Ancient Philosophy and Contemporary Problems

Sunday, April 30, 2006

Heya everybody,

I want to keep talking about what we were talking about today in class...

If I were Moses, does that mean that Moses was me before I was me? Furthermore, would that mean that I was here forever prior to my actual birth etc? I think that we really can't define a thing or person solely by the set of materials which comprise it or them.

One more thing...

If we take the fifth argument farther, what form would I be? Do I resemble the form "Lisa", or do I represent the form "human"? Maybe I represent both...? Just some things to think about. Is the relation between the form of a person different from the relation of the form of an ordinary object to the actual object? If so, how?


Thanks for your help on my previous post. I have another question open to anyone.

This is the first argument I have presented in my paper and I am trying to figure out which premise would be the easiest one to object to. (Also, I THINK it's valid, but if it's not please let me know!) So, which premise looks the easiest to object to and why?

1. If there is time, then there is a 4th dimension.
2. There is time.
3. ,', There is a 4th dimension (MP).
4. If there is a 4th dimension, then all things have temporal parts.
5. "3"
6. All things have temporal parts (MP).
7. If an object has temporal parts, only one object exists at any place at any given time.
8. "4"
9. ,', Only one object exists at any place at any given time.



Friday, April 28, 2006

This question will most be easily answered by those working on the Material Constitution paper, but please feel free to help out even if you are not focusing on Material Constitution:

I am worried about how my first argument opens...

"1. If there is time, then there is a fourth dimension."

I am unsure of whether these two are related. Is this statement necessarily true?



Monday, April 24, 2006

I've reached a point in my paper where I can't resolve a conflict between two lines of though. First off, I'm writing about fatalism and central to that is Aristotle's argument about making predictions. It goes:

1. A sea battle will happen tomorrow.
2. A sea battle will not happen tomorrow.

He concludes that since the two predictions are contradictory, one must be true and the other must be false. This pertains to fatalism in that if a prediction can be true, then the future is closed (like the past is 'closed' because it is unchangeable). This is the first line of thought.

The competing idea is that a prediction really isn't a statement, but an utterance. Therefore, the logic that Aristotle uses does not even apply. Remember the Parmenides argument that if something can be spoken of, it exists? The same logic goes here: since a prediction speaks of the future and the future doesn't exist (yet?) then we're just talking about something that doesn't exist--merely uttering nonsense.

I like Aristotle's argument more than the second one simply because it's easy for me to understand. If you're making statements about reality and you say S and ~S, one has to be true and the other false.

I'm envious of everyone who isn't working on their paper right now...

Sunday, April 23, 2006

Hey guys, i need some help - i have some idle premises in my argument and i cant seem to figure out how to fix them... the idle premises are somewhere in (1-3) and (7-9) - heres the argument (sorry for the lengh...)

Heres the Background,

*This sentence is false.

The starred sentence is

(a) True

(b) False

(c) All of the Above

(d) None of the above

And heres the actual argument,

  1. If (a) is the right answer, then the sentence is true.
  2. If (a) is true, then it is false.
  3. Supppose (a) is the right answer
  4. If (a) is true and false there is a contradiction in (a)
  5. (a) is true and false
  6. .’. There is a contradiction in (a)
  7. If (b) is the right answer, then the sentence is false
  8. If (b) is false, then it is true
  9. Suppose (b) is the right answer
  10. If (b) is true and false there is a contradiction in (b)
  11. (b) is true and false
  12. .’. There is a contradiction in (b)
  13. If there is a contradiction in (a) and (b) then they are not correct.
  14. There is a contradiction in (a) and (b)
  15. .’. (a) & (b) are not correct
  16. If (a) & (b) are not correct, then (c) cannot be correct
  17. .’. (c) is not correct
  18. If (a), (b), and (c) are not correct, (d) must be correct
  19. .’. (d) is correct
  20. If (d) is correct, then the sentence is neither true nor false
  21. .’. the sentence is neither true nor false

Any help would be much appreciated. Thanks alot.

- Derek

Wednesday, April 05, 2006

Proof of the Existence of Infinity

In doing research for my paper, I came across a proof in Bertrand Russell’s “Essays in Analysis” which I think is particularly important in the discussions we had before on whether it is logically possible to perform a super-task. One of the problems that was brought up was that infinity as well as infinitely small things are defined in terms of limiting operations. However, Russell manages to prove that infinity exists without ever making use of any limiting operation what so ever. He wrote the proof as a response to (quote) “Professor Keyser’s very interesting article ‘On the Axiom of Infinity’” (end quote), which claimed that all accounts of infinity essentially involve some sort of limiting operation, which, Keyser claims, is not sound. Keyser also claimed that all arguments involving infinity are circular arguments, which Russell refutes as well.

Russell’s proof goes something like this:

Definitions and assumptions:

1. Every set has some perfectly well-defined number of terms.

2. Zero is defined to be the number of things fulfilling any condition which nothing fulfils. So, for instance, the number of statements which are both true and false, a condition which nothing fulfils, is zero.

3. Zero exists.

4. The number 1 is the number of members of a set such that there is a member of that set such that when that member is removed the resulting set is identical to zero (i.e. 1-1=0.) A set which contains only zero will have only one member; therefore, the number 1 exists.

5. The set containing 0 and 1 has two members; thus, 2 exists.

6. n is any finite integer.

Russell then moves onto a proof by mathematical induction. The principle of mathematical induction states that any property possessed by the number 0, and possessed by n+1 when it is possessed by n, is possessed by all finite numbers (by “numbers” Russell means integers – i.e. the natural numbers. What he’s really refering to, and he says so later on in the article, are cardinal numbers. But for our purposes we can simply assume that he means integers.)

7. If n is any finite integer, the number of integers from 0 to n, both inclusive, is n+1.

8. If (7), then if n exists, so does n+1.

9. n exists.

10. Therefore, n+1 exists.

11. If (10) and (3) then all finite integers exist.

12. Therefore, all finite integers exist.

13. If m and n are two finite natural numbers (integers), other than 0, then m+n is not identical (i.e. not equal) to m or n.

14. If (13) then if n is any finite number, n is not the number of finite numbers, for the number of numbers from 0 to n is n+1 and (due to (12)) n+1 is not identical to n.

15. If n is any finite number, then n is not the number of finite numbers, for the number of numbers from 0 to n is n+1 and (due to (12)) n+1 is not identical to n.

16. n is any finite number (true by definition.)

17. Therefore, n is not the number of finite numbers.

18. The definition of cardinal numbers (what I’ve been referring to as integers) requires the existence of a number which is the number of the finite numbers (again, what I’ve been referring to as the integers.) This is basically identical to premise (1).

19. If (17) and (18) then at least one non-finite number exists.

20. Therefore, at least one non-finite number exists.

21. If at least one non-finite number exists, then at least one infinite number exists.

22. Therefore, at least one infinite number exists.

I’ve tried to quote most of the argument above straight from Russell; so if there are any premises that I don’t use, it’s because I was trying to stick with the form of Russell’s argument which he presents in his paper. One of the biggest parts where I strayed away from Russell’s original argument was in his use of the word “number” to mean the cardinal numbers. I simply replaced just about everywhere Russell uses the word “number” with the word integer, but this is because Russell’s cardinal numbers are restricted to describing the integers; they cannot describe irrational numbers, for instance, or complex numbers (and thus when Russell says “numbers” he isn’t really referring to all numbers, but rather a subset of the numbers.) But I believe that Russell’s proof still works despite this minor change in wording, namely because there is no change in the meaning of the argument.