A formalization of the argument from mental causation
1. Physical states are indeterminate with respect to intentional content. Given the state of the physical, there is a plurality of intentional states that are logically compatible with the state of the physical. In fact, any set of physical facts is logically compatible with the complete nonexistence of intentional states whatsoever.
2. If a broadly materialist world-view is correct, then the physical is causally closed. Nothing over and above the physical state of the world can be responsible for a subsequent physical or mental state.
3. Therefore, if there are mental states, and those mental states have determinate mental content, then that determinate mental content is causally irrelevant to the future course of nature.
posted by Victor Reppert @ 11:55 PM
79 Comments
79 Comments:
Premise 1 seems more contentious than the conclusion you are trying to establish.
This isn't quite a formalization yet, so it isn't even clear that it is deductively valid. Perhaps you could fill in the enthymeme.
I agree with BDK.
Suppose I consider the proposition "My dog is on the porch."
How do I know what this proposition is about? If I see the neighbor's cat on the porch instead of my dog, how do I know that the proposition is false? And how can I assert the proposition in advance of actually making the observation?
There's a simple and elegant (and natural) solution. Intentionality is about my own cognitive abilities, and my cognitive abilities are in a physical brain that does exist as the thought is processed. A proposition has meaning in light of me knowing (approximately) what experiences would increase or decrease my confidence in the truth of that proposition. That is, the proposition isn't a physical reference to actual dogs and porches (which may not exist), but is about my presently-existing faculties for recognizing dogs on porches if those things existed.
Rocks and CD-ROMs lack intentionality because they lack thought and recognition. Deep Blue lacks intentionality because Deep Blue does not formulate propositions about its abilities to recognize states of affairs. It just recognizes them. For example, Deep Blue does not ponder the proposition that it will lose the game (in some abstract way), even though it is capable of recognizing a great many specific ways of losing a match. Deep Blue's intelligence is fish-like or insect-like. It does not have ability to recognize its own mental states.
So the argument that we cannot see how one lump of matter could be about another just doesn't hold up under scrutiny. If the first lump has recognition and expectation, and the ability to recurse those abilities on its own faculties, then that lump can have intentional thought.
BDK & DL
I think we can get at Victor's first point by considering what kinds of necessity can be observed and confimed between propositional content and associated physical events/states.
It may be as logically necessary that salt + water = brine as it is that 1 + 1 = 2, but we cannot see or confirm in any scientific sense the logical necessity of salt plus water equalling brine. I think Hume made this point convincingly and has not been overturned on it.
A state or system or process is physical to the extent that its properties and relations can be observed/confirmed empirically, and logical necessity is consequently excluded. It is not simply that a succession of physical states (A followed by B) cannot be observed to be a logically necessary succession. It is that nothing in those states can be seen to be causally sensitive to logical necessity. If physical states were causally sensitive to logical necessity, then such necessity would be empirically confirmable--the two go hand in hand.
We know that thought processes sometimes ARE sensitive to logical necessity. In that respect we know something about those processes that can never be empirically confirmed, putting them to a significant extent outside of the physical domain.
Darek,
We know that thought processes sometimes ARE sensitive to logical necessity.
I guess we've covered this before.
Minds are not compelled to obey logical laws. They are not forced by logic. They evolved to take advantage of consistency relationships. And they do that some of the time.
Minds are certainly not beyond physical verification. We can (in principle) verify that a machine thinks rationally.
Finally, Hume's point works on thoughts too. Does 1 + 1 = 2 necessarily? If 1+1=2 yesterday, why think that 1+1 still equals 2 today? Induction is necessary for all rationality, not just for science.
DL
Hume distinguished between the degree of certainty of inductive as opposed to analytic reasoning, as did philosophers in the British empirical tradition such as A. J. Ayer and Bertrand Russell.
Hume made the point that we have no empirical basis for ascribing the certainty of 1+1=2 to such a proposition as salt+water=brine. Or, as C. S. Lewis said, we do not believe that two quantities both equal to a third are equal to each other because we have never caught them behaving otherwise, but because we see that it "must" be true.
We can confirm from observation both that one plus one DO equal two and that salt plus water DO equal brine. But we also go further in the first instance and say that one plus one MUST equal two, but not that salt plus water MUST equal brine. The trouble is that we never have empirical license for the "must" in any proposition.
I am trying to tease out the implication of this lack of empirical license for any ascription of logical necessity. The empirical license by definition accompanies all physical properties and relations. Therefore the ascription of causative power to logical necessity--to say that we believe C because it MUST be true given A and B--poses a conundrum for run-of-the-mill naturalism.
You must grasp this concept of what I here call the "empirical license" of all physical properties and relations to appreciate my point.
Darek,
Just to keep us on track... The issue about minds obeying logical laws is separate from the induction issue.
It's not that minds are constrained by logical laws, but that you think minds ought to think logically. It's the same difference as between is and ought. If we were constrained by logic to think rationally, we would never make a mistake, yet we all make logical mistakes.
There's a lovely naturalistic story that explains what we observe. The natural laws are non-contradictory (because you can't have contradictory natural laws). There's evolutionary advantage to be able to think abstractly about lawful systems, and that means there's evolutionary advantage to thinking logically. Thus, we don't need separate universal laws of logic to constrain us. We just need a world filled with a myriad of natural laws and regularities wherein it is advantageous for a being to have abstract reasoning ability.
As for induction, you may be right that, upon reflection (mental experimentation, if you will), I find that arithmetic equality is transitive, for any A,B or C. This doesn't impact my point.
If I reflected upon this yesterday and found that arithmetic equality was transitive at that time, why should I believe that it is still the case without reflecting on it again (i.e., without re-running the experiment)? Who knows, maybe mathematics will be different today than it was yesterday.
Of course, if logic and mathematics really changed every day, the world would likely be unintelligible. But then the same would be true if physics changed daily. So it is fundamental to intelligibility that past experience is a guide to future experience, whether that experience be mental or physical.
It may look like mathematical intuitions are in a wholly different class, but they are not wholly different. Analytic judgments are arbitrarily precise because, in experimental terms, they are totally controlled. I can become arbitrarily certain that 7+7=14 by performing the computation over and over again. I know the laws, and just have to compute the theorems. In contrast, physical experiments are not totally controlled because we don't know the laws in advance.
DL
Sure, we can quibble over whether awareness of logical necessity entails infallibility (it doesn't). And we can speculate as many have that the actual laws of nature (whatever they are) are in fact logically necessary. That doesn't change the crux of the issue, which turns on the following questions:
1) Is logical necessity real?
2) Does the awareness of logical necessity ever make a difference in the course of thought?
3) Is logical necessity an empirically confirmable property of physical states, events, or relations?
It does not help to push logical necessity back from the level of operations to the that of axioms. I've seen it argued, in effect, "1+1=2 merely if certain axioms are adopted." That just results in the proposition that, given certain axioms, certain results necessarily follow. But the "necessarily follow" part of the proposition expresses logical necessity. It is logically necessary that, given certain axioms, certain operations yield certain results. And mental reflection--even aided by pencil and paper or other memory aids--is not the same as empirical observation.
DB: that is more than what Victor has in his argument. There could be illogical minds with causal efficacy, and he should be able to make his point as long as those minds influence behavior. I think we have many examples of such minds in politics :)
So, I'm gonna sidestep logical necessity unless Victor needs it for his argument (perhaps you have discovered one of the terms in the enthymeme, though it doesn't appear that way).
BDK
Fair enough. I have endeavored to find a juncture where the intentional state cannot be "connected up" in a causally correlative manner with any conceivable physical state. This may not be the way Victor would go about demonstrating his point and it goes well beyond his statements.
That said, my own argument has been refuted.
DL
To my response above I might add that your speculation that you can conceive of waking up tomorrow and finding mathematics to work differently would seem to fly in the face of possible worlds arguments regarding logical necessity. That seems to me like a hard road to hoe.
BDK
Uh oh! Please correct the above to read, "My own argument has NOT been refuted." Although my fallibility is amply demonstrated!
Darek,
Logical consistency is necessary for intelligibility. It is not somehow uber-necessary all by itself. If a natural universe is logically consistent, then it already meets the necessity requirement. The necessity does not have to be of a supernatural nature just because we're not sure which possible world we're living in.
The natural story is a simple one. The universe is governed by natural laws, and is, therefore, largely consistent. Humans are physical machines that evolved the ability create abstractions and predictions. One such abstraction is logical consistency. The abstraction recognizes consistent systems, of which there are very many in the physical universe. Human machines recognize that they can only know about consistent systems, so they call logical consistency a necessity for intelligibility.
Thus, I think your argument is refuted. Your argument is that we are sensitive to something independently real and non-physical, therefore, we cannot be purely physical. However, if logical consistency is a mental abstraction in a physical mind, then we are actually just aware of a pattern that can be matched in a physical mind, and there's no need for anything non-physical.
One more example. Does geometric circularity exist out there as an absolute non-mental abstraction? Does it have to? No. Our minds recognize circular things, and there are external physical instances of circular things, but there is no requirement that circularity exist independently of all of these things. Instead, circularity can be a mental abstraction (a pattern our minds can match against). We can then speak about circles as "that which would trigger my circularity recognition circuit."
Now, the thing about mental abstractions is that we can combine them together. We can know that an external thing that would qualify under one mental abstraction, must (or must not) qualify under a second mental abstraction. We can know that a circle cannot be a square, even if we have never seen an instance of either. This reasoning does not require some supernatural sensitivity. It only requires a mind that can recognize the properties of its own abstractions.
DL
Remember my three questions? Here they are again:
1) Is logical necessity real?
2) Does the awareness of logical necessity ever make a difference in the course of thought?
3) Is logical necessity an empirically confirmable property of physical states, events, or relations?
I believe the answers are yes, yes, and no. Where have you demonstrated a different answer ought to be given for one of them?
You seem to be saying that humans create "logical consistency." Are you claiming that human brains create logical necessity? This seems to be at odds with earlier claims you have made that logical necessity obtains in the physical universe (i.e., a physical state cannot both exist and fail to exist in the same way at the same time).
If your claim is now that logical necessity is generated by human brains, then it should be an empirically confirmable property or state or relation of human brains.
You cannot get around the issue simply by talking about abstractions, patterns and recognition without specifically engaging the issue of the empirical confirmability or lack of confirmability of logical necessity.
Darek,
As I explained, "logical necessity" translates to "logical consistency is necessary for intelligibility." There is no "logical necessity" floating out there. This means your first premise is vague at best, and most likely false.
In principle, we could show that a reasoning machine cannot conclude facts within logically inconsistent systems. To show this would be to show that logical consistency is necessary for the machine to find the system intelligible. We could also show that such a machine can be aware that it cannot reach a conclusion about such systems.
Why ought I assume logical consistency?
Answer: if I don't assume this, I won't have knowledge or facts or beliefs, etc. It means that the world would not be discoverable. However, by this little exercise, we have not shown that the world must be discoverable. We merely said that the world we're interested in investigating is discoverable.
Now you are turning this on its head and saying that the particular, physical, discoverable world in which we live is not good enough because it lacks discoverability in the universal abstract.
I'll explain abstractions again because it's very important. I can train a neural network to recognize rabbits. It will be trained on one or more particular rabbits. Once trained, what can we say about the neural network? We can say that it is an abstraction of rabbits because it will recognize more than just the particular rabbits on which it was trained. There are countless possible rabbits (and likely a few non-rabbits) that would cause the neural network to say "That is a rabbit!" In other words, capacity for recognition of class membership is the same thing as abstraction.
The question is, is this rabbit recognizer sensitive to rabbits that do not actually exist? Yes. We can simulate a non-existent rabbit, and show that the network would recognize it. So you might say that the network has awareness of rabbitness.
But is that rabbitness awareness caused by those non-existent rabbits? No! The non-existent rabbits don't cause the network to be "aware" of them. Rabbitness is an abstraction of some particular physical rabbits, and that abstraction (the trained network) is physically caused by those same particular rabbits.
And so it is with logically consistent systems. Our awareness of consistency can be causally explained by our experience with particular consistent systems. "Logical necessity" is our demand that the world be consistent so that we may comprehend it. We are not being causally affected by non-existent consistent systems any more than we are causally affected by non-existent rabbits. However, we ARE causally affected by these circuits in our brains that implement those abstractions.
For example, suppose that I think that a hypothetical rabbit can't be both in a hat and not in a hat at the same time. Does this thought have to be caused by the non-existent rabbit in the non-existent hat? No. I can simply simulate both possibilities simultaneously, and my inconsistency abstraction will trigger, telling me that the possibility is unintelligible. And so I don't need to be causally affected by some invisible "logical necessity field" external to my physical body. The mere fact that I can recognize inconsistency using a physical circuit is adequate.
By the way, neural networks that perform this kind of abstraction do exist and are empirically confirmable. They're called auto-associative neural networks.
DL
You have resorted to the claim that logical necessity is unreal or at least highly questionable. I could rest my case right there.
>>Why ought I assume logical consistency?
Answer: if I don't assume this, I won't have knowledge or facts or beliefs, etc.<<
Look at your answer. It entails an inference. The inference depends upon logical necessity. It is necessarily the case that if we do not assume consistency we don't have knowledge or facts.
>>Now you are turning this on its head and saying that the particular, physical, discoverable world in which we live is not good enough because it lacks discoverability in the universal abstract.<<
When did I say that? I can't even tell exactly what you mean by "lacks discoverability in the universal abstract." I said that logical necessity cannot be empirically confirmed, in which opinion to my knowlege the empirical philosophical tradition
as a whole concurs.
>>Our awareness of consistency can be causally explained by our experience with particular consistent systems.<<
Huh? Our experience with systems we assume to be consistent? Or with systems whose consistency we actually experience? Or with systems about which we must draw inferences that depend upon logical necessity, which you are choosing to identify with "consistency"?
Your account about the rabbit and the hat depends upon inference and therefore on logical necessity.
>>telling me that the possibility is unintelligible.<<
"Me" meaning a certain neural network as opposed to others that are in your brain but are not part of the "me," I assume?
Accounts like this must be envisioned physically as circuit switching and chemical reactions. But logical necessity cannot be confirmed through any number of observations of neural events or reactions. Neither can it be confirmed by any of the observations of responses that are interpreted in terms of auto-associative networks. Yet your account and your argument depend upon inference, i.e., logical necessity.
Many paraconsistent logics don't include consistency as axiomatic. A&~A is possible, and doesn't lead to all theorems. Some describe this as saying paraconsistent logics are 'nonexplosive'.
Such logics can be useful for modelling belief systems in which people believe contradictory things, but do not believe everything. They can also be used to model systems of experts that give contradictory recommendations.
You could model these things using Bayes nets or something, too, but the fact that there are paraconsistent logic systems (they aren't just possible, but actual) is interesting.
It is hard, perhaps impossible, to give a non question-begging argument for the importance of consistency. I'm not saying I don't try to be consistent, or advocating inconsistency in one's arguments. However, when confronted with things like the liar's paradox, there are many options at your disposal. You can either say it is meaningless, that there is a third truth value, that it's truth is indeterminate, or even that it is both true and false (this could be a special case of a third truth value).
If ordinary language were peppered with liar's paradox type statements, we might be more open to paraconsistent logics, it may seem natural and helpful for dealing with strange semantic behavior.
At any rate, I think it important to distinguish formal, public, symoblic logic from claims about internal 'logic of thought' (to the extent that the properties of public logic don't apply to internal representations, such claims are category mistakes).
When people make claims about logical thought, I usually just translate it into claims about public symbolic representational systems, as I am agnostic about whether our minds operate in the right format to even talk about logic (though I am starting to take more seriously that the brain (unconsciously) uses statistical decision rules).
Darek,
I notice that you didn't answer my question. For what is logical consistency necessary?
Thus far, you seem to interpret logical necessity to mean that we somehow know something about the world (and every possible world) that must be true, no matter what. This interpretation is wrong.
Logical necessity is a reflection of our own cognitive limitations. A desire/demand that the world be comprehensible does not imply that the world must be comprehensible or that every possible world must be comprehensible.
So your first premise is wrong in the sense you're taking it. You're taking logical necessity as if it is something we know about the external world without empirical knowledge. That's just not the case. We don't know it. We just hope it's the case because the alternative is cognitively hopeless.
Your account about the rabbit and the hat depends upon inference and therefore on logical necessity.
It depends upon logical consistency, not on logical necessity. Physicalism is a possible world (or collection of possible worlds) that is logically consistent. You may not realize it, but you are arguing that logical necessity (which is an expression of our demand that the world, whatever it turns out to be, be consistent) somehow rules out the possibility that the world is physical and consistent.
I think the reason you don't see my position is that you have not considered what logical consistency might actually be necessary for. Even if you're eventually going to disagree with me about what it is for, you still have to consider the question.
Oops, wrong link for paraconsistent logic. Here it is, a pretty good overview.
Looking over it more closely, that's the best intro to paraconsistent logic I've seen. Bravo to Priest.
I know this is getting a bit off track, but what are the arguments that we should accept the law of noncontradiction (LNC)? (I.e., for any A, ~(A&~A) is true).
I've been looking over Priest's new book Doubt truth to be a liar, and he has an interesting discussion of Aristotles' argument for LNC, mentioning that Aristotle realized he couldn't prove LNC, but did give several arguments for it, all of which Priest says beg the question. The first chapter of his book is a detailed analysis of all of Aristotle's arguments.
The usual modern-day argument is that accepting A&~A leads to an explosion of truths, that everything follows. However, this is not the case in paraconsistent logic, so that blocks the main objection.
I am outside my specialty with this topic, but it is pretty interesting stuff. The sort of things Sophomore philosophy majors would get very excited about. :) That worries me a little bit.
He also has a very interesting discussion of some Indian philosophers, who argued that for any proposition there are four possibilities, it is true, false, both, or neither.
He basically argues that LNC is a dogma that was begun by Aristotle (who was indeed responding to those who denied the LNC), perpetuated by the Scholastic philosophers because of their undue respect for Aristotle, and has since been a dogma.
I'm not sure I go along with all his arguments, but it is very interesting stuff!
One of his other interesting arguments is that whether we should accept A, ~A, both, or neither, depends on the evidence, not a priori restrictions on the truth values a single proposition can have.
BDK,
I'm pretty sure I know less about this than you, but I think you're right... up to a point. If we take the LNC to be the claim that a system should be completely free of contradictions, then the LNC would indeed seem like too strong a claim.
It seems like the paraconsistent logics are generally showing us that we can find non-contradictory facts in systems that possess some contradictions or paradoxes. In other words, they are asking how we might find some non-contradictory stuff even in the presence of contradictory stuff.
IMO, advocates for the LNC are (by their example) rejecting what we might call global violations of non-contradiction rather than local violations.
My point in my response to Darek is that the LNC (or a partial LNC) is imposed by our own desire to understand systems. Physical systems are not caused to be consistent because of the LNC, but are consistent because they are lawful, and laws are consistent by definition. If I have a law L that describes X, I do not need a meta-law in the form of the LNC that will force L (and every other possible lawful description of X) to be consistent. L is consistent all by itself. The LNC is just a search heuristic that minds use to find stuff they can comprehend.
DL: I'm not sure. It probably depends on the paraconsistent logic and logician.
DL
>>Thus far, you seem to interpret logical necessity to mean that we somehow know something about the world (and every possible world) that must be true,<<
Do we know it to be true about some worlds that they are indeed possible? How do we classify worlds as possible or not? By empirically confirming that they are possible?
>>So your first premise is wrong in the sense you're taking it.<<
You mean, I am wrong in taking logical necessity to be real? Or that I'm wrong in taking it to affect the course of human thought? Or that I'm wrong that it cannot be confirmed empirically.
>>You're taking logical necessity as if it is something we know about the external world without empirical knowledge.<<
Well, that's how A. J. Ayer took it.
I'm taking it as something real, something that makes a difference (at least at times) to the course of thought, and something that cannot be empirically confirmed. You seem to classify it with the tooth fairy--something "real" to the extent that we dreamt it up because it appeals to us. Yet you seem to take it as objective in continuing to pose arguments as you do.
>>That's just not the case. We don't know it. We just hope it's the case because the alternative is cognitively hopeless.<<
How do you know that "the alternative is cognitively hopeless"? Can you confirm that proposition empirically?
>>You may not realize it, but you are arguing that logical necessity (which is an expression of our demand that the world, whatever it turns out to be, be consistent) somehow rules out the possibility that the world is physical and consistent.<<
I am arguing that if the physical consists of states and relations that can be confirmed empirically, then logical necessity is not physical, yet it can make a difference to thought processes. Consistency may be a matter of logical necessity, but if so it cannot be empirically confirmed that necessary truths are necessarily consistent.
Darek,
You didn't answer my question. For what is logical consistency necessary?
If you cannot say what logical consistency is necessary for, then you don't know the meaning of the term "logical necessity". And if you don't know what "logical necessity" means, then how do you know it's not empirically testable?
If it means that we humans cannot reach conclusions within logically inconsistent systems, then that seems quite testable to me.
You seem to classify it with the tooth fairy--something "real" to the extent that we dreamt it up because it appeals to us. Yet you seem to take it as objective in continuing to pose arguments as you do.
I think you should analyze the line of argumentation you are pushing here.
Clearly, I regard my future existence as necessary for my own decision-making. I embark on chains of thought and action in the hope and expectation of finishing those lines. That is, the assumption of my future existence is necessary for me to do anything goal-oriented. However, the assumption of my future existence doesn't guarantee my immortality, right? My future existence is necessary for me to work towards a goal, but it is not physically necessary (or metaphysically necessary).
Furthermore, the necessity of the assumption of a person's future existence to their goal-oriented thinking is empirically testable.
So...
We have to distinguish "assumption of X" from "X", and distinguish "necessity of assumption of X" from "necessity of X".
Logical consistency of the world is a necessary assumption for our thinking. Logical consistency of the world is not necessary.
Darek,
>>You didn't answer my question. For what is logical consistency necessary?<<
You're the one who insists on the term "logical consistency," not me. Then you demand that I expound your own term back to you.
Logical necessity is inseparable from "understanding" as opposed to "knowing" in the simplest sense. Even in the case of paraconsistent logics, conclusions still necessarily follow from premises in certain ways even though the conclusions might not be what we normally consider consistent. So I think that logical necessity is on as firm if not firmer ground than consistency.
Logical necessity is the relation between premises and the conclusions that follow from them. We can expand this to include rules or axioms: certain conclusions follow from premises given certain axioms, system rules, etc. In other words, we invoke necessity even to understand the role of axioms and rules.
Logical necessity, and to a large degree consistency, are necessary to a discussion such as we are having right now. Do you that you are somehow arguing for objective truth in this blog, or just sharing with me your assumptions? Do you think the Socrates syllogism is empirically confirmable? Or does the conclusion follow from the premises?
>>Clearly, I regard my future existence as necessary for my own decision-making. I embark on chains of thought and action in the hope and expectation of finishing those lines.<<
I don't believe that my existence tomorrow is logically necessary, nor do you. It sure wasn't necessary when I took out life insurance! It may be logically necessary that if I make no plans today for the possibility of my being alive tomorrow, I will if alive tomorrow find my circumstances to be unplanned for.
>>However, the assumption of my future existence doesn't guarantee my immortality, right?<<
Obviously not. Perhaps you are saying this: "An assumption is necessarily unproven." Unless you mean that it is merely your subjective opinion that assumptions are unproven. Or that it is merely probable that assumptions are unproven. Perhaps we can empirically confirm that assumptions are unproven?
>>Furthermore, the necessity of the assumption of a person's future existence to their goal-oriented thinking is empirically testable.<<
Necessity is never empirically testable. We test for what simply is, not for what necessarily is. We reason to what necessarily is.
>>We have to distinguish "assumption of X" from "X", and distinguish "necessity of assumption of X" from "necessity of X". Logical consistency of the world is a necessary assumption for our thinking. Logical consistency of the world is not necessary.<<
In naturalism, our thinking IS part of the world. That's a key point of naturalism, at least in its common physicalistic form.
DL, you are saying that logical necessity (or to have it your way, consistency) is necessarily assumed in our thought processes, and because of that its reality is questionable. But this is self-refuting. First, we must invoke logical necessity to make the observation itself. The claim may be put in the form, "Logically, certain assumptions are necessary for understanding the world." Second, if the necessity of the assumption of, say, consistency, calls it into question, then we must also call into question the reasoning, "If necessarily assumed, then possibly unreal." The very conclusion you are advocating is, by your own account, nothing but an artifact of the way your brain works.
DB said:
Do you think the Socrates syllogism is empirically confirmable? Or does the conclusion follow from the premises?
Yes.
But now we'd come full circle on previous discussions.
BDK
To be subject to confirmation, the syllogism must be corrigible. Is there a conceivable empirical observation that even though Socrates is a man and even though all men are mortal, Socrates nevertheless is not mortal?
If you maintain that there is, I think at the very least you have to admit that your view is idiosyncratic among your fellow naturalists.
If to maintain coherence naturalists must choose between either denying the objective reality of logical necessity or else arguing that the Socrates syllogism is corrigible, a great many of them will be disappointed with their options.
DB: I think modus ponens is a good argument, it's one I use. But that doesn't mean it isn't something we didn't discover, that it isn't the result of an arduous screening and searching for good inference rules.
Of course, many people aren't very good at modus ponens considered abstractly. (Wason), so it doesn't seem to be carved into our cognitive apparatus. It rather is a cognitive corrective lens that we use to elevate above and beyond our innate apparatus.
So I'm not saying there is no logic, and I'm not saying that for any logical rule I can find a counterexample. I'm just saying that this isn't metaphysically interesting.
That said, as described here, in some paraconsistent logics, modus ponens fails. So this isn't just an abstract possibility, but an actuality!
By what criteria would you decide whether to buy the paraconsistent logic, or the more standard classical logic? Perhaps would you let a little of the world in? Pragmatics? A priori, is there a foolproof method to pick a system of logic?
I wrote about these issues here under my real name, and while my main Godelian argument I now think is wrong, in the comments I adumbrated what I now think is a better approach.
As I've said (and mentioned at that previous link) before, Gila Sher has done the coolest work on this topic. I think readers would find much of interest there, and of course a little to disagree with. She is better versed than I am in this stuff, and I don't want to rehash all of her arguments here.
Also, Penelope Maddy has a book Second Philosophy, which based on reading one chapter looks excellent. She is really good in mathematical logical and philosophy of mathematics, and seems to have put her finger on the pulse of what naturalism amounts to. Very impressive, as logicians are usually horrible naturalists.
Darek,
I agree with BDK that we're coming full circle now.
What I think you should do is distinguish between two things here.
The first is our inability to prove (without circularity) that rules of inference (or rules of rationality) are what we think they are.
The second is our perfectly straightforward ability to show that machines can function according to those rules.
Naturalism only has to show the latter, not the former.
Indeed, while it may be true that naturalism cannot explain the former, neither can supernaturalism or theism. There cannot be a logical argument for logic without circularity.
DL, you are saying that logical necessity (or to have it your way, consistency) is necessarily assumed in our thought processes, and because of that its reality is questionable.
Knowledge is justified belief. Logical inference cannot be justified logically without circularity. Therefore rules of inference are not knowledge, and not something we "know".
And, again, it is not naturalism's burden to show that rules of inference are correct. It is naturalism's burden to show that physical systems can think according to those rules, and that machines can have the same intuitions and cognitive limitations that we have.
This means that your argument that naturalism cannot work doesn't work. We can turn your argument right back around against theism. Theism cannot explain the rules of inference without circularity. Does theism's inability to explain the rules cast doubt on the rest of theism?
DL
>>The first is our inability to prove (without circularity) that rules of inference (or rules of rationality) are what we think they are.<<
I proposed that logical necessity is real. I believe we both effectively concede this merely by our discussion here, and if we do then "proving" the rules of inference is not at issue. You cannot argue against the reality of logical necessity without employing it.
>>The second is our perfectly straightforward ability to show that machines can function according to those rules.<<
Yet again, let's look at my third question:
3) Is logical necessity an empirically confirmable property of physical states, events, or relations?
Nothing in the operations of a computer can be empirically confirmed as logically necessary. The only way we can bring logical necessity into computing might be to claim that it is logically necessary to design computers a certain way if their output is to be interpreted symbolically a certain way. Even that is a questionable strategy, but in any case it relies on the effect of logical necessity on human thought processes, which is the very point at issue.
Remember, machines of all kinds are just physical systems operating according to laws of nature that can be empirically confirmed. And logical necessity cannot be empirically confirmed . . . although BDK would argue otherwise.
Darek,
I proposed that logical necessity is real. I believe we both effectively concede this merely by our discussion here, and if we do then "proving" the rules of inference is not at issue. You cannot argue against the reality of logical necessity without employing it.
If "logical necessity" means "assumptions necessary for rational thinking as determined by rational thinkers" then it is certainly real. But that is useless.
Your argument is this. We can put rules of rationality into the category of rationally-known facts (like laws of physics), but the rules of rationality cannot be rationally-known empirically, therefore, there is something supernatural about them. Since our minds have rational instincts, we are "aware" of the supernatural rules, therefore, minds are supernatural too.
The argument fails because the assumptions of rationality aren't rationally-known to be true. They are assumed by all rational thinkers, not rationally-known by all rational thinkers. That makes them completely different from the laws of physics and not real in the same sense of the word.
Logical necessity doesn't cause anything here. Our instincts for logical necessity are what cause things. There's no evidence that we sense some external logical necessity field, and respond to it in the same way we might respond to the heat of a flame.
And you've completely ignored the distinction I was talking about. You responded by saying that a computer does not demonstrate that the rules of rationality are correct. I totally agree that looking at computers won't prove that the rules of rationality are what our instincts tell us they are. That was my point. But looking at computers (or brains) will prove that a machine can think according to those rules. And this is what naturalism claims. Naturalism does not claim to explain the inexplicable.
Even if your argument showed that the rules of rationality were supernatural, it would not prove that minds are supernatural. As long as a machine can think according to rational rules and can have rational instincts, it fits with what we observe.
It is easy to imagine a machine with rational instincts. The machine won't rationally be able to explain why its instincts are correct, but it will be able to use them.
DB: How do you define logical necessity? Is it a property of propositions, inference rules, entire logical sytems?
DL
>>If "logical necessity" means "assumptions necessary for rational thinking as determined by rational thinkers" then it is certainly real. But that is useless.<<
Why useless if real?
We have to be careful here. When we talk about assumptions we ordinarily mean propositions that need not be affirmed by a rational thinker.
Logical necessity is intuitive, yes. But take my example of the Socrates syllogism. Do we simply assume that if major and minor premises are true then the conclusion follows? This stretches the meaning of "assume" quite a bit.
>>They are assumed by all rational thinkers, not rationally-known by all rational thinkers. That makes them completely different from the laws of physics and not real in the same sense of the word.<<
We don't know that the conclusion of the Socrates syllogism follows from the premises? That is also a stretch.
You yourself said that logical necessity is real. Now you say that it is not real in the same way as the laws of physics. But that is exactly what we require for refutation of naturalism--a side of reality not known in the same way as the physical.
You cannot demand that a supernatural reality be natural before you will concede that it lies outside of nature!
>>Logical necessity doesn't cause anything here. Our instincts for logical necessity are what cause things.<<
If it is real, and if we have an "instinct" or intuition for it, and if the intuition for it makes a difference in the course of our thinking, then clearly logical necessity itself makes a difference in the course of our thinking.
>>There's no evidence that we sense some external logical necessity field, and respond to it in the same way we might respond to the heat of a flame.<<
No physical evidence? That only shows that it's not physical--which is exactly the point. Are you saying that we have an instinct for it and yet we do not respond to it? It's not like the heat of a flame because a flame is physical. Again.
>>You responded by saying that a computer does not demonstrate that the rules of rationality are correct.<<
Well, that is not precisely my point. Take a calculator. We might ask, why does the calculator give the answer "2" to the input "1+1." The answer from the standpoint of physics would simply refer to the layout of the circuits and the nature of electromagnetic theory.
What if we try to say instead, "The calculator says 1+1=2because logical necessity requires that answer." That analysis would only work by backing up to what was in the minds of the engineers who set up the calculator to give certain results, which gives logical necessity a causal role only because of the role it played in human minds.
>>As long as a machine can think according to rational rules and can have rational instincts, it fits with what we observe.<<
Well, the calculator can give the right answer, but to offer that as proof that it "thinks" in the sense of seeing that certain answers are logically necessary goes way beyond the evidence. See my analysis above.
BDK
I have to get to an appointment tonight but I will try to respond to your question when I get back.
Darek,
Harry Potter is real in a sense because we own several of J.K. Rowling's books. However, that fact that Harry Potter is real in this sense does not make him existent in the same way you and I are existent.
Logical necessity is intuitive, yes. But take my example of the Socrates syllogism. Do we simply assume that if major and minor premises are true then the conclusion follows? This stretches the meaning of "assume" quite a bit.
But in the major and minor premises, you are not including the implicit premises, namely the assumptions of the axioms of rationality itself. If those assumptions are implicit, then the syllogism holds absolutely, without proving the premises. Our assent to the validity of the syllogism no more proves "logical necessity" than it proves that Socrates actually is a man. What we agree upon is that IF Socrates is a man, and IF all men are mortal and IF the rules of rationality are in effect, THEN Socrates is mortal.
Let me give this to you another way. Before every argument, there are a bunch of implicit assumptions. Those assumptions are the axioms of the system in which the inference is taking place. For example, for the calculation 1+1=2, we assume the rules of rationality and the rules of standard decimal arithmetic. (For example, in some alternative systems, 1+1 would equal 0.)
Logical necessity is the observation that every rational argument relies on certain common axioms. This observation does not prove the axioms true. Even if these axioms are merely assumed, we can still know with near certainty that the conclusion is valid if the assumptions are true.
In common algebra, let us start with the axioms that x+y=7, and x=3. We can know with certainty that y=4 given these explicit axioms, and the implicit axioms regarding inference and common algebra. But does our universal assent that y=4 here prove that our original axioms (e.g., x=3) are absolutely true? No. In our next algebra problem, x might equal 9 (because the axioms vary from problem to problem).
So universal assent to the conclusions of an argument based on assumed premises does not prove the assumed premises. So you do not know that the rules of rationality are absolutely true because you will never have rational justification for their truth.
If it is real, and if we have an "instinct" or intuition for it, and if the intuition for it makes a difference in the course of our thinking, then clearly logical necessity itself makes a difference in the course of our thinking.
Harry Potter is real and makes a difference in the course of our thinking. What does that say about Harry Potter? Is Harry Potter "out there", causally affecting our thinking? No.
Another example. We know that an unstable configuration of snow causes an avalanche. But this is just a case of "grammatical" causation. "Unstable configuration of snow" (in the abstract) does not cause the avalanche. Rather, a particular (not an abstract) configuration of snow causes a particular avalanche.
Abstractions (like abstract unstable configurations of snow) exist only within abstracting systems, of which our mind is an example. And it is absurd to say that abstract snow configurations have causal effect because they impact our thinking. It would be mistaking the map for the territory.
(The brain is full of abstractors, and to talk about the brain's abstractions as existing outside the brain is absurd.)
What if we try to say instead, "The calculator says 1+1=2 because logical necessity requires that answer." That analysis would only work by backing up to what was in the minds of the engineers who set up the calculator to give certain results, which gives logical necessity a causal role only because of the role it played in human minds.
Calculators are not machine minds, and calculators are not instinctively aware of "logical necessity". Calculators do not know what an axiom is, so a calculator is not a demonstration of much when it comes to machine minds. Nothing that you have said here says that machine minds are impossible or that they are necessarily reflections of human intellect.
I have (numerous times) spelled out how rational minds can evolve without the need to be designed by some prior rationality. The argument that mechanistic minds are only reflections of their rational creators is a canard.
Let's remember that the AfR purports to show that naturalism is wrong because it cannot ever explain minds. That is a strong burden on the AfR. It is not necessary for the naturalist to prove that minds are machines to refute the AfR.
DL
Harry Potter is a fictive construct of the human imagination. I leave other readers of this blog to judge the appropriateness of your comparison.
>>Our assent to the validity of the syllogism no more proves "logical necessity" than it proves that Socrates actually is a man.<<
This amounts to saying, "Our assent to logical necessity does not prove logical necessity." My first point simply asserts that logical necessity is real. It does not assert that logical necessity is justifiable or provable. Since you yourself assent to the reality of logical necessity (when you're not comparing it to Harry Potter), my initial point goes through.
>>What we agree upon is that IF Socrates is a man, and IF all men are mortal and IF the rules of rationality are in effect, THEN Socrates is mortal.<<
No one--certainly not me--claimed that the Socrates syllogism proves Socrates to be mortal. Logical necessity simply requires the very "IF" statements you make.
I am pointing out that your "assumption" language amounts to saying "We merely assume that if Socrates is a man and if all men are mortal, then Socrates is mortal." Throw in the relevant axioms if you like. And it remains true that this stretches the verb "assume" beyond its normal limits.
>>Even if these axioms are merely assumed, we can still know with near certainty that the conclusion is valid if the assumptions are true.<<
You are just moving the lump around under the rug. If logical necessity is merely an assumption, then the "knowing with near certainty" that you refer to is itself just an assumption.
>>So you do not know that the rules of rationality are absolutely true because you will never have rational justification for their truth.<<
I don't need to know they are "absolutely true" for my argument to go through. All I need is your assent, along with that of any other rational interlocutor, which I (sort of) have.
>>Harry Potter is real and makes a difference in the course of our thinking.<<
The idea of Harry Potter as a fictive creation is real, not Harry Potter. The attempt to classify logical necessity as a fictive creation of the human imagination scarcely needs refutation.
>>And it is absurd to say that abstract snow configurations have causal effect because they impact our thinking. It would be mistaking the map for the territory.<<
This is going far afield. Needless to say, maps do have effects. But the relationship to the current argument is sketchy at best.
>>Calculators are not machine minds, and calculators are not instinctively aware of "logical necessity".<<
So instinctive awareness of logical necessity is not required to give outputs that accord with logical necessity? That's an important point to remember.
>>Calculators do not know what an axiom is, so a calculator is not a demonstration of much when it comes to machine minds. Nothing that you have said here says that machine minds are impossible or that they are necessarily reflections of human intellect.<<
Well, you are the one making the claim about machines--that they can have the same intuitions that we do. I said that in principle no set of mechanical responses can be observed to be logically necessary, which claim you have yet to refute.
Darek,
If logical necessity is merely an assumption, then the "knowing with near certainty" that you refer to is itself just an assumption.
So any conclusion based on an assumed premise is no more certain than the assumption?
Assuming the axioms of geometry, we can prove the Pythagorean Theorem. But you seem to be saying that since the axioms of geometry are not necessarily true, then we ought to doubt our proof and justification of the Pythagorean Theorem. But theorems are always contingent on assumptions. While we may not be certain that the Theorem holds across differing assumptions and axioms, we ARE certain that it holds when our assumptions are as stated. So there is certainty even in the presence of an assumption because the certainty is contingent upon the assumption.
As for reality, what do you think reality means in this context? You appear to be taking it to mean that logical necessity is "out there" in some supernatural way, which begs the question.
Logical necessity can be a real instinct or a real limitation of thinking mechanisms and still be real. And that instinct or limitation does causally affect thought. And science can show (in principle) that a thinking machine can have this instinct and limitation.
I said that in principle no set of mechanical responses can be observed to be logically necessary, which claim you have yet to refute.
Once again, logically necessary for what? If you can't say what it is that is necessary, then there's nothing for me to refute.
If logical necessity is about limitations of thinking machines, then we can observe a machine to reach a logically necessary conclusion.
Finally, let's just expand on the naturalistic picture.
Suppose we show scientifically that, due to the laws of physics, a particular machine will think rationally. That is, the machine will make the same kinds of rational decisions you and I would make in the same situation. The machine will have an instinct for what solutions are consistent, and instinctively prefer the consistent ones over the inconsistent once. And suppose the machine is also aware that it performs this selection, and intentionally applies this filter when evaluating its conclusions.
So what? How is naturalism refuted in this sort of picture?
Note that you cannot say that the machine doesn't think rationally because that would contradict one of the premises. Rational thinking is already defined as a set of instinctive mental behaviors, and you cannot redefine rational thinking to mean a set of supernatural instinctive mental behaviors.
Moreover, the machine thinking picture does not contradict our own reasoning because the machine has the same instincts we do.
BDK
You asked how I would define logical necessity. That's tricky just because of its strange nature. It could be described as the certain implication of some propositions by others (or as near to certain as human minds can come), which implication can be transferred to a different level of analysis but not eliminated. We can back it out of a particular set of axioms or logical framework, but only at the price of moving it to a level in which we can draw implications about that set of axioms or logical framework.
DL
I'm too dizzy at the moment with the stomach flu to respond to your latest post in detail, but I will in due course.
DL
>>But you seem to be saying that since the axioms of geometry are not necessarily true, then we ought to doubt our proof and justification of the Pythagorean Theorem.<<
Well, the theorems of geometry are no more certain than are the axioms. But I never said that only necessary truths (those grounded in logical necessity) are worthy of belief.
Also, we have to distinguish reasoning from a certain axiom set and reasoning about that set. And I stressed that logical necessity itself is not an assumption in the usual sense of the word.
It was you, remember, who seemed to classify logical necessity with assumptions that are not "rationally-known." Then later you said that logical necessity was an "observation."
>>Once again, logically necessary for what?<<
You misconstrue my claim. I said that no empirically confirmable (i.e., mechanical) response can be observed to be logically necessary. For example, it cannot be observed that it is logically necessary for an unrestrained billiard ball to move after being struck by another billiard ball. Or that like magnetic poles repel and unlike poles attract. Or that sniffing pepper causes sneezing. All this goes back to Hume and I can't believe you've never heard of it.
It is because the effects of physical causes are not evidently logically necessary that we have to make observations of them to know what they are. And sensory observation of events cannot show them to be logically necessary results of antecendent events.
However, in our thought processes we experience that we arrive at certain conclusions because they are logically necessitated by certain premises. In other words, the effect of logical necessity can be introspected but not inspected.
It's frustrating for me to have to defend to you, of all people, one of the most widely accepted conclusions of more than three centuries of the empirical philosophical tradition.
Since we assume that computers like all machines operate strictly by physical cause and effect, and since physical effects cannot be observed to be logically necessitated by physical causes, in principle we can never empirically confirm a role for logical necessity in the state-by-state causal sequences of a computer.
>>Suppose we show scientifically that, due to the laws of physics, a particular machine will think rationally. That is, the machine will make the same kinds of rational decisions you and I would make in the same situation.<<
As I have just explained, it is impossible to "show scientifically," that is, confirm empirically, that logical necessity makes a difference to the cause-and-effect sequential states of a machine.
The calculator, as I pointed out, does make the same "rational" decisions as you and I do about a narrow class of arithmetic questions. The principle does not change as we widen the class of questions with more circuitry. The machine can parallel or mimic rational decisions in the same preemptive way as the calculator. In fact, the computer could consist of banks of calculators all wired together to achieve increased computing power.
>>And suppose the machine is also aware that it performs this selection, and intentionally applies this filter when evaluating its conclusions.<<
This amounts to saying, "Suppose the machine has a mind while remaining nothing more than a machine." Talk about begging the question!
Suppose instead that the computer merely simulates rational responses. No awareness needed. Kasparov was aware of the chess moves he made, Deep Blue was not. But lack of awareness doesn't stop computers from playing great chess.
You seem to be heading toward a behavioral definition of "awareness" or consciousness. That's a dead end. Do you know you are thinking only by observing in the mirror that you have a knitted brow?
Darek,
Every time we try to deconstruct the term "logically necessary", you reject the idea that logical necessity reflects something being necessary for something else. I propose we drop the term "logically necessary" and replace it with something we can formally define.
Better still we ought to devise multiple rigorous definitions, and see what it is we're really saying about experience.
For example, we can define the following:
1. Logical Intuition: That it feels like a conclusion ought to follow from its premises.
2. Law of Computing: After specifying rules for symbol manipulation, and specifying initial states, certain final states follow consistently and with regularity. It means that, starting from known axioms, some theorems can be known with effective certainty.
There are potentially other terms we can define with rigor. Now your "logical necessity" might be one of these two, both of these two, or some assortment of other rigorously defined ideas. So let's define your term rigorously.
If logical necessity means Logical Intuition, then it remains true that I cannot say that one billiard ball absolutely ought to move in a particular way when struck by a second billiard ball by way of my logical intuition. However, this definition does not preclude naturalism because naturalism need only account for (and be in accord with) my intuitions.
If logical necessity means Law of Computing, then it is also true that the behavior of billiard balls is not necessitated by any law of computation. This is because we don't know the axioms of the physical world, and so it cannot be said that a physical outcome is necessitated by laws of computing. However, naturalism is not contradicted by this. In naturalism, those physical axioms may exist (as laws of physics), in which case, physical outcomes are indeed necessitated by axioms of physics, even if we cannot see their necessity. Or, in naturalism, there may be outcomes that are not necessitated by prior states (e.g., in radioactive decay, perhaps). None of this precludes us from creating a naturalistic model of human cognition. If human minds can compute, then they can discover "laws of computing".
Now I expect that you don't want to define logical necessity as either of these things, but at least we've ruled these two out.
Personally, I think that definition #2 is quite pertinent. Naturalism means that stuff is governed by rules. Naturalism should not be confused with physicalism. Physical stuff is natural because it is lawful, but we can imagine non-physical stuff that is lawful too. There's no contradiction in a naturalistic theory that has both laws of computing and laws of physics. In each case, the laws imply that certain conclusions (or physical final states) are determined by the laws and by premises (or initial states). And again, the reason that physical final states do not seem to be necessary given past experience is that our past experience does not allow us to tease out the axioms of physics (at least, not easily).
How do we know that 234 + 678 = 912? We know it because we defined and controlled the axioms of the computation. And we can work out the theorem enough times that our uncertainty falls to some very low level. Yet in physics, we do not have the luxury of defining or controlling the axioms. The axioms are very complex, and we can only observe the theorems. If we could only observe the theorems of mathematics (and not fix axioms), results of mathematical experiments would be as unpredictable as results of physical experiments.
You talk about computers simulating responses, but if we're talking about laws of computing (as I think we are), then the simulation is the very same thing as thinking.
Can you think of a way to establish that your "logical necessity" is not a matter of laws of computation?
Feel free to respond, but I'll be away from the blog for a few days, and will get back to it later.
Cheers,
DL
DL
>>Every time we try to deconstruct the term "logically necessary", you reject the idea that logical necessity reflects something being necessary for something else.<<
No, I reject that it can be empirically confirmed that any physical effect is logically necessitated by any physical cause. And this claim is not unique to me or particularly controversial philosophically.
>>Better still we ought to devise multiple rigorous definitions<<
One would think logical necessity to be hopelessly vague. It isn't. Logical necessity is that which makes necessary truths necessary. The Socrates syllogism is venerable example, as is 1+1=2. It may be objected that in both these cases the necessity is dependent upon unstated axioms, but the objection falls when we simply include the axioms: "Given base 10 arithmetic, etc., it is necessarily the case that 1+1=2."
We probably ought to distinguish between necessity itself and our means of knowing about it. To say that we know intuitively that certain truths are necessary is not the same as saying that the necessity itself is an intuition. My intuition that I am conscious, for example, is different than the fact of my consciousness.
>>However, this definition does not preclude naturalism because naturalism need only account for (and be in accord with) my intuitions.<<
Let's say that our knowledge that certain truths are necessary is an intuition. Through this intuition the property of necessity possessed by those truths affects the course of our thought.
In naturalism, only that which is empirically confirmable can be allowed causal efficacy. Whatever causes the chemicals in my brain to change their configuration must be capable of empirical confirmation, at least in principle.
Our intuition that certain truths are necessary is not, however, an empirical confirmation of the necessity of those truths. In principle there can be no empirical confirmation of that property.
In other words, through our logical intuition a property that can never be empirically confirmed affects the course of our thought. That property is possessed by those truths that are necessary.
To that extent naturalism does not account for or accord with the causal role played by our awareness that certain truths are necessary.
>>Naturalism means that stuff is governed by rules.<<
Naturalism goes a bit farther than that. Theism countenances rules across reality, but not within a single causal context that is fundamentally non-purposive and non-intentional.
>>Naturalism should not be confused with physicalism. Physical stuff is natural because it is lawful, but we can imagine non-physical stuff that is lawful too.<<
Most naturalism is physicalistic. But crucial to naturalism in general is closure of the physical. Only properties and relations that can be empirically confirmed can be seen as making a difference to the causal story of a physical system.
>>How do we know that 234 + 678 = 912? We know it because we defined and controlled the axioms of the computation.<<
This implies that we are at liberty to make any axioms support any theorems. That's not the case. We are constrained (dare I say by necessity) to acknowledge that certain axioms will support only certain theorems. We don't invent the relationships between axioms and theorems.
>>Can you think of a way to establish that your "logical necessity" is not a matter of laws of computation?<<
To the extent that laws of computation are necessary truths, their property of being necessary cannot be empirically confirmed. Yet that same property affects the course of our own thoughts about laws of computation.
If laws of computation are viewed merely as regularities, not necessary truths, then they obviously leave out of account the effect of the necessary property of certain truths on our thought processes.
>>You talk about computers simulating responses, but if we're talking about laws of computing (as I think we are), then the simulation is the very same thing as thinking.<<
Awareness of the necessary property of certain truths requires consciousness. Computer simulations of conscious behavior (Turing machines) need not be conscious. That alone is a clue that simulation does not capture the essence of rationality.
This talk of logical necessity, as I stated in my first response to DB, seems to be one big red herring as far as philmind goes. But I'm playing along for fun nonetheless.
"We probably ought to distinguish between necessity itself and our means of knowing about it."
If beings with minds didn't exist (this includes gods and humans and rats and monkeys), would the property of logical necessity still exist?
Also, are there any special causal consequences of X being logically necessary versus not logically necessary? If logical necessity has no special causal consequences, then I'm not sure why you keep going on about it as important for behavior or mind. If it does, then we should be able to perceive it, interact, and measure it.
Which horn do you choose?
Darek,
One would think logical necessity to be hopelessly vague. It isn't. Logical necessity is that which makes necessary truths necessary.
I hardly need to point out that this is circular.
Logical necessity is a necessary requirement on propositions for comprehension by rational agents. Why? Because rational agents are agents that seek out logically necessary conclusions. So the whole concept is definitional and conventional.
Moreover, humans are not ideally rational agents. They are frequently irrational. So there is no law of logical necessity which constrains human thinking. Otherwise, we would be justified in saying that there is a law of timekeeping that constraints wristwatches, even when some wristwatches fail to keep time reliably.
It is not impossible for there to be something that is incomprehensible (paradoxical) to rational agents. So it is not a necessity about states of affairs in general. Logical necessity isn't out there. Logical necessity is something that rational agents ought to assume if we are to call them rational agents.
You are begging the question by assuming that logical necessity is "out there" when it is just an arbitrary moral goal (like keeping good time).
Naturalism goes a bit farther than that. Theism countenances rules across reality, but not within a single causal context that is fundamentally non-purposive and non-intentional.
I disagree. A lawful thiesm could be natural. Causal context is not a problem for naturalism. The reason that Christian theists reject a natural mind is that a natural mind would be an deterministic and predictable mind. That destroys the scheme of Christian morality in which punishment is deserved, and not meted out on the basis of utilitarian concerns.
Christian theology is incoherent because it proposes a third choice after determinism and randomness, when randomness is the logical complement of determinism.
Most naturalism is physicalistic. But crucial to naturalism in general is closure of the physical. Only properties and relations that can be empirically confirmed can be seen as making a difference to the causal story of a physical system.
I disagree. I don't think that electromagnetic fields would have been considered physical in Ancient Greece. The definition of "physical" is very vague. I think this is called "Hempel's dilemma".
How do we know that 234 + 678 = 912? We know it because we defined and controlled the axioms of the computation.
This implies that we are at liberty to make any axioms support any theorems.
No. Not all systems are consistent. And sometimes we intend to operate within a particular axiomatic system, so we deny ourselves the ability to add axioms. But you cannot say that my arithmetic is valid outside of particular axiomatic systems. Arithmetic theorems are not true out of context. 1+1 is not 2 without specifying the axioms.
If laws of computation are viewed merely as regularities, not necessary truths, then they obviously leave out of account the effect of the necessary property of certain truths on our thought processes.
I don't think there are any absolutely necessary (context-free) truths because you have to specify for what the truths are necessary.
Your statement above is question-begging. If minds compute, and laws of computation are regularities, then the necessity we perceive is necessity for computation and comprehension, and that is most certainly verifiable. I see no problem here whatsoever.
Awareness of the necessary property of certain truths requires consciousness. Computer simulations of conscious behavior (Turing machines) need not be conscious. That alone is a clue that simulation does not capture the essence of rationality.
I don't think this is at all obvious. If a frog can be aware of a fly, then awareness does not require consciousness.
BDK
>>If beings with minds didn't exist (this includes gods and humans and rats and monkeys), would the property of logical necessity still exist?<<
Well, I think that God is the necessary ground of all existence.
But, assuming a materialistic universe in which there are no minds, would it still be the case that, necessarily, 1+1=2? If we are talking about a possible world, then yes. That's one way of distinguishing between possible and impossible worlds, I believe.
>>Also, are there any special causal consequences of X being logically necessary versus not logically necessary?<<
It has consequences for the course of thought. For purposes of science, for example, we assume that mathematical relations could not, even hypothetically, change over time. That's helpful.
>>If it does, then we should be able to perceive it, interact, and measure it.<<
We perceive it and interact with it in the course of thought. If it could be measured in the sense required by the hard sciences, it would be physical or natural. Logic and mathematics would advance by experimentation just as does physics.
DL:
Since 'necessity' is a property of propositions or sets of propositions, I think it didn't exist before minds. Similarly, the property of being a kidney didn't exist during the first few billion years of the universe's life. Or perhaps even more appropriate, the property of being a healthy kidney didn't exist.
Similarly, the properties of truth/falsity/necessity didn't exist until strange proposition-trading creatures emerged on the cosmic landscape.
As for your specific claim about 1+1=2 being necessary and true independently of minds (by which I mean proposition-trading agents):
If I am modelling water drop number, then 1+1 is not 2, it is 1. I add one drop to another, and end up with a single water drop.
So we get back to the same problems I've been pointing out with logic (e.g., how to choose paraconsistent versus classical). Namely, the choice of a mathematical or logical system depends on the target domain being modelled, so the choice depends on pragmatic factors. Once such a choice is made, certain properties flow such as being a tautology, necessary, true, etc..
Math may be a particularly bad example for you to use, as it is possible that axiomatized mathematics is inconsistent (Godel's second proof showed you can't prove the consistency of any axiomatization of mathematics). This suggests no axiomatization of arithmetic is necessarily true (if X is logically possible that means ~X is not logically necessary).
BDK
>>Since 'necessity' is a property of propositions or sets of propositions, I think it didn't exist before minds.<<
Put it this way. If a universe were possible apart from all minds, could that universe nevertheless contain a particular number of atoms or energetic particles?
>>Godel's second proof showed you can't prove the consistency of any axiomatization of mathematics<<
Only insofar as the proof itself depends upon necessity. This is what I said before, it amounts to shifting the level of analysis, not escaping from or negating necessity.
Per DB:
Put it this way. If a universe were possible apart from all minds, could that universe nevertheless contain a particular number of atoms or energetic particles?
Sure. But that doesn't mean the number abstractly considered, or mathematics, or propositions exist in that universe.
>>Godel's second proof showed you can't prove the consistency of any axiomatization of mathematics<<
Only insofar as the proof itself depends upon necessity. This is what I said before, it amounts to shifting the level of analysis, not escaping from or negating necessity.
My point was that you should be careful of using mathematics to make your point, as it has these types of problems.
I'm not denying that we seem to be able to perceive (judge) that X follows from Y given certain definitions of the terms being used. I'm saying this isn't interesting metaphysically, and doesn't pose any more problems than an illogical mind with no awareness of the 'follows from' operator.
For simple two to three move inferences, we can judge the 'follows from' pretty easily (given the rules, and given that the rules are those we understand quickly--no Scheffer strokes allowed).
However, if I give you a set of propositions 200 long and a putative conclusion, you won't be able to tell if it follows necessarily from the premises. Indeed, a computer would spit out an answer much faster than you. (I'm not saying the computer has an awareness or knowledge of necessity, just that it would kick our ass in spitting out the right answer).
Of course, you could follow each step of the proof, slowly working through to make sure it is valid in the logical system within which you have defined logical necessity. I don't see why that is interesting or mind-blowing or what special role necessity plays there except our ability to recognize the following of the rules. How is that different cognitively from our ability to recognize a friend's face? It's still just a special instance of pattern recognition, a skill which doesn't seem to have interesting consequences.
DL
>>I hardly need to point out that this is circular.<<
In that necessity is irreducible, of course a description of it is going to be some kind of tautology. I was trying to identify it in a way that made it even less controversial philosophically. That there are necessary truths is seldom denied in my experience. (As usual, Quine may be an exception.)
>>Because rational agents are agents that seek out logically necessary conclusions. So the whole concept is definitional and conventional.<<
If it is conventional, it is invented, not "sought out." You do not "seek" after that which you simply imagine or create.
>>Moreover, humans are not ideally rational agents. They are frequently irrational. So there is no law of logical necessity which constrains human thinking.<<
It constrains it to the extent that humans can become aware of it as an objective reality. Humans may or may not be aware that electrical charge exists, for example. They were unaware of it for a long time. In that sense, it did not force itself upon the human mind. But humans can become aware of electrical charge as an objective reality, not as something they merely dreamt up.
>>Logical necessity isn't out there.<<
You keep saying that, as if I'm implying that necessity exists at some spatiotemporal location such as the corner of Park and Main Streets in Omaha, Nebraska. Can you come to grips with the idea of something that doesn't exist that way and yet is still objectively real?
>>Logical necessity is something that rational agents ought to assume if we are to call them rational agents.<<
Why, if it's conventional as you claim? Why couldn't we simply all agree tomorrow that rational agents need not assume it? It's conventional that the dollar bill is a certain length and width, but the US treasury could change that in the future.
>>You are begging the question by assuming that logical necessity is "out there" when it is just an arbitrary moral goal (like keeping good time).<<
There is a sense in which caesium atoms keep good time, yet I don't believe that the characteristics of caesium atoms are conventional or arbitrary. There are aspects of time-keeping that are conventional, but nevertheless there are facts that time-keeping must respect. We have some choice in the ends to which we put our reasoning ability, but necessity itself is not a matter of choice.
>>I don't think there are any absolutely necessary (context-free) truths because you have to specify for what the truths are necessary.<<
How about, "There are no absolutely necessary (context-free) truths." Is that likewise not a necessary truth? If so, then perhaps there are such truths. I take it you understand, at least, that it is unusual in the fields of philosophy and logic to deny that there are necessary truths.
>>I don't think this is at all obvious. If a frog can be aware of a fly, then awareness does not require consciousness.<<
Chalmers with his "hard problem," Searle with his Chinese room, even Dennett with his multiple drafts will be embarrassed to find that consicousnessness is so easily explained--frogs and flies. Thermostats are aware of temperature, too, I take it. Running water is aware of elevation. Leaves are aware of the afternoon breeze. The moon is aware of gravity--how else would it stay in orbit? I think there is a problem trying to define conscious awareness as simple cause-effect, but if that satisfies you . . . welcome to it.
>>That destroys the scheme of Christian morality in which punishment is deserved, and not meted out on the basis of utilitarian concerns.<<
If you are like me, you've probably done some things in your life that you feel guilty about. Justifiably. I don't mean we obssess about them, but feel a sense of moral responsibility for them. I don't see how that squares with determinism that obviates moral responsibility.
BDK
>>Sure. But that doesn't mean the number abstractly considered, or mathematics, or propositions exist in that universe.<<
I take that as a "yes." In such a mindless universe, there could be a certain number of elementary particles.
Would that "certain number" be double what half of it would be? I think that's hard to deny.
Would it be the case, in such a mindless universe, that there are no minds? In other words, are there certain ways this mindless universe would have to be in order to be what it is? Again, I think that's difficult to avoid.
>>However, if I give you a set of propositions 200 long and a putative conclusion, you won't be able to tell if it follows necessarily from the premises.<<
Of course. But whether I can tell or not, there is a fact of the matter as to whether it does follow necessarily from the premises. And we can conceive of what it would mean for it to follow necessarily.
>>I don't see why that is interesting or mind-blowing or what special role necessity plays there except our ability to recognize the following of the rules.<<
What's interesting and mind-blowing is often what we take for granted, what's right in front of us but we never question.
By "following of the rules" do you mean simply observe a regularity? In addition to regularity, there are such real things as rules and necessity. So that, for example, Godel's proof is more than Godel's fantasy.
>>How is that different cognitively from our ability to recognize a friend's face?<<
We recognize a friend's face by seeing it. But there are some things we recognize by thinking about them as opposed merely to seeing them. We don't recognize the necessary character of the commutative law of addition (given axioms, if you insist) by seeing it with the eyes.
In other words, are there certain ways this mindless universe would have to be in order to be what it is? Again, I think that's difficult to avoid.
Yes, of course. What is your point?
Rules are defined within the axiomatic system in the inference rules. It doesn't require noticing "necessity" in any interesting way. If I teach you boolean logic using the Scheffer stroke you won't understand it, but will be able to follow proofs nonetheless. Eventually you will understand it and it will feel intuitive, you will "feel" the necessity of a conclusion from a premise.
Where is the magic there? And how is anything you've been saying different from learning logic using the Scheffer stroke? Is the 'if..then' construction in Boolean logic any different? Try teaching the if--then truth table to undergrads if you want to say it is intuitive ("Hey, wait, if the antecedent is false the conditional is true? WTF? I don't get it!").
So, within an axiomatic system there is an induced logical necessity. Fine. But nothing radical follows metaphysically.
I don't think I can be clearer than that.
Note I came off a bit cocksure in my last one. I realize there are issues here! I think my general perspective works, but is not without problems. I think some kind of nominalism (where by 'nominalism' I just mean a rejection of platonism) is the best route, as any reader here would predict. So I don't have to deal with the 'problem' of abstract objects and how they interact with nature.
However, I'm left with the problem of explaining in virtue of what facts mathematical statements are true (or if I think they are literally false, I must explain this seemingly crazy view).
BDK
>>Yes, of course. What is your point?<<
You said that in a universe without minds there would be no mathematical truths, and perhaps no necessary truths at all.
I asked if there could be a mindless universe containing a certain number of particles. You said yes (but without "abstract" mathematics). Then I pointed out that if there were such a universe and it did contain a certain number of particles, that number would be double what half of it would be. In other words, those truths of relation and proportion that allow for any significant meaning of the description, "containing a certain number of particles," would necessarily be true in such a universe.
To be fair, you seem to acknowledge this as a problem at least in your last post.
>>Rules are defined within the axiomatic system in the inference rules.<<
Could you by any chance mean that, necessarily, rules are so defined? What experiment could potentially disconfirm your statement? Or what experience?
>>Eventually you will understand it and it will feel intuitive, you will "feel" the necessity of a conclusion from a premise.<<
>>Try teaching the if--then truth table to undergrads if you want to say it is intuitive<<
We could equally claim that there is no such thing as "knowing" anything, there is only the "feeling of knowing" things. Except that that would be a claim of knowledge beyond mere feeling.
I cannot intuit that 1482 + 8673 = 10155. I can blindly follow a procedure to give me the result. But I can conclude that the procedure is likely to give me an answer that I could appreciate to be as necessary as "a + b = b + a" if I had more conceptual power. But to do that I have to understand the necessity of the commutative law.
When we analyze necessity as habit or game-playing or conditioned response, we don't notice that we are presuming our analysis to be other than habit or game-plaing or conditioned response. We have to stand on some logical ground or unwittingly invoke necessity, in other words, to analyze logical analysis.
When we analyze necessity as habit or game-playing or conditioned response, we don't notice that we are presuming our analysis to be other than habit or game-plaing or conditioned response. We have to stand on some logical ground or unwittingly invoke necessity, in other words, to analyze logical analysis.
Why? You have defined necessity as
"the certain implication of some propositions by others." Why does my analysis of necessity have to be certain or necessary? It is part of my naturalistic, fallible, theory of the world and how things fit together. Propositions that 'follow from' others are just another bit of the universe that I seek to understand. Such properties aren't fundamental in any way in my nonfoundationalist picture of knowledge.
You also said:
"We can back it out of a particular set of axioms or logical framework, but only at the price of moving it to a level in which we can draw implications about that set of axioms or logical framework."
I'm not sure what this means. It seems moving necessity out to the level of a system opens up all sorts of interesting questions about how we choose the system. And again, I say this isn't something that is necessary. It is guided by pragmatics, fit with evidence, the kind of stuff scientists like, that naturalists like.
In bumper sticker form, choosing between standard and paraconsistent logics is not a logical matter, is not a matter of necessity.
Trying to understand what you are saying about the universe having N particles. You could say, if we existentially quantify over numbers in such a description of this mindless universe, aren't we ipso facto claiming that numbers exist in that universe? Is that what you are getting at?
BDK
>>Why does my analysis of necessity have to be certain or necessary?<<
I didn't say it had to be certain, I said it had to invoke necessity. Somone can be incorrect in a proof and still be attempting to give a proof.
Below seemed to be a part of your analysis:
>>Rules are defined within the axiomatic system in the inference rules.<<
I asked if you can conceive of experimental disconfirmation of that statement. If not, I presume you were invoking necessity.
>>Propositions that 'follow from' others are just another bit of the universe that I seek to understand. Such properties aren't fundamental in any way in my nonfoundationalist picture of knowledge.<<
Then there ought to be a potential disconfirmation that some propositions follow from others. But it seems to me that any such disconfirmation would have to presume that some propositions do follow from others. If you must keep the implication of some propositions by others around in order to have confirmations or disconfirmations, it sure would seem to be necessary, don't you think?
>>In bumper sticker form, choosing between standard and paraconsistent logics is not a logical matter, is not a matter of necessity.<<
If the implication of some propositions by others is necessary to understanding the difference between standard and paraconsistent logics, it would seem necessary to choosing between them.
>>You could say, if we existentially quantify over numbers in such a description of this mindless universe, aren't we ipso facto claiming that numbers exist in that universe?<<
That is supposed by clearer than my simple question? I asked if in a mindless universe there could be a certain number of particles. You (sort of) said yes. I then asked if this number would necessarily be double what half of it would be. I assumed a yes answer, and on that basis asserted that there would be mathematical facts ("truths of proportion and relation") in that universe.
Would those mathematical facts be known in that universe? Necessarily not, since it is a universe without minds. Unless you think we need to perform an experiment to test the hypothesis that mathematical facts cannot be known in a universe without minds.
Darek,
If it is conventional, it is invented, not "sought out." You do not "seek" after that which you simply imagine or create.
I am not saying that consistency is purely invented (whatever that means). I am saying that what a "rational thinker" ought to do is conventional to the definition of "rational thinker". That is, the definition of rational thinker is spelled out in terms of what a rational thinker does. There's no other reference point by which we can say "Fred is rational when he concludes X" other than by reference to the consistency of Fred's conclusion. It's not as if we think Fred is rational and later discover that he happened to pick out consistent solutions. Saying Fred is rational is equivalent to saying he picks out consistent solutions.
But humans can become aware of electrical charge as an objective reality, not as something they merely dreamt up.
Okay, but the analogy to electromagnetism here is consistency, not necessity.
Why, if it's conventional as you claim? Why couldn't we simply all agree tomorrow that rational agents need not assume it? It's conventional that the dollar bill is a certain length and width, but the US treasury could change that in the future.
Because it is integral to the definition of rational thinking that we seek out consistent solutions. Dollar bill size is analogous to a logical notation. To say that rational thinking means seeking inconsistent solutions would be like declaring the dollar to be of no particular value (and, therefore, not a currency.
There are aspects of time-keeping that are conventional, but nevertheless there are facts that time-keeping must respect.
But what would happen if the time-keeping aspects of device X were not respected? We would say that X is not a time-keeper. X must only conform to the aspects of a timekeeper if X is to be consistently called a timekeeper.
Chalmers with his "hard problem," Searle with his Chinese room, even Dennett with his multiple drafts will be embarrassed to find that consicousnessness is so easily explained--frogs and flies.
I'm not explaining consciousness. I'm saying rationality doesn't necessarily require it.
BTW, sorry for the delay. I'm still on vacation, and can only sneak off to the blogosphere now and then.
DB:
Me:
>>Rules are defined within the axiomatic system in the inference rules.<<
DB:
I asked if you can conceive of experimental disconfirmation of that statement. If not, I presume you were invoking necessity.
I'm not invoking necessity or a positivistic confirmationism. Let's say it's a hypothesis about the nature of necessity. That it is a property of inter-proposition transitions within certain formal languages. Note this is a syntactic notion of necessity. I also have a semantic notion of necessity, in which a proposition can be true or false based on the meanings of the terms used.
Then there ought to be a potential disconfirmation that some propositions follow from others. But it seems to me that any such disconfirmation would have to presume that some propositions do follow from others.
Why? Just because affirming the consequent doesn't work, that doesn't imply that there are other inference rules that will always work.
Me:
>>In bumper sticker form, choosing between standard and paraconsistent logics is not a logical matter, is not a matter of necessity.<<
DB:
If the implication of some propositions by others is necessary to understanding the difference between standard and paraconsistent logics, it would seem necessary to choosing between them.
I would be fine if you said that choosing between the logics is a matter of choosing which types of inference rules will count as necessary. My point is that the choice of said system is not dictated by some independent consideration of necessity. I.e., one of them isn't necessarily true, the other necessarily false. We need to step outside of necessity to pick the system that induces the set of necessary rules.
On the math stuff, I've already replied to your number objection then. Sure, our propositions about that universe use numbers, but that doesn't mean the universe we are talking about has numbers. Say there are two objects in the universe. That doesn't mean the number two is also in the universe! Or the number one (which is half the number of things in that universe, again a true proposition, entertained by proposition-trading creatures, about that universe).
Reductio: because I have two eyes the number two abstractly exists in my body.
I think my formulation in terms of existential quantification is more standard, so to me it is more clear, familiar, and frankly makes it harder for me! Your question about the cardinality of the universe seems less threatening because it seems relatively easy to block.
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How does Reppert get off scott-free from these discussions. I have a feeling his blog is for note taking. If true, gotta love that! What a compliment to you three.
DL
>>I am saying that what a "rational thinker" ought to do is conventional to the definition of "rational thinker".<<
Is the above statement necessarily true, or true by convention? And if true only by convention, why couldn't it be otherwise?
>>Because it is integral to the definition of rational thinking that we seek out consistent solutions.<<
Doesn't "integral" in the above mean the same thing as "necessary"?
>>To say that rational thinking means seeking inconsistent solutions would be like declaring the dollar to be of no particular value (and, therefore, not a currency<<
That the dollar has a particular value is a convention. Conceivably, the dollar could be declared no longer to have a particular value. Are you claiming that unavoidably it would be either false or meaningless to say that "rational thinking means seeking inconsistent solutions"? And if so, doesn't "unavoidably" mean "necessarily"?
BDK
BDK
>>Let's say it's a hypothesis about the nature of necessity. That it is a property of inter-proposition transitions within certain formal languages.<<
OK, if it is a hypothesis, then it must be testable against experience. In order to be testable against experience, it must be capable of disconfirmation. But is it? This sounds positivistic, but that is still the gold standard of science.
More broadly, are there hypotheses about syntactical and semantic properties that cannot be conceived, communicated, tested and evaluated without assuming or intuiting those very properties in the course of such conceiving, communicating, testing and evaluating?
>>I would be fine if you said that choosing between the logics is a matter of choosing which types of inference rules will count as necessary.<<
What is necessary is that certain results (theorems, what have you) are determined by certain rules, or axioms, or rules derived from axioms. The results could not be otherwise given the axioms chosen. Sure, we can choose among different axiom sets or logical systems. But we cannot arbitrarily decide or choose which theorems will follow from which axioms. We cannot decide that a paraconsistent logical framework will give us results that are identical with those of classical logic. We find ourselves constrained, limited, in terms of the results that follow from a given logical framework or axiom set.
Insofar as the axiom set and its derivations can be expressed as propositions, this limitation works itself out in terms of the relations between propositions. To say we are limited or constrained in this way is just another way of saying that necessarily thought must run along certain rails, as it were, to get certain places.
>>We need to step outside of necessity to pick the system that induces the set of necessary rules.<<
If we could step outside of necessity, we could pick any system and pick any rules, results, etc. that we wanted for that system. But quite obviously, we cannot do that, i.e., "necessarily" we do not do that. But look at the task itself, that is, picking the system. Doesn't the "picking" depend upon an evaluation of some kind, upon understanding to some degree what the various systems logically entail. And if it depends upon that entailment it is also constrained by it. To say that I have to pick oranges to make orange juice and lemons to make lemon juice constrains my choice, even if I'm free to pick between them.
To put it yet another way, the manner in which axiom sets and logical systems inevitably work is something we discover, not something we invent. But these discoveries cannot all be empirically tested. To test them we have to be able to question them coherently. But we need to assume some of them to form coherent questions about anything. To ask what conclusions necessarily follow from what inference rules, for example, we have to assume we know what we mean by "necessarily follow from."
I'll defer on the question of mathematical entities, since I'll easily get out of my depth. To summarize my point, we live in a universe that has the property of being capable of mathematical description. If a universe could indeed exist without minds, it nevertheless could have that same property.
Me (with arrows):
>>Let's say it's a hypothesis about the nature of necessity[: it] is a property of inter-proposition transitions within certain formal languages.<<
DB (in italics):
OK, if it is a hypothesis, then it must be testable against experience. In order to be testable against experience, it must be capable of disconfirmation. But is it? This sounds positivistic, but that is still the gold standard of science.
I look at my view as an inference to the best explanation. It should mesh with the evidence: accurately capture how the idea of 'necessity' is invoked, be naturalistically reasonable, and help demarcate what makes logically necessary statements different from non-necessary statements. I think it does all these things.
It would not work if logical necessity didn't apply to inter-proposition transitions, for instance.
More broadly, are there hypotheses about syntactical and semantic properties that cannot be conceived, communicated, tested and evaluated without assuming or intuiting those very properties in the course of such conceiving, communicating, testing and evaluating?
Perhaps. It is also not possible to do neuroscience without having a brain.
>>I would be fine if you said that choosing between the logics is a matter of choosing which types of inference rules will count as necessary.<<
What is necessary is that certain results (theorems, what have you) are determined by certain rules, or axioms, or rules derived from axioms. The results could not be otherwise given the axioms chosen.
Sure. I'm fine with this.
To say we are limited or constrained in this way is just another way of saying that necessarily thought must run along certain rails, as it were, to get certain places.
Now you've switched from the topic of logic to the topic of transitions among mental states. We could imagine a perfectly mental creature that was quite illogical. Indeed, I think humans are such a creature.
>>We need to step outside of necessity to pick the system that induces the set of necessary rules.<<
If we could step outside of necessity, we could pick any system and pick any rules, results, etc. that we wanted for that system. But quite obviously, we cannot do that, i.e., "necessarily" we do not do that.
Is this obvious? How do you choose among the various "deviant" logics such as paraconsistent logics versus classical boolean versus predicate logic?
But look at the task itself, that is, picking the system. Doesn't the "picking" depend upon an evaluation of some kind, upon understanding to some degree what the various systems logically entail. And if it depends upon that entailment it is also constrained by it.
I agree with the first point: we should have some understanding of the commitments the logical system entails. But this doesn't imply that our thinking is constrained, or our choice is so constrained. I can step back and look at which looks more reasonable given the domain I am modelling. It's a question of evidence, which as I've stated brings in pragmatic and empirical considerations.
To put it yet another way, the manner in which axiom sets and logical systems inevitably work is something we discover, not something we invent.
Sure. The same is true of any mathematical equation like F=ma.
But these discoveries cannot all be empirically tested. To test them we have to be able to question them coherently. But we need to assume some of them to form coherent questions about anything. To ask what conclusions necessarily follow from what inference rules, for example, we have to assume we know what we mean by "necessarily follow from."
Sure, and I've provided a general explanation of necessity that transcends particular logical systems--all logical systems have inference rules and axioms, and what is necessary is what follows from the two (ignoring, for now, special terms defined in the language of the logic, such as 'set'). This isn't an analytic truth, but a hypothesis about the nature of logical necessity.
So, the question, which has to be informed by extra-logical considerations, is which logical system (or systems) we wish to latch onto for our present epistemic goals, including the target domain we are modelling. If I am working on modelling a domain peppered with liar's paradoxes, I might go paraconsistent. If I'm modelling statements about medium-sized dry goods, I'd probably go with standard predicate logic. If I'm modelling quantum systems, I'd consider using quantum logics. Finally, I would probably not employ formal symbolic logic at all as a substantive theory of human thinking (though I would, perhaps, of public human language and argumentation).
BDK
>>Rules are defined within the axiomatic system in the inference rules.<<
>>I look at my view as an inference to the best explanation.<<
Given the terms you use in your hypothesis, could it really be false? That is, could there be an alternate explanation of necessity within an axiomatic system that would entail that your statement is untrue with respect to the relationship between "rules" and "axiomatic system" without a change of defintions of your terms?
>>Perhaps. It is also not possible to do neuroscience without having a brain.<<
Sarcastically this may be effective, but it doesn't speak to my point. Suppose that it were not possible to confirm empirically the proposition that humans have brains in their skulls without either assuming or intuiting the truth of the proposition that humans have brains inside their skulls. In that case, we could not in fact, make the empirical confirmation, could we? We can confirm that we have brains and need them for thinking precisely because we do not need to intuit or assume those propositions in order to test them against experience.
>>Sure. The same is true of any mathematical equation like F=ma.<<
Did humans discover F=ma to be necessarily true the same way they discovered a+b=b+a to be necessarily true? I seem to remember some debate over the definitional content of F=ma. In any case, the necessary truth of a proposition cannot be discovered empirically. That certain propositions are not only true, but necessarily true, is discovered by other than empirical means.
>>I agree with the first point: we should have some understanding of the commitments the logical system entails.<<
"Should have" or "must have" in order to choose in a manner appropriate to our epistemic goals? Do we "need" to understand the commitments or necessities of the systems to choose appropriately? Isn't it necessarily the case that our ability to choose appropriately covaries with our understanding of the necessities within the system we are considering?
>>all logical systems have inference rules and axioms<<
Is this claim inductive or deductive? Aren't the terms "logical system," "inference rule" and "axiom" definitionally interdependent?
>>This isn't an analytic truth, but a hypothesis about the nature of logical necessity.<<
Did you determine that analytically? Is it a truth of analysis that your explanation of necessity is not analytic? And if so, has it really helped you to step outside of necessity?
>>So, the question, which has to be informed by extra-logical considerations<<
Again, doesn't this amount to a check written against logic? Aren't you implying, "Logically, the question has to be informed by extra-logical considerations"?
DB:
Before getting to specifics, I'd be curious about how you look at the decision to operate using a paraconsistent versus a more classical logic. Would you not take into account pragmatic or evidentiary considerations in making this choice? Is one of the logical systems right, the other wrong? How would you arrive at this conclusion?
>>Rules are defined within the axiomatic system in the inference rules.<<
>>I look at my view as an inference to the best explanation.<<
Given the terms you use in your hypothesis, could it really be false? That is, could there be an alternate explanation of necessity within an axiomatic system that would entail that your statement is untrue with respect to the relationship between "rules" and "axiomatic system" without a change of defintions of your terms?
Rather than get into that, I think it would not hurt my theory if it were true by definition! But we'd be getting into semantic necessity, analytic truths, and I want to keep this post focused on the syntactic notion of necessity, the type of necessity induced by the 'syntax' or rules of inference in a system.
>>Perhaps. It is also not possible to do neuroscience without having a brain.<<
Suppose that it were not possible to confirm empirically the proposition that humans have brains in their skulls without either assuming or intuiting the truth of the proposition that humans have brains inside their skulls. In that case, we could not in fact, make the empirical confirmation, could we? We can confirm that we have brains and need them for thinking precisely because we do not need to intuit or assume those propositions in order to test them against experience.
My point is that just because we use X to discover things about X, that doesn't imply that we can't have knowledge about X. How is logic different? How, specifically, is it different than the brain case? You could say I'm not allowed to justify claim Z by assuming claim Z, but that is different, and I haven't done that.
I don't just assume logic is true, and I don't trust intuitions (e.g., they sure break down with liars' type paradoxes for most people). We trust various logical forms partly because of extralogical considerations (as I've discussed ad nauseum and linked above.
>>Sure. The same is true of any mathematical equation like F=ma.<<
Did humans discover F=ma to be necessarily true the same way they discovered a+b=b+a to be necessarily true? [...]In any case, the necessary truth of a proposition cannot be discovered empirically. That certain propositions are not only true, but necessarily true, is discovered by other than empirical means.
I disagree. While an inference rule isn't a low-level empirical claim like 'I am 6 foot four' that can be verified by a simple one-off observation, inference rules aren't oblivious to pragmatic/evidentiary considerations. Again, this gets back to our previous discussions meta-linked above.
>>I agree with the first point: we should have some understanding of the commitments the logical system entails.<<
"Should have" or "must have" in order to choose in a manner appropriate to our epistemic goals? Do we "need" to understand the commitments or necessities of the systems to choose appropriately? Isn't it necessarily the case that our ability to choose appropriately covaries with our understanding of the necessities within the system we are considering?
Sure. It's not like we suddenly understand a logical system. Even like a theory in physics, ya' gotta play around with it, explore its implications, move about it in, do some proofs, examine how well it works in the domain of interest.
>>all logical systems have inference rules and axioms<<
Is this claim inductive or deductive? Aren't the terms "logical system," "inference rule" and "axiom" definitionally interdependent?
It's an observation of modern logic, but you are probably right that it is so entrenched that some of my claims would be considered definitional truths.
>>This isn't an analytic truth, but a hypothesis about the nature of logical necessity.<<
Did you determine that analytically? Is it a truth of analysis that your explanation of necessity is not analytic? And if so, has it really helped you to step outside of necessity?
It's a description of my psychology. I've proposed this theory, and I don't mean it to be an analytic truth, but something open to logical practice. In the quote you reference, I was talking more generally about my model of logic, its openness to evidence, etc., not any narrow definitional stuff.
And the model has helped me make sense of talk about logical necessity, so far, so I consider it a reasonable view until evidence counter comes my way.
>>So, the question, which has to be informed by extra-logical considerations<<
Again, doesn't this amount to a check written against logic? Aren't you implying, "Logically, the question has to be informed by extra-logical considerations"?
Sure. I never said I avoided being logical or making logical arguments. I just have a little proto-framework within which such practices take place.
For practical purposes, I think we can get by pretty darn well with boolean or predicate logic, and to step back, with every argument, and say, "Aha, I'll Quine-Duhem your sorry butt and question the very logic you are using" would be an extreme waste of time. However, if I were a philosopher of logic I certainly wouldn't take it to be a waste of time!
One little amendation:
DB said:
Isn't it necessarily the case that our ability to choose appropriately covaries with our understanding of the necessities within the system we are considering?
I agreed to this, but I should have struck through the bold word. You sure like to put necessity operators in front of things in this discussion. :)
My previous posts have discussed logical necessity in the sense of what inter-proposition transitions are valid.
There is also a different type of necessity that could be called logical necessity, but which I call semantic necessity. This applies to individual sentences. E.g., 'A triangle has three sides' is often taken to be knowable based only on the meanings of the terms. This is a whole different, in some ways more complicated topic, but I am OK with there being such 'analytic' truths, and think it is fine for a naturalist to believe in them.
Giving a proper account would require giving a semantic theory. Of course, modern logic also is not silent on truth, since Godel and especially Tarski's formalization of model-theoretic semantics. I'm sure people have written on this cool topic (relation between analyticity and model-theoretic semantics), but I know absolutely nothing about it.
Hence, since I don't have time to learn about it right now, I am just going to stick with arguing about syntactic necessity rather than semantic necessity, even though they are probably related in interesting ways. Not least of all, we don't care about syntactic engines that don't preserve truth values the way they should, i.e., the way they are preserved in the target domain.
Funny, Tarski himself called his logical truths 'analytic' truths, as can be found on his entry at Stanford:
In terms of the defined notion of satisfaction, Tarski introduces the notion of a model of a sentence. A model of a sentence S is an interpretation that satisfies the sentential function S′ determined by S; more generally, a model of a set of sentences K is an interpretation that satisfies all the sentential functions determined by sentences of K. And in terms of the defined notion of model Tarski proposes his defined notion of logical consequence. A sentence X is a (Tarskian) logical consequence of the sentences in set K if and only if every model of the set K is also a model of sentence X (cf. Tarski 1983c, p. 417). Tarski proposes also a defined notion of logical truth (he uses the expression "analytic truth") using the same apparatus: a sentence S is a (Tarskian) logical truth if and only if every interpretation of S is a model of S. Analogous notions of Tarskian logical consequence and logical truth can be defined for other languages using the same method we have followed with LAr, just making the obvious changes.
This is for those who have had some model-theoretic semantics, a beautiful subfield of mathematical logic. Really, to address the full topic in this thread, I'd have to retool much of it in terms of such concepts, and frankly I haven't studied them in many years and it would take a bit of a time commitment.
BDK
Sorry to be late getting back to you. Computer woes.
>>Would you not take into account pragmatic or evidentiary considerations in making this choice? Is one of the logical systems right, the other wrong? How would you arrive at this conclusion?<<
Doesn't your first question presume a relationship between evidenciary considerations and reasonable choice such that a choice that disregards relevant evidence cannot be--i.e., necessarily is not--reasonable?
Doesn't your second question imply that there is a right or wrong answer to the question, "Is one of the logical systems right and the other wrong?"
I'm not trying to send experience packing. But raw experience is not evidence, it becomes evidence when we drop it into a grid that includes necessity. Because the grid is what transforms raw percepts into evidence, we can never confirm all the properties of the grid itself from evidence.
That which is learned from experience can be confirmed from experience, because confirmation is the process of revisiting the the learning. However, experience might catalyze or trigger an understanding that cannot be confirmed and therefore was not learned--not in the sense of drawing conclusions from evidence, anyway.
For example, Helen Keller's memory began with the moment that she understood that a sign meant water, or more importantly, that a thing can have a meaning. But the proposition that a thing can "mean" cannot be tested. In the very act of asking, "Can something have a meaning?," we assume or intuit that it can--otherwise the question itself has no meaning.
I think the same can be said of definitional truth or semantic necessity or whatever we choose to call it. If we dig we will find it there in the mix whenever we analyze, and simply asking questions about the relationship between evidence and logical systems is a step of analysis.
Your brand of naturalism may accept inference to the best explanation apart from empirical confirmation (note that confirmation is weaker than verification). But such is not the case with science. Science requires testability or possibility of confirmation. And garden variety naturalism hitches its epistemic wagon to science, attributing scant value to propositions that are incapable of being empirically tested.
I do accept, however, that we are unlikely to have a meeting of the minds and that this thread may have run its course . . .
This comment has been removed by the author.
Hrm, this seems to completely ignore the relevant science about mental states. I'm about to leave town, but I will return on Thursday and explain why.
In the meantime, I have an entry on my site that explains the physical nature of cognizance.
JT: You mean neuroscience has solved the mind-body problem and we've missed it all this time! :)
I wrote:
>>>Before getting to specifics, I'd be curious about how you look at the decision to operate using a paraconsistent versus a more classical logic. Would you not take into account pragmatic or evidentiary considerations in making this choice? Is one of the logical systems right, the other wrong? How would you arrive at this conclusion?<<<
DB:
But the proposition that a thing can "mean" cannot be tested. In the very act of asking, "Can something have a meaning?," we assume or intuit that it can--otherwise the question itself has no meaning.
[...]
I think the same can be said of definitional truth or semantic necessity or whatever we choose to call it
[...]
If we dig we will find it there in the mix whenever we analyze, and simply asking questions about the relationship between evidence and logical systems is a step of analysis.
So looking for evidence about necessity in logic is analogous to asking if anything exists that has semantic properties? I agree that asking for evidence is often entering the space of reasons which invokes some sort of "logic" (in the informal sense). (Though this isn't always clear such as for low-level empirical claims like 'The TV is on my table right now').
But agreeing for the time-being, what does that imply? It suggests we come to any problem with a pre-existing set of epistemic standards already in place.
We begin en media res, we tend to trust certain types of proposition-chains better than others. We have a bunch of flexible and revisable rules of thumb, heuristics, and things that seem to work, which we have come to trust. Is that necessity? Your definition of necessity involved 'certainty' that one thing follows from something else. Is this really required to navigate, argue, give and accept reasons for things? It doesn't look like necessity to me.
Let me come full circle. While the answer may be buried in there (I'm still not sure what you think as you seem to keep trying to throw out these "gotcha" lines and avoid the direct question), I am still unclear: How exactly would you choose between paraconsistent and classical logic? Do you think one system of logic is better than the other, that one (but not the other) has the property of being logically necessary? And by what inference process would you decide either of these questions? Would you use classical logic, paraconsistent logic, or something else to decide between the two? Or would you just say 'Let a thousand logics bloom' and embrace logical pluralism?
My suggestion: we use that set of informal heuristics, rules of thumb to decide such matters. The ultimate meta-logic is not really a logic at all, but is a raft that we start out upon in this enterprise, a raft that we are constantly rebuilding, trading parts, and improving as we navigate the epistemic landscape. (I steal the idea of the raft from Otto Neurath).
Your brand of naturalism may accept inference to the best explanation apart from empirical confirmation (note that confirmation is weaker than verification). But such is not the case with science. Science requires testability or possibility of confirmation.
I can't resist nibbling at this bait(ing). There are a few reasons this is confused.
First, I could be a naturalist and think there are a priori conceptual truths that are immune to revision. E.g., I could think that 'A bachelor is a male' is true by definition, and no amount of evidence will change it. I am actually agnostic on this topic, as my view on concepts isn't settled enough to take a strong stance. So, if it turns out that my view is true by definition, that doesn't mean I'm not a naturalist! I happen to think my view is more substantive than all that, that it isn't just stating definitions, but if you were to argue that I'd be OK.
Second, I didn't say there shouldn't be evidence for my claim, and I discussed that explicitly. One thing you haven't discussed directly is my questions above about choosing between paraconsistent and other logics. One reason I brought it up is because it suggests ways I might be wrong (e.g., there could be some ultimate and necessarily true meta-logic that we use to choose from among logical systems--a prediction of my view is that there is no such thing, but if it were discovered I'd be wrong).
Finally, this claim is ironic since what has been killed by the evidence is the view that there exist logically necessary inference rules simpliciter, that there exist universally necessary rules of inference. My views are simply a logical reaction to the evidence that this view is incorrect. If there were no alternative incompatible logical systems with different inference rules that would make my position less tenable.
Darek,
I'm back. I'll just try to sum up.
First, let's go back to what naturalism means. It means that the world can only be explained by predictable, causal rules. X occurs because Y predictably caused X (at least statistically). In naturalism, if X occurs without a predictable cause, then X is unexplained.
Physicalism is a subset of naturalism because physical laws are natural laws.
Now let's consider consistency. All natural systems have consistency as a property. If they did not, then they would not have predictive, causal rules.
In particular, mathematics and computation are natural. They represent predictive regularities in computation. Every time I follow self-imposed rules of computation, I get the same answer. (Well, statistically!)
Naturalism goes beyond physicalism. Naturalism can apply to thought as well as to the five senses. Indeed, the division between mental and physical is not a philosophically fundamental one, IMO. Every physical experience comes at us as a mental experience. We just partition off a certain set of subjective mental experiences as belonging to the set of physical experiences.
Your argument is that naturalism fails if a regularity cannot be seen by the physical sciences. This seems like a a folk-philosophic notion to me, and it's certainly not a requisite test for naturalism. Just like every other system, there are some things that remain unexplained under naturalism. What matters for naturalism is predictability, not physical predictability. Naturalism works whenever there is a regularity that can be experienced, whether physical or not. For example, mathematical predictions are natural predictions.
There could be natural psychic powers, natural gods, natural souls, etc. However, there's no compelling evidence for these things because there are no predictive theories of them. Moreover, most Christians reject a natural god for moral or theological reasons. Specifically, they reject the idea that god (or human agents) would be deterministic.
Let's apply all this to the mind. We can tell from our experience that one set of propositions is consistent, and another set of propositions is not. This is all that is required for us to have a notion of truth and necessity. Also, I can impose rules of logic upon myself, and find that certain conclusions always follows when the rules are followed consistently. So it seems clear to me that even physicalism supports the notion of perceived necessity.
As I said before, there's also no reason to rule out the possibility that what we see in the world is just as necessary as the theorems of arithmetic. If the world is natural, then the world has axioms, and everything we see is a theorem. The only reason that physical outcomes don't appear necessary is that we don't know the axioms. But if the world is deterministic, and we knew the rules, then the physical outcomes would be necessary.
Let's suppose that we apply your argument against physicalism rather than naturalism. Well, under physicalism, everything that I'm thinking (rules, concepts, etc) are functions of my physical being. So, to say that a person is doing arithmetic is like saying that a sea current has an undertow. So, showing that a physical model of a human is functionally the same as a thinking human, is enough to to show that physical has explained how we think. So even physicalism can find a way to physically prove the appearance of necessity.
Nonetheless, like all systems, naturalism and physicalism do have things that are unexplained. Naturalism cannot prove rationality is what we think it is (naturalism as a rational doctrine relies on definitions of rationality for its existence). Specifically, though I can show that a physical system is rational, I cannot show that axioms of rational thinking ought to be assumed. Also, a complete natural system cannot explain itself because an explanation for the complete set would require another external law to explain the set.
In my opinion, your argument gives us no reason at all to believe that necessity isn't merely the appearance of consistency, especially as it applies to self-imposed rules. Your claim is about a moral choice ("we ought to think in this way"), not about what is.
Now, you could argue that there is a moral reality that cannot be shown to be in any reliable or scientific fashion, but I'm sure you would be using that argument instead of the AfR if it held any water at all.
Just to preempt it... it's not convincing philosophically to say that my agreement that we ought to think rationally makes rational thinking correct. If I think eating puppies is good, and you happen to agree, your agreement does not signify that eating puppies is a morally correct thing to do. We are self-selecting, and I wouldn't be here if I didn't think rational thinking was a good moral choice.
I guess this is my last word on this thread unless you have a specific question for me. Thanks for debating!
BDK
>>It suggests we come to any problem with a pre-existing set of epistemic standards already in place.<<
Sort of. If "coming to a problem" necessarily entails presuppositions (that words have meanings, that some questions can be answered, etc.), then not all relations and properties that are real are testable/confirmable.
>>We have a bunch of flexible and revisable rules of thumb, heuristics, and things that seem to work, which we have come to trust. Is that necessity?<<
Your statement necessarily implies that "rules" are things we have some conception of. Otherwise you would not have any idea of what you meant by what you just wrote. Likewise, what it is for them to "seem to work."
>>Your definition of necessity involved 'certainty' that one thing follows from something else.<<
>>E.g., I could think that 'A bachelor is a male' is true by definition, and no amount of evidence will change it.<<
If a bachelor is a male by defintion, then it follows with certainty that if Fred is a bachelor then Fred is a male.
>>The ultimate meta-logic is not really a logic at all, but is a raft that we start out upon in this enterprise, a raft that we are constantly rebuilding, trading parts, and improving<<
If there is a common thread to this "enterprise" (and if not, how can it be identified with a single term?) of continual revision, a sense of what "improvement" must consist of to mean anything, then this doesn't refute me.
>>I'm still not sure what you think as you seem to keep trying to throw out these "gotcha" lines and avoid the direct question<<
They are not intended as rhetorical devices. I would choose a logical system in the same way you would, bringing evidence and necessity together as fully as possible in order to make a reasoned judgment. I am just trying to point out that you are, in fact, posing your questions within a rational grid that obviously includes and subsumes the logical systems you are referring to.
>>There are a few reasons this is confused.<<
To begin with, do you really think I am confused to claim that that science requires empirical testability of hypotheses? Or that it is common for naturalists to invoke scientific standards for belief?
>>First, I could be a naturalist and think there are a priori conceptual truths that are immune to revision.<<
I would guess that most reflective naturalists would admit there are necessary truths. I am trying to point out a largely unacknowledged inconsistency between this admission and a common naturalist position on testability of beliefs. Science generally requires hypotheses about physical properties and relations to be testable. It is not that necessary truths cannot be observed to be true, it is the necessity of their being true that cannot be observed.
>>So, if it turns out that my view is true by definition, that doesn't mean I'm not a naturalist!<<
No, but it may mean that you are a naturalist with an unresolved inconsistency or paradox in your philosophy. Granted, everybody's philosophy has these, but they are still not desirable. Each of us hopes we hold a world view in which the number and severity of these is minimal.
>>Finally, this claim is ironic since what has been killed by the evidence<<
Do you mean empirical evidence? Or logical argument . . . including argument from, dare I say it, necessity? Even in quantum mechanics, the counterintuitive aspects of the theory have been demonstrated through mathematics that presupposes necessity. The commutative laws of addition and multiplication, among others, are assumed for the purposes of forming the equations of quantum theory.
Same conventions as above for quotes...
>>It suggests we come to any problem with a pre-existing set of epistemic standards already in place.<<
Sort of. If "coming to a problem" necessarily entails presuppositions (that words have meanings, that some questions can be answered, etc.), then not all relations and properties that are real are testable/confirmable.
Not all at once, anyway.
>>We have a bunch of flexible and revisable rules of thumb, heuristics, and things that seem to work, which we have come to trust. Is that necessity?<<
Your statement necessarily implies that "rules" are things we have some conception of. Otherwise you would not have any idea of what you meant by what you just wrote. Likewise, what it is for them to "seem to work."
Not necessarily. People can have these expectations etc without being conscious of them. They often have crappy (implicit) rules that can be questioned, revised. That's pretty much how I look at the enterprise of science, logic, philosophy. Making explicit what is already there so we can revise, extend, jettison, and make progress. This is one of the main thrusts of Brandom's book Making it explicit that I actually agree with.
>>The ultimate meta-logic is not really a logic at all, but is a raft that we start out upon in this enterprise, a raft that we are constantly rebuilding, trading parts, and improving<<
If there is a common thread to this "enterprise" (and if not, how can it be identified with a single term?) of continual revision, a sense of what "improvement" must consist of to mean anything, then this doesn't refute me.
OK, then we are in agreement then. We've talked about the truth-goal before. That's what seems to individuate the epistemic enterprise from others--the aim to find methods for knowledge-building.
I would choose a logical system in the same way you would, bringing evidence and necessity together as fully as possible in order to make a reasoned judgment. I am just trying to point out that you are, in fact, posing your questions within a rational grid that obviously includes and subsumes the logical systems you are referring to.
For me, that "rational grid" is the ship we are on, so as long as you don't think the grid is some kind of sacrosanct immutable touchstone meta-logic, we'd agree.
>>There are a few reasons this is confused.<<
To begin with, do you really think I am confused to claim that that science requires empirical testability of hypotheses? Or that it is common for naturalists to invoke scientific standards for belief?
Naturalism is broader than scientism, and scientism is broader than logical empiricism or its offshoot Popperianism. On the other hand, I do look at this as an empirical question about science. I think we are talking about conceptual issues here, which science doesn't yet have much to tell us about.
>>First, I could be a naturalist and think there are a priori conceptual truths that are immune to revision.<<
I would guess that most reflective naturalists would admit there are necessary truths. I am trying to point out a largely unacknowledged inconsistency between this admission and a common naturalist position on testability of beliefs. Science generally requires hypotheses about physical properties and relations to be testable. It is not that necessary truths cannot be observed to be true, it is the necessity of their being true that cannot be observed.
Perhaps, but a science of concepts should be able to ground claims of analyticity.
>>Finally, this claim is ironic since what has been killed by the evidence<<
Do you mean empirical evidence? Or logical argument . . . including argument from, dare I say it, necessity?
Paraconsistent logics are motivated partly by quasi-empirical concerns about liars' paradoxes, by related mathematical-logical concerns with Godel's incompleteness theorems, and such. As with most things in science, there are multiple avenues that suggest something is a good idea, conceptual, empirical, and usually a mosh of the two.
Even in quantum mechanics, the counterintuitive aspects of the theory have been demonstrated through mathematics that presupposes necessity. The commutative laws of addition and multiplication, among others, are assumed for the purposes of forming the equations of quantum theory.
Yes. As I've said many times, I have no problems with the idea of necessity per se, but with its reification and the universalization of local models. But it is hard to maintain this because there is a reductio in Godel as he proved, using those beloved techniques, that they can't be proven consistent using those same techniques. So we are again left with the folksy informal "rational grid" to rely upon, but either way, logically speaking, it is possible that arithmetic is inconsistent. And using the standard logics (not that this is necessary), this would suggest it is false. And if it is logically possible that A is false, then we know that A cannot be necessarily true. But again, you aren't forced to use standard logic.
>>Your definition of necessity involved 'certainty' that one thing follows from something else.<<
[clip, rearrange]
>>E.g., I could think that 'A bachelor is a male' is true by definition, and no amount of evidence will change it.<<
If a bachelor is a male by definition, then it follows with certainty that if Fred is a bachelor then Fred is a male.
OK, so you've given us a good rule from classical logic which works wonderfully in most domains. Interestingly, modus ponens isn't actually a valid inference form in paraconsistent logics--it has different rules. Is leaning on your rational grid sufficient reason to say that the deviant logic is BS?
But stepping back, let's assume an all-knowing oracle told us that modus ponens never failed in any logic, that it always worked. I'd be fine with that. I wouldn't be surprised if some such rules existed that we could discover. I just wouldn't want to go to the extreme of saying it proved naturalism false, or that this necessarily good inference rule exists as a platonic object. That's my main motivation here, is avoiding Platonism.
BDK
>>Not necessarily. People can have these expectations etc without being conscious of them.<<
I meant "rules" in general, not the specific rules at issue. For you to make the statement you did and for me to understand it, we must have a conception of what a "rule" is.
>>Not all at once, anyway.<<
If certain presuppositions are inherent in the testing process itself, then those presuppositions can never be tested singly, together, or any other way. They are intuited.
>>That's what seems to individuate the epistemic enterprise from others--the aim to find methods for knowledge-building.<<
Unless there is something undeviating here, some necessary core to the terms "epistemic," "methods," "aim," and "knowlege-building," then this is just meaningless. It amounts to saying, we are seeking a goal that is yet to be determined by means that are yet to be determined. Actually, it means even less than that!
And if we confess that there must be such an undeviating core to these terms/concepts, then we are acknowledging that immutable touchstone meta-logic that you so wish to avoid.
>>Paraconsistent logics are motivated partly by quasi-empirical concerns about liars' paradoxes<<
The liar's paradox is partly a physics problem???????
>>So we are again left with the folksy informal "rational grid" to rely upon, but either way, logically speaking, it is possible that arithmetic is inconsistent.<<
Sure, it could be a matter of necessity that arithmetic is possibly inconsistent. But as I say, this is just moving necessity around like a lump under the carpet.
>>Interestingly, modus ponens isn't actually a valid inference form in paraconsistent logics--it has different rules.<<
Yes, but this a matter of necessity I think. Necessarily, modus ponens doesn't hold in paraconsistent logics as it does in classical logic.
>>I just wouldn't want to go to the extreme of saying it proved naturalism false<<
No! Heaven forbid that we go to extremes. ;)
Same conventions.
For you to make the statement you did and for me to understand it, we must have a conception of what a "rule" is.
You said to follow a rule you must be conscious of it, and that is false. Yes, us talking about this phenomenon means we have some sort of idea what a rule is.
>>[We can't reject our epistemic raft] all at once, anyway.<<
If certain presuppositions are inherent in the testing process itself, then those presuppositions can never be tested singly, together, or any other way. They are intuited.
Only if they are all used with equal weight each time there is an investigation. Which seems unlikely. And I never claimed all people had the same raft, so there is intersubjective conflict and resolution. There are lots of possible ways to rebuild the raft upon which you are afloat.
This doesn't have to be complicated or esoteric. One assumption could be that objects do not change size at different temperatures (a good example of a "rule" we are probably not conscious of). But then we do the experiment to isolate this claim, based on some anomalous results, and find that it is false.
For a more "logical" example, obvously deviant logics show how you can even retool some of the basic assumptions about how to make inferences while starting out in a classical logical sea. Given the liar's paradox, one possibility is to update your "rule" that sentences have one of two truth values.
I took this idea of the piecemeal updating of knowledge from my favorite analytic philosopher Wilfrid Sellars. In his amazing essay Empiricism and the Philosophy of Mind, he writes presciently:
"One seems forced to choose between the picture of an elephant which rests on a tortoise (What supports the tortoise?) and the picture of a great Hegelian serpent of knowledge with its tail in its mouth (Where does it begin?). Neither will do. For empirical knowledge, like its sophisticated extension, science, is rational, not because it has a foundation but because it is a self-correcting enterprise which can put any claim in jeopardy, though not all at once." (Section 8, his italics).
Unless there is something undeviating here, some necessary core to the terms "epistemic," "methods," "aim," and "knowlege-building," then this is just meaningless.
I'd largely agree (of course striking through the "necessary" adjective). Even the study of digestion, which the Midevils had a very different definition for, had a core of looking at what happens between food going in and waste coming out.
And if we confess that there must be such an undeviating core to these terms/concepts, then we are acknowledging that immutable touchstone meta-logic that you so wish to avoid.
This is just a non sequitor. Let's assume Plato and I are both interested in how people "know", that there is some kernel of meaning that Plato and I share. That doesn't imply that we share an immutable touchstone meta-logic. At all. This is just a non-sequiter. It would mean we had a similar concept in our minds, but wouldn't imply anything about how our minds work otherwise.
>>Paraconsistent logics are motivated partly by quasi-empirical concerns about liars' paradoxes<<
The liar's paradox is partly a physics problem???????
Another nice one liner. I used the term "quasi" on purpose, and I think you don't want to restrict the real of empirical to the realm of physics. I consider the liar's paradox a datum that must be dealt with by logicians (since their province is truth and inference) the way a recalcitrant fact about a weight falling must be dealt with by physics.
>>So we are again left with the folksy informal "rational grid" to rely upon, but either way, logically speaking, it is possible that arithmetic is inconsistent.<<
Sure, it could be a matter of necessity that arithmetic is possibly inconsistent. But as I say, this is just moving necessity around like a lump under the carpet.
It was a reductio, as I said in the post, that used the assumption of necessity of the system as a whole to kill itself. I never said I didn't like necessity (relative to a system).
Necessarily, modus ponens doesn't hold in paraconsistent logics as it does in classical logic.
Fine, you have made my point again about necessity: it is relative to a logical system as we've now discussed ad nauseum.
Thanks for the discussion. At this point I'm repeating things so I'll bow out.
BDK
>>You said to follow a rule you must be conscious of it, and that is false.<<
When did I say that? I sure don't believe it. I accept that I must have said something that could be interpreted that way, but that was not my intended point. I merely think that we have a conception of what a rule is. (We can follow rules consciously on occasion. But we would go crazy being aware of all rules we follow at all times.)
>>For empirical knowledge . . . is a self-correcting enterprise which can put any claim in jeopardy, though not all at once."<<
I cannot help but notice that if the above statement is true, then it itself can be put in jeopardy. That is what I was attempting to do by pointing out that necessity is not empirically testable. And a claim such as the above cannot be used preemptively without becoming incoherent.
Or take the claim, "Human knowledge can progress" or "Human knowledge can increase." We could not disconfirm it except by adding the disconfirmation to the sum of human knowledge, which would then rather confirm it. Even if we were to conclude that is probably undecideable, we would increase the sum of knowledge and confirm it. If it cannot be put in jeopardy, it must lie outside the scope of empirical knowledge.
BDK
Oh, I should clarify my point about presuppositions necessary to testing. You made a fair objection. I should have specified to presuppositions or intuitions necessary to ANY empirical test.
But while the commutative law of addition may not be necessary to any and all empirical tests, I still doubt that any empirical test could be devised that would test its property of necessity.
DB:
Yes, you are right that even Sellars' resolution to the serpent versus the tortoise problem is open to revision. He would heartily agree!
Pretty much every third paragraph of that essay has spawned a subfield of philosophy. In it, he develops the language of thought hypothesis, the view that our ideas about mental states are part of a 'theory of mind' rather than just 'given' by virtue of having the experiences, develops a coherentist theory of meaning and justification, an inferential role semantics, and functionalist theories of meaning (not to mention older stuff we now accept such as bashing behaviorism, logical positivism, and Cartesian everythingism).
Here's another example that brings up normativity in epistemology, or at least an analogy with normativity, another now-booming subfield:
"Now the idea that epistemic facts can be analyzed without remainder -- even "in principle " -- into non-epistemic facts, whether phenomenological or behavioral, public or private, with no matter how lavish a sprinkling of subjunctives and hypotheticals is, I believe, a radical mistake -- a mistake of a piece with the so-called "naturalistic fallacy" in ethics." (From Section 1)
It was tempting to put the full quote of his in context, because it is quite beautiful, but I just included the link so as to not take up another 400 pages in Victor's blog comments.
I look at his essay as the systematic, metaphysically sensitive naturalist's complement to Quine's Two Dogmas, which has very similar themes. Sellars is my philosophical hero, in my top five all time (he was the PhD advisor for Paul Churchland, Brandom, and Millikan among others--funny how different they are).
This has been useful for me. I'm sure some of what I said is utter BS, but there is a core there that I think works. It makes me really want to read all of Penelope Maddy's book 'Second Philosophy' which articulates a similar vision but I'm sure much better than I ever could.
BDK
The discussion was just getting interesting! I feel like you and I talk past each other only about half the time, which is an encouraging percentage for these parts.
We will have to continue somewhere down the line. You feel like a change of topic and for the near future I have to devote time to other endeavors.
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