Wednesday, February 28, 2007

The most famous fallacy?

I was talking with my roommate over dinner and the conversation turned to mistakes in reasoning. He pointed out to me that the opening line of the Nichomachean Ethics is fallacious. It is: "Every art and every inquiry, and similarly every action and pursuit, is thought to aim at some good; and for this reason the good has rightly been declared to be that at which all things aim." The fallacy is inferring from \forall x \exists y to \exists y\forall x. Having never read the Nichomachean Ethics (We read the Eudemian Ethics in my Greek Philosophy class for some reason.), I was shocked. Were those the perils of syllogistic reasoning?

I think another good fallacy is in the Critique of Pure Reason. In the paralogisms of pure reason (B422-423), in a footnote on Descartes, Kant seems to make the modal fallacy (is there a Latin name for this?) of inferring from [](p->q) and p to []q.
The quote is, "I cannot say 'Everything that thinks, exists'; for then the property of thinking would make all beings possessing it into necessary beings."
Again, I was surprised when I saw that.

What other great fallacies are there...

Saturday, February 24, 2007

Cause quotes are awesome

And quotes from Wittgenstein are really awesome. From Rhees's review of Anscombe's book on the Tractatus:
"In a remark written considerably later than the Tractatus Wittgenstein said 'No philosophical problem can be solved by a calculus.' He had no longer spoke quite as he had in the Tractatus, but he always thought that 'meta-languages' were an evasion. This was not because he did not feel that logic was important, but because he was convinced that it was."
Whatever one thinks of the use of a calculus, too often people make the knee jerk inference to the idea that formal tools are worthless, period.

The protestant work ethic fallacy

There are a couple of interesting posts here and here by Nigel Warburton. In discussing whether blogs are conducive to doing philosophy (my short answer is yes!) he talks about what he calls the protestant work ethic fallacy. This fallacy is that the more time you put into something the better it will get. The fallacy, Warburton claims, is to think that this is always the case. This seems right to me. Generally things do get better with more work and time put into them, but this isn't always the case. Things can be polished and improved, but revision doesn't entail improvement.

In calling this a fallacy, one shouldn't swing too far the other direction and jump to the conclusion that more time and work doesn't improve things and it is better to do things quickly. This would be the slacker fallacy. One should avoid this one too. The pair of these indicates, I think, the need to carefully weigh the costs and benefits of one's work. It also points to the need of recognizing when one is improving one's work and when one is (merely) changing it. This seems particularly difficult as it is hard to get an honest perspective on one's work. The way around this then is to work with other people and try to get feedback as much as possible.

Friday, February 23, 2007

Different formalisms for different reasoning?

In his "What is logic?" Ian Hacking attributes to William Tait a comment about how natural deduction is more suited towards intuitionistic reasoning while the sequent calculus is more suited to classical reasoning. At first, this comment struck me as odd because the sequent calculus didn't seem suited to anything but proving cut elimination in a nice way and showing a system has the subformula property. Then it occurred to me that Tait might have been talking about the one-sided sequent calculus. This is a neat little thing that one can develop out of the normal two-sided calculus. Since in the classical calculus one can move formulas across the sequent arrow by adding a negation, one can treat all formulas as though they were on the same side of the arrow. I believe this is because since in classical logic everything is equivalent to a formula in negation normal form and you can eliminate double negations, you can always convert a formula to an equivalent one in a nice form. In effect, you get a one-sided sequent ~A_1,...,~A_n,B_1,...,B_n from a two-sided sequent A_1,...,A_n=>B_1,...,B_n by sticking a negation in front of the A_i in the one-sided version. The one-sided version is then read as the disjunction of all the formulas, i.e. at least one of these holds, much like the consequent of the classical two-sided calculus says that at least one of those formulas holds given that all the antecedent formulas hold. Using the one-sided calculus lets you cut down on rules; you only need intro rules for &,v, and \forall and a way of taking care of negations (I will have to review my notes to clarify that). The proofs for the one-sided calculus are much easier and more intuitive than the proofs for the two-sided calculus. This is what makes me think that Tait was right and what makes me think that he was talking about the one-sided calculus.

As for why natural deduction is suited to intuitionistic reasoning, I'm not particularly sure. It certainly feels right, but there isn't a better reason I have off hand. I think I learned about the nuts and bolts of intuitionistic logic in the same setting in which I learned about natural deduction (a proof theory class), so the two are linked in my mind. This is just an accidental feature of my educational history though. I'm not sure what the clearer connection is that Tait sees. Maybe it has something to do with Prawitz's work on the introduction rules of natural deduction defining the intuitionistic connectives.

Thursday, February 22, 2007

From an ontological point of view

[This post is partially in jest, but only partially.] Suppose we are good Quinean ontologists, and we admit sets into our ontology, since Science needs Math, and set theory takes care of that. We can use sets to define real numbers and we can represent all of physical space with quadruples of real numbers. Objects in space and time are representable as sets of real numbers and predicates,etc. are representable as sets of those. So all we need to satisfy the quantifiers for our best theories are sets.

But, I like my chair, and putting my chair into the ontology doesn't make it any bigger. There is already continuum many things in the ontology. So, I add my chair. Continuing, adding one more (or a countably infinite number) of physical things won't make the ontology any bigger. So, I'll go ahead and add all the physical things in the world. But, ponies are nice and everything is better if it comes with a pony. Therefore, I'll add an extra pony in my ontology. Being a good Quinean, I end up with a sparse ontology of sets, all physical things, and a pony.

Tuesday, February 20, 2007

Making our ideas clear

Thinking about some things in the Tractatus together with things I've been reading for other classes (mostly the Moral Problem) has led me to think about clarity in writing again. It is still somewhat elusive. One of the virtues of analytic philosophy, I have been told, is that the writing is clear and the arguments are explicit. The importance of clarity in writing seems to me more and more odd. There are many things one might be looking for in reading a philosophy book or article. One of these is good philosophy. There isn't much reason to see clear writing as particularly indicative of good philosophy (an amorphous term which won't be defined here). Placing a high premium on clear writing could lead to the following two sorts of errors. One is the error of mistaking clear writing for good philosophy. The other error is mistaking unclear writing for bad philosophy.

One could take the Searle approach and claim that unclear writing is indicative of poor understanding. There is something right in this. For a lot of cases, this is true. It seems like a good heuristic for grading undergraduate papers. As an across the board maxim, it seems likely to lead to error. There are a lot of people who understand abstract subjects very well but are bad at communicating this to others. It isn't particularly hard to think of TAs who clearly understood things but could not explain them appropriately. Similarly, a presentation might be unclear because the presenter is loading the presentation with so many qualifications and subtleties as to lose the audience. But, this is just because the presenter is being very careful, overly so. At a certain level, it doesn't make sense to hold to Searle's maxim. Clarity of presentation becomes something of an accidental feature rather than indicative of understanding. As another example, some people, I hear, accuse John McDowell of being somewhat opaque, but I would be extremely hesitant to make the leap to saying that this is because he doesn't understand what he is talking about. Doing that seems like a reductio of the Searle maxim.

Going the other way, clear writing isn't always indicative of good philosophy. It is certainly less frustrating to read an article that is well structured so that the dialectic is easy to follow than it is to read an article that is not well structured. The danger is that the author gets caught up making the article clear at the expense of focusing on the philosophical issue, e.g. explicitly naming all the principles, numbering all the steps of the argument, using variables in different scripts for terms whose particular values don't matter, etc. These things all help keep one honest, and I am a fan of them. I use them a fair amount in writing my own papers. But, they go a ways toward giving an illusion of rigor that can lead the reader/author into a false sense of security. If clarity by itself meant philosophical issues were on full display and under control, then philosophy of logic and philosophy of math would not exist, it seems. (That is probably a bit of a hasty assertion but I'm going to leave it for now.)

To head off a worry (possibly a worry only I have about what I wrote), I don't want to endorse any kind of deep vs. (merely) clever dichotomy, something which Wittgenstein himself apparently endorsed (a fact which saddens me). I'm not sure these have to be seen as a dichotomy or even in opposition. Philosophical merit is one thing, and stylistic merit is another. Sometimes the two go together, as in David Lewis. Sometimes they come apart, as in... a lot of philosophers. Confusing one for the other seems like a bad move. Trying to use one to cover for the other seems like an even worse move. There are myriad benefits to writing clearly, and there are reasons enough to keep teaching and endorsing that practice.

The way forward in thinking about this is, probably, to hack away at the idea of clear writing for a bit. I'm not going to attempt to go at the idea of good philosophy. I mean, really, that would be pure hubris.

Best. Proof. Ever.

A few pages into his "Display Logic", Nuel Belnap gives a few equivalences between forumlas. Since it is a logic paper, the equivalences must be proved. So, he gives the proof: "Proof: by diddling."

I hope to have enough logic cred someday to write a paper featuring a proof like that.

Humpty Dumpty was a Wittgensteinian?

When Alice is talking to Humpty Dumpty, Humpty Dumpty says that he doesn't sing after singing the first verse of a poem for Alice. Alice responds "I see you don't." To this Humpty Dumpty remarks severely, "If you can see whether I'm singing or not, you've sharper eyes than most." This reminded me of the anecdote about Wittgenstein and his friend. The friend, who had just had surgery, says, "I feel just like a dog that has been run over." Wittgenstein gets irritated and says, "You don't know what a dog that has been run over feels like." Same impatience with slightly metaphorical usage.

Wednesday, February 14, 2007

Theoretical adequacy in three easy steps

In one of the first lectures in the syntax class I'm taking, the prof discussed this three way distinction found in Chomsky's Aspects. Chomsky claimed there were three levels of adequacy for any grammar: observational, descriptive, and explanatory. A grammar is observationally adequate if it tells you whether any given string of words comprises a sentence in the language. A grammar is descriptively adequate if it associates with each grammatical sentence a syntactic structure (not sure if it also associates a structure indicating why the string is not grammatical if it isn't). A grammar is explanatorily adequate if it explains why descriptive grammar works. Chomsky thought that syntactic theories should ideally meet all three levels, although they must only meet the first two. The first two certainly look easier, but I was a bit puzzled what made that the natural boundary. Looking at the levels of adequacy reveals a pretty natural reason. Observational and descriptive adequacy are the sorts of things that are naturally completed by an algorithm. They are clearly mechanizable. An observationally adequate grammar would be a program that took a string and ran through sentences of the language until it found the sentence or exhausted the sentences of the proper length. It would be the characteristic function of the set of sentences of the language. Similarly, the descriptively adequate grammar would build a syntactic structure for each sentence that the observationally adequate grammar told it was good. That's a bit more difficult, but still mechanizable. Explanatory adequacy crosses the boundary (barring some assumptions about the mind being a Turing machine) into what one wouldn't expect a program to do. It would need to bring in stuff outside the language the grammar is designed to describe. In particular, it would need to be able to cite (on a Chomskyan way of looking at things) universal grammar, parameters, language modules, and a host of other things about the ins and outs of language and linguistics. That'd require creativity on the part of a full blown artificial intelligence with a fair amount of world knowledge (that's an awful wastebasket phrase). Chomsky, rightly, thought it might be a bit demanding of the syntacticians to have their grammars do all that.

Momentarily victorious

I recently finsihed my outstanding (as in late, not as in great) Kant seminar paper. Although I declared victory over fall semester back in December, there was a sense in which that was in bad faith. Kant was left undone then, but now I have finished all my classes. To celebrate this, I've updated the list of links and attempted to go ice skating. The rink was closed due to ice. Seriously.

Saturday, February 10, 2007

A kind of history of philosophy

[This one is kind of rough.] There's an essay by Dan Garber on the history of philosophy I rather like. The essay is "What's philosophical about the history of philosophy?"[edit: It appears in Analytic Philosophy and History of Philosophy, edited by Sorell and Rogers.] In it, Garber distinguishes two approaches to the history of philosophy: collegial and antiquarian. Roughly the distinction is that collegial history of philosophy treats the philosophers as sources of problems and a context in which to situate or contrast a view while the antiquarian treats the wider context, including the surrounding chapters, other works by the author, historical events and correspondence, etc., as necessary for understanding the philosopher. The latter tries, as nearly as possible, to recapitulate the perspective of the philosopher, so we can get into their heads, so to speak. The former takes some element of a theory as a foil or jumping off point for a new position. The example of this that Garber gives is John McDowell, although I'm sure there are better examples. The point of the article is to argue that antiquarian history of philosophy is relevant for philosophers that don't have exclusively historical interests. He does this by explaining what it is he sees antiquarian history of philosophy doing and pointing out how that is worthwhile. A large part of this is to more fully understand an argument and to provide prospective on how to think about problems. This seems fairly correct to me, but he was preaching to the choir somewhat in my case.

There is one kind of, roughly, antiquarian history of philosophy whose approach I rather like. It tries to approach a philosophy book by trying to figure out the problems from the perspective of the author. What problems did they tackle and why? How did they try to solve them? On one interpretation, this might just sound like any sort of history of philosophy, and in a way it is. I think a good way to put it is that there is a lot of focus on what is being reacted to as well as the reaction. The Wittgenstein class I'm taking now is a good example of this. It started with reading a bunch of the post-Principles of Mathematics Russell, particularly the stuff that Wittgenstein read. From this, we look at Wittgenstein's notes and the Tractatus to see how he reacted and how he tried to solve the problems he attempted to solve. (I am having a little trouble getting nice clear necessary and sufficient conditions for this approach.) The Kant class I took last term was somewhat similar. The focus on was on reconstructing Kant's trails of thought in the first Critique by concentrating on the Critique rather than secondary literature. Secondary literature has its place, and some of it is quite good (E.g. Ricketts's "Wittgenstein against Frege and Russell"). Some of it is less good, and very little of it compares with the original material. The mighty dead are mighty for a good reason (and dead for a good reason too I suppose).

What makes this sort of approach worthwhile? I think one of the main values in it comes from thinking through what the philosopher in question was trying to do. But, isn't this just what doing philosophy is, in large part? I suppose. Trying to see how the printed views followed from (or were thought by their authors to be entailed by) the collateral commitments that constitute the beliefs of the philosopher in question seems like a very edifying exercise. It seems like this splits into at least two parts. One is reconstructing their arguments and the other, which usually goes on in tandem, is to figure out those collateral commitments. Of course, each informs the other. Another payoff from this is that in reconstructing the perspective of the philosopher in question, one can (might?should?) get enough distance on one's own view (or proto-view, or conceptual stumblings around [as a lowly grad student]) of things that one can more clearly see what rests on what and what follows from what. This is fairly close to the justification that Garber gives for antiquarian history of philosophy, because it is pretty close. The main difference I see (or think I see) is that antiquarian history of philosophy often approaches the subject from "outside" the philosopher in question, looking back from now, in a way. This approach tries to tackle the problems from "inside" the philosopher, trying to see how one would view problems and possibilities given a certain tool set, as well as figuring out what tools one has. The inside and outside approaches to antiquarian history are closely related, but I'm digging the inside approach, reconstructing the internal perspective of the philosopher. I see it as sort of like working through proofs, but that isn't a perfect analogy. At the very least, this approach seems good at doing what Wittgenstein's friend O.K. Bouwsma said was an aim of philosophy: to "quicken the sense of the queer."

Wednesday, February 07, 2007

A note on philosophy of science and syntax

The structure of syntactic theory classes is interesting. (By the end of the term I will have taken two, so take an appropriately sized grain of salt with this post. For anyone interested, the books I have in mind are Syntactic Theory by Sag, Wasow, and Bender and Syntax by Carnie.) To my memory, most science classes start off in some accepted theory and get you more-or-less caught up with what that says. You'll start off with a bit of a simplified version, maybe, but you get up to speed as you go. Syntax classes seem to be different. You start off with an obviously toy theory. This will be something very simple, e.g. only rules for S, NP, VP, N, and V. As the class progresses, you look at certain phenomena and change the theory as you go. This sort of test indicates constituency patterns, so we need more structure. This sort of thing indicates a difference in verb arguments, so we need hierarchical structure. These things violate the theoretic neatness (of X-bar, for those that care), so we should add new categories. This sort of reflexive violates our binding principles. Etc. etc.

This is interesting because it seems to me to be an explicit instance of theory construction, including the things that motivated the changes; conjectures and refutations. After a few weeks/chapters, the theory with which you work is very different than the one with which you began. Not just expanded with new pieces. There are several underlying differences as well as expansion with new pieces. This approach illustrates the ideas about scientific theories and testing that Duhem, Kuhn, Popper, and the rest of that gang discussed. I rather enjoy it. The wildest ride of this sort I've been on comes in Syntactic Theory. About halfway through the book there is a large shift in the theory. Then, again, in the final chapters, the authors tell us that the brand of HPSG that we've been working with is insufficient for a few reasons and sketch a version of the then-state-of-the-art HPSG. The homework problems in the chapters gave you the sense that you were developing the theory as you went (in a couple of cases pretty explicitly), and then at the end, it is still inadequate. Pedagogically this is kind of fun. Philosophically it seems like an interesting approach. I don't know if there is any discussion of this in the literature in philosophy of science, but then, I am quite close to completely ignorant about philosophy of science. i wouldn't be terribly surprised if it wasn't in there some where, since philosophy of linguistics gets even less attention than linguistics itself (a travesty to be sure.)

Tuesday, February 06, 2007

Overly strong statement of the day

Michael Smith takes it as a conceptual truth about fully rational agents that they have no false beliefs. This is a view he picks up from Bernard Williams (Ch. 5 of the Moral Problem; p. 156 actually). This strikes me as too strong and hard to motivate. The reason Smith gives in its defense comes from Williams. Suppose an agent, Wilfrid, has a cup of tonic in front of him and what he thinks is a cup of gin but in reality it is a cup of petrol. He wants to mix the petrol with the tonic and drink it cause he thinks it is gin. According to Smith, it is odd to say he has a reason to do this. In fact, Wilfrid has no reason to do so even though he might think to the contrary. The conclusion that Smith draws from this line of thought is that a fully rational Wilfrid would not have reason to mix the liquids because he would have no false beliefs. The argument he gave doesn't really support that conclusion. It would support the conclusion that were he fully informed (and rational) he would give up his reason to mix the liquids. Maybe the concept of full rationality is supposed to support the idea that one can, given a set of beliefs, rationate them in such a way that the true ones are preserved and the false ones are weeded out by the powers of logic alone. It isn't insane to think that a fully rational agent could weed out most false beliefs given some time and access to a fair amount of resources. But, it doesn't seem supportable to hold that the machinations of pure reason alone rule out the very possibility of false belief. I feel like there are some collateral premises Smith is relying on that I can't quite get.

In any case, the argument he gives is rather poor. There is a difference between a fully rational agent and a fully informed one. Since we're stipulating the situation, we are fully informed. Even though I'm not fully rational I can say that Wilfrid shouldn't mix the liquids, that he has no reason. But, this is just because I know what Wilfrid does not. The concept of rationality does not seem to be pulling any weight in the example. Because of this, it really can't pull any dialectical weight in the argument. That being said, this particular requirement of rationality doesn't seem to figure in the rest of Smith's positive account of non-Humean normative reasons in any big way.

[Addition: Nate continues this discussion here.]

Sunday, February 04, 2007

I'm just saying

There is an invalid step in this dialogue somewhere.

Willard: Look, p. I'm just saying.
Donald: Ah, but on a Gricean analysis, saying is a kind of non-natural meaning. So by just saying, you are just meaning in the sense of speaker meaning. Therefore you meant p. I take offense at that.
Willard: Oh no, you have foiled my attempt to evade commitment to p! You've bested me again Donald.


In Russell's work, Russell's paradox is called "the Paradox." By parity of reasoning, in Hawaii, Hawaiian pizza is called "Pizza."

Saturday, February 03, 2007

Links: all the benefits of theft over honest toil

For some reason, I think that people that read my blog also read the other blogs I read even though I'm fairly certain this is not the case. On the off chance that someone does not, there are a few posts I've read recently that are definitely worth checking out. One is Nate's provocative question about methodology in semantics. Andreas has a pair of posts on Kaplan's "Demonstratives" on necessitation and proper contexts. And Ole has a post on Field on logical primitives. Of course, I think everything in the sidebar of links is worth reading. Especially the Philosophy Talk blog which features John Perry's delightful post on truth and bullshit.
(On a side note: my lame spell checker does not recognize "blog" as a word. I could excuse it for not recognizing "impredicateively", but "blog"?)

The world is everything that is the case

The Tractatus opens with the line "The world is everything that is the case." To this, Wittgenstein adds at 1.11, that the world is made of those facts and the fact that those are all the facts. This is a "stop"-clause of sorts. Frank Jackson uses one in his From Metaphysics to Ethics, which one might see as problematic. Barwise and Perry discuss this in Situations and Attitudes and decide to reject a stop clause. They think it is alright to not have an upper limit on what constitutes the world.

Why bring this up? There is an odd part in Russell's intro to the Tractatus. He says "We touch here one instance of Wittgenstein's fundamental thesis, that is, it is impossible to say anything about the world as a whole, and that whatever can be said has to be about bounded portions of the world." (p. 17 of my version) This is odd because Wittgenstein starts off saying something about the world as a whole. Then he says, no really, that is the whole world. Wittgenstein not only says something about the whole world, he adds another proposition saying that's everything. That looks like two violations of the thesis Russell attributes to him.

One might think that there could be a self-reflexive proposition or fact in the world. This is ruled out because of what Wittgenstein sees as the "fundamental truth" of type theory (that's from his Notes on Logic). That "truth" is that a proposition cannot contain itself, which can plausibly be understood by saying that a proposition cannot be impredicatively defined. Since reflexive propositions cannot exist by Wittgenstein's lights, he has to add another proposition to a "complete" specification of the world saying that it is complete. But, it seems like he'd need another proposition saying that those really are all the facts, and so on.

I'm having trouble squaring what Wittgenstein says with Russell's explanation of Wittgenstein. The quote from Russell follows up a discussion of Wittgenstein on the idea of objects in general. Short version: Wittgenstein thinks "object" is a pseudo-concept and that it is legitimate to talk about objects only in connection with another property. Interestingly, this property need not be a sortal, e.g. person, dog, cat, copy of the Moral Problem by Michael Smith. It can be a mass term or adjectival property, e.g. water, blue, red, light. There's more to untangle in the connection between these ideas, and it is possible that Russell got the interpretation wrong, but, it does seem like this is something Wittgenstein was sympathetic to.

Thursday, February 01, 2007

Brilliant

Following others, I thought I'd comment on the recent links to the photos of philosophers. My favorite quote is definitely Searle's: "If you can't say it clearly, you don't understand it yourself."
There is certainly some truth in that. I'd like to say that it connects up clearly with my previous posts on clarity, but I haven't made it clear enough to myself to say that.
My favorite pictures are probably Davidson, Lewis, and
McDowell. Davidson's is kind of spacy. Lewis's is kind of happy. McDowell's reminds me of a comic book cover, although I'm not sure which one. Just some possible one. That being said, he looks seriously philosophical.