Tuesday, October 02, 2007

The reality of rational inference

VI. The Reality of Rational Inference
The argument from reason focuses on cases where we infer one proposition from another proposition. I will not deny that there are other ways of acquiring true and justified beliefs. Many have argued that, for example, I can have a justified belief that my eyeglasses are here on my computer table without drawing any inferences at all, but rather, just by perceiving my glasses. I should add that this “direct realist” view of perception is by no means universal amongst philosophers; there are many who maintain that what we are directly aware of are “sense data” and that we infer physical objects from sense data. The reason this entire issue can be sidestepped for the sake of this discussion is that an “error theory” concerning rational inference leads inevitably to skepticism about some beliefs that naturalists cannot give up.
Naturalists maintain, of course, that what is real are the sorts of things that lend themselves to scientific analysis, but they also cannot escape believing that there are scientists and mathematicians whose minds are capable of performing those scientific analyses. Consider, for example, a doctrine I call “hyper-Freudianism,” the view that all beliefs are the product on unconscious drives, and that no one believes anything they believe for the reasons that they think they believe it. An atheist could say of the theist “You think you believe in God because of the arguments of Christian apologists, but you really believe it because you are searching for a cosmic father figure to calm your fears.” Or, a theist can say “You think you are an atheist because of the evidence of evolution and the problem of evil, but I know that you just want to kill your father. But this, of course, can be pushed still further to include all beliefs. But that’s just the trouble, if it is pushed that far, then it has to be extended to the belief in hyper-Freudianism itself. If someone tries to present evidence for hyper-Freudianism, they are doing something that can only be done if hyper-Freudianism is false.
Consider the classic syllogism:
1. All men are mortal.
2. Socrates is a man.
3. Therefore, Socrates is mortal.
If it is a consequence of naturalism that nothing like this ever happens, that no one ever draws these types of conclusions from premises, then naturalism is in a lot of trouble. Consider, for example, the role of mathematics in science. Mathematical inferences were critical in making it possible for Newton to discover gravity and Einstein to discover relativity. If we believe that natural science gets the truth about the world, then we must not deny that mathematical inferences exist. If we are persuaded that the argument from evil is a good argument against theism, then we must not accept a position that entails that no one is ever persuaded by an argument.
In my previous treatment of the argument from reason, I presented nine presuppositions of rational inference.
1. States of mind have a relation to the world we call intentionality, or about-ness.
2. Thoughts and beliefs can be either true or false.
3. Human can be in the condition of accepting, rejecting, or suspending belief about propositions.
4. Logical laws exist.
5. Human beings are capable of apprehending logical laws.
6. The state of accepting the truth of a proposition plays a crucial causal role in the production of other beliefs, and the propositional content of mental states is relevant to the playing of this causal role.
7. The apprehension of logical laws plays a causal role in the acceptance of the conclusion of the argument as true.
8. The same individual entertains thoughts of the premises and then draws the conclusion.
9. Our processes of reasoning provide us with a systematically reliable way of understanding the world around us.

It seems to me that naturalists and theists can agree that these things actually occur. Naturalists can't afford to deny them. They must, therefore, try to explain them, and to show that their understanding is the best explanation of the data.

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46 Comments:

At 10/02/2007 06:41:00 PM , Blogger exapologist said...

Logical laws are a *problem* for Christian theists, not an *asset*.

 
At 10/03/2007 09:36:00 AM , Blogger Alan Rhoda said...

Exap: Logical laws are a *problem* for Christian theists, not an *asset*.

Why?

 
At 10/03/2007 01:10:00 PM , Blogger exapologist said...

I guess in at least a couple of ways. For example, how to avoid the sorts of problems that plagued Descartes' view of "The Eternal Truths". Plus, even if, perhaps per impossibile, God didn't exist, modus ponens would still be a valid argument form, in which case it seems odd to say that they depend on God in any interesting way. Also, the Apostle Paul (if he wrote the relevant epistle) has God as the creator of all things. Well if the laws of logic are as they seem to be, viz., utterly independent of God, then it's not true that God is the creator of all things. Now you could say that that's not what Paul *meant*, but the problem is that's what he *said*, in which case what he said was just plain false.

Relatedly, logical laws are necessarily existent abstracta, and all views about God as the ground of abstracta are implausible, as now many young christian philosophers are saying in print (e.g., Bergmann and Brower, and Matt Davidson). If so, then you have some nasty problems with the doctrine of absolute creation, as well as the fact that God *isn't* the explanation of the laws of logic.

So for these sorts of reasons, I think the laws of logic are a problem for christian theism.

 
At 10/03/2007 03:42:00 PM , Blogger Alan Rhoda said...

Thanks for the reply, Exap.

I just read Davidson's SEP essay on "God and Other Necessary Beings" and I don't see why this is such a problem for the theist. Seems to me that it is Chisholmian/Plantingian-style metaphysics that creates these kinds of problems and not theism per se.

In reply to Davidson I would argue, first, that the Lewis semantics for counterpossibles is simply wrong. Instead of going Vander Laan's direction and trying to hold onto an extensional semantics for counterpossibles, I'd teke an intensional, relevance logic approach.

Second, Davidson assumes throughout that properties are abstract objects. I think that's wrong. Property-concepts are abstract, but properties themselves are, so I say, concrete causal powers.

Third, unlike Morris and Menzel I wouldn't say that God "causes" abstracta. Rather, I would say that abstracta are more like conceptualizations of essential aspects of God's being (his thoughts and/or capacities).

 
At 10/03/2007 05:37:00 PM , Blogger exapologist said...

Hi Alan,

Davidson's "A Demonstration Against Theistic Activism" is also worth a look. Also, Bergmann and Brower give a version of the problem that doesn't turn on a Platonist construal of universals. But as a related aside, what would you say about the property of being abstract? And what about necessarily unexemplifiable properties (e.g., being a married bachelor)?

I'm inclined to agree with you about the appropriateness of a relevance semantics account of counterpossibles. A fellow faculty member is currently working on an account of relevance semantics that doesn't have the crazy implications of most accounts. But even on his account, there is still a problem with the claim that various sorts entities depend on God.

Isn't it just obvious that neither God nor his nature (assuming the medievals were wrong that these are identical) doesn't *make*, say, Modus Ponens a valid argument form?

 
At 10/03/2007 06:25:00 PM , Blogger Alan Rhoda said...

Hi Exap,

The property of being abstract. Hmmm. Interesting question. I'm not really sure what to say about that. I'm not even sure I should admit as a bona fide property. On the other hand it does seem to be one. Offhand I guess I would say that "being abstract", as well as "being a married bachelor", are merely general concepts in some mind or other. In general, I have a strong metaphysical aversion to locating abstracta of any sort outside of a mind. Given the necessary existence of certain abstracta, that commits me to the necessary existence of some mind or other - a bullet I'm willing to bite.

Regarding your last point, I'd beg to differ. I would grant that the validity of MP is not obviously dependent on God, but I don't think it's right to say that the validity of MP is obviously not dependent on God.

As for the relation between God and his nature, I think the prospects for identifying these depends on what we mean by God's "nature". If it is exhausted by God's "essence" (the properties God exemplifies in every possible world in which God exists), then God cannot be identical with his nature since if God himself has any freedom at all then he cannot be entirely the same in all possible worlds. But if God's "nature" means "the entirety of God's being" then it seems clear to me that God must be identical to his nature.

 
At 10/03/2007 10:32:00 PM , Blogger exapologist said...

Hi Alan,

I'm not sure I've overstated it. So, for example, consider the proposition that 1+1=2. Is the truth of that proposition dependent on God? To say so makes it sound as though "twoness" is *extrinsic* to the sum of one and one.

Similarly, to say that Q's following from P and (if P, then Q) depends on God makes it sound as though it's extrinsic to the nature of the set of those two premises that Q follows from them.

At any rate, I think that's the sort of intuition that makes me say it's obvious that logical facts don't depend on God.

Maybe I'm missing something, though? I wouldn't put it past me. ;-)

 
At 10/04/2007 09:00:00 AM , Blogger Alan Rhoda said...

Hi Exap,

I see what you're saying, and I agree that what we definitely don't want to say is that "twoness" is extrinsic to the sum of one and one. Deductive validity and invalidity are grounded in purely internal relations among propositions.

It follows that if necessary truths depend on God it can't be by way of grounding a relation between two already established abstracta, say, 1+1 and 2. Instead, it must be by way of grounding the abstracta themselves, such that if God (per impossibile) did not exist, then neither would anything else, including the concepts of "twoness", "oneness", "addition", and "equality".

That doesn't strike me as absurd, especially if one grants my conceptualist thesis that there can be no abstracta apart from minds.

So my proposal is this: Break necessary truths (propositions) down into their conceptual constituents. The necessity of those propositions is grounded in internal relations among their conceptual constituents, whereas those constituents derive their necessity from being ideas in the mind of God.

 
At 10/04/2007 12:14:00 PM , Blogger exapologist said...

Hi Alan,

That was a very helpful reply. So you get around Descartes' problem by granting that the relations among the entities are internal. That's good. And then to account for the necessity, you ground them in God's mental activity, which you construe as something like Swinburne's notion of an act of essence. So you hold to something like Plantinga's theistic conceptualism in "How to Be an Anti-Realist" (and if I remember correctly, Warrant and Proper Function and Does God Have a Nature?), correct? So from this point, we can take Plantinga's (and Craig's) cue re: the ensuing dialectic:

Abstracta can't be causally inert, non-spatiotemporal entities, for then we can't get around Benaceraff's objection. So there's pressure to reject realism about abstracta and look for an account that allows for causal contact with abstract objects. Conceptualism fits that bill. But wait! There are *too many* abstract objects -- in fact, infinitely many (in fact, non-denumarably infinitely many!). So there's pressure to accept an infinite mind to account for all the abstracta. So how can we be anti-realists? Easily enough: by being theists.

Is this right?

I sympathize with this view, but I think Bonjour's *In Defense of Pure Reason* (well, at least the stuff just before he gets into that weird Aristotelian account at the very end), and (believe it or not) Moreland's *Universals*, provide accounts of or relation to abstracta (construed along realist lines) that get around Benecaraff's objection. And these are, I think, at least as plausible, and more economical, than Plantinga's theistic conceptualism.

But at any rate, it looks as though the dialectical path we're on ends with each of us saying "I see how you could responsibly hold your view, but I'm not persuaded". Does this seem right to you?

 
At 10/04/2007 05:35:00 PM , Blogger Rino said...

Hi Exapologist,

You make some interesting points. I have always thought that the argument from reason was effective at dismantling physicalism, without it necessarily proving that theism was true. Do you think the existence of logical laws poses problems for physicalism?

 
At 10/04/2007 06:27:00 PM , Blogger exapologist said...

Hi rino,

Physicalism? Yes. Naturalism, no. On my view, abstracta are necessarily existent entities. As such, they need no explanation for their existence whatsoever. Even an adherent of PSR should agree with that, I should think. I still think that abstracta are a problem for christian theism (though not for theism per se), as they are entities that God doesn't create or sustain. You might be able to come up with an account that makes abstracta *consistent* with theism, but I doubt one could make a widely convincing case that abstracta are *best explained* in terms of theism.

 
At 10/04/2007 10:13:00 PM , Blogger Blue Devil Knight said...

A great discussion, unusually illuminating for the blogosphere.

 
At 10/05/2007 11:39:00 AM , Anonymous Anonymous said...

I am *way* out of my league here, being no philosopher but simply an interested party. However, I think the point alan rhoda made saying "...if God (per impossibile) did not exist, then neither would anything else, including the concepts of "twoness", "oneness", "addition", and "equality"..." is a point that has quite a bit of weight that I don't think has been explored enough in this discussion.

As a layman, I'd ask those more well versed, if there could possibly be a set of "laws of logic" in an *empty* universe. I'd imagine not.

It seems that on the surface, without "something" there can be no laws of logic at all. Is it true, my intuition, that all laws of logic depend ultimately on (physical) things, even if only abstract representations of (physical) things? If so, then if one takes the stance that God created all *things* then would it not be true that "laws of logic" *emerge* from God due to their being contingent on the "things" He created? If true, would we not therefore contribute the existence of laws of logic to God?

Forgive my naivety, but exaplogist's example of 1+1=2 is contingent on some*thing* being added to another, no? And therefore would have no meaning and no existence in an empty universe?

Again, as a layman here I wouldn't be surprised if I'm wrong, or am missing something. But I'd most appreciate illumination if it can be provided.

 
At 10/05/2007 12:54:00 PM , Blogger Rino said...

Hi Exapologist,

Thanks for your comments. I'd like to understand your view more. So, abstracta are immanent? Is there a transcendent element at all? Are abstracta unchanging and eternal?

 
At 10/05/2007 02:31:00 PM , Blogger Alan Rhoda said...

Hi Exap,

I'm not familiar with Benaceraff's objection. Can you summarize it for me?

If I follow you, you grant that theistic conceptualism is defensible, but you find it less plausible than a realistic account of abstracta for reasons of metaphysical economy. As you put it, there are “too many” abstract objects.

First, if indeed there are “too many” abstracta, then why isn’t that just as much a problem for your view?

Second, why think there are “too many” abstracta? Are you suggesting that a non-denumerable infinity of them would overwhelm God? If so, why? Or is it just that think there’s a more parsimonious account that avoids non-denumerable infinities? If so, then I’d like to know what account you have in mind.

Third, it’s not obvious to me that the theistic compatibilist is committed to a non-denumerable infinity of abstracta. I would distinguish between complex abstracta and simple abstracta, with the former built up out of the latter. Propositions, for example, are complex abstracta because they involve both a subject and a predicate, which are (relatively) simpler.

Now, I grant you that there are non-denumerably many complex abstracta, but those can be reduced to simpler abstracta, and I don’t see why there have to be non-denumerably many of those. For example, give me as basic concepts “one”, “equals”, and “plus” and I can define all of the positive integers (1+1=2, 1+1+1=3, etc.). In short, given the reducibility of complex abstracta to simpler abstracta, I don’t see any reason to think that my account of abstracta is bound to be less parsimonious than yours, whatever that is.

 
At 10/05/2007 02:58:00 PM , Blogger Alan Rhoda said...

Anonymous: I'd ask those more well versed, if there could possibly be a set of "laws of logic" in an *empty* universe. I'd imagine not.


Hi Anon,

I'm inclined to agree with you. If by an "empty world" you mean one that is void of everything, including the laws of logic, then I'd say that that's not a coherent possibility. It is a contradiction in terms to speak of there being a "logically possible" world in which the laws of logic do not apply.

But I wouldn't say, with you, that the laws of logic "emerge" from God, or that they are "contingent" upon created things.

Since the very notion of "logical possibility" presupposes the laws of logic, the laws of logic must be logically necessary. Hence, they can't be contingent on creation (esp. in light of the fact that creation is itself contingent).

 
At 10/05/2007 03:09:00 PM , Blogger exapologist said...

Hi you guys,

Wow -- lots of questions!

Anon,

I think those are great questions. I think it would take a lot of stage-setting to get to the sorts of answers you're looking for, but I just want to say this for now: if you're going to go that route, why bring in God at all? What explanatory work is God doing that other hypotheses can't do equally well? So, for example, I'm a Platonist -- I think properties, propositions, possible worlds, etc., are non-spatiotemporal, abstract objects that exist independently of everything, and they exist of necessity. Well, if (perhaps per impossibile) abstract objects didn't exist, then we lose the logical and mathematical laws (for then they wouldn't exist at all). In other words, we get the same results as Alan's view, but without the need to bring in God as their ground. So what is it about theism that makes an advance over straight Platonism? What work is God doing that can't get done without him on this issue?

Rino,

Perhaps my reply to Anon applies to your question as well? Thus, I'm a Platonist about properties, propositions, possible worlds, etc. I think they're necessarily existent, transcendent entities. They can stand in something like Plato's "participation" relation with concreta.

I'm not a "true believer", though: if some other account of these entities can do a better job of explaining what *needs* to be explained, then I'll jump ship.

Alan,

Beneceraff was arguing against Platonism about numbers in particular, but his argument is equally applicable to Platonism in general. He argued that a necessary condition on knowledge is standing in some appropriate causal relation to the thing known. Unfortunately, Platonic entities can't stand in causal relations of any sort; therefore, if numbers (or properties, or possible worlds, or...) are non-spatiotemporal entities, then they're unknowable. But they're not unknowable; so, whetever they are, they're not Platonic entities.

We can quibble with his externalist assumptions about knowledge, but I'm an externalist about knowledge. But in Warrant and Proper Function and elsewhere, Plantinga gets around the Benaceraff problem by construing properties, propositions, possible worlds, etc. as concepts. But (and this goes to your last set of comments) there are way to many such entities to account for them in terms of *human* concepts; therefore, there must be an infinite Mind that entertains them (strictly speaking, this isn't quite Plantiga's view -- he takes numbers to be divine sets, properties to be divine concepts, propositions to be divine thoughts, etc.).

Bonjour (and if I remember correctly, Moreland) get around the Benaceraff problem by denying the causal requirement. Bonjour says that while we can't have causal contact with abstracta, we *can* have such contact with concreta that *instantiate* them. See the last chapter (or so) of his In Defense of Pure Reason for the rest of the details of his account.

But to address your main commnent more directly: I think there's a bit of a misunderstanding here. I was arguing on behalf of the *theistic conceptualist* when I said that there are too many concepts. That is, too many if they are to be accounted for by *human* concepts. Therefore, there must be an infinite mind that has them.

Best,

EA

 
At 10/05/2007 04:59:00 PM , Blogger Rino said...

Hi Exapologist,

As a Platonist, would you accept the Platonic conclusion that abstracta (or Ideas) cannot exist if there weren't a Mind to think them?

"STRANGER: Can we imagine that being is devoid of life and mind, and exists in awful unmeaningness an everlasting fixture?
THEAETETUS: That would be a dreadful thing to admit, Stranger." -Plato, The Sophist

 
At 10/05/2007 06:36:00 PM , Blogger exapologist said...

Hi Rino,

For my part, I just don't see the explanatory point of tacking on God to Platonism. If you have entities that can't fail to exist, then what need is there for an explanation?

 
At 10/05/2007 08:14:00 PM , Blogger properly basic said...

Gosh, Exa! neo platonism sounds as eerie as belief in God, don't you think?

 
At 10/05/2007 08:15:00 PM , Blogger Alan Rhoda said...

Thanks for the reply, Exap.

I'll have to take a look at the Benaceraff vs. BonJour/Moreland debate in the near future.

Now, if I understand the nature of our disagreement, it all boils down to this: Can abstracta exist independently of a mind? I say 'no', and so opt for theistic conceptualism. You say 'yes', and so opt for Platonism.

If that's right, then it seems to me that my position has at least one advantage over yours, namely, that it yields a more unified metaphysics. On my account God is the ground of being such that everything that exists, exists in virtue of being either God, an aspect of God, or a creation of God's. On your view, however, there is a brute and ultimate metaphysical dualism with abstracta on one side and concreta on the other.

 
At 10/05/2007 08:23:00 PM , Blogger exapologist said...

Hi Alan,

It seems odd to me how you put it: it makes it sound as though the necessary beings -- the abstracta -- are "brute" in a way that cries out for explanation, when in fact they don't. And as for the existence of the concrete world, its existence seems odd only to those who hold to versions of PSR that require that all explantory chains terminate in necessary beings. But so far as I've been able to make out, there is no tenable version of PSR that has that implication. If so, then my view leaves nothing to be explained that needs explaining.

Best,

EA

 
At 10/06/2007 12:49:00 AM , Blogger exapologist said...

This comment has been removed by the author.

 
At 10/06/2007 12:59:00 AM , Blogger exapologist said...

HI Properly Basic,

I see your point, but I'm not in the camp of naturalists that has a visceral reaction to immaterial entities.

There are several versions of naturalism. Naturalists share in common the view that the natural world is all there is -- there is no supernatural realm of spiritual beings. However, naturalists differ in how they define 'the natural world'. Now there are at least three broad ways of characterizing "the natural world", and so there are at least three kinds of naturalists -- let's call them 'Conservatives', 'Moderates', and 'Liberals'.

Conservative naturalists are straight physicalists -- nothing exists but the physical, and the physical is characterized by all and only the properties listed in physics and chemistry textbooks.

Moderate naturalists differ from Conservative naturalists, in that they expand their conception of natural world so as to include abstracta (e.g., propositions, properties, possible worlds, etc.).

Finally, Liberal naturalists differ from Moderates and Conservatives, in that they admit into their ontology of the natural world the abstracta of the Moderates, but they also allow for a conception of concreta according to which they have more properties and powers than the Conservatives and Moderates allow. Thus, perhaps they're straight Spinozists, or type-F monists, or panprotopsychists, etc.

In light of this sketch of the varieties of naturalism, we see that from the fact that one is a naturalist, it doesn't follow that one is averse to entities that don't belong to the ontology of Conservative naturalism. To put it differently: naturalism doesn't entail Conservative naturalism. And I am no Conservative naturalist -- I'm a Liberal naturalist, in fact.

 
At 10/06/2007 08:38:00 AM , Blogger properly basic said...

Thanks for clarifying, EA! Though I'm not altogether sure what to think about it all. It still sounds to me like a full blown metaphysic too awkward for any naturalist to hold.

 
At 10/06/2007 12:16:00 PM , Blogger exapologist said...

Hi PB,

Really? Even given the fact that many prominent naturalists *have* held such views, and many prominent contemporary naturalists *do* hold such views? What about Liberal naturalists like Spinoza, and more recently, Donald Davidson, Thomas Nagel, David Chalmers, and Daniel Stoljar? What about Moderate naturalists like Bertrand Russell, and more recently, W.V. Quine, Roderick Chisholm, Tyler Burge, Kit Fine, and Jeff King?

Is there any *reason* one could give for why Conservative naturalism is to be preferred to the other sorts? I suspect the answer will be 'no'.

 
At 10/06/2007 01:53:00 PM , Blogger Alan Rhoda said...

Hi Exap,

I see you don't like the word "brute" as applied to abstracta. I take it then that you believe that abstracta are "self-explanatory".

If these abstracta exist independently of each other, then that leaves you with an infinite multitude of entia necessaria? Hardly a parsimonious metaphysics I would think. Or perhaps you think that all abstracta somehow fuse together into something like Plato's Form of the Good. It's rather opaque how that's supposed to work.

Regarding the existence of the concrete world, I don't need a heavy-duty, Leibnizian-style version of PSR according to which all explanatory chains terminate in necessary beings to argue that it needs an explanation for its existence. All I need is a version of PSR that picks out some feature of the concrete world as standing in need of explanation. For example, "everything that begins to exist has a cause".

The options are limited. Either the universe has an explanation or it doesn't. If the former, then it's existence is "brute". If the latter, then it either has an internal explanation or an external one. If the former, then it is "self-explanatory". But that seems both conceptually (why doesn't it seem absurd to suppose its nonexistence?) and cosmologically (Big Bang, etc.) implausible. So that creates pressure to look to an external explanation. If that explainer is itself something that is non-self-explanatory, then either it is simply "brute" or it, too, has an external explanation. And so on. Either we terminate the series with a "brute" posit. Or we terminate it with a self-explanatory entity. Or we don't terminate it at all, in which case it's "turtles all the way down".

Suffice to say, I think you're too quick in concluding that you've got no explaining left to do. Nor have you dealt with the problem of metaphysical unification, much less acknowledged it as a genuine cost of your system.

Regards,
Alan

 
At 10/06/2007 02:39:00 PM , Blogger properly basic said...

Exa,

While I appreciate your mind, I just haven't the slightest idea what the LNC (for instance) looks like, if it looks like anything at all. I wasn't poking fun at Platonism, just confused.

 
At 10/06/2007 06:20:00 PM , Blogger exapologist said...

Properly Basic,

Sorry if I came off a little snippy!

Alan,

Good points. My family is heading out for the evening, but I hope to reply late this evening, or perhaps tomorrow.

I'm very much enjoying our discussion, all!

All the best,

EA

 
At 10/06/2007 08:19:00 PM , Blogger properly basic said...

Thanks, Exa =)

 
At 10/07/2007 01:47:00 AM , Blogger exapologist said...

Hi Alan,

Re: abstracta: I take them to be the best explanation of a variety of data, and I attribute to them the properties required to get the relevant explanatory work done. So, for example, consider numbers, and math generally. There are infinitely many numbers, and mathematical truths are necessary truths -- they're true at all possible worlds. I seem unable to account for them in terms of finite, contintent concreta. And math is indispensible to the sciences and many practical matters -- I can't get along without them; so, I posit that mathematical entities are abstract, there are infinitely many of them, and they exist of necessity.

I think the above account is a satisfactory explanatory terminus in a way akin to the Leibnizian cosmological argument if it were sound. Thus, the latter appeals to the apparent data of the contingency of the universe, and then posits an entity to account for it, viz., a necessarily existent substance. Similarly, the former appeals to the data of the infinity and necessity of mathematical truths, and posits necessarily existent abstracta as the entities that account for those truths.

If one comes at me and says, "but *why* do they (the numbers) exist of necessity?", that sounds like a weird question to me, as if they could imagine 1+1 equalling something *other* than 2.

Perhaps there is *some* sense in which it's mysterious that abstracta (e.g., numbers) exist of necessity -- e.g., I don't have a synthetic a priori intuition that their essence is identical to existence, or something of that sort. But the same thing goes with God: unfortunately, we don't have a persuasive version of the ontological argument to get us that result. So if one remains puzzled about the necessary existence of abstracta, then it seems to me that it's a puzzle that applies equally to the necessary existence of God. This leads me to your second point:

Re: explanatory principles and theism: you say that all you need is Craig's premise that whatever begins to exist has a cause of its existence. I have no trouble with that premise, although I have no reason to believe that either the realm of abstracta or the realm of concreta began to exist. Craig's philosophical arguments don't seem to work (by that I mean not that they're all unsound, but rather that it's very dubious whether any of them are sound). And while his big bang argument does seem to be sound, it only gets the conclusion that our universe began to exist; it doesn't get the conclusion that the real of concreta began to exist. There are a number of theories on offer that don't entail that the beginning of our universe was the beginning of the realm of concreta per se. So, for example, M-Theory entails that our universe is just one membrane in 10-dimensional spacetime, within which there may well be many, many other membrane universes. On this theory, the 10-dimensional spacetime didn't begin with the Big Bang; it may well be eternal for all we know.

(To anticipate the claim that such a "superspace" is purely speculative, without direct observational support: of course, the same thing goes for the theistic hypothesis; they're on a par in this respect. In science, as in detective work, you often have to resort to hypotheses incapable of direct experimental confirmation or disconfirmation. You just have to make abductive inferences to the best explanation. Each theory accrues support in terms of embodying theoretical virtues, such as simplicity, explanatory scope and power, etc. Now consider the two hypotheses of theism and M-Theory. Both explain the data of the origin of our universe. Which one is the better explanation? One could argue that theism is simpler/more parsimonious, as it posits just one extra entity, while M-Theory posits many. But as David Lewis has taught us, there are at least two kinds of simplicity/parsimony: quantitative (postulates fewer entities) and and qualitative (postulates fewer *kinds* of entities), and it's not clear at all which type of parsimony is more important. And while theism may be more *quantitatively* parsimonious, M-Theory is more *qualitatively) parsimonious. Indeed, it's breath-takingly parsimonious, ultimately reducing all physical reality to vibrating filaments of energy.)

In short, Craig's a priori arguments don't work, and Craig's a posteriori argument may well work, but it doesn't force the theistic conclusion he wants -- it doesn't entail that all natural *concreta* had a beginning, and therefore needs an immaterial originating cause of its existence.

Re: the existence of the universe: again, I would re-formulate the issue in terms of the the existence of concreta -- in particular, material objects -- and not in terms of the universe, for the two may not necessarily be co-extensive, and the re-formulated issue is the most important one for our purposes. On my view, I think it's more explanatorily economical and less metaphysically extravagant to say that the realm of concreta is an eternal, factually necessary being. That is, it's a logically contingent, yet metaphysically independent, "free standing" stuff. So there are possible worlds in which it doesn't exist, but given that it does exist, it's free-standing, and there's nothing in the actual world that can destroy it (which is reminiscent of the 1st law of thermodynamics). So it doesn't fit neatly into traditional categories of either "brute" (in the sense of lacking no explanation at all as to why it exists -- after all, there is a sensible explanation for why it exists, viz., there it's free-standing, and nothing in the actual world has what it takes to make it go out of existence), and "self-explanatory: (since it's not a logically necessary being, i.e., there are possible worlds at which it doesn't exist). In other words, it's very much like Swinburne's notion of God, except that it's material, and it's not a person.

 
At 10/07/2007 04:17:00 PM , Blogger Alan Rhoda said...

Hi Exap,

Thanks for the extended reply. I suspected you might say something along those lines.

I agree with you about the inconclusiveness of Big Bang cosmology and about the ambiguity of "simplicity". For my part, I think that at least one of Craig's a priori arguments is sound (which one depends, I think, on the correct metaphysics for time, whatever that happens to be). But I'll set that aside.

I still think you've got to bite a bullet in positing two ultimate categories, viz. abstracta and concreta. For one thing, that raises issues about how to correlate them. Since you can't appeal to the intentions of a Creator to account for the intrisic intelligibility of the concrete world, it seems to me that the applicability of math to the physical world, say, becomes rather fortuitous.

 
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Hi Exapologist,

Can I just ask a question related to a comment you made in a previous forum about externalism. Would you say that the content of our mental states are concreta or abstracta. Explain. Thanks.

 
At 10/08/2007 08:49:00 PM , Blogger exapologist said...

Hi Alan,

I'm not sure if my accepting two ontological categories is a problem. Why is that? If it's the simplest one can get one's ontology without loss of explanatory scope, then I think it's a very simple theory. One could try a theistic conceptualist/activist account, but as I've said, I think those accounts are incoherent (Davidson points out the problem with some versions; Bergmann and Brower finish the critique by refuting the other versions; recall my worries about the property of being abstract, about necessarily unexemplifiable properties, etc.). So I don't think one could unify one's ontology any further without loss of coherence, which is to say it's a simple theory.

I don't see how Steiner's "applicability of mathematics" problem affects my view (that's the argument you had in mind, correct?). I haven't read his book, but I understand that it's supposed to be a problem for naturalists who are conceptualists about mathematical objects. But I'm not a conceptualist, and so I don't see the problem. And given that mathematical truths are necessary truths, they're true in all possible worlds. So why is it mysterious that they're applicable in the actual world? In any case, I can't even imagine what a world would have to be like for mathematics *not* to be applicable to it.

Hi Rino,

As I've mentioned before in another thread, I'm not settled on a semantic theory, and so I can't give a determinate answer. Some days I'm a hardcore semantic externalist, like Howard Wettstein. Other days I'm sympathetic to two-dimensionalism. Yet other days I think Jeff King is closest to the truth. By the way, King has done come recent work on naturalism and his theory of propositions as structured entities -- some more stuff on my "to read" list. :-)

Well, I better get back to work. It's been very stimulating and enjoyable talking to you all! I hope to come back in about a month or so when I get a break. In the meantime, be well!

All the best,

EA

 
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