David Hume and the Problem of Induction

Some of my detractors have claimed that David Hume said, "Only a madman would be a complete skeptic."  Who is David Hume?  Why would anyone think I was a complete sceptic?

First of all, let's set the story straight; David Hume never made the above comment.  What he said was, "...though none but a fool or madman will ever pretend to dispute the authority of experience, or to reject that great guide of human life, it may surely be allowed a philosopher to have so much curiosity at least as to examine the principle of human nature, which gives this mighty authority to experience, and makes us draw advantage from that similarity which nature has placed among different objects."  As we can see, David Hume's quote (when not taken out of context) seems to indicate that a healthy scepticism is a good thing and that a degree of delving into the value of experience was meritted and worthwhile.

David Hume is important because he was the first person to officially touch on what is now known as the "Problem of Induction," although he never used that term.  The problem is this: There is no logical reason to believe that the future will resemble the past.

At first people may vigorously object to this idea.  "Just you wait," they may say.  "The sun has risen every day and it will rise again tomorrow.  You watch and see!"  Then, appearing triumphantly on the following day they state, "A-ha!  So you see, the sun has risen as I predicted.  Now, surely, you must realize that the past is a good guide to the future."

Unfortunately for these well-meaning people, they are committing a logical fallacy called "begging the question."  They are saying that the past is a good guide to the future because it has worked in the past (and will therefore work in the future).  This is circular logic and proves absolutely nothing.

Over the centuries since David Hume first encountered the problem many great minds have struggled with the problem and to date there is no answer to the problem of induction.  David Hume resolved the problem for himself by deciding that mankind was irrational and that it was impossible to avoid using induction.  As such he is known as the father of anti-rationalism.  Rationalism has been defined as "any view any view appealing to reason as a source of knowledge or justification."  Anti-rationalism is the view that even though something conflicts with reason, logic and good-sense that this is no reason to abandon the procedure.  As you might guess, I heartily disagree with this notion.

In fact, I should like to point out that the basis on which David Hume argues that humans are irrational and that induction is unavoidable is based on the past and the assumption that the past is a good guide to the future.  As such, he basically justified induction and the irrationality of humans by using induction.  This, as we have already mentioned, is begging the question.

Scientific apologists generally try to sweep the problem of induction under the carpet, and with good reason.  Accepting the idea that the past is not necessarily a good guide to the future means that science itself is suspect.  After all, the idea of science is that after dropping a rock a few dozen times and noting the acceleration downwards that this observation can be applied not only in that same spot, but everywhere in the universe both in the past and in the future.  What scientist would like to admit that there is no rational basis for his craft?  Perhaps it is even more unappealing when lucrative scientific funding is at stake.

Those who have seriously delved into the matter, however, have advanced two possible solutions to the problem.  Karl Popper proposed 'falsificationism' in which induction is abandoned.  It is true, he argued, that science cannot prove any theory right - but it can and has proved a number of apparently good theories to be faulty.

So simply by objecting to the illogical nature of induction does not mean that someone completely abandons experience as a guide nor does it mean that a person who insists on using logic is a complete sceptic.  It just means that I don't place stock in things that are blatantly irrational and that I'm not going to sacrifice logic and common sense on the altar of science just because I'm told to do so.

The second proposed solution to the problem of induction is Bayesian statistics.  This argument proposes that although you cannot use induction to say that just because you have observed 6 white swans in a row that all swans are white, that you CAN say with a degree of statistical precision that it is very likely that the next swan you see will be white.  This n+1 workaround is what most scientists fall back on if they are pushed on the problem of induction.  In another article, I plan to take the time to criticize this claim.

But for now I will suffice by saying that naive reliance on induction, as the vast majority of science-ophiles do and the willful ignorance of the problem is just another reason to realize that science... is BS.

Big Bang Theory

I once asked my uncle, who is an astronomer, if he believed in the Big Bang Theory.  He told me that he did because of the discovery of the Cosmic Background Radiation (CBR).  Although I don't believe in the Big Bang Theory, I let it drop at that.  I could have continued with any number of reasons why the CBR isn't consistent with the Big Bang Theory like the smoothness, that the theory originally predicted a temperature closer to 50ºK, or something else but I didn't.

Instead I thought about science - what it really is and how it works.

Let's follow my uncle's logic process from start to finish.  First we have a theory called the Big Bang Theory (BBT).  The theory predicts things about the CBR.  Then we find the CBR so my uncle concludes the BBT is correct.  Unfortunately, however, this is a classic case of a logical fallacy.

Thanks to Wikipedia it's easy to find an absurd example following the same pattern of logic.  If Bill Gates owns Fort Knox, then he will be rich.  Bill Gates is rich, therefore he owns Fort Knox.  This logical fallacy, called affirming the consequent, is the basis of the so-called "scientific method."  We can express it in symbols, as follows:

If P, then Q ( or P=>Q )
Q
therefore P

This pattern is reflected in almost every aspect of scientific "knowledge" that we find nowadays.  If Einstein's theory of relativity is correct then the orbit of Mercury will be such-and-such.  The orbit of Mercury is, indeed, such-and-such, therefore Einstein's theory is true.

If the Earth is 4.5 billion years old (give or take) then we will find a certain ratio of uranium-238 to lead.  We find that ratio, therefore the Earth is indeed 4.5 billion years old.

Realizing this, a sensible person will say, "Well, all of these are just theories," but don't say that too close to a true scientific believer.  He will assure you that a scientific theory is a special thing - not a hunch, a guess, or anything else.  It's well-documented, well-supported, and well-tested.

Unfortunately all this documentation, support, and testing follows the above logic-challenged pattern.  I guess they feel that although one logical fallacy proves nothing, a large number of logical fallacies do indeed prove something.

And that's why Science... is BS.

How to Calculate the Odds of Something

Some people didn't understand my post about why induction is self-refuting.  I believe this may be because they don't know exactly how the odds of something are calculated.  By way of illustration, we shall imagine that a person takes a cancer test, which turns out positive.

We know that the cancer test has a 95 percent confidence level - that is that it generates false positives and false negatives only 5 percent of the time.  Some people might think because of this that the person has a 95 percent chance of having cancer.  That is not true.  As a matter of fact, there is not enough information in the problem to know what the person's chance of having cancer is.

Let us assume that the person has an 8 percent base chance of having cancer.  Perhaps this is merely an informed guess by the doctor or perhaps it comes from the percentage of people in the general population who have cancer.  As such, anyone walking in the door might be expected to have cancer based on their age, their symptoms, or whatever.  This is the piece of information we will need to calculate the chance of having cancer.

So if 8 percent of the population has cancer then out of every 10,000 people that come to be tested 800 of them will have cancer and 9,200 will not.  After the test we will have four groups: 760 people who have cancer and tested positive for cancer (800 x .95) and 40 people who have tested negative for cancer, but really do have it (800 x .05).  We will also have 460 people who have tested positive for cancer, but do not have cancer.  We will also have 8,740 people who do not have cancer and have tested negative for it.

What then is chance that the person really does have cancer after receiving a positive test result for cancer?  The answer is 760 / (760+460) ... that is, the number of people who have cancer and have tested positive, divided by the size of the whole number of people who have tested positive for cancer (the 760 plus the 460 who falsely tested positive).  Accordingly we can say that the person has a 62.3 percent chance of really having cancer.

It may seem strange to you that a test that is 95 percent accurate results only in a 62.3 percent chance of the person having cancer.  However, you need to look at it this way:  The person's initial chance of having cancer (8 percent) has now increased to 62.3 percent and a second positive test would let us increase the probability accordingly.  The more tests we do, the greater the chance of the person having cancer if, indeed, they do have cancer.

A Stupid Argument

How would you feel if someone said to you, "Hey... since you don't accept Thor why don't you stop using your computer!  After all, you wouldn't have electricity if it weren't for the God of Lightning.  Log off now and stop wasting my time!"

I bet you'd think that was a pretty stupid argument.  I agree - it's a dumb argument because it presupposes something as true that is not known, namely that Thor is responsible for lightning and thereby electricity.  Electricity could easily exist without Thor having been responsible, right?  Ok, good.

So now you understand how I feel when someone says, "Hey!  Since you don't accept science you should stop using your computer, never take penicillin or aspirin, and stop bothering us!"

Really that's the same argument, isn't it?

Plus it shows that the person is woefully ignorant of history.  First of all, penicillin was first made by microorganisms.  It is far more likely that we have God, Vishnu, or Allah to thank for penicillin than science.  Secondly, aspirin is nothing more than the bark from a white willow tree and has been in use for centuries before science reared its ugly head on the scene.

Similarly there's no proof that science is responsible for computers, electricity or our understanding of them either.  Science's main claim to fame is retroactively proclaiming people they agree with scientists while doing everything they can to sabotage them during their lives.  A simple look at http://amasci.com/weird/vindac.html#list will give you an extensive list of those who have suffered thusly.

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.