[Computational Complexity] A new logical fallacy
- Those of us who have taught logic to students are familiar with some of the fallacies they make: (1) confusing OR with XOR (reasonable given English Lang use), (2) thinking that (a--> b) --> (b-->a) and (3) thinking thatfrom
A1 AND A2 AND A3 --> B
you deduce something about the writer's opinion of A3.
This recently happened, though it wasn't a student. It was a commenter on this blog. In a recent blog I wrote about McCain's concession speech:
If he has that way the entire time he might have won (if he also didn't pick Palin and we didn't have the economic crisis and we were more clearly winning the Iraq War).This is an IF-THEN statement. There is no logical way to deduce what I think of any of the premises. One of the commenters committed error (3) above:
A country is destroyed and half million people are killed, and yet the only thing you feel regret about is not "more clearly winning". Excuse me, Professor Gasarch, I never held hope for the humanity of US, but a comment like this from an intellectual in this country, just taught me how coldblooed the americans can be."The commenter raised an interesting question: If a writer says A-->B then what can you deduce about the writers opinion of A?
- If the work is in Large Cardinals then likely the writer thinks that the Large Cardinal hypothesis is true. Note that we do not know this logically.
- In papers that prove things contingent on P\ne NP or that factoring is hard or the usual derand assumptions the authors thing the assumption is true. Note that we know this by sociology, not by logic.
- (I may be off on this one- if so please correct.) Non-Euclidean Geometry was started by assuming the Parallel Post was false, hoping to prove that that assumption was FALSE, and seeing what can be derived from it. Let A be For a line L and a point p not on that line there are an infinite number of lines through p that do not intersect L. Let B be The sum of the angles of a triangle are LESS THAN pi. When someone proved A implies B they may have thought that A was false.
Pat Buchanan said (I am paraphrasing)
If McCain had presented more ties about Obama to Ayers and Wright then he would have won.While this could be a simple IF-THEn statement, given who he is we know that he things these ties are relevant. Keith Oberman may have expressed a similar sentiment differently:
If McCain had presented more lies about Obama to Ayers and Wright then he would have won.In this case we can tell what Keith Oberman thinks of the assumption.
- SO- if someone says A-->B then you can't really deduce what the speaker thinks of A LOGICALLY, but you can use other things he has said and his reputation to discern what he thinks of A. Reasoining from context and personality can be useful, though it is not as rigorous as we are used to. Students in a logic course should not use it.
Posted By GASARCH to Computational Complexity at 11/07/2008 12:11:00 PM