## Sunday, November 23, 2003

### Philosophical Buzzword: Modus Ponens

Savannah said, in reference to my Curry paradox post: I think I need to know what modus ponens means, because I don't see how your argument goes from 3) to 4). It looks to me like since 3) is the same as 1), you might as well have gone from 1) to 4) and it would have made just as much (or little) sense. The argument in question was this:
C: If this sentence (C) is true, then Santa Claus exists. (1) If C is true, then If C is true, then Santa Claus exists. (1') If if C is true, then Santa Claus exists is true, then (if C is true, then Santa Claus exists). (2) If if C is true, then Santa Claus exists is true, then Santa Claus exists. (3) If C is true, then Santa Claus exists. (4) Santa Claus exists.
I said that to go from (3) to (4), we used modus ponens on (3) and (3). Modus ponens is one of the basic rules of logic. Basically, it says that any time you know A, and also know "if A, then B", you can conclude "B". Here's an example of valid use of modus ponens:
1. If Jonathan is rich, I'm a monkey's uncle.
2. Jonathan is rich.
3. Therefore, by modus ponens on (1) and (2), I'm a monkey's uncle.
So how's this work in the Santa case? Let A be C, and let B be "Santa Clause exists". So sentence (3) above is equivalent to "if A, then B". But, because of the self-reference in C, sentence (3) is also equivalent to A. So we can invoke (3) as both antecedent and conditional (that is, as both "A" and "if A, then B"). This gets us to B by modus ponens. UPDATE: Thank you Alexis for catching a very bad error. It's now fixed.