Tuesday, October 30, 2007

Get thee to a punnery

Why are there not more discussions of the instrumental value of music? *drum roll* But seriously, Aristotle seems to want to say that music isn't final without qualification because it has some instrumental value.

I'm not sure if that is a standard pun among ethicists and other value theorists, but I hadn't heard it before. I think it is a shame, if not.

Monday, October 29, 2007

This is neat...

I just stumbled across this repository of online .pdfs. Apparently Stanford is putting online the text of their CSLI lecture notes and other books as well. There are some things that look nice in there. Among the things I found were Barwise and Moss's Vicious Circles, Troelstra's Lectures on Linear Logic, and Link's Algebraic Semantics in Language and Philosophy. Best part: they're all free.

Saturday, October 27, 2007

Pitt-CMU conference update

We've lined up our faculty speakers, Gordon Belot and Peter Machamer. They will be giving talks in addition to the keynote by Bas van Fraassen. The submission deadline is December 10, 2007. For more information, see the website.

The limits of the first-order

Why has standard first-order logic occupied philosophers so much? In particular, why take it as the basis for forays into the foundations of math or the nature of language or metaphysics? It has its good points to be sure. It is complete and compact. The negative that I'm thinking of is non-trivial though. First-order logic (with identity) has some pretty large expressive limitations. In particular, it cannot express the general concept of finitude. It can express trivial finiteness conditions, e.g. "there are exactly n things that are such and such" or "there are at least m things that are so and so". It cannot express "there are finitely many things that are so and so", so it also is incapable of expressing "there are infinitely many things that are so and so". Of course, if we want we can make up our own quantifiers that express infinitude. This comes at the expense of some of the niceties of first-order logic; in this case the Loewenheim property. If finite sentences are too limiting, we can always add infinitary conjunctions or disjunctions. These force us to give up standard forms of compactness. However, these seem like good moves to make in many applications. Why would we saddle ourselves with expressive limitations from the outset?

Wednesday, October 24, 2007

Van Fraassen's Manifest Image

I had a thought about how to motivate van Fraassen's constructive empiricism (the view that we need only accept theories as empirically adequate, that is, believe what they say about observables and be agnostic about what they say about the unobservables) since anti-realist views can seem at times, unmotivated. The thought I had was that he is responding to Sellars's Philosophy and the Scientific Image of Man. (Apologies for poor Sellars reconstruction.) In that essay, Sellars contrasts two images of man, the manifest and scientific images. The manifest one is, roughly, the commonsense conception of ourselves and the world. The scientific image is that which contemporary science gives us. I think it is roughly the difference Eddington finds between the everyday idea of tables and chairs and the view of them as composed mostly of empty space and composed of small, small particles and fields, etc. Sellars thinks that one important job of philosophy is to spell out the relation between the images. In the end, he says that they don't need to be reconciled but that the manifest image needs to be joined to it. Sellars is also a realist of a rather extreme kind. He was also van Fraassen's teacher at Pitt.

Now, my crazy idea is that van Fraassen's constructive empiricism is an attempt to go the other way. It is an attempt incorporate the scientific image into the manifest. The manifest image seems to roughly correspond to the sort of thing that van Fraassen views as observable. Especially when viewed through empiricist lenses, the macroscopic level at which we normally find ourselves lends itself to being viewed as the world of the manifest image. Of course, van Fraassen doesn't talk much about intentions and norms that Sellars's manifest image also concerns itself with. Putting that aside for now, if one is agnostic about everything that is not observable, in van Fraassen's sense, then one is agnostic about the traditional way of understanding the scientific image. Eddington gets just the manifest table. Constructive empiricism says to be agnostic about the scientific table. Everything science says about the observable is incorporated into our beliefs about the world of the manifest image. This seems like it is one way of cashing out the relation between the relation between the two images of man. The scientific image helps us to understand the manifest image, but we need only believe in the world of the manifest image.

I floated this in my philosophy of science class today. A couple of good points were raised against it. One is that apart from the title, van Fraassen doesn't really mention the Sellars piece. Another is that what I have been calling the manifest image in van Fraassen's book is somewhat different than the manifest image in Sellars's essay. This is true, but it doesn't seem that far from what you'd get if you took Sellars's manifest image and tried to cast it in an empiricist vein. Depending how exactly observable gets spelled out in the end, this might not be tenable at all. I think that if the idea of observable is constrained to the roughly medium-sized macroscopic things and processes, then it is a possibility.

Saturday, October 20, 2007

Are there any software platonists?

A formulation of mathematical platonism is that mathematical entities exist independently of us and when we do math we are exploring the realm of the mathematical entities and discovering new things about them. This is a fairly basic or naive formulation of it, but it gets the flavor roughly right. A software platonist would think that programs exist independently of us and when we do computer science or programming (not sure which would be the better formulation) we are exploring the realm of programs and discovering new things about them. A mathematical platonist would say that the natural numbers would exist even if humans never did and a software platonist would say, e.g., that LISP or Apple OS X would exist even if humans never did. Further, the natural numbers were around long before there were humans, and, similarly, LISP and Apple OS X were around long before there were humans. We started exploring the natural numbers a long time ago but only recently started exploring LISP and even more recently Apple OS X.

It seems to me that software platonism is nuts. There is a fairly strong sense, I would think, in which Apple OS X would not have existed were we (broad, inclusive 'we') not around to create it. It was created by engineers and is changing over time. But, it is still just a program. However, as such, there is a Turing machine equivalent to it. Now, LISP was also created by a computer scientist, but it is a bit more abstract and so the platonist intuitions are maybe stronger for it. Engineers have changed LISP over time, and I don't know how a software platonist would explain what links the various versions of LISP (or, for that matter, how programs of any sort run on hardware, but that might not be so different than us counting with the natural numbers). LISP has, I believe, been shown to be able to compute the same functions as Turing machines; the term is Turing-complete, I think.

The question is: are we creating or exploring an antecedently existing realm of programs? There is a related question: are we creating or exploring an antecedently existing realm of Turing machines? I'd hope the two fall together, given the tight connection between programs and Turing machines. However, there seems to be a little bit of room to drive a wedge between the two. I suppose that would allow one to be a Turing machine platonist without being a software platonist. Although, one could try to use the Turing machines, which may be able to draw on mathematical platonist leanings, to argue for platonism about programs.

I don't have any worked out ideas in this area, but it does seem to me that software platonism is hopeless. Are there any software platonists?

Thursday, October 18, 2007

Structure is as structure does

Philosophers like structural comparisons for various reasons. Establishing these are often important. For example, in the Tractatus, Wittgenstein seems to be trying to set up an isomorphism between language and the world. In other contexts, philosophers try to establish that structures are isomorphic. It seems like outside of model theory the only notion of structural comparison that gets any play is isomorphism. The model theory class I'm taking has started making me wonder why this is. There are lots of other interesting and useful sorts of comparisons: back-and-forth games, bisimulation, homomorphisms of various sorts, etc. We could even through out a lot of the homomorphisms, the ones that are one-way. I'm not sure why the others don't see more philosophical action. Bisimulation is the key notion of modal logics, at least in the Amsterdam school. Yet, philosophical discussions of modality don't mention it as far as I know (which, admittedly, isn't very far). Back-and-forth games (meant here in a more general sense of games of any finite length) seem like they would be fruitful and usefully combined with ideas from computability theory. This is because they emphasize the idea of being able to differentiate two structures using only a certain number of checks. The two structures could be non-isomorphic, but discovering this fact could take an infinite number of checks, something that finite little agents could not do. What lead to the popularity of isomorphism? It often seems a little heavy handed. Is it just that it gets covered in the standard logic classes, like induction, and so is the tool of choice amongst philosophers?

Wednesday, October 17, 2007

Call for papers: Pitt-CMU philosophy grad conference

I'm pleased to announce the 2008 Pitt-CMU Graduate Philosophy Conference.

Keynote speaker: Bas van Fraassen
Theme: Relativism and rational reflection
Facutly speakers: TBA
When: March 1, 2008
Where: The University of Pittsburgh

Call for papers: The deadline for submisisons is December 10, 2007. More information can be found here.

Tuesday, October 16, 2007

We are sorry to inform you...

I just came across a wonderful link again. This is a page of rejection letters of famous papers. It includes papers by Turing, Shannon, and Dijkstra. I will quote the Turing letter for those that don't want to click through:
""On Computable Numbers, with an Application to the Entscheidungs Problem." This is a bizarre paper. It begins by defining a computing device absolutely unlike anything I have seen, then proceeds to show—I haven't quite followed the needlessly complicated formalism—that there are numbers that it can't compute. As I see it, there are two alternatives that apply to any machine that will ever be built: Either these numbers are too big to be represented in the machine, in which case the conclusion is obvious, or they are not; in that case, a machine that can't compute them is simply broken!
Any tabulating machine worth its rent can compute all the values in the range it represents, and any number computable by a function—that is, by applying the four operations a number of times—can be computed by any modern tabulating machine since these machines—unlike the one proposed here with its bizarre mechanism——have the four operations hardwired. It seems that the "improvement" proposed by Turing is not an improvement over current technology at all, and I strongly suspect the machine is too simple to be of any use.
If the article is accepted, Turing should remember that the language of this journal is English and change the title accordingly."
I love the last line. Turing should remember that the journal is in English, so he shouldn't call the Entscheidungsproblem by its German name. I wonder how amusing this will be when I start sending things to journals...

How fast does time go?

I seem to have fallen off the blogging bandwagon for a bit. A combination of recent events conspired to eat up time that might otherwise be used for writing, but there shouldn't be much to prevent me from writing about things in the nearish future.

The title of this post comes from a question I always thought was a little weird, namely what is the rate at which time passes. I've always liked the uninformative answer of one second per second. Often it seems like it goes much faster, like the lightning quick weekend I just had. Other times it slows down. For example, recently I went skydiving and I was warned that during the free fall it feels like time stops. I was looking out for this, so I was concentrating on it as I jumped out of the plane. Time really does seem to grind to a halt for those, apparently, 50 seconds. I'm not quite sure what to make of the feeling of time stopping together with my seeming ability to entertain thoughts at that point. The kantian in me is very confused by this since time is the form of inner sense and it seems like stopping that would interfere with inner sense. Nonetheless, it certainly seemed like time stopped then it started again. Truly odd. This ends my rambling on time perception. I'd like to return to the philosophy of time at some point since I really dig on McTaggart. I'm not sure when that will be. I promise to try to avoid further forays into phenomenology though. (Bonus points to anyone that caught the underlying motivation for this post.)

From the looks of my posts, one would think that I've spent most of my time thinking about Making It Explicit and the Tractatus. This is in part true. I've been thinking about other things but these haven't yet made their way into posts. This will hopefully change this week.

For those interested in the Pitt-CMU grad conference in the spring, the website is up but the new call for papers isn't done yet. Bas van Fraassen is the keynote speaker, which should be pretty sweet.

Sunday, October 07, 2007

Making It Explicit: Incompatibility problems

Throughout MIE, we are told what incompatibility is. Two claims are incompatible when commitment to one precludes entitlement to the other. We are also told that incompatibility is a modal notion. In fact, it plays are rather central and rather modal role in the later part of MIE and Brandom's later work. Now, my problem is I don't understand where the modality comes from. Commitment and entitlement are normative but they aren't, at least at this point in the story, modal. The preclusion isn't modal either; it is just straightforward non-modal precluding.

There is a modal sense of incompatibility that is used in other philosophical papers. This is, I think, a sense in which two propositions are not jointly possible; non-compossible is the term I think. This is clearly modal. If that is what Brandom means, then there should be some demonstration that this sort of incompatibility and the kind defined in MIE coincide. There isn't any such demonstration, which makes me think that this is not on the right track. However, if it isn't on the right track, then I don't know how in the world incompatibility is modal. If it is on the right track though, then I'm also not sure how the argument is supposed to run since these two notions don't seem coextensional. I'm doubtful that the latter implies the former either, but then this is just denying that I'm on the right track.

Saturday, October 06, 2007

Semantic Externalism

You know you've had a cultural impact when your ideas make it into a dinosaur comic. Hilary Putnam must be proud of this.

Tuesday, October 02, 2007

Making It Explicit: Notes on reading ch. 4

I want to write some in depth posts about the material in chapter 4, but I have precious little background in the philosophies of action or of perception. Instead, I will try to sort out a few things about the structure, mostly in an expository vein, mostly sketching some of the major themes. The chapter covers a lot of ground; in particular, action, perception, and epistemology. Most of the epistemological background in the book is in the chapter, preceding the perception stuff. The perception and action sections are supposed to present the theories of the book on those topics. It seems like neither is entirely satisfactory and a lot more could be said about all three parts.

The perception section bears most of the weight. Conceptually, action is identified with (I think that is right) language-exit moves while perception is identified with language-entry moves. Perception bears most of the weight because the model for perception is reused for action. The order of things is just, in a sense, reversed.

The model of perception is what Brandom calls the two-ply account. It consists of having an appropriate reliable differential responsive disposition and applying the appropriate concept. There is a two part structure here to reflect the interactions of the causal order of things and the rational order of things, with dispositions for the former and concepts for the latter. For action, instead of passively accepting a stimulus, the causal side of things is motivational. There is a further story to tell on the action side about practical reasoning and practical commitments, but this leans heavily on the established ideas of doxastic commitments, theoretical reasoning, and the two-ply model for perception.

Brandom is primarily concerned with materially good practical reasoning, like theoretical reasoning. This means that the inferences will in general be non-monotonic. Similarly to his views on material inference in the theoretical case, the practical case features multiple sorts of formal goodness. Whereas the different sorts of conditionals express different sorts of endorsements of inference on the theoretical side, the different sorts of oughts (instrumental, unconditional, etc.) express different sorts of endorsements of practical reasoning on the practical side. In a big way, the account of action is what you get if you take the structure for the theoretical side, i.e. inference, logic, perception and the rest, and change as few bits as possible to make it about action. The symmetry is both lovely and kind of creepy.