4 ms·

no, this is really begging the question. youve reduced "the proposition is true" to "the algorithm is correct, and the algorithm returns 'true'". once you prove

by hc 17y ago

no, this is really begging the question. youve reduced "the proposition is true" to "the algorithm is correct, and the algorithm returns 'true'". once you prove the former you still have to do the hard part of actually _proving_ the latter. i suppose this amounts to mathematically proving, among other things, that your pentium 4 or whatever is incapable of executing a program incorrectly.

justin_vanw 17y ago
You miss my point completely. You are thinking that mathematical proofs are like airtight and completely unassailable and locked in for all time. In reality (practice) they are pretty sloppy, and are really just a form of persuasion. Now, persuading a group of mathematicians to believe a claim is a high bar, and they are very good at finding logical holes, gaps, and mistakes. As Nietzsche points out in Beyond Good and Evil, it is quite possible that humans as a species have all sorts of blind spots in our reasoning abilities, and that such blind spots are essential for life itself. In fact, we know of many of these blind spots, or failures of human reason. One great example is the Monty Hall problem. Others are the lottery, gambling, stock market events, advertising (the effects of), and all sorts of experiments that economists do these days. So before you get concerned about the Pentium IV's accuracy, and 'mathematically proving' it is correct, consider that your brain is a very imperfect reason engine, and there is no reason to suspect that our intuition is accurate except in (and still imperfectly in) those situations where those intuitions improved the reproductive chances of our ancestors.
- justin_vanw 17y ago
  Oh, I just made a huge howler. >...our intuition is accurate except in (and still imperfectly in) those situations where those intuitions improved the reproductive chances of our ancestors That actually contradicts my point. Our intuition and reasoning powers did not evolve toward accuracy or better understanding the world, it evolved purely toward whatever kept our monkey ancestors out of lion mouths. Sometimes that could have caused our primitive ancestors to believe that they could only safely cross the plains while holding magic rubaduba fruit. This would of course be reinforced, since perhaps the rubaduba fruit only is on trees in the one month a year that lions are far away looking for water. The proto-humans who believed the rubaduba bullshit survived because they were able to pick up on a correlation, but they only acted on it because they believed in causation, meaning we our ancestors who thought the rubyduby fruit theory was idiotic got eaten by lions, while the credulous saps who filled sacks with 50 pounds of inedible crap and carried it across the plain were fine. This is a just-so story, but the point is illustrated, which is that not only do humans have terrible reasoning ability when it comes to money and anything remotely scary, it's quite possible we evolved specifically towards irrationality in certain situations. There is billions of dollars spent studying this every year, it's called marketing.
- hc 17y ago
  "[proofs] are pretty sloppy, and are really just a form of persuasion." yes... with one of these computer brute force proofs, you must take it on faith that the result of executing an algorithm is as someone has claimed, be it the paper author or your own machine. this is proof by handwaving.

by hc 17y ago

justin_vanw 17y ago

You miss my point completely. You are thinking that mathematical proofs are like airtight and completely unassailable and locked in for all time. In reality (practice) they are pretty sloppy, and are really just a form of persuasion. Now, persuading a group of mathematicians to believe a claim is a high bar, and they are very good at finding logical holes, gaps, and mistakes. As Nietzsche points out in Beyond Good and Evil, it is quite possible that humans as a species have all sorts of blind spots in our reasoning abilities, and that such blind spots are essential for life itself. In fact, we know of many of these blind spots, or failures of human reason. One great example is the Monty Hall problem. Others are the lottery, gambling, stock market events, advertising (the effects of), and all sorts of experiments that economists do these days. So before you get concerned about the Pentium IV's accuracy, and 'mathematically proving' it is correct, consider that your brain is a very imperfect reason engine, and there is no reason to suspect that our intuition is accurate except in (and still imperfectly in) those situations where those intuitions improved the reproductive chances of our ancestors.

justin_vanw 17y ago
Oh, I just made a huge howler. >...our intuition is accurate except in (and still imperfectly in) those situations where those intuitions improved the reproductive chances of our ancestors That actually contradicts my point. Our intuition and reasoning powers did not evolve toward accuracy or better understanding the world, it evolved purely toward whatever kept our monkey ancestors out of lion mouths. Sometimes that could have caused our primitive ancestors to believe that they could only safely cross the plains while holding magic rubaduba fruit. This would of course be reinforced, since perhaps the rubaduba fruit only is on trees in the one month a year that lions are far away looking for water. The proto-humans who believed the rubaduba bullshit survived because they were able to pick up on a correlation, but they only acted on it because they believed in causation, meaning we our ancestors who thought the rubyduby fruit theory was idiotic got eaten by lions, while the credulous saps who filled sacks with 50 pounds of inedible crap and carried it across the plain were fine. This is a just-so story, but the point is illustrated, which is that not only do humans have terrible reasoning ability when it comes to money and anything remotely scary, it's quite possible we evolved specifically towards irrationality in certain situations. There is billions of dollars spent studying this every year, it's called marketing.
hc 17y ago
"[proofs] are pretty sloppy, and are really just a form of persuasion." yes... with one of these computer brute force proofs, you must take it on faith that the result of executing an algorithm is as someone has claimed, be it the paper author or your own machine. this is proof by handwaving.