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Ratiocination

The Onion on "That Guy"


Everyone who reads this blog has been in a philosophy class with (or been) "that guy." Read all about him on The Onion! This was recently linked to in a comment, but I think it's funny enough to deserve its own post. =)

Anselm and the 'Greater Than' Relation


If something has a property, it exists. There is nothing such that it doesn’t exist and also has some property. Put formally, for every x and every F, if Fx, then there is some x such that Fx. Call this the Exemplification Implies Existence thesis (EIE). There are arguments for EIE, but I will not present them here;, I simply assume its truth for now.

Properties come in at least two flavors—qualities and relations—and EIE holds for both of them. Qualities can be attributed with a simple statement of the form ‘Fx’—that object x has quality F. Relations, similarly, can be attributed to objects with a simple statement of the form ‘Fxy’ or (perhaps less commonly) ‘xFy’—that object x stands in the F relation to object y.

Given EIE, every statement of the form ‘Fxy’ implies at least two things: that x exists, and that y exists. Since the ‘F’ in such statements says something about (attributes a property to) all relata (eg, both x and y), it follows from EIE and Fxy that there is some x and there is some y (they exist). So for every true attribution of a relation, there are relata.

With this in mind, I shall advance a novel objection to Anselm’s ontological argument. It is novel only in this sense. It is not one of Kant’s, Hume’s or Gaunilo’s objections or mantras. For an intelligent rehearsal of one of these perennial objections, check out this post at Philosophy, et cetera.

Anselm’s argument is a familiar one, so I will not rehearse any primary source material here. Instead, consider the following formalization of an ontological argument that could be found somewhere in the vicinity of Prologion II (care of Alvin Plantinga):

1.God exists in the understanding but not in reality. (Assumption for reductio)
2. Existence in reality is greater than existence in the understanding alone. (Premise)
3. A being having all of God's properties plus existence in reality can be conceived. (Premise)
4. A being having all of God's properties plus existence in reality is greater than God (From (1) and (2).)
5. A being greater than God can be conceived. (From (3) and (4).)
6. It is false that a being greater than God can be conceived. (From definition of "God".)
7. Hence, it is false that God exists in the understanding but not in reality. (From (1), (5), (6).)
8. God exists in the understanding. (Premise, to which even the Fool agrees.)
9. Hence God exists in reality. (From (7), (8).)

What exactly does premise (2) mean? It seems to be claiming that a greater than relation obtains between some object that exists in the understanding alone and the same object, should it exist in reality. This does not amount to the stronger claim that everything that exists is greater than anything that does not (although that claim, too, will prove false if my critique is sound).

The second "existence" referred to in (2) is not really existence, we must note. An object which exists in the understanding alone (to use Anselm's language) does not exist simpliciter; it is instead merely thought of as existing. Similarly, an object which exists in the understanding alone does not have any properties; it is merely thought of as having certain properties. To say, for example, that Schmlions are fictional creatures exactly like lions except for their long, furry, hand-bearing tails is to speak of things that exist in the understanding alone. When normal people speak of Schmlions, we may take their words as shorthand for something like, "though Schmlions do not actually exist, I think of Schmlions as existing and having Schmlionic features... If my thoughts were to correspond with reality, then there would be creatures with Schmlionic features..."

Premise (2) amounts to the following claim, where G stands for the greater than relation, x is an object that exists in reality, and y is some object, the same as x, save that it exists in the understanding alone: For every x and y (meeting these conditions), Gxy.

From the conjunction of premise (2) and EIE, we may now derive a contradiction. (2) says of some object or some range of objects x that x exists and says of another object or range of objects y that y does not exist, and that some relation (the greater than relation) obtains between x and y. But EIE tells us that if a relation obtains, all relata exist. So, from EIE, x and y exist. But from (2), x and y do not exist. So either (2) or EIE must go; the two are mutually inconsistent. Assuming EIE, (2) is false.

Of course, if (2) could be modified in such a way that it does not contradict EIE in the way I have outlined, positing that God exists (simpliciter). But this is the very point under the microscope, whether God exists; sneaking it into the premise is thus a dialectical sin.

The Rising Dualist Tide?


Leading philosopher of consciousness David Chalmers notes that Jaegwon Kim has rejected full-blown physicalism in his latest book. This is interesting, given Kim's reputation for (militant?) physicalism. Chalmers writes,

Tone aside, this makes at least three prominent materialists who have abandoned the view in the last few years.  Apart from Kim, there's Terry Horgan and Stephen White (balanced, of course, by Frank Jackson moving the other way).  One still sometimes sees the claim that almost everyone these days is a materialist (e.g. in Peter Carruthers' new book, p. 5: "Just about everyone now working in this area is an ontological physicalist, with the exception of Chalmers (1996) and perhaps a few others").  I don't think one can get away with saying this any more.  Apart from the four counterexamples just mentioned, here are a few other contemporary anti-materialists about consciousness who come quickly to mind: Joseph Almog, Torin Alter, George Bealer, Laurence BonJour, Paul Boghossian, Tyler Burge, Tim Crane, John Foster, Brie Gertler, George Graham, W.D. Hart, Ted Honderich, Steven Horst, Saul Kripke, Harold Langsam, E.J. Lowe, Kirk Ludwig, Trenton Merricks, Martine Nida-Rumelin, Adam Pautz, David Pitt, Alvin Plantinga, Howard Robinson, William Robinson, Gregg Rosenberg, A.D. Smith, and Richard Swinburne.  There are plenty of others, and then at least as many again agnostics.  If I had to guess, I'd guess that the numbers within philosophy of mind are 50% materialist, 25% agnostic, 25% dualist.

This is certainly an interesting shift. I note, however, that substance dualism remains a (minisucle) minority position among philosophers of mind, despite the traction that more modest forms of dualism have recently found. Substance dualists like J.P. Moreland (and the rest of the Biola crew) do not yet have reason for triumphantist celebration, then. It seems to me that claims like this are still patently true: "Kim's point was that among philosophers of mind... there is nearly a consensus that substance dualism is false."

Closure Principles


I have spent a good deal of time thinking about one closure principle, viz., closure under entailment for ‘N’, a modal operator such that Np reads “p and No one has or ever had a choice whether p,” (the early van Inwagen) or, alternatively, “p and no one is even partly morally responsible for p” (Eleanor Stump), or “p and no matter what anyone does, p.” (Michael Huemer and the later van Inwagen)

As recent posts have suggested, is not always a clear matter whether these closure principles are valid. It turns out that van Inwagen’s original reading of N is not closed under conjunction introduction (and hence not closed under entailment); this is a surprising and counter-intuitive result. On all readings of N, I'm inclined to initially think that if Np and Nq, then N(p & q) after all, how could one have a choice over something, the constituent parts of which one has no choice over? But this prima facie intuition was misleading. Might other intuitions have a similar fate?

Similar closure principles have figured prominently in contemporary epistemology debates; the general verdict, so far as I can tell, is that knowledge is not closed under entailment, conjunction introduction, and maybe not even for known entailment or known conjunction introduction either, though a version of closure may hold when additional conditions are stipulated.

It seems to me that the parallel deontic principles also are clearly invalid. To see why this is so, let ‘W’ express the predicate, “Is wrong.” Closure under conjunction introduction for W looks something like:

C1. Wa & Wb |— W(a & b),

while closure under conjunction elimination for W looks something like:

C2. W(a & b) |— Wa & Wb

Clear-cut counter-examples to both C1 and C2 are not hard to concoct. Take C2; it is impermissible for me to flog an innocent baby and eat pepperoni pizza—that is, W(a & b). But the wrongness doesn’t transfer to the second conjunct—there is no reason to think that it being wrong to (flog an innocent baby and eat pepperoni pizza) implies that it is wrong to eat pepperoni pizza (Wb). Quite the opposite, in fact. Now take C1; any case in which two impermissible actions “cancel each other out” or are jointly a permissible action will do to unseat it.

This is all to say that closure principles are tricky things. It is on these grounds that as of late (and excepting the distribution axiom for K, similar modal logics, and those closure principles that can be formally proven from them), I’m increasingly agnostic about them.

Soames Review


Scott Soames has completed and published his two-volume history of analytic philosophy, Philosophical Analysis in the Twentieth Century, and an interesting critical review can be found at NDPR.

Update: As Michael Pakaluk points out, this last paragraph to the review is a bit odd; I can't help but wonder about the personal circumstances that gave rise to it:

I will end this review with a confession. As I read these books, I often found myself persuaded on one or another point, and I could not help admiring the clarity and power of the presentation. Yet I also experienced a growing feeling of irritation and frustration, slipping at times into anger. Perhaps this review displays too much residual irritation, frustration, and even anger. I hope that it also conveys some of the ground for these feelings.

Philosophers' Carnival


A new issue of the Philosophers' Carnival is up, including a post from yours truly.

Nonsense Alert


Update: this exchange has produced too much heat and not enough light. It has proven unproductive and, evidently, hurtful, something I never intended. Those who did not read the original exchange need read no further.

Shortly after the initial posting, I did some research on Chris Gibson (having never known him), and discovered a number of bloggers mourning his untimely death. That this many this soon have publicly mourned is a tribute to Chris' memory. I was just reading today a commentary on Wittgenstein's Investigations and I thought to myself, "I wonder what Chris Gibson would think about this." It is a tragedy that many who counted him as a dear friend or even just as an interesting acquaintance will know the joy of knowing Chris no more. I am sorry for the loss his friends have suffered and wish to impose no additional pain upon them.

Any further critique of Jeff McMahon's editorial decision or Chris' writing is likely to only cause just this unnecessary pain, and this suggests to me that the exchange should be put to rest. Unfortunately, the matter does not end here. It will continue now, however, behind closed doors and in private correspondence. This is as it should be, I think.

Can Rejecting PAP Get the Compatibilist Anywhere? (Part II)


I argued in Part I that β* generates non-trivial and worrisome results. I turn now to the question of its validity. It seems that whether β* is valid can be evaluated on at least three grounds: examples, counterexamples, and provability. I address these in reverse order.

I grant that Beta-Star is not provably valid under any widely accepted modal logic. For brevity’s sake, I won’t go into the details as to why this is the case. It’s important to remember that this does not thereby make it invalid, though.

I cannot demonstrate that no counterexamples to β* will emerge. There are two things to be said on the point, though. First, no obvious counterexamples are apparent to me, and quite the opposite. β* just seems to me to be the sort of principle to which there are no counterexamples. Though this sort of evidence may no longer seem quite so luminous as it did in 1983, it still has some weight, I think. Second and more importantly, the most potent counterexamples to its plainer cousin, β, have no application—I refer to the Agglomeration cases advanced by Johnson and McKay. Johnson and McKay offer an indirect counterexample to β by proving invalid one of its logical consequences, Agglomeration, or, closure under conjunction introduction. Johnson and McKay’s proof that β implies Agglomeration:

1. Np (Assumed)
2. Nq (Assumed)
3. o(p ⊃ q ⊃ p&q) (conjunction introduction)
4. N(p ⊃ q ⊃ p&q) (3, α)
5. N(q ⊃ p&q) (1, 4, β)
6. N(p&q) (2, 5, β)

But the inference from Np and Nq to N(p&q) is subject to counterexample: where S in the actual sequence does not, but could have tossed a (fair) coin, let p express ‘the coin does not fall heads’, and q, ‘the coin does not fall tails.’ Johnson and McKay observe of this case:

"Both premises of agglomeration are true, ‘Np’ and ‘Nq’: no one can choose to falsify p (no one can choose to make the coin fall heads) and no one can choose to falsify q (no one can choose to make the coin fall tails). The conclusion, ‘N(p&q)’, is false, however. I could have chosen to make ‘(p&q)’ false by choosing to toss the coin, so I had a choice about whether ‘(p&q)’ is true."

β is thus invalid; but β* is not subject to the Agglomeration case. Plugging in the same values for p and q, Np and Nq come out false; and without these premises, the proof does not get off the ground. Suppose that S is a rational agent, who acted with due deliberation, and, through reasons-responsive mechanisms and so forth (you may again plug the details of your favored account of MR here), actually refrained from flipping the coin, so where c is ‘the coin is not flipped’, S → c. It is not the case, then, that Np, nor is it the case that Nq, for S is responsible for c, and c entails both p and q.

I see no way of reconstructing any coin-flipping case such that Np and Nq will both be true. Without these premises, a proof of the validity of closure under conjunction introduction seems hopeless. β* remains unscathed by Johnson and McCay’s strategy. This is some evidence in its favor.

Furthermore, like β, examples of β* have intuitive force. Let p express ‘Hurricane Katrina ravages the gulf coast’, and q, ‘Countless lives are lost.’ On the supposition that Np and N(p ⊃ q), is it not reasonable to infer Nq? That is, there is no one who brought about p in a morally responsible way, and no one who brought about ‘p ⊃ q’ in a morally responsible way. It seems obvious on these grounds alone to conclude that no one is morally responsible for q, either. This is β* in action.

All the best evidence suggests that β* is valid. Given this and what I have argued above, even the semi-compatibilist who rejects PAP must find a way to undercut or defeat the Modal Argument as I have reimagined it. Indeed, anyone interested in preserving the possibility of MR in the face of determinism would be wise so to do.

Can Rejecting PAP Get the Compatibilist Anywhere? (Part I)


My independent study with Tom Crisp has already begun to prove productive, I think. The next two posts summarize one line of thought I've pursued in the last several days.

van Inwagen advances three formal versions of the following Consequence Argument for the incompatibility of free will and determinism in An Essay on Free Will:

“If determinism is true, then our acts are the consequences of the laws of nature and events in the remote past. But it is not up to us what went on before we were born, and neither is it up to us what the laws of nature are. Therefore, the consequences of these things (including our present acts) are not up to us.”

The third Modal argument has received the most attention in recent years. It ostensibly demonstrates that for any true proposition p, given determinism, Np, which reads, “p and no one has, or ever had any choice about whether p.” Having a choice whether p has most often been understood by defenders of the argument in terms of alternate possibilities; for S to have a choice whether p just is for S to have an action A within her power such that if she were to perform A, ~p, or something along those lines.
Consider now the Principle of Alternate Possibilities:

PAP: A person is morally responsible for what he has done only if he could have done otherwise.

Some find PAP dubious, on the basis of the so-called Frankfurt counter-examples. These involve a counter-factual intervention that closes off certain kinds of alternate possibilities, while apparently preserving moral responsibility. To this crowd, the conclusion of the Modal Argument is inconsequential. That alternate possibilities (or even “free will”) are precluded by determinism is no real worry—after all, the thing we really care about, Moral Responsibility (MR), is not ruled out by the argument. So the semi-compatibilist line goes.

But getting around the Modal Argument isn’t quite so easy. Let us suppose with the semi-compatibilist that PAP is false. On this assumption, the Modal Argument can still demonstrate the threat determinism poses to MR, for its essential operator, ‘N’, can be reformulated in terms of MR such that it is every bit as pressing for the compatibilist who denies PAP as it is for those who affirm PAP. This reformulation in terms of MR has one side-benefit, too; it neatly sidesteps a powerful challenge to the original Modal Argument, the Agglomeration counter-examples.

Following a suggestion of van Inwagen’s original text, I show how the ‘N’ operator may be reformulated to pack in concepts of MR. I make use of a special symbol. Let ‘→’ stand for the relation between a subject and a proposition just in case the subject is morally responsible for that proposition’s truth value. I invite my reader to read into ‘→’ whatever conditions are necessary and sufficient for a subject’s being morally responsible for truth-value of a proposition—for example, the subject having brought it about that p in just the right way, through a reasons-responsive mechanism, with due deliberation, with the right sorts of second-order volitions, and so forth. The details are not important for my purposes; fill them in as you like, provided that those details do not presuppose that moral responsibility implies or precludes determinism. So, supposing a subject S has murdered Jones in the first degree, S has brought about the truth of ‘Jones is dead’ (‘j’) in a morally responsible way, we may say that ‘S → j.’

I now formulate an interpretation of the ‘N’ operator using ‘→’. Let Np express ‘p, and ~(∃x such that x→p).’ That is, p is true, and no one is morally responsible for p’s being true. I suggest that on this interpretation of N, the following is a valid rule of inference.

β*: Np & N(p ⊃ q) — Nq

β*, together with the uncontroversial α (op — Np), is sufficient to generate an MR-laden Modal Argument structurally identical to van Inwagen’s original, where ‘Pº’ expresses the state of the world at a time before there were any humans (conjoined into a single proposition), L expresses the conjunction of the laws of nature into a single proposition, and "o" logical necessity ("the box"):

1. o (Pº & L) ⊃ p (Assumed, determinism)
2. o Pº ⊃ (L ⊃ p) (1, exportation)
3. N(Pº ⊃ L ⊃ p) (2, α)
4. NPº (Assumed, no responsibility over the distant past)
5. N(L ⊃ p) (3, 4, β*)
6. NL (Assumed, no responsibility over the laws)
7. Np (5, 6, β*)

No one brought it about in a morally responsible way that Pº, nor did anyone bring about the laws of nature, so NPº and NL seem true. Hence, for any true proposition p, ~(∃x such that x→p). That is to say, no one is morally responsible for any proposition’s truth value, a worrisome result indeed, even for those who deny PAP.

Having seen that B* can generate interesting and non-trivial results, I turn in Part II to the question of its validity.

The Problem of the Criterion


Following is my summary of Roderick Chisholm's classic article, "The Problem of the Criterion."

The problem of the criterion is this: there are two sorts of questions we may ask about knowledge, and it is unclear which question ought to be asked first. Indeed, this unclear priority threatens the possibility of knowledge. The questions are:

Q1: What are the instances of knowledge?
Q2: By what criteria are we to pick out the instances of knowledge?

Three responses to this problem are skepticism, methodism, and particularism. The skeptic believes there is no satisfactory answer to either question; the methodist begins with Q2 and proceeds to Q1, while the particularist begins with Q1 and proceeds to Q2.

The skeptic might say: we cannot discern what knowledge instances are without criteria to pick them out. Nor can we discern knowledge criteria. If we were to favor some criterion C on the basis of its success, this would be mistaken, for we could only know that C successfully picks out knowledge instances if we could already detect what the instances of knowledge were (which we can’t). So, we cannot answer question Q1 or Q2, and hence cannot know anything.

Methodism posits that there is an answer to Q2, and proper inquiry begins there and then moves to Q1. Empiricism, the thesis that a belief is known only if it is derived from sense experience, is a leading form of methodism. It answers Q2, “by the criterion of sense experience,” and answers Q1 by applying this criterion to beliefs, counting as knowledge only those beliefs that are derived from sense experience.

Chisholm advances one objection to methodism, viz., that whatever criteria advanced, they are sure to be both arbitrary and generalizations. It is puzzling how one is to arrive at these sort of generalizations, especially when methodism is so careful and modest in admitting only those beliefs as knowledge that pass the test imposed by criteria. A second objection targets empiricism. Supposing empiricism to be true, we hardly seem to know anything at all, even about physical objects; all that can be known are sensory experiences.

Chisholm develops a particularist alternative, supposing that there are many things that we know (an answer to Q1). Surveying these instances of knowledge with the following technical vocabulary, he thinks, will help formulate knowledge criteria (an answer to Q2):

A mental state A is preferable to state B if it is objectively proper to prefer A to B.

A proposition p is beyond reasonable doubt if believing p is preferable to withholding belief that p.

A proposition p is evident for S if p is beyond reasonable doubt for S and including p among the propositions upon which S’s decisions are based is preferable to excluding it.

A state R is self-presenting to S iff S is in R and it is necessarily true that if S is in R, then it is evident to S that S is in R.

A proposition p is axiomatic for S iff p is necessarily true and it is necessarily true that if S believes p, then p is evident to S.

Chisholm posits that some instances of knowledge are states like thinking thoughts and being appeared to in some way. These are self-presenting (in the above technical sense). A priori beliefs like the “truths of reason” are axiomatic. Finally, over the most vexing beliefs (those generated by memory and sense perception), Chisholm proposes that the following criteria preside:

M: For any subject S, if it is evident to S that S seems to remember that a was F, then it is beyond reasonable doubt for S that a was F.

P: For any subject S, if it is evident to S that S thinks that S perceives that a is F, then it is evident to S that a is F.

Principles M and P are not sufficiently precise; to adequately serve us, conditions and qualifications must be added. This is proper inquiry, to amend these principles in light of the body of knowledge we have, fitting these general criteria to particular instances.

This particularist approach begs the question against the skeptic and methodist, Chisholm admits. But it has this much going for it; there are many instances of knowledge, and particularism accommodates that fact.

A Theft


The passenger-side window of my car has never rolled up and down quite right. The same is now true of my driver-side window.

Shite.

The window was forced last night, and a number of things are now missing--a $10 MP3 player, a bag of zippo lighters, and my ashtray. My frickin' ashtray. That's right; this dingbat left behind an $80 AC/DC adapter, a box of applesauce, a sweet leather jacket, a few expensive textbooks, and even an airhorn (with hours of fun left in it!), but took the ashtray from my 1991 Toyota Corolla...

Did she have a Corolla of her own that was missing an ashtray? Is there a black market for these things? Is there a trade-in value? Or maybe she was just a smoker and needed place to put the ashes. To this I can only say, "get your own damn ashtray, you smoking car-burglar!"

Damn those thieves... damn those smoking thieves to hell.

A Poem


From David Friedman's The Machinery of Freedom:

A saint said "Let the perfect city rise.
Here needs no long debate on subtleties,
Means, end,
Let us intend
That all be clothed and fed; while one remains
Hungry our quarreling but mocks his pains.
So all will labor to the good
In one phalanx of brotherhood."
A man cried out "I know the truth, I, I,
Perfect and whole. He who denies
My vision is a madman or a fool
Or seeks some base advantage in his lies.
All peoples are a tool that fits my hand
Cutting you each and all
Into my plan."
They were one man.

A Treasure Trove


Peter van Inwagen's An Essay on Free Will, like Plantinga's The Nature of Necessity is a "treasure-trove," not just of arguments, but of astute observations or humorous asides. Here are two of my favorite:

"When a philosopher says, 'The burden of proof lies on you' he means, 'You must deduce your conclusion from the truths of immediate sense experience by means of an argument that is formally valid according to the rules of elementary logic; I, on the other hand, may employ any dialectical tactic I find expedient.'" (p.18)

"The concept of a possible world is an extremely useful one. Yet a considerable number of philosophers who seem to be otherwise intellectually responsible have taken to amusing themselves and their graduate students by engaging in what can only be described as Philistine sneering at this harmless and fruitful notion. Well, as poor Paley said, who can refute a sneer?" (p.79)

A Broken Window


I was planning on posting about Hurricane Katrina and the Broken Window fallacy—but it looks like Tom Palmer beat me to the punch. Here's the short version: a common economic fallacy employs the following inference: material goods are being destroyed, and this is good, since it will stimulate economic activity, viz., the rebuilding of those material goods. Unfortunately for proponents of this kind of thinking, Frederic Bastiat blew this line of reasoning out of the water 150 years ago with his acclaimed essay "What is Seen and What is Not Seen."

Bastiat's argument draws his readers' attention to the opportunity costs involved with window fixing. Sure, a hurricane may break a few windows and thereby give business to window-fixers. But the money used to hire the window-fixers would have gone somewhere else should the window not have been broken. In that sense, there is no net economic gain. When all is considered, there is a net loss, in fact: the broken window!

It's silly to suppose that wealth can be created by destroying things, and this is just what the broken window fallacy does. That's why we call it a fallacy!