Coelispex
11-05-2007, 06:09 PM
Let me begin by saying that I am not a mathematician, and therefore may make minor errors in my explication of certain 'problems', but I feel that there is something in the philosophy of numbers (mathematics) that applies to dualism.
I will begin by explicating Benacerraf's dilemma. Paul Benacerraf believed that for mathematics to have truth we must have two things:
A. A plausible semantics for mathematics.
B. A plausible epistemology for mathematical knowledge.
For A to occur, the most plausible way is to use numbers as abstract entities.
For B to occur, the most plausible way is for numbers not to be abstract entities.
Therefore, Benacerraf was left with a dilemma. (He was trying to reject a Platonist view)
In layman's terms:
To have a plausible semantics for mathematics, we need numbers that never change. For an example out of the Platonist view, imagine the number 3. Now imagine there is one perfect 3 floating around in some dimension that we cannot see, and every instance of 3 on earth or in the universe is just an instance of the 3 in the other dimension, and can only be like the number 3 in the other dimension, because it is the ideal 3 and therefore all instances of 3 aren't themselves THE 3, but just A 3.
To have epistemic knowledge of numbers, we have to be able to prove they exist, or Know that we Know them. So therefore THE number 3 can't be off somewhere that we can't see, or we couldn't KNOW for sure that we know what it is. It follows that we must have instances of 3 that we rely on for knowing that 3 exists, like seeing 3 cows or 3 boats.
This may not seem like a problem for some people. Why can't we just choose one or the other?
Well, here is my explanation. If THE 3 is in another dimension somewhere, how does it touch all the other threes in "reality" as we know it? But, it does allow for congruity between all the threes in the world. Why do we need congruity between all the threes in the world? Well, because there are no threes that are exactly the same, right? Take for instance the 3 cows and 3 boats. Other than the abstract number, what is the same? Boats aren't cows, nor vice versa. They don't weigh the same, they don't look the same, aren't made of the same materials. Even if you have 3 cows and 3 other cows, the 3 is never going to be exactly the same, or they would not be separate entities. There would always be a difference, even if the second 3 cows were cloned from the first 3. Even if all six were cloned from one and then raised in the same environment, weighed exactly the same, and then split into two groups of 3. The difference, you ask? Location. Three cows would be here, and the other three there (or at point a and point b, to be more neutral).
So you can't point to one instance of 3 in reality as we know it that can stand in for all the other threes, but you can't know that a perfect 3 exists in another dimension, either. So how do you know mathematical truth if you need both to reconcile in order to attain it? Well, you don't.
This leads me to the mind(soul)/body problem, which is more complicated because of the human element. When people argue about numbers, personal beliefs don't tend to get involved, and the search for unbiased truth seems more direct and less of an attempt to justify existing beliefs.
This is my translation of Benacerraf's dilemma into dualism:
A. To have intelligent bodies, we must have an abstract form of intelligence, or what I consider words/thoughts to be. This must exist beyond our realm of understanding, or people would never be self-aware or able to make complicated abstract thoughts. This means for many that we must have a mind (soul) that is more than the mass of flesh and bones that make up our body.
B. If we do have intelligence and our brain is where the source of it by all accounts appears to be, then we must conclude that our intelligence is in our brain and not an abstract entity that we cannot touch/see/sense.
I was wondering if this makes sense to any one else, or if you have any feedback on the similarities between these two dilemmas.
I will begin by explicating Benacerraf's dilemma. Paul Benacerraf believed that for mathematics to have truth we must have two things:
A. A plausible semantics for mathematics.
B. A plausible epistemology for mathematical knowledge.
For A to occur, the most plausible way is to use numbers as abstract entities.
For B to occur, the most plausible way is for numbers not to be abstract entities.
Therefore, Benacerraf was left with a dilemma. (He was trying to reject a Platonist view)
In layman's terms:
To have a plausible semantics for mathematics, we need numbers that never change. For an example out of the Platonist view, imagine the number 3. Now imagine there is one perfect 3 floating around in some dimension that we cannot see, and every instance of 3 on earth or in the universe is just an instance of the 3 in the other dimension, and can only be like the number 3 in the other dimension, because it is the ideal 3 and therefore all instances of 3 aren't themselves THE 3, but just A 3.
To have epistemic knowledge of numbers, we have to be able to prove they exist, or Know that we Know them. So therefore THE number 3 can't be off somewhere that we can't see, or we couldn't KNOW for sure that we know what it is. It follows that we must have instances of 3 that we rely on for knowing that 3 exists, like seeing 3 cows or 3 boats.
This may not seem like a problem for some people. Why can't we just choose one or the other?
Well, here is my explanation. If THE 3 is in another dimension somewhere, how does it touch all the other threes in "reality" as we know it? But, it does allow for congruity between all the threes in the world. Why do we need congruity between all the threes in the world? Well, because there are no threes that are exactly the same, right? Take for instance the 3 cows and 3 boats. Other than the abstract number, what is the same? Boats aren't cows, nor vice versa. They don't weigh the same, they don't look the same, aren't made of the same materials. Even if you have 3 cows and 3 other cows, the 3 is never going to be exactly the same, or they would not be separate entities. There would always be a difference, even if the second 3 cows were cloned from the first 3. Even if all six were cloned from one and then raised in the same environment, weighed exactly the same, and then split into two groups of 3. The difference, you ask? Location. Three cows would be here, and the other three there (or at point a and point b, to be more neutral).
So you can't point to one instance of 3 in reality as we know it that can stand in for all the other threes, but you can't know that a perfect 3 exists in another dimension, either. So how do you know mathematical truth if you need both to reconcile in order to attain it? Well, you don't.
This leads me to the mind(soul)/body problem, which is more complicated because of the human element. When people argue about numbers, personal beliefs don't tend to get involved, and the search for unbiased truth seems more direct and less of an attempt to justify existing beliefs.
This is my translation of Benacerraf's dilemma into dualism:
A. To have intelligent bodies, we must have an abstract form of intelligence, or what I consider words/thoughts to be. This must exist beyond our realm of understanding, or people would never be self-aware or able to make complicated abstract thoughts. This means for many that we must have a mind (soul) that is more than the mass of flesh and bones that make up our body.
B. If we do have intelligence and our brain is where the source of it by all accounts appears to be, then we must conclude that our intelligence is in our brain and not an abstract entity that we cannot touch/see/sense.
I was wondering if this makes sense to any one else, or if you have any feedback on the similarities between these two dilemmas.