Electronic communities build nothing. You wind up with nothing. We are dancing animals. How beautiful it is to get up and go out and do something. We are here on Earth to fart around. Don't let anybody tell you any different.
- Kurt Vonnegut, A Man Without a Country, 62
Wednesday, April 30, 2008
Monday, April 21, 2008
Confucius, Music, Character
Therefore, the superior man tries to create harmony in the human heart, by a rediscovery of human nature, and tries to promote music as a means to the perfection of human culture. When such music prevails, and the people’s minds are led towards the right ideals and aspirations, we may see the appearance of a great nation. Character is the backbone of our human nature, and music is the flowering of character.
- Confucius (? - Can't find the source)
- Confucius (? - Can't find the source)
Saturday, April 19, 2008
Is Existence a First-Order Property?
I think I’ve found a not-so-bad argument for construing existence as a first-order property. Here goes:
Begin with the principle that first-order properties are those things in virtue of which a sentence of the form “x is not identical to y” is true, for some substitution of individual-symbols for “x” and “y”. So existence is a first-order property if some such statement is true solely in virtue of the truth of a corresponding sentence of the form “x exists” or “x does not exist” – or, if you like, corresponding sentences of the form “there is a z, such that x = z” and “there is no z, such that x = z.” Let c1 =def the bottom tennis ball in a certain canister that can contain as many as three tennis balls; let c2 =def the middle tennis ball in that same canister; let c3 =def the ball immediately above c1 in the canister. Now suppose that there are actually only two balls in the canister. Then c3 is above c1, but c2 is not, since c2 does not exist. It seems that ~(c2 = c3).
I would suggest that this is the case just because c2 does not exist. Supporting this contention is the apparent fact that if c2 did exist (i.e. if there were some ball, such that that ball is the middle ball in the canister; if there were some ball, such that that ball is c2), then it would be the case that c2 = c3. But if ~(c2 = c3) just because c2 does not exist, then by our initial principle about first-order properties, existence is a first-order property.
Does this work? Am I missing something? I don’t really understand the necessity of identity. Is some abuse of that principle at work here? Or is my beginning principle about first-order properties false? Or is it actually not the case that ~(c2 = c3) – say, because “~(c2 = c3)” lacks a truth-value?
___________
Update:
In a comment at the Maverick's, Ockham, writes: "You cannot say 'c2 =def the middle tennis ball in that same canister' and then say 'but c2 does not exist'" Here's my response, which is too long and too irrelevant to the discussion of the Maverick's post to leave on his blog.
I suppose that, in classic FOL, you can't introduce a term through a definite description that doesn't refer. FOL aside, though, do you mean to say that this is incoherent in natural English? "The middle ball in that same canister doesn't exist" does sound strange to me. Admittedly, it sounds more natural to say "There is no middle ball in the canister," which we might formalize "~(Ex)(Middle ball in the canister(x))." It doesn’t sound unnatural to introduce a proper name through that definite description, however. Nor does it sound unnatural to me to say “c2 doesn’t exist” (even though “the middle ball in the canister” is the definition of “c2”), just the same way it doesn’t sound unnatural to say that “Pegasus doesn’t exist.” The big difference between “c2” and “Pegasus” seems to be that “c2” was obviously introduced by a definite description, whereas “Pegasus” was not obviously so introduced. I’m not sure that this difference is enough to make “c2 doesn’t exist” incoherent and “Pegasus doesn’t exist” coherent. Still, we might imagine situations in which a term like "c2" is introduced – say, by a group of people who believe, incorrectly, that there are three balls in the canister – otherwise than by the definite description “the middle ball in the canister.” (Briefly: maybe the group could use a function from canisters to the middle ball in the canister. Maybe they could just start using “c2” to (try to) refer to what they believe to be the middle ball by stating facts that would be true of such a ball, were it to exist.) In any event, I’m not sure that “c2 doesn’t exist” is incoherent, and if it is, we can use other stories about how something like “c2” comes to have a certain meaning, and then tell a story similar to the one I tell about ~(c2 = c3).
Begin with the principle that first-order properties are those things in virtue of which a sentence of the form “x is not identical to y” is true, for some substitution of individual-symbols for “x” and “y”. So existence is a first-order property if some such statement is true solely in virtue of the truth of a corresponding sentence of the form “x exists” or “x does not exist” – or, if you like, corresponding sentences of the form “there is a z, such that x = z” and “there is no z, such that x = z.” Let c1 =def the bottom tennis ball in a certain canister that can contain as many as three tennis balls; let c2 =def the middle tennis ball in that same canister; let c3 =def the ball immediately above c1 in the canister. Now suppose that there are actually only two balls in the canister. Then c3 is above c1, but c2 is not, since c2 does not exist. It seems that ~(c2 = c3).
I would suggest that this is the case just because c2 does not exist. Supporting this contention is the apparent fact that if c2 did exist (i.e. if there were some ball, such that that ball is the middle ball in the canister; if there were some ball, such that that ball is c2), then it would be the case that c2 = c3. But if ~(c2 = c3) just because c2 does not exist, then by our initial principle about first-order properties, existence is a first-order property.
Does this work? Am I missing something? I don’t really understand the necessity of identity. Is some abuse of that principle at work here? Or is my beginning principle about first-order properties false? Or is it actually not the case that ~(c2 = c3) – say, because “~(c2 = c3)” lacks a truth-value?
___________
Update:
In a comment at the Maverick's, Ockham, writes: "You cannot say 'c2 =def the middle tennis ball in that same canister' and then say 'but c2 does not exist'" Here's my response, which is too long and too irrelevant to the discussion of the Maverick's post to leave on his blog.
I suppose that, in classic FOL, you can't introduce a term through a definite description that doesn't refer. FOL aside, though, do you mean to say that this is incoherent in natural English? "The middle ball in that same canister doesn't exist" does sound strange to me. Admittedly, it sounds more natural to say "There is no middle ball in the canister," which we might formalize "~(Ex)(Middle ball in the canister(x))." It doesn’t sound unnatural to introduce a proper name through that definite description, however. Nor does it sound unnatural to me to say “c2 doesn’t exist” (even though “the middle ball in the canister” is the definition of “c2”), just the same way it doesn’t sound unnatural to say that “Pegasus doesn’t exist.” The big difference between “c2” and “Pegasus” seems to be that “c2” was obviously introduced by a definite description, whereas “Pegasus” was not obviously so introduced. I’m not sure that this difference is enough to make “c2 doesn’t exist” incoherent and “Pegasus doesn’t exist” coherent. Still, we might imagine situations in which a term like "c2" is introduced – say, by a group of people who believe, incorrectly, that there are three balls in the canister – otherwise than by the definite description “the middle ball in the canister.” (Briefly: maybe the group could use a function from canisters to the middle ball in the canister. Maybe they could just start using “c2” to (try to) refer to what they believe to be the middle ball by stating facts that would be true of such a ball, were it to exist.) In any event, I’m not sure that “c2 doesn’t exist” is incoherent, and if it is, we can use other stories about how something like “c2” comes to have a certain meaning, and then tell a story similar to the one I tell about ~(c2 = c3).
Wednesday, April 16, 2008
Davidson, Belief
I think there might be something like an inconsistency in Davidson’s theories of meaning and belief. Consider the following set of claims, all of which, I think, Davidson has to accept:
1. Intentional indeterminism: the apparatus of folk-psychology always underdetermines the total set of beliefs and desires that we attribute to an intentional system. The non-psychological facts and the commitments of psychology as such (i.e. the common commitments of any psychological theory in virtue of which the theory is psychological) underdetermine – inductively, deductively, and abductively – what beliefs and desires an intentional system has.
2. General agreement: in general, folk that are equally well-informed about an intentional system in non-psychological terms agree, in the individual cases, both on what beliefs and desires the system has, and how to determine further what beliefs and desires the system has.
3. We must explain (2) in terms of the commonly-held beliefs of the folk.
4. These beliefs are not among the basic commitments of psychology as such. (From (1) and (2).)
5. Facts about commonly-held beliefs that determine the evidential procedures governing the proper application of a word (like “believes) are among the facts that constitute, in part, the meaning of that word. (I take this to be one of the reasons that Davidson says that meaning and belief are so closely related. I also take it to be a consequence of most varieties of semantic holism.)
6. Facts about the meaning of “believes” are among the basic commitments of psychology as such.
But then, from (3), (5), and (6), it seems we can derive the conclusion that the facts that explain (2) are facts about the meaning of “believes,” and so among the basic commitments of psychology as such. This is immediately contrary to (4).
I think Davidson might get out of this by denying (3), but it still seems that the sort of meta-semantics underlying (5) is going to make it difficult to say that the commonality that explains (2) is not, in part, constitutive of the meaning of “believes.”
1. Intentional indeterminism: the apparatus of folk-psychology always underdetermines the total set of beliefs and desires that we attribute to an intentional system. The non-psychological facts and the commitments of psychology as such (i.e. the common commitments of any psychological theory in virtue of which the theory is psychological) underdetermine – inductively, deductively, and abductively – what beliefs and desires an intentional system has.
2. General agreement: in general, folk that are equally well-informed about an intentional system in non-psychological terms agree, in the individual cases, both on what beliefs and desires the system has, and how to determine further what beliefs and desires the system has.
3. We must explain (2) in terms of the commonly-held beliefs of the folk.
4. These beliefs are not among the basic commitments of psychology as such. (From (1) and (2).)
5. Facts about commonly-held beliefs that determine the evidential procedures governing the proper application of a word (like “believes) are among the facts that constitute, in part, the meaning of that word. (I take this to be one of the reasons that Davidson says that meaning and belief are so closely related. I also take it to be a consequence of most varieties of semantic holism.)
6. Facts about the meaning of “believes” are among the basic commitments of psychology as such.
But then, from (3), (5), and (6), it seems we can derive the conclusion that the facts that explain (2) are facts about the meaning of “believes,” and so among the basic commitments of psychology as such. This is immediately contrary to (4).
I think Davidson might get out of this by denying (3), but it still seems that the sort of meta-semantics underlying (5) is going to make it difficult to say that the commonality that explains (2) is not, in part, constitutive of the meaning of “believes.”
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