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Truth values of the following sentences
aka more on the present King of France

Truth values of the following sentences

nb
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Posted 05/07/06 - 03:56 PM: Subject: Truth values of the following sentences	#1
Hi, this is my first post here. I'm a junior in college in the U.S. (majoring in Philosophy) and just finished my final paper for my Philosophy of Language class, which had to do with the meaning of (relatively :P) simple sentences containing empty definite descriptions. Here are the truth values I came up with for a bunch of sentences and brief reasons. Here are the sentences I analyzed, in the paper or on my own: (1) "The present King of France lives under your bed" = clearly false This sentence asserts a physical relation between a "non-entity" and a physical thing, which could not possibly hold. Russell would say this is false and Frege would say this is neither true nor false. (2) "The present King of France is numerically distinct from the present Queen of England" = clearly true My hypothesis is that this relation can only hold between a non-entity and an existing thing because it is synonymous with another sentence that denies a relation that could not possibly hold. Namely, it is synonymous with the negation "The present King of France is numerically identical to the present Queen of England," which is is "It is not the case that the present King of France is numerically identical to the present Queen of England." This sentence is true because numerical identity is not something that could hold at a particular time between a non-entity and a physical thing. By Leibniz's law, "two" things that are numerically identical must have all the same properties at a particular time, and this is clearly not the case. The present Queen of England has the property of being a queen, living in England, and having mass, while the present King of France clearly does not. (3a) "The present King of France is moving" = clearly false (3b) "The present King of France is not moving" = clearly true The present King of France is not the sort of thing that could move. Only physical things that exist in space and time can move, because motion means the change in position in space in a particular time. Therefore the negation, interpreted as "It is not the case that the present King of France is moving" is true. (3c) "The present King of France is stationary" = clearly false (3b) and (3c) are not synonymous on my interpretation, because to be stationary implies that something has a physical position that is not changing. Therefore, it is a physical property and cannot be possessed by the present King of France. "The present King of France is not moving," on the other hand, merely denies a property without implying another property. (4) "The present King of France is nonexistent" = clearly true This is true because it is synonymous with "It is not the case that present King of France exists" which denies a property of the present King of France without also asserting one. (5) "The present King of France has hair" = clearly false This is false because the present King of France is not physical and having hair by definition is a physical property (or a physical relation between a non-entity and a physical thing). There is no hair in the universe such that it is possessed by the present King of France. Therefore, the present King of France does not have hair. (6) "The present King of France is hairless" = clearly true I interpret this as being synonymous with "It is not the case that the present King of France has hair." Hairlessness simply means "lacking hair" which to me does not imply any physical properties. Thus I would say that the sentence "The number 7 is hairless" is true because it is not the case that the number 7 has hair. Sure, it seems like an odd thing to say, but that's because we don't normally have any reason to talk about the lack of hair of non-physical things. (7) "The present King of France is bald" = clearly false I think this is clearly false because it asserts a physical property. For something to be bald it does not simply have to (partially or completely) lack hair, but it also has to have a head, because the primary definition refers to a head. Being bald, like being stationary is therefore a physical property in itself, unlike hairlessness on my view. Since the present King of France does not have a head, he is not bald. (8) "The present King of France has hair on his head" = neither true nor false While "The present King of France has hair" is false in isolation and so is "The present King of France's head has hair," this sentence is neither true nor false. If it was true, it would imply that the present King of France's head has hair on it which is clearly false. However, I don't think it can be said to be false either, because the intuitive basis for believing it might be false is based on the fact that the present King of France does not have a head. The present King of France's head has no hair, but that's not because it is bald (it isn't) but because there is no such head. However, this sentence presupposes that such a head exists, which means that we can no longer assume that "The present King of France's head has hair" is false in the context of sentence (8). The negation of (8), "It is not the case that the present King of France has hair on his head" is also neither true nor false. Therefore, it is not synonymous with (7) ("The present King of France is bald") because that sentence is false. The distinction is that while (7) requires that the present King of France have a head in order to be true, it does not presuppose that he has a head, which (8) and its negation do. Other sentences: "The present King of France is a king" = false (a non-entity cannot have the property of being a king) "The present King of France is not a king" = true "The present King of France reigns over France" = false (this is also a property that a non-entity cannot have) "The present King of France does not reign over France" = true "The present King of France is male" = false "The present King of France is not male" = true "The present King of France is female" = false "The present King of France is the present King of France" = neither true nor false (because it falsely presupposes that there is a present King of France for the non-entity to be identical to) "The present King of France is not the present King of France" = neither true nor false "The present King of France has people in his Kingdom" = neither true nor false (because it falsely presupposes that he has a Kingdom) "The present King of France has a wart" = false "The present King of France has no wart" = true "The present King of France has a wart on his body" = neither true nor false "The present King of France has no wart on his body" = neither true nor false "The present King of France has a wart on his mind" = neither true nor false "The present King of France has no wart on his mind" = neither true nor false "The largest prime number is greater than 1" = false This is the one that has been giving me trouble because it does not seem false to me. It almost even seems true, because EVERY prime number is greater than 1 (at least every one that exists! ). I guess it cannot technically be true though, because there is no largest prime number. However, I thought of reinterpreting this as "The largest prime number has a value greater than 1," which is neither true nor false because it falsely presupposes that the largest prime number has a value. OK, that's all. Feel free to share your thoughts or other examples that you think either support or refute my theory. Nick Edited by nb on 05/07/06 - 04:02 PM

Lodestone
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Posted 05/08/06 - 12:42 AM:	#2
I don't think you've fully appreciated Russell's solution, which deals with exactly what you're hypothesising: that if you can find a reason beyond non-existence that a sentence containing a non-existent entity is false, then that sentence's negation must be true. But this, according to Russell, is a mistake. You claim that "The present King of France is not moving" is clearly true, as its negation would entail stating that something which cannot move (the present King of France) is moving. However, Russell claims that both sentences are false, as they both entail claiming that there is one and only one present King of France. They are in fact: (3a) "There is a present King of France, and only one present King of France, and he is moving" (3b) "There is a present King of France, and only one present King of France, and he is not moving" Or, in predicate logic: (3a) ∃x∀y (Kx & (Ky->y=x) & Mx) (3b) ∃x∀y (Kx & (Ky->y=x) & ~Mx) Since both sentences include a false claim (There is a present King of France / ∃xKx), they are both false. Personally, I don't agree with this interpretation, but if you are to present an alternative then you at least need to show why it is false.
Where once my wit, perchance, hath shone, In aid of others let me shine; And when, alas! our brains are gone, What nobler substitute than wine?

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Posted 05/08/06 - 05:07 AM:	#3
It would seem that nb's account of meaningfulness is based upon a rather confusing idea of "physical existence". I think Lodestone is correct here. Russell's account of definite descriptions of non-existent entities posit as false any proposition where a predicate is attributed to a non-existent entity. So "The present King of France has a wart" would be paraphrased into "There is an x, such that it is tpkof & it has a wart", which is false "The present King of France has no wart" would be paraphrased into "There is an x, such that it is tpkof and it does not has wart", which is also false Any statement which contains "There is an x, such that x is tpkof..." will be false on virtue of a false supposition. nb wrote: "The largest prime number is greater than 1" = false This is the one that has been giving me trouble because it does not seem false to me. It almost even seems true, because EVERY prime number is greater than 1 One thing is to say "every prime number is greater than 1", and another different thing is to say that "the largest prime number is greater than one". This second sentence implies that "there is a number, which is prime and is greater than all other prime numbers". Since there is no such thing, the sentence is false.
""Physics investigates the essential nature of the world, and biology describes a local bump. Psychology, human psychology, describes a bump on the bump." W.V.O. Quine

Owen
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Posted 05/08/06 - 05:44 AM:	#4
nb wrote: Hi, this is my first post here. I'm a junior in college in the U.S. (majoring in Philosophy) and just finished my final paper for my Philosophy of Language class, which had to do with the meaning of (relatively :P) simple sentences containing empty definite descriptions. Here are the truth values I came up with for a bunch of sentences and brief reasons. Here are the sentences I analyzed, in the paper or on my own: (1) "The present King of France lives under your bed" = clearly false This sentence asserts a physical relation between a "non-entity" and a physical thing, which could not possibly hold. Russell would say this is false and Frege would say this is neither true nor false. (2) "The present King of France is numerically distinct from the present Queen of England" = clearly true My hypothesis is that this relation can only hold between a non-entity and an existing thing because it is synonymous with another sentence that denies a relation that could not possibly hold. Namely, it is synonymous with the negation "The present King of France is numerically identical to the present Queen of England," which is is "It is not the case that the present King of France is numerically identical to the present Queen of England." This sentence is true because numerical identity is not something that could hold at a particular time between a non-entity and a physical thing. By Leibniz's law, "two" things that are numerically identical must have all the same properties at a particular time, and this is clearly not the case. The present Queen of England has the property of being a queen, living in England, and having mass, while the present King of France clearly does not. (3a) "The present King of France is moving" = clearly false (3b) "The present King of France is not moving" = clearly true The present King of France is not the sort of thing that could move. Only physical things that exist in space and time can move, because motion means the change in position in space in a particular time. Therefore the negation, interpreted as "It is not the case that the present King of France is moving" is true. (3c) "The present King of France is stationary" = clearly false (3b) and (3c) are not synonymous on my interpretation, because to be stationary implies that something has a physical position that is not changing. Therefore, it is a physical property and cannot be possessed by the present King of France. "The present King of France is not moving," on the other hand, merely denies a property without implying another property. (4) "The present King of France is nonexistent" = clearly true This is true because it is synonymous with "It is not the case that present King of France exists" which denies a property of the present King of France without also asserting one. (5) "The present King of France has hair" = clearly false This is false because the present King of France is not physical and having hair by definition is a physical property (or a physical relation between a non-entity and a physical thing). There is no hair in the universe such that it is possessed by the present King of France. Therefore, the present King of France does not have hair. (6) "The present King of France is hairless" = clearly true I interpret this as being synonymous with "It is not the case that the present King of France has hair." Hairlessness simply means "lacking hair" which to me does not imply any physical properties. Thus I would say that the sentence "The number 7 is hairless" is true because it is not the case that the number 7 has hair. Sure, it seems like an odd thing to say, but that's because we don't normally have any reason to talk about the lack of hair of non-physical things. (7) "The present King of France is bald" = clearly false I think this is clearly false because it asserts a physical property. For something to be bald it does not simply have to (partially or completely) lack hair, but it also has to have a head, because the primary definition refers to a head. Being bald, like being stationary is therefore a physical property in itself, unlike hairlessness on my view. Since the present King of France does not have a head, he is not bald. Non-referring descriptions have no properties at all. We cannot say what it is, we can only say what it is not. F(the present king of France) is false for all properties F. ie. ~(F(the present king of France)) is true for all properties F. Even (~F)(the present king of France) is false! (8) "The present King of France has hair on his head" = neither true nor false While "The present King of France has hair" is false in isolation and so is "The present King of France's head has hair," this sentence is neither true nor false. If it was true, it would imply that the present King of France's head has hair on it which is clearly false. However, I don't think it can be said to be false either, because the intuitive basis for believing it might be false is based on the fact that the present King of France does not have a head. The present King of France's head has no hair, but that's not because it is bald (it isn't) but because there is no such head. However, this sentence presupposes that such a head exists, which means that we can no longer assume that "The present King of France's head has hair" is false in the context of sentence (8). I don't agree. If there is no king of France then there is no head of the present king of France either. All primary statements about 'the present king of France's head' are false. The present King of France has hair on his head, is false. It is not the case that the present King of France has hair on his head, is true. The negation of (8), "It is not the case that the present King of France has hair on his head" is also neither true nor false. Therefore, it is not synonymous with (7) ("The present King of France is bald") because that sentence is false. The distinction is that while (7) requires that the present King of France have a head in order to be true, it does not presuppose that he has a head, which (8) and its negation do. ?? Other sentences: "The present King of France is a king" = false (a non-entity cannot have the property of being a king) "The present King of France is not a king" = true "The present King of France reigns over France" = false (this is also a property that a non-entity cannot have) "The present King of France does not reign over France" = true "The present King of France is male" = false "The present King of France is not male" = true "The present King of France is female" = false OK. "The present King of France is the present King of France" = neither true nor false (because it falsely presupposes that there is a present King of France for the non-entity to be identical to) "The present King of France is not the present King of France" = neither true nor false Wrong. The present King of France is the present King of France, is false. There is no-thing that the present king of France is. ~(The present King of France is the present King of France) is true. "The present King of France has people in his Kingdom" = neither true nor false (because it falsely presupposes that he has a Kingdom) "The present King of France has a wart" = false "The present King of France has no wart" = true "The present King of France has a wart on his body" = neither true nor false "The present King of France has no wart on his body" = neither true nor false "The present King of France has a wart on his mind" = neither true nor false "The present King of France has no wart on his mind" = neither true nor false The present King of France has people in his Kingdom, is false. The present King of France has a wart, is false. The present King of France has no wart, is true ..if it is interpreted as ~(The present King of France has a wart). The present King of France has a wart on his body, is false. The present King of France has no wart on his body, is true. The present King of France has a wart on his mind, is false. The present King of France has no wart on his mind, is true. "The largest prime number is greater than 1" = false Agreed This is the one that has been giving me trouble because it does not seem false to me. It almost even seems true, because EVERY prime number is greater than 1 (at least every one that exists! ). I guess it cannot technically be true though, because there is no largest prime number. However, I thought of reinterpreting this as "The largest prime number has a value greater than 1," which is neither true nor false because it falsely presupposes that the largest prime number has a value. If there is no largest prime number then there is no property that 'the largest prime number' has. There cannot be exactly one largest prime number if there are none.

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1 of 1 people found this post helpful Posted 05/08/06 - 07:12 AM:	#5
Lodestone wrote: I don't think you've fully appreciated Russell's solution, which deals with exactly what you're hypothesising: that if you can find a reason beyond non-existence that a sentence containing a non-existent entity is false, then that sentence's negation must be true. But this, according to Russell, is a mistake. Where does Russell claim this? Clearly according to Russell ~EyAx(x=y <-> Fx) -> ~(G(ix:Fx)) is true, for all G. You claim that "The present King of France is not moving" is clearly true, as its negation would entail stating that something which cannot move (the present King of France) is moving. However, Russell claims that both sentences are false, as they both entail claiming that there is one and only one present King of France. They are in fact: (3a) "There is a present King of France, and only one present King of France, and he is moving" (3b) "There is a present King of France, and only one present King of France, and he is not moving" Or, in predicate logic: (3a) ∃x∀y (Kx & (Ky->y=x) & Mx) (3b) ∃x∀y (Kx & (Ky->y=x) & ~Mx) Since both sentences include a false claim (There is a present King of France / ∃xKx), they are both false. Wrong. nb interprets "The present King of France is not moving" as: It is not the case that The present King of France is moving. You seem to interpret "The present King of France is not moving" as: "The present King of France is non-moving". Clearly ~Ey(Ax(x=y <-> Kx) & Mx) is not equivalent to Ey(Ax(x=y <-> Kx) & ~My). Note, it is tautologous to say: The present King of France is moving, or, ~(The present King of France is moving). But, it is not tautologous to say: The present King of France is moving, or, The present King of France is non-moving.

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Posted 05/09/06 - 12:34 AM:	#6
Owen wrote: Where does Russell claim this? Clearly according to Russell ~EyAx(x=y <-> Fx) -> ~(G(ix:Fx)) is true, for all G. You're right, I got a little bit confused. I meant what you outlined as well: that Russell argues that all (~F)(The present king of France) statements are false, rather than accidentally saying that Russell argues that all ~(F(The present King of France) statements are false. Anyway. nb interprets "The present King of France is not moving" as: It is not the case that The present King of France is moving. Absolutely not. He says: The present King of France is not the sort of thing that could move. Only physical things that exist in space and time can move, because motion means the change in position in space in a particular time. Therefore the negation, interpreted as "It is not the case that the present King of France is moving" is true. clearly conflating the two and failing to see the distinction. He argues for the statement "It is not the case that the present King of France is moving" being false by saying that "The present King of France is not the sort of thing that could move" which would be a (bad) argument for the statement "The present KIng of France is non-moving" being false.
Where once my wit, perchance, hath shone, In aid of others let me shine; And when, alas! our brains are gone, What nobler substitute than wine?

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