Russell, Existence and Description, pt. 2
“What is the ‘simple logical mistake’ that metaphysics makes in its traditional treatment of sentences like ‘Homer existed’?”
Traditional metaphysics assumes that, in the claim, “Homer existed”, Homer is a constituent. However, nothing could be further from the truth. If Homer was a constituent of that claim, then it could not be falsified, for, since Homer is a constituent of a phrase, he exists. This can be seen more clearly when we look at the negation of the claim, “Homer did not exist.” The logical form is the same, but (assuming Homer is a constituent), we have a meaningless statement. The claim is that a constituent of the sentence does not exist. But if Homer does not exist, then what in the world is the constituent constituted of?
In reality, the claim “Homer existed” should be translated as “There existed exactly one x who had certain properties, such as being the author of The Iliad and The Odyssey, and being a Greek.” The word “Homer” is not being used as a name, but as a reference for a definite description.
“*What would Russell say about identity statements with two names?”
Russell would (most likely) say that an identity statement with two names is either false, or a tautology. Take “c is f”: if c and f are names for the same object, then we have a tautology. If c and f name different objects, then the claim is false. Nothing metaphysically interesting or meaningful can ever come from an identity statement between two names. That does not preclude “c is f” ever being important epistemologically, or in a proof as a step. (For example, we can imagine it being interesting to find out that Josh Frear is Freezer, or that a step in a proof might involve a=b).
“Is Russell’s claim that “ ‘x is F’ is sometimes true” a temporal claim?”
Russell’s claim is clearly non-temporal. On page 33a, he laments the vulgarity of tense in English verbs. The fact that possibility and necessity are expressed in temporal-sounding language is also a deplorable vulgarity. “ ‘x is F’ is sometimes true” means that for some x, x is F, and for others, it is not. We can attempt to remove temporality by changing the claim to “ ‘x is F’ is true for some, but not all x”. If you are really hung up on the ubiquitous use of temporal language for claims of possibility, I recommend thinking of it this way: imagine a computer running through all the objects in the domain of x, and seeing if they make “x is F” true. In this scenario, temporality is added to the “sometimes”. Of course, this may just confuse the issue even more.
“What is the ‘double denial’ of ‘The present King of France is bald’? Why is there no double denial of ‘Scott is human’ (supposing ‘Scott’ is used as a name)?”
The double denial of the claim ‘The present King of France is bald’ is that there are two conditions that falsify the claim: first, the present King of France may indeed have a full head of curly locks, or second, there may not be a present King of France. It is easy to overlook the second possibility because form of the claim is suspiciously similar to “Scott is human”, to which there cannot be made the rebuttal “Scott doesn’t exist” (assuming Scott is a name). “The present King of France is bald” can be expressed more accurately as “There exists a c such that ‘x is the present King of France’ and ‘x is bald’ are both true when x is c and at least one is false when x is not c.” Now it is easier to see that there are two claims being made, and that either one can be falsified. c could either not be the present King of France or not be bald.
There is no double denial of “Scott is human” because Scott is a name and cannot be denied like a definite description (the present King of France) can. In this claim, “Scott” is being used to refer to an object, and then we are trying to figure out if that object has the property of being human. It is absurd and meaningless to retort “That object doesn’t have that property because it doesn’t actually exist!” Perhaps this can be seen more clearly when the claim is expressed longhand, as in the previous case. “Scott is human” is more accurately, “ ‘x is human’ is true when x is c”, where c is Scott. There is no double denial possible here.
Could we try to write “Scott is human” in the way we did for the previous claim? Let’s try. “There exists a c such that ‘x is d’ and ‘x is human’ are both true when x is c.” We have two claims; the second one is not problematic. It is possible thatc is not human. However, could c not be d? c ≠ d is possible to write and understand, but what does it mean? It means that the object we are examining, c, or Scott, is not the same object as Scott, d, or the object we were claiming to be human. This is complete nonsense. We can now clearly see that there can be no double denial of “Scott is human”.
I hope I didn't muddy the water too much with my first post!
Traditional metaphysics assumes that, in the claim, “Homer existed”, Homer is a constituent. However, nothing could be further from the truth. If Homer was a constituent of that claim, then it could not be falsified, for, since Homer is a constituent of a phrase, he exists. This can be seen more clearly when we look at the negation of the claim, “Homer did not exist.” The logical form is the same, but (assuming Homer is a constituent), we have a meaningless statement. The claim is that a constituent of the sentence does not exist. But if Homer does not exist, then what in the world is the constituent constituted of?
In reality, the claim “Homer existed” should be translated as “There existed exactly one x who had certain properties, such as being the author of The Iliad and The Odyssey, and being a Greek.” The word “Homer” is not being used as a name, but as a reference for a definite description.
“*What would Russell say about identity statements with two names?”
Russell would (most likely) say that an identity statement with two names is either false, or a tautology. Take “c is f”: if c and f are names for the same object, then we have a tautology. If c and f name different objects, then the claim is false. Nothing metaphysically interesting or meaningful can ever come from an identity statement between two names. That does not preclude “c is f” ever being important epistemologically, or in a proof as a step. (For example, we can imagine it being interesting to find out that Josh Frear is Freezer, or that a step in a proof might involve a=b).
“Is Russell’s claim that “ ‘x is F’ is sometimes true” a temporal claim?”
Russell’s claim is clearly non-temporal. On page 33a, he laments the vulgarity of tense in English verbs. The fact that possibility and necessity are expressed in temporal-sounding language is also a deplorable vulgarity. “ ‘x is F’ is sometimes true” means that for some x, x is F, and for others, it is not. We can attempt to remove temporality by changing the claim to “ ‘x is F’ is true for some, but not all x”. If you are really hung up on the ubiquitous use of temporal language for claims of possibility, I recommend thinking of it this way: imagine a computer running through all the objects in the domain of x, and seeing if they make “x is F” true. In this scenario, temporality is added to the “sometimes”. Of course, this may just confuse the issue even more.
“What is the ‘double denial’ of ‘The present King of France is bald’? Why is there no double denial of ‘Scott is human’ (supposing ‘Scott’ is used as a name)?”
The double denial of the claim ‘The present King of France is bald’ is that there are two conditions that falsify the claim: first, the present King of France may indeed have a full head of curly locks, or second, there may not be a present King of France. It is easy to overlook the second possibility because form of the claim is suspiciously similar to “Scott is human”, to which there cannot be made the rebuttal “Scott doesn’t exist” (assuming Scott is a name). “The present King of France is bald” can be expressed more accurately as “There exists a c such that ‘x is the present King of France’ and ‘x is bald’ are both true when x is c and at least one is false when x is not c.” Now it is easier to see that there are two claims being made, and that either one can be falsified. c could either not be the present King of France or not be bald.
There is no double denial of “Scott is human” because Scott is a name and cannot be denied like a definite description (the present King of France) can. In this claim, “Scott” is being used to refer to an object, and then we are trying to figure out if that object has the property of being human. It is absurd and meaningless to retort “That object doesn’t have that property because it doesn’t actually exist!” Perhaps this can be seen more clearly when the claim is expressed longhand, as in the previous case. “Scott is human” is more accurately, “ ‘x is human’ is true when x is c”, where c is Scott. There is no double denial possible here.
Could we try to write “Scott is human” in the way we did for the previous claim? Let’s try. “There exists a c such that ‘x is d’ and ‘x is human’ are both true when x is c.” We have two claims; the second one is not problematic. It is possible thatc is not human. However, could c not be d? c ≠ d is possible to write and understand, but what does it mean? It means that the object we are examining, c, or Scott, is not the same object as Scott, d, or the object we were claiming to be human. This is complete nonsense. We can now clearly see that there can be no double denial of “Scott is human”.
I hope I didn't muddy the water too much with my first post!
posted by Joshua Frear at 9:15 AM
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