# phil 101 on probability and Hume's problem of induction

Here’s a simple question that i came up with in exasperation at students whom upon attending the lecture on Hume’s problem of induction felt that they cleared understood the issue and knew something that students of other departments did not .

What’s the probability of the sun rising tomorrow ?

All i have is my own answer to this , but does anyone have a more rigorous approach to the question?

Ok well lets see…

A large object could hit earth and hit it so it stops it’s rotation. Lets call that arbitraily. 1 in 10^23

Either the sun or earth could disappear in what is known as a “quantum miracle.” Let’s say 1 in 10^144

Any one of the laws of physics could change tomarrow, or end a cycle where all of human history has been in one phase. (This is the Humeian bit.) Let’s say 1 in 10^10.

Finnially, we could all be in a computerised historical simulation and they are not interested in anything after 2008. I’ll put that at a 1 in 10^5.

So my finial calulation is aproximately 99.998%.

Really, hume didn’t figure in much. The historical simulation thing really dwarfed it. Anyway, I’ll bet you 10,000\$ the sun rises tomarrow.

hume wasn’t concerned with probability…

the claim that the future will resemble the past because of past experiences, begs the question. it is a logical error.

-Imp

Well, more importantly that he thought induction was nonetheless reasonable. So, his point was not all our truth telling ability came from Cartesian style deductive reasoning. He was putting the death nail in Rationalism. Of course Kant really declaired it dead when he took all its stuff and combined it with Epiricism.

There is no meaningful way to reckon that probability. Probability obtains only when all the possibilities are known. If you keep the model simple enough (and ignore everything we know about the Universe) then the probability is 50/50 - either it comes up or it doesn’t. But that seems like a sucker bet.

Is this something that everybody agrees upon? I am discussing this issue with my friends, and I’d like to be throwing out factual points on Hume’s problem.

everybody who reads hume agrees that this is what he said… not everyone agrees with hume’s conclusions however… and I’ve not found any valid arguments that overcome the problem of induction…

-Imp

Except for more or less of course.

Let’s see. I have to think back, but I think how this was how it was explaned to me in class.

Hume catagorises truths in two catagories, analytic and synthetic.

Analytic truths can be know by only looking at the meaning of the terms. For example, “All bachelors are male.” Because bachelor means unmarried male, we don’t even have to look at a bachelor to know all bachelors are male.

Synthetic truths requre you to look at the world. For example, “That swan is white.” Nothing about swan means white, so to see if it is white we must use our senses.

Ok?

Well then we get to problematic statements like “All swans are white.” First of all, it’s synthetic. So we must need sense data. What sense data do we have?
We have, “All 100 swans I’ve seen are white.” But does that lead directly to “All swans in the world are white,”? Not quite we need something else. We need the Principle of Universality of Nature.

The PUN: Things I haven’t seen are similar to things I have seen. (Tommarow is like today, ect.)

Ok, well how do we know the PUN is true. First of all it too is synthetic. There is nothing in the definition of nature that means universal. So whats the sense evidence?
“Things I’ve seen for the first time in the past have been similar to things I had already seen before.” But agian this is insufficent, so we need then PUN.

But then we are using the PUN to prove the PUN. That is circular. So here, according to Hume, inductive logic is not justified by deductive logic.

Another way to put it is that Hume sees Deduction as the logic of Analytic truths, and Induction as the logic of Synthetic truths, and that the two systems are seperate forms of logic that we use.

I think this interpretation of Hume is pretty uncontroversal- I’m sure I’ll be corrected if it’s not.

As for arguments to overcome Hume, look for Quine’s paper Two Dogmas of Empiricism.

As much as Hume does not talk about probability he should have for …If the sun rose in the past there is definitely a probability of it rising tmr. In fact ceteris paribus , it will ceryainly rise tmr given that it rose today and noyhing changes till tmr .

The probability of the sun rising is therefore 1/(total no.of possible sets of conditions whereby the sun does not rise) .

My ans to the original question is simply ‘uncertain’ . But if we take the past into account then the ans has to be some mumber between 0 and 1 .

Yeah, that’s the PUN right there. The deep question is why? Why do things keep happening the same way? And why are we so confident they will keep happening the same way?

Hume’s answer was that it was part of being human. (His skeptical solution.)

the problem is how do we/philosophers evaluate the truth value of non-scientific probabilistic claims . All we have right now is this notion of an agreed upon reasonability . Its easy to point out logical errors with regards to deduction ; children implicitly and unknowingly do that all the time by asking ‘why’ .

Actually, Lewis Carrol wrote a paper showing that deductive logic was circular. I think it was called “Archimedes and the Tortouse” something like that. Anywho, I lot of this gets solved by Kant, the Pragmatics, and the Analytics. But Hume was good enough to bring up the question.

kant never solved anything.

-Imp

Kant did offer solutions which have been improvised , extended or are still being debated upon till today . If we interpret ‘solve’ in strict terms then only the scientists and mathematicians can be seen to have solved anything . Hume posed a problem and kant took in on .

no, the real implication iirc is the relation of the cause in the past to the effect in the future. ie, to expect the relation of the two events to hold without its evidence.

now, after your conclusion has been affirmed time after time, then the habit of reasoning causing one to assume the connection as then being cause and effect. THAT was the meat of the problem, not the expectation itself.

kant’s “solutions” don’t solve anything (there is no synthetic a priori…)… nor have scientists and mathematicians…

speaking in circles…

-Imp

no, the problem is that inductive logic is fatally flawed as hume pointed out. his explanation why one believes in cause and effect was that the constant conjunction of events imprints itself habitually, NOT logically; the nature of human thought believing in a connection that isn’t demonstrated logically but is derived from habit for hume isn’t the problem of induction in itself, but it is the result of it…

-Imp

well i would really like to know what the word solve means . If no one solved anything why does this term exist ? If nothing was solved u would not be here now .

And is mathematical induction flawed ?

Speaking in circles…Do u mean the fallacy of assuming my conclusion in my premises . When ? How ? Use some intellect please …Philosophy is not that easy though what Hume says appears so .

Mathematical Induction is perfectly logically valid .

Answer this obvious question and you will see your error : Why is induction not valid in Hume’s point of view ?
Its all to do with the premises , and as i said in an earlier post if the premises (conditions) of the past were to be entirely repeated , Nothing more or less (ceteris paribus), then logically the exact same conclusion must infer . THIS is my argument for induction. The past gurantees the future if and only if Nothing changes at all.( i am not implying nietzche’s eternal recurrence at all , i still don’t get that.) If the anything is variable then change is possible and of course the past cannot gurantee the future in that case.

The whole problem is about what students infer from Hume ( Hume is not wrong , some of us might be).
Hume was not an analytical philosopher , he never said or even gave an argument as to the invalidity of induction as a method of reasoning, he only showed through examples that the the way we humans use it in Everyday Thought does not produce deductive conclusions . in mathematics this is not the case …as its not observation based. Anyway going further here might bring Godel into the picture , i certainly wouldn’t want that.

Did any preceding philosopher ever commit Hume’s error of induction ?

Btw inductive logic is an emerging field in many forms , one of them being Fuzzy logic . Pls stopping saying its invalid and that Hume said that .

Can I replace the world ‘solved’ with ‘developed’ or something? I was just trying to hint that in contemporary philosophy it’s not considered as much a poblem because the analytic/synthetic division is now much fuzzier. Once you knock out that stark division the problem begins to dissolve.