Thursday, June 12, 2008

Intellectual Cheaters

A deductive disproof would give us the strongest possible example of “proving the negative.” But there are a wide range of other circumstances under which we take it that believing that X does not exist is reasonable even though no logical impossibility is manifest. Juries decide that defendants are not guilty, doctors conclude that patients are not ill, mechanics infer that a car is not in need of repair, computer technicians conclude that a computer is not malfunctioning, and biologists conclude that an animal species is extinct. None of these cases achieve the level of deductive, a priori or conceptual proof. Nevertheless, these and countless other instances like them are instances where concluding that X is not true, or X does not exist is entirely justified and reasonable. These cases are, for the most part, inductive. That is, under a wide range of circumstances it is reasonable to conclude that X does not exist on the grounds that X is improbable. Inductive atheological arguments purport to make just such a case against the existence of God or of gods.

When the critic of atheism objects on the grounds that the justification for non-belief doesn’t achieve deductive certainty—“You can’t prove atheism! How can you be so sure? You’re being unreasonable”--he has invoked an artificially high epistemological standard of justification that creates a much broader set of problems not confined to atheism. If one must achieve deductive proof in order to be justified in believing any claim p, then not being able to justify atheism is the least of one’s worries. This high standard of justification undermines the vast majority of what people believe and normally consider to be justified. It generates a broad, pernicious skepticism against far more than religious and irreligious beliefs. Mackie says, “It will not be sufficient to criticize each argument on its own by saying that it does not prove the intended conclusion, that is, does not put it beyond all doubt. That follows at once from the admission that the argument is non-deductive, and it is absurd to try to confine our knowledge and belief to matters which are conclusively established by sound deductive arguments. The demand for certainty will inevitably be disappointed, leaving skepticism in command of almost every issue.” (The Miracle of Theism, 7)

If the atheist is unjustified for lacking proof, then so are the beliefs that planes fly, fish swim, air contains oxygen, electrons exist, or the Cubs are baseball players, not robots. This critic presents a problem for everyone, believer and non-believers alike. If we are to take it seriously, at all (we shouldn’t) then the challenge is not just the atheist’s to answer because the general problem of skepticism is not uniquely the atheist’s to solve. Addressing it is not more of a problem for atheism than for any other view about an empirical, inductive, or non-a priori matter. Skepticism is an interesting and historically influential problem in epistemology, and it is as old as philosophy itself. But part of what makes it interesting is that no one really takes it seriously. That is, even though the occasional earnest philosophy students presses the issue and makes himself or herself into a pain in the ass, we all talk, act, and think under the pervasive presumption that we do have knowledge. The widespread assumption is that we are justified in believing that planes fly, fish swim, and that oxygen exists even though no one can satisfy the stringent deductive proof standard to support them. It would be a mistake, therefore, to object to inductive atheology or to try to defend it against this charge as if the problem is particular to non-belief in God. Throwing this problem up at the non-believer is a flagrant case of the pot calling the kettle black.

We can also understand this attack on disbelief as an example of the more general mistake of applying a sliding scale of proof. When we encounter an idea, we form rapid reactions to it, many of which happened beneath our conscious awareness. Psychologists have shown that the gears of belief formation are set into motion long before the subject is even aware of what is going on (in one recent study the gap was 7 seconds!!). Then if our immediate reaction is a positive one, we are prone to much more forgiving with reasons or justifications that are given in favor of it. As long as a speaker or writer is drawing a conclusion you agree with—as long as he or she appears to be on your side—then they can do no wrong. But if we are averse to the conclusion they are drawing, then we a high degree of scrutiny to bear on every inferential move they make. We jump on the slightest appearance of mistake and draw the satisfied conclusion that they are mistaken—“See, I knew it all along. What he’s suggesting is outrageous.”

It should be noted that it’s not just serious believers criticizing atheists who are guilty of playing this crooked game of poker. Its just as often the case that a self-professed agnostic who is guilty of stacking the deck. This critic of atheism doesn’t subscribe to the religious excesses of the hard-core believer. But he thinks that the atheist is just as guilty of going to extremes that the evidence cannot support. But for many agnostics, the high standard of justification that they invoke against believers and non-believers is one that few of their other beliefs would satisfy. They are being highly selective about which matters they will apply this epistemic standard to and which they won’t. The agnosticism, as a result, is arbitrary and disingenuous. This double-standard agnostic amounts to a sort of closet believer, holding out some false hope for something he’s reluctant to give up. He’s not so much an agnostic because it’s what the evidence indicates but because he doesn’t have the courage and consistency to follow through. (Just pull the band-aid off quick!)

The atheist, I have been arguing, has been subjected to a great deal of this inconsistency. In Darwin’s Dangerous Idea, Daniel Dennett gives an example of a believer and a non-believer playing tennis. When the believer serves, he lowers the net on his own behalf. The beauty of faith after all is that it doesn’t play by any rules of reason. It’s virtue is abandoning the dictates of reason and evidence. But when the non-believer tries to return the serve and challenge some preposterous claim, suddenly then net is raised high, making it nearly impossible to successfully return the volley. It gets even worse when two believers get together to play and exchange ideas, Dennett says. Philosophical theology amounts to “intellectual tennis without a net” at all.


Anonymous said...

Jeremiah Johnson says it's OK to believe anything at all on no evidence whatsoever. Or at least that 's the way I read it.

Anonymous said...

I have kind of an off-topic question, but does apply here. You say a deductive proof would be the strongest proof. That is generally accepted because a deductive proof carries with it a "100% guarantee." However, that guarantee is that of an inference coming out of its premises. An inductive proof only provides some lesser degree of certainty about the conclusion inferred. Now something that has caught my attention to research in the future (so, I wouldn't min getting some other philospher's experience or feedback on it) is whether or an inference meaningfully applies to something.

Now, I'm not going to get into any advanced logic or metamathematic stuff here, but lets just say an a priori argument (i.e., a deductive inference) may or may not say anything about the real-world. I can make a modus ponens argument that we would all find completely absurd, but it's a 100% guaranteed truth under interpretation! This raises the question whether or not deductive arguments actually infer anything meaningful at all, because once they apply to the real-world we will see it becoming inductive. It takes idealized assumptions and modeling to turn, say, an applied mathematical problem into a nice mathematical equation. In truth, it is only ever going to be an approximation.

If that's the case, is the deductive proof really the "strongest example" we have? It seems more like the weakest! It's strength seems to go hand in hand with it's obscurity. One such example I found completely unrelated was in [Elijah Millgram. 2000. Mill's Proof of the Principle of Utility. Ethics 110 no. 2: 282-310.]; as quoted:

Mill was embarked on the radical empiricist project of showing that there is no such thing as deductive inference; it is one of the more important burdens of the System to argue that all inference (and consequeiltly all proof) is inductive (pg. 292, see related footnote 18).

I find such a project appealing, and goes hand-in-hand with another one I have considered in regard to the extent and limit of applied mathematics (from a philosophical perspective, not any kind of actual or practical standpoint working mathematicians would provide, and something metamathematics stays away from since it is far from the axiomatic systems of pure mathematics). What is your take?

If we consider these sentiments to hold some weight, then how it might apply here, very generally and very briefly, goes in hand with your critique of "When the critic of atheism objects on the grounds that the justification for non-belief doesn’t achieve deductive certainty." Furthermore, it also immediately discounts all deductive proofs for God, and puts the religious person in quite a spot for having to show a supernatural conclusion (i.e., God, or related issues that run contrary to naturalism) from natural premises. In other words, they'd have to use inductive proof, evidence, to demonstrate God with any real or meaningful inference. That alone may be more than any religious person believing in the supernatural might be able to obtain, leaving them with no tools whatsoever.

I think such a project could be important because the claim that "the atheist is unjustified for lacking proof" would be absolutely wrong. The atheist would be the only one with proof! The consequence of the project is that the deductively certain arguments would not constitute a proof (in Mill's sense) at all.** This would put the issues in an appropriate context that the "variables" taken by those using deductive "proofs" would be taking them as assumptions, maybe on faith, maybe metaphysically. They would be ideals that may not apply to reality at all. But this does not mean one might not reasonably find a way to make an argument based on those kind of assumptions if they can justify their applicability; e.g., showing one of them to be properly basic (under a foundational theory of epistemology). That is something the author demonstrates is Mill's ultimate failing in his argument for utilitarianism, i.e., the metaphysical assumptions and the role they play.

Also, that tenis analogy is hilarious. I love it. Find a crafty student to make a gif animation to present it and it will really brighten your page! haha

**Note, the paper referenced was analyzing Mill's arguments in Utilitarianism, chapter four, when taking about what kind of proof one has for the Principle of Utility, and how he claims it is not what we can really consider a proof at all, because the factors used are basic (foundational epistemology) and thus tautological. They derive from experience still, but are thus a conditional proof P implies P, essentially. Thus, as the author clarifies, his position was not fallacious (logically). On the contrary, it is for that reason that it does not constitute a proof!

Anonymous said...

An inductive proof only provides some lesser degree of certainty about the conclusion inferred.

Right. Like our inductive, scientific conclusion that the Earth is not flat. It's not 100% certain, it's only 99.999...% certain.

Matt McCormick said...

Thanks Bryan and all for the comments.

Bryan, this is a really interesting set of points. And, if I understand you right, I think I agree with you. Let's keep the distinction between deductive validity, as a property of an argument, and truth, as a feature of propositions, clear. If an argument is valid, then the premises, if they are true, will guarantee the truth of the conclusion. Period. What you are getting at, I think, is that we typically do not have 100% certainty about the truth of any of the propositions that would form an argument. So without that, our confidence in the conclusion is undermined to the extent to which we are not certain about the premises. But let's not conflate two things--there is objective probability or validity, and there's a person's epistemic justification for believing premises and accepting an argument.

In the end, I think I agree with you and Mill on the hardcore empiricist line. I want to naturalize even logic and a priori knowledge too. So when push comes to shove, I'd say that all knowledge is inductive. The arguments that we call deductively valid and sound are ones that we just apply a very high degree of confidence to. But we should be prepared to revise what we think about those propositions, and even logic itself in the light of new evidence. If a better model comes along that fits with the evidence overall (I am hedging a whole bunch of points here) better than the old one, then the empiricist has got to accept it. That would mean, and this is going to be weird for most people, that even if the new model revises, changes, or throws out what we thought were foundational, a priori truths of logic and logical principles, then we've got to go with the new model. As you say, in the end we are always making idealized assumptions and adopting certain axioms without argument for our models. The only way that we can discriminate between those different systems is the extent to which they make successful predictions on the basis of the broadest classes of evidence.

Now you can see the deeper point I was getting at with the "Sinking the Raft I'm Standing On" post a bit back. In midstream, we all construct a raft that incorporates as much empirical data as possible, and then continually rebuild that raft, making it possible to look for and describe new kinds of empirical data, and while changing the rules about what is important to look for.

I think this is a pretty standard post-Quinean scientific pragmatism/naturalism.

Thanks again. Killer provocative comments.


Anonymous said...

Thanks, I should have been more clear about separating those two concepts. I agree with Mill (though I have yet to read his complete System, mainly because it's so damn long!), but metaphysical assumptions definitely prevent him from making it work; plus, he required, or at least allowed, a foundational theory of epistemology to function. I am against that, personally. It leads to queer conclusions like taking sense data to be self-evidently justified. A product of his time, no doubt. I shudder at such thoughts! I think a modern apparoch with new models of epistemology and logic (and math) allow us to have a much more complete and coherent system to naturalize philosophy. My real curiosity is how much of philosophy even thinks of such things let alone fancy the idea.

The one thing that the Mill example brings out, however, is not so much comparing a logical system's truth under interpretation versus an epistemic claim to truth about reality, but it challenges the very notion of what we mean by proof. Many people will tout (especially students) that they have a definitive answer about something (at least for that week! haha). Why? Because they have shown by some model of logic that X implies Y, QED. But logic is (1) about interpreting something under a system, which requires more than most people even realize (and metamathematics is one of the hardest subjects I've ever learned; granted, I'm having to teach it to myself). Logic is also (2) divorced from reality until applied in some manner. Like math, you can play with abstract objects (rings, fields and groups, e.g.), but it will say nothing about reality. People seem to neglect the fact a deductive proof says nothing until it can be shown to relate real-world variables. In other words, the logical model needs to be grounded on real-world relations for which the variables in the model correspond to variables of real objects (or concepts, depending on the kind of system used and level of analysis). Few, I have seen, will connect the two. They act like a priori "proofs" are actually proofs. I think Mill's project really brings that to the fore by challenging the very notion that proof needs to be tied to inferring a conclusion "greater" than its premises. I express it as we take as premise our current knowledge-set K for which our inference builds off of (i.e., the data), to conclude an expanded knowledge set K' for which the inference has provided new information. A deductive proof mapes from K to K only; i.e., deductive (a priori) inferences add no new content or information.

Does that sound like a reasonable position? I think so. How does the philosophical community feel about it though? My intuition tells me when I research it that I'll find many people on the other side of the fence, but I could be wrong.

The other thing is that logic itself is system relative while induction is information relative (though the method or tools are built from a system). Logic doesn't care what the information is, it's just about relating the ideas. Induction itself is concerned with getting B from some set of information A, and I think that illuminates its unique importance as a real system of proof. Like applied mathematics can, when appropriate, use pure mathematical concepts (sets, functions, calculus) in supporting conclusions, I think inductive "logic" is a valid system of logic that is distinct in that it is "applied" and can still use logical principles when appropriate. It is that appropriateness that seems to not escape the lips of people appealing to a priori claims, but they are not meaningful until they make that association.

If anyone wants to discuss these kinds of concepts (since I don't want to hijack your blog here), feel free to visit my blog on Xanga. Though I worn, dry economic and political topics do spring up from time to time (it's where I apply my philosophy).

Anonymous said...

We live in a probabilistic world and deductive proofs are largely meaningless (in terms of their ontological value). What logic provides us is simply a pragmatic and useful form for establishing empirical knowledge in the world -- but all empirical knowledge is contingent.

The old idea of logic or mathematics as metaphysical tools of certainty are dead. Now a better analogy would simply be as tools in creating a kind of virtual reality we use to carve up "facts" in the world.

So, yes, you are absolutely right when you say some theists and agnostics ask for too much by making all or nothing epistemic demands for either 100% certainty or 100% skepticsm.

We live in the era where 85% is "certainty."

We don't need faith anymore, as faith is only necessary if we presuppose a radical inability to know.

However, these days we have the ability determine nearly all human action and physical laws on the basis of relatively high probabilities.

So the skeptics and the faithful are both still living in an Epistemological Dark Age.


Matt McCormick said...

Thanks to all again for the interesting comments. I don't want to give the wrong impression. I don't have some sort of old school medieval view about deductive logic giving us some sort of epistemological certainty with disproofs or with proofs. But I don't think the atheist should be so quick to abandon the usefulness of the so-called modern (post-Russell, post-Godel) deductive disproof. It's certainly a gross overstatement to say, as Steve does, that they are largely meaningless. We've got a tremendously long list of reasons and arguments for concluding that God does not exist. I don't think we should permit the theist to even assume that what they are saying about God even makes sense, much less is true, if there are good reasons to doubt it. And there are. So far, the consensus seems to be among the best and brightest logicians and philosophers of our time that we simply do not have a coherent definition of omniscience or omnipotence that can withstand any serious scrutiny. And those are a priori arguments that make that clear. Should the atheist just walk away from those arguments because of these vague concerns you guys are expressing about the power of logic? No. Those arguments put an enormous burden of proof square in the lap of the believer who, along with billions of other people, has been assuming all this time that the concept of God is coherent and makes sense. It turns out that no one has been able to cash that check. I'm not inclined to let them off the hook for that because of the metamathematical and meta-theoretical concerns that you guys are voicing, even if I agree with you both in the end. I want the theist to pay dearly for the privilege of even talking about God as an intelligible being. We should be calling them on every mixed up and incoherent claim they make, not equivocating about certainty and proof.


Anonymous said...

My quote before:

"We live in a probabilistic world and deductive proofs are largely meaningless (in terms of their ontological value)."

I agree that deductive proofs are worth something in terms of disproving traditional _concepts_ of god.

We can get a hold of concepts and carve them up based on their inconsistencies. And yes, this is very useful, and necessary.

But this is purely in regard to concepts. There is no metaphysical value to logic; it cannot magically conjure up all the beings that exist in the world; it cannot peer into reality itself and deliver us a non-conceptual Truth.

As I said in my last post, logic provides a form in which we can more accurately investigate the world conceptually, and here there is some ontological value:

Based on what we know about the world now, it appears that logic is a good guide for sorting out which of our concepts more accurately reflect reality.

But to presume that logic really proves anything absolutely is to misrepresent its real value: it is purely a conceptual tool.

If we came up with a valid logical proof against god, that would be great in our conceptual debate against the theists, but it wouldn't follow that we have in our hands a genuine ontological proof.

That is, prooving a concept to be inconsistent is not that same as disproving the existence of an entity.

It might give us sufficient justification to believe god does not exist.

But it may or may not coincide with the actual facts of the matter. My own belief is that it would, but that is not the same thing as pushing a magic button, looking into the navel of reality, and knowing (magically) with certainty that god does not exist.


Anonymous said...

I have to agree with what steve has been saying. I don't see that we're giving the theist some kind of ground to stand on by realizing the limits of using a deductive argument to make a claim against the ontological status of this thing named God. At most all you can show is that the relation between the information about what X believes is inconsistent. Say, X believes in God (G) and X believes in some other thing S (science?). When we put together these two specific concepts based on the person's first-order descriptions (our data), we can show G is inconsistent with S and that he has to reconcile his beliefs. But there is nothing definite about the status of G or S in this analysis. All we were able to do is infer something about the relation of these two things. Since God cannot even be defined adequately, I find it hard to see where a deductive proof is going to be all that useful in generalizing disproofs of different definitions of God.

Steve mentions that they are good for conceptual debates with the theists. I have to step back from that a little. Consider the fact that the debate would essentially be like trying to argue about logical systems. We can talk about geometry and say that we're advocating the standard and the theist is advocating the non-standard (hyperbolic, e.g.). At most all we can do is demonstrate the limits of the system, where contradictions may arise, etc. But what does that mean about applying it to reality? In the case of geometry it is shown that both apply appropriately in some respects to the real world relations. But how do we assess that? That requires us to consider the axioms, presuppositions or primitive beliefs of the system. Maybe there is no grounding for them, or maybe there is some data, some facts of the matter, that lend themselves to accept certain axioms. That needs to be assessed, and that is where the real meat of any debate is going to be meaningful, but that instantly removes itself from being merely a deductive discussion. That requires an inductive analysis.

Therefore, I can only see deduction working as laying the ground work for potential problems or inherent conflicts (or limits) within a defined system. But where anyone accepts that system or in its totality or whether it applies (or not) to reality is an inductive endeavor. To have a list of deductively laid out relations is like having tools made but nothing to apply them to. They may be good to have ready for when they can be applied, but that is the extent of it. The problem is, however, that like when holding a hammer all problems begin to look like nails (or however that saying goes), people tend to tunnel into their views based on these deductive tools before they can even be shown applicable to anything or the scope and limitations of their applicability.

In the end, I do not discount the interpretations they provide, I just discount their applicability. When they are expressed as being applicable when merely deductive, that is simply wrong. Applicability is an inductive treatment that I find necessary, especially for any kind of meta-analysis on these deductive interpretations.

Anonymous said...

I should add the caveat that when I mention discounting deductive arguments I mean as such in terms of intended conclusions. If we intend to disprove something (about the world), then deduction fails to apply. It certainly applies when dealing in relations of concepts. But there is to be noted a certain unintended value in any investigation; those outcomes which were not expected. In examining inductive or deductive arguments we can find unseen relations or inspiration to new concepts and relations which may be applicable (inductively or deductively). Even if something seems only remotely useful, it can be found that unintended results may drift into other areas of interest. But my initial statements do not discount this fact, since I was referring to specifically the kind of disparity between a proof as something about the world, and merely forms of argument as found in relations of ideas. Proof, I would say, concerns matters of fact, and appealing to deductive inferences (for intended outcomes) I would discount as being useful since there is no inherent applicability (that would need to be inductively proven, i.e.).