Date: Dec 27, 2012 10:47 AM
Author: Paul A. Tanner III
Subject: Re: A Point on Understanding
On Wed, Dec 26, 2012 at 11:38 PM, kirby urner <firstname.lastname@example.org> wrote:
In all these posts in this thread you have yet to actually state what the contradiction is supposed to be, since you have not actually put forth a contradiction, which is by definition a statement that is false in all its substitution instances - that is, for instance when doing truth tables, in the main column there would be nothing but but F's. (A tautology is by definition a statement that is true in all its substitution instances - when doing truth tables, in the main column of its truth table there would be nothing but but T's.)
One standard form of a contradiction is a statement of the form p & ~p, (the conjunction of some statement p and its negation ~p), and since you have yet to explicitly put forth any statement form that is false in all its substitution instances - much less prove that said statement is false in all its substitution instances, you have yet to put forth the form p & ~p and tell us what statement p is supposed to be.
This is a common problem when people put forth claims of contradiction, the sloppy argumentation of claiming that some contradiction exists but never actually doing the careful work in crafting an argument such that the one crafting the argument would be able to give the actual statement of a contradiction, a statement that is false in all its substitution instances, and prove that it is false in all its substitution instances, where one way to do this would be to simply put forth a statement form like p & ~p and prove that this form necessarily derives from the argument.
I would think that those who engage in such sloppy argumentation and wrongly make claims of contradiction would find the error in their thinking if only they were to actually try to put forth an argument such that a known contradiction form like p & ~p necessarily derives from the argument - that is, they would soon find that they cannot put forth such an argument and why they cannot.