### Thursday, October 13, 2005

## AskPhilosophers.org Question of the Day: Is self-contradiction still the prima facie sign of a faulty argument?

Opening remark:

"prima facie" evidence is just something that apears as it is on first sight, or on its face: there's no priority as such, no "before others", so a better question would be whether self-contradiction is still

It looks as though the answer to the question in this form is an unqualified "yes", and what is left open is what the other prima facie signs are, and where the implicit re-evaluation of the force of logic would lead us. The first of these is too open, so I'll concentrate on the second.

The crucial logical theorem which asserts the dismissive power of self-contradiction is this: if, in a logical system, you can derive both a proposition P, and its contradiction not-P, then you can derive any proposition about the system at all - including the negation of any of the axioms.

Bertrand Russell famously once demonstrated at a dinner that a mathematical contradiction would let him show that he was the Pope like this: "If 2 + 2 = 3, then, subtracting two from each side, it follows that 2 = 1. The Pope and I are two, and therefore, the Pope and I are one. Therefore I am the Pope."

The argument is obviously no more true of Russell than it is of me or you - even if you are indeed the Pope, because it is based on a false premise. And if you are the Pope: I'm sorry, it's nothing personal.

In general (and in general, when people generalise from the particular like this, one should not take the generalization for granted), self-contradiction is a sign that the speaker is capable of expressing views which are expedient at the time of expression, and so the speaker may be well suited for a career in Politics - which does not let such people off the hook for the logical consistency of their views, as many Politicians down the ages have discovered to their cost.

Or not. At one and the same time, I say I am a fish, and I am also not a fish. Now, where does that leave you, your Holiness (or not)? I could say I am left with a duty to evaluate the logic of assertions I am presented with, and if I should find that contradiction in the arguments of others undermines their conclusions, then I should also be watchful of my own precepts so that I can ensure that I am not contradicting myelf. Then again, I could forgive the self-contradictory, faulty arguments of others because my own arguments are prone to be self-contradictory and faulty.

And at this point I find I am drawn back to the expedient. The risk of this is that I may lose touch with reality, as I follow a chain ofreasoning to its conclusion; and in my experience and observation,reality asserts itself forcefully when contradicted in this way. So Ido my best to seek out contradiction in myself, and find resolution bychanging my precepts. I don't know any other way to proceed: do you?

The AskPhilosophers blog is at http://www.amherst.edu/askphilosophers/, but there's also a google group, AskPhilosophers, which is much like an old fashioned Newsgroup. As a philosophical blog, how do the panel members become members?

"prima facie" evidence is just something that apears as it is on first sight, or on its face: there's no priority as such, no "before others", so a better question would be whether self-contradiction is still

**a**prima facie sign of a faulty argument.It looks as though the answer to the question in this form is an unqualified "yes", and what is left open is what the other prima facie signs are, and where the implicit re-evaluation of the force of logic would lead us. The first of these is too open, so I'll concentrate on the second.

The crucial logical theorem which asserts the dismissive power of self-contradiction is this: if, in a logical system, you can derive both a proposition P, and its contradiction not-P, then you can derive any proposition about the system at all - including the negation of any of the axioms.

Bertrand Russell famously once demonstrated at a dinner that a mathematical contradiction would let him show that he was the Pope like this: "If 2 + 2 = 3, then, subtracting two from each side, it follows that 2 = 1. The Pope and I are two, and therefore, the Pope and I are one. Therefore I am the Pope."

The argument is obviously no more true of Russell than it is of me or you - even if you are indeed the Pope, because it is based on a false premise. And if you are the Pope: I'm sorry, it's nothing personal.

In general (and in general, when people generalise from the particular like this, one should not take the generalization for granted), self-contradiction is a sign that the speaker is capable of expressing views which are expedient at the time of expression, and so the speaker may be well suited for a career in Politics - which does not let such people off the hook for the logical consistency of their views, as many Politicians down the ages have discovered to their cost.

Or not. At one and the same time, I say I am a fish, and I am also not a fish. Now, where does that leave you, your Holiness (or not)? I could say I am left with a duty to evaluate the logic of assertions I am presented with, and if I should find that contradiction in the arguments of others undermines their conclusions, then I should also be watchful of my own precepts so that I can ensure that I am not contradicting myelf. Then again, I could forgive the self-contradictory, faulty arguments of others because my own arguments are prone to be self-contradictory and faulty.

And at this point I find I am drawn back to the expedient. The risk of this is that I may lose touch with reality, as I follow a chain ofreasoning to its conclusion; and in my experience and observation,reality asserts itself forcefully when contradicted in this way. So Ido my best to seek out contradiction in myself, and find resolution bychanging my precepts. I don't know any other way to proceed: do you?