Induction is Self-Refuting

Recently I was talking to Riemanngalois on FICS and he tried to argue that although the only way to justify induction was using inductive reasoning (and agreed that induction was circular) he claimed that you could avoid the problem by just postulating induction.

I disagree.  I believe that induction is self-refuting and therefore cannot be accepted.  The logic is simple: since induction has failed in the past, induction predicts that induction will fail again in the future.  However, we went round and round on the point so I have created this document to establish for once and for all that induction is self-refuting.

So in order to do that we need to start by postulating induction and lead around from that to the conclusion that induction is false.  To do that I will be using Bayesian statistics but since this is mostly written for a lay audience I won’t clutter up the page with lots of symbols that most people cannot understand.

Bayesian statistics requires us to start with an initial probability of induction and since we are postulating induction as true we will start with an initial probability of 100 percent or, in other words, 1.  Using this initial probability we will examine induction to see how well it works.

So using this as a starting point we find that things initially work very well.  We start making some inductive predictions.  In my case, I speak Spanish, my wife speaks Spanish, my boss speaks Spanish, my maid speaks Spanish and my mother-in-law speaks Spanish so I conclude that the next person I speak to will speak Spanish.

And, at first, everything works fine.  The security guard speaks Spanish, the receptionist speaks Spanish, the janitor speaks Spanish, the office staff speak Spanish, etc.  But then we run into Martin, the Essex-born English teacher.  He doesn’t speak Spanish… not a lick.

So at this point we have 9 cases of induction working and 1 case of it not working.  At this point some people might argue, “That’s what we’ve been telling you!  Induction may not be 100% but it still works most of the time and it’s a good system.”

Not so fast… remember that we are USING induction to PROVE induction.  So now that induction is showing a 90% success rate our confidence in induction has dropped from our postulated 100% to 90% and will continue to go down.

So the next person we speak to speaks Spanish.  So now we have measured that induction works 90.9% of the time BUT remember that we’re using a system that we know is not 100% accurate (namely induction).  We had previously figured that induction worked 90% of the time so now we calculate that induction works 81.8% of the time (90% times 90.9%) so our confidence in induction continues to drop.  On and on it goes, with our next successful test we measure as induction successful 91.7% of the time and our confidence in our method is at 81.8% so our new confidence in induction drops to 75 percent.  On and on it goes until the 20^th test shows our confidence in induction drops to 47.4 percent.  At that point we can say that flipping a coin is better than using induction.

As the tests continue to go on… even if induction NEVER fails again, our confidence in induction will continue to drop until our confidence in induction approaches zero.

And that’s why you cannot postulate induction as a starting axiom and avoid the problem of induction.