Anti-Quinean Hoaxers?

This NYT article quotes a letter in which Quine tells his friend’s kid about an arithmetic trick. http://freakonomics.blogs.nytimes.com/2007/09/05/a-little-math-puzzle-to-ponder/#more-1836

It is interesting to hear about the private life of the great man, but I think the comment section is even more interesting: rather than proving to themselves via normal elementary school math why the trick *must* work for all positive integers many posters seem to just try a bunch of cases. e.g. “The algorithm does not work for 29 x 31.” “In fact, it does not work for the number 29 at all. Why is that?” Then, sometimes they forget to take into account the first column (which causes trouble only when the first number you are trying to multiply is odd) so these cases seem to ‘falsify’ the claim, from which they conclude that the algorithm has “holes”. They even guess (apparently purely inductively) what the holes might be e.g. ‘all pairs of numbers starting with 29’. Other responders disagree by going through their observations of the particular instance in question. Then the same thing happens with another pair of numbers!

Is this just a case of decaffeinated blog posting or a bit of sly performance art which envisages what the state of mathematics would be like if we *did* form and revise mathematical beliefs in the same way as other more traditionally empirical parts of our web of belief?

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realist Pen Maddy, waffles

I just bought "Organic Vanilla Mini-Waffles 8 sets of 4 waffles". Hopefully the ur-elements are in the same box. Read more!

from L.W.'s notes on Culture and Value

"If it is true that Mahler’s music is worthless, as I believe to be the case, then the question is what he ought to have done with his talent. For obviously it took a set of very rare talents to produce this bad music. Should he, say, have written his symphonies and then burned them? Or should he have done violence to himself and not written them? Should he have written them and realized that they were worthless? But how could he have realized that?"

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incompatible complaints?

A traditional objection to empiricism is that you couldn’t learn math empirically because math doesn’t make empirically testable predictions. On the other hand a traditional objection to formalism is that it would be surprising if a mere formal game had the scientific applications which math does. So prima facie it seems like on the one hand we are saying that the problem with empiricism is that math *doesn’t* make empirically testable predictions while on the other hand the problem with formalism is that math *does* seem to make such predictions and these predictions turn out right. So it seems like these traditional objections can’t both work.

One natural/obvious thing to say here would be that the applications problem for formalism is not that math itself makes empirical predictions (as the empiricist would like) but that it can be combined with a lot of empirical stuff to make predictions. But if the “applicability of math” just consists in the fact that mathematical statements can be usefully combined with a lot of empirically discovered stuff to make correct predictions this doesn’t seem like much of a problem for the formalist. Given two complex systems like the game of producing mathematical proofs on the one hand and the physical world on the other hand it would be more surprising if we *didn’t* find some parallels between the two. Newton et al just noticed the bits of math that seem to match certain transactions in the physical world. For all we know you *could* do just the same with any sufficiently complex formal game.

Specifically, the feature of math which (immediately seem to) pose a problem for the formalist are the *direct* applications – the claim that when there are 2Fs and 2Gs there are 4 F-or-Gs and predictions about what a computer will do so long as its electricity behaves in a certain way, or whether you will literally be able to tile a certain floor with certain physical features and certain tiles or whether a someone doing a certain kind of formal manipulations will get a certain string. It’s not surprising that some connection can be found between a complex formal game and what goes on in the external world, but here the ‘arbitrary formal manipulations’ of mathematical practice seem to call the shots and directly make predictions –and then these predictions turn out to be correct. If one allows that the formalism of math has direct predictive applications then it does indeed seem miraculous that the particular mathematical game which we ended up with makes the right predictions.

But if math does have these *direct* predictive applications (if this program halts you should expect to find a mouse in the wiring, no one will ever manage to cover a flat floor with tiles in those shapes) which turn out to be correct when tested then how can we make the other traditional objection that ‘you can’t learn math empirically because math doesn’t make empirical predictions’?

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umm...free will

this really speaks for itself, i think
http://www.msnbc.msn.com/id/18684016/ Read more!

Win Sharon’s Money #4

Quine, Backsliding

It’s been a while since I have come to a philosophical question such that knowing the answer to it was worth $5 to me but here we have the latest Win Sharon’s Money with a prize of $5 to the first answer that convinces me (I will send out an email saying so) or what I think is the best one if none of them convince me. This one is about defending a very famous position of Quine's, so it should be on the easy side…

If you are feeling public feel free to post your answers as comments here on the blog, otherwise email me:

So, as happens with alarming frequency whenever I think about stuff in the neighborhood, my grasp of Classic Quine has gotten unstuck. What did it this time was reading a bit of Davidson, in case that helps you see where this is question is coming from (not to imply that Davidson would agree with this point, as I understand it he wouldn’t, which is what got me thinking)…

The question:

Why can’t you take into account facts about whether a person says S in situations where it would be appropriate/normal to say that P as well as those about whether they assent to S in situations where P in deciding whether or not to attribute someone the belief that P? (If you did it, seems like this would cut down on a lot, though probably not all, indeterminacy)

Specifically, what if our ideas about when it is appropriate/normal to say P are sometimes not just some kind of empirical/sociological knowledge about what 21^st century western humans like to say but are part of our very conception of what it is to mean that P.

Consider the example –from W I think, though I don’t remember where - of a person who is trained to say the words ‘I think that…’ before every assertion. A person who was taught language in this way wouldn’t be a person who refused to make claims about anything which extended beyond their own epistemic state (wouldn’t you agree?). Rather, using the words ‘I think that’ in this uniform way would deprive them of their usual meaning. So this person’s sentence ‘I think it is raining’ would be much closer in meaning to my sentence ‘It is raining’ than to my homophonic sentence ‘I think it is raining’.

I think this example shows us (among other things) that the evidence relevant to whether a given person’s sentence S means ‘I think that it is raining’ goes beyond their *assenting* to S in the right circumstances. For, the conditions under which one should *assent* to ‘I think it is raining’ and ‘It is raining’ are the same. However the conditions under which one should *assert* ‘It is raining’ and ‘I think it is raining’ are quite different (we use the latter to signal respect and the existence of disagreement or hint that there is a certain kind of relevant justification which one doesn’t have). Now I claim that there is a difference between meaning ‘It is raining’ by your sentence and meaning ‘I think it is raining’ and we are rationally required to attribute the former state and not the latter one to the person described in the paragraph above.

If one allows that these notions of appropriate assertion (as opposed to merely assent) as being part of what is necessary for a person to mean P by their sentence S then it seems like a lot of traditional indeterminacy disappears. So, for example, there are definite (though relatively limited) conditions under which it is appropriate to assert ‘here is an undetached rabbit part’ or ‘the spatial complement of a rabbit is presently avoiding this spot’ which differ from those under which it is appropriate to assert ‘here is a rabbit’. Thus one might think that more detailed consideration of the way that a person’s linguistic behavior constrains their meaning (it’s not just a matter of assenting to what’s true but of asserting what’s appropriate) removes a lot of apparent indeterminacy of reference.

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Fun with Quotes

Back when I was TFing for QR22 I used to pass the time by making up puzzles. At some point, I came up with some quote puzzles (of the standard use/mention type) which I proposed to Peter as extra credit problems. He thought we had best not use them, which in retrospect was a wise decision. Anyway, no reason they should go to waste, so here they are!

To answer these puzzles, all you have to do is put a certain number of quotes into the given sentence to transform it into a truth. To give you a feel for the locutions I use, the following sentence has two quotes in it, the first of which is an opening quote, and the second of which is a closing quote.

“Boston” names Boston

Puzzle (1) below is my attempt to create a slightly more challenging limerick puzzle than the well known one given in most logic classes which features the sentence about Boston above. One of (2) - (4) throws self-reference into the mix. One of the nice things about puzzle (4) is that (so far as I know) it has a unique solution. (6) is inspired by part of Dave Gray's recent Eminees presentation. I might post hints in the comments. Enjoy!

(1) A few quotes placed right help construe
the sense of this jumbled word stew:
James names names names James
names names names James names
names names James names names, which is true.

(2) This sentence has the quoted expression this in it, but there is no instance of it unquoted.

(3) This sentence has exactly two instances of in it.

(4) The number of quotes in the sentence on this page beginning with the words the number of quotes on this page is three, and moreover, they are all opening quotes occurring before the first letter t in it.

(5) This sentence uses but has no mention of the word akimbo.

(6) Names name names name name.

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