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

3 Comments:

Blogger linford86 said...

One of the primary problems of your argument is that it appears to me that you worked backwards; i.e. you came up with the argument first, and then tried to force it to fit a valid form. When I approach an argument, what I usually try to do is to only make those statements which I know will fit a valid form; i.e. I work from the form of the argument, rather than the content of the argument. With a long argument such as yours, with a number of sub-conclusions, this isn't always easy. However, I have created what I believe to be a valid version of your argument below:

1. If (a) is true, then the sentence is true.
2. If (a) is true, then the sentence is false.
3. .’. (1) and (2) (1, 2 Conj)
4. If (3) then it is the case that if (a) then the sentence is true and it is the case that if (a) then the sentence is false.
5. .’. If (a) then it is the case that the sentence is true and it is the case that if (a) the sentence is false.
6. If (4) then there is a contradiction is a contradiction in (a).
7. .’. There is a contradiction in (a).
8. If (b) is true, then the sentence is false.
9. If (b) is false, then the sentence is true.
10. If (7) and (8) then it is the case that if (b) is true then the sentence is false and it is the case that if (b) is false then the sentence is true.
11. .’. Therefore, if (b) is true then the sentence is false and it is the case that if (b) is false then the sentence is true.
12. If (11) then there is a contradiction in (b).
13. .’. There is a contradiction in (b).
14. If there is a contradiction in (a) and (b) then they are not correct.
15. .’.(7) and (13) (7, 13 Conj). <= This states: “There is a contradiction in (a) and there is a contradiction in (b).” (Note: we are allowed to do this because we can make a sub-conclusion wherever we like so long as the premises that validate the sub-conclusion precede somewhere in the argument; obviously, 7 and 13 precede 15.)
16. If (15) then there is a contradiction in (a) and (b).
17. .’.There is a contradiction in (a) and (b).
18. If (17) then (a) & (b) are not correct.
19. .’. (a) & (b) are not correct.
20. If (a) & (b) are not correct, then (c) cannot be correct.
21. .’. (c) is not correct.
22. If (a), (b), and (c) are not correct, (d) must be correct.
23. .’. (d) is correct.
24. If (d) is correct, then the sentence is neither true nor false.
25. .’. The sentence is neither true nor false.

10:53 PM  
Blogger linford86 said...

I would also like to make the point that when working with these kinds of arguments, one has to very important in what it is that one says; for instance, we have the statements:

There is a contradiction in (a) and there is a contradiction in (b).

And:

There is a contradiction in (a) and (b).

It would seem like these are the same statements; however, we are still required to link them by the statement:

If (15) then there is a contradiction in (a) and (b).

Simply because they are not precisely the same statement.

Also, the terms "right answer" and "wrong answer", although intuitively correct, are noticeably ambiguous. Presumably, you don't mean "morally right" - but simply by removing "right" and putting something along the lines of "true" you remove this ambiguity.

The same problem exists for the word "correct" - once more, you mean "true", and not "morally correct."

11:00 PM  
Blogger Undercover Sheep said...

I concur.

1:32 PM  

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