Alright, it’s time for me to stop beating around the bush and dive head first into some deeper philosophy.
My first step was Hume’s problem of induction, thanks to a thread by shotgun. He claims that the possibility of science and logic are destroyed by this problem…
I think I get the problem of induction: basically, there’s no reason as to why we should expect something to behave in the future as it has in the past, except through induction. And induction can’t validate itself.
So I have a few questions. First, what relevance, if any, does the problem of induction have in regards to the usefulness of science?
Secondly, does this problem make all of science unreasonable, or is it simply the relationship between two propositions that’s unreasonable?
Thirdly, when is deductive reasoning used instead of inductive reasoning, and what problems does deductive reasoning pose?
Not induction, habit. We never see the necessary connection, we never see that the billiard ball hitting the other one causes the other to move. We just come to expect it because we have seen correlation so many times that it becomes a habit of ours. We cannot induct causation because we never see causation, we only see correlation, and habit leads us to expect future correlation.
So you’re saying that we see one ball hit the other, we see the other one move, but it’s unreasonable to say one affected the other? Or did you just go completely over my head…
Pretty much, we see one ball move and then another ball move. According to Hume we don’t see a necessary connection between the two but only a correlation. Further, according to Hume, we think we see causation because we see this correlation consistently over the course of many billiard games, and from habit we assume they are related in terms of cause and effect. However, I don’t think Hume would claim that it is unreasonable to assume a causal relation between the billiard balls.
To me, and given that Hume abandoned his radical skepticism later in life it would seem to Hume, the Problem of Induction serves as a warning against taking logic too far. Logic is built on tautologies and its relation to the real world is only as valid as those tautologies relate to the real world. In his brash younger days, Hume saw no reason why causality ought hold beyond induction (which he had a rather sever allergy to) and he was able to logically demonstrate that such a relationship need no hold. Hume’s formulation of the self (interestingly, quite similar to a Buddhist view of the self) is a good demonstration of his view of the situation.
So, it really depends on your flavor. As the N-man said, “All is a matter of taste and tasting”. Hume’s fork showed that deductive and inductive reasoning are at odds with each other (at least when both are reified as complete systems, but that is a different discussion entirely). So which way do you go? Do you go with ‘truth’ as being a logical construct and thereby limit yourself to a purely noumenal reality or do you accept a contingent ‘truth’ that may merely be an accident due to your own particular perspective? You needn’t reject both to become a nihilist (though that often happens in ill-informed vulgar nihilism) all you need do is reify both of them and point out their incompatibility.
As per your questions:
If both deductive and inductive reasoning represent complete systems, they are incompatible. If science is based on reason, it contains within itself a fundamental contradiction that cannot be resolved. Induction leads to the production of theories but theories are, by their nature, deductive.
Depends on how you view it. “Reason” is a human construct and is therefore incomplete. Likewise, the systems of deductive and inductive logic are incomplete. If you treat any of those as complete, the contradiction is indeed irresolvable. And if science is based on reason, then it follows that science is based on an irresolvable contradiction. It is an absolutist, almost religious, mindset that leads to this schism: “Humans are finite, but somehow systems created by humans are not!”
Both have their place and people use each all the time. What are the problems with deductive reasoning? Just that is only relates to the world as well as its tautological bases do, a relationship that is often quite tenuous. For me, I think deductive reasoning is all about Chuck D, “Check yourself before you wreck yourself.” Look at what you’ve inductively demonstrated and put it together. Does it hold? If not, there is something missing you ought discover! But using deductive logic as a model of reality, by itself, is a terrible idea.
Dorky - I think Xunzian has covered all the bases here, but that has never stopped me before.
In general, the usefulness of science is not affected by Hume. The usefulness of science is usually judged by the results, and the technology provided by science speaks for itself.
There is nothing unreasonable about a brand new Maserati, except maybe its price.
Use either as you see fit. Deductive reasoning provides proofs, and inductive reasoning provides probabilities.
As for your first 2 questions, the induction problem does not involve science whatsoever. The inductive reasoning problem is an argument based upon pure discursive reasoning.
The ‘solution’ to Hume was to go with sensory experience and not pure reasoning, which we otherwise refer to as empirical evidence.
I see no problem with deductive reasoning as long as the claims are qualified.
Inductive reasoning takes a specific case, or cases, and derives a general rule. It derives logical conclusions from premises known or assumed to be true from observations in order to make said generalized rules.
Deductive reasoning takes a general instance or case and reasons by tracing connections to arrive at specific cases.
Because of this, deduction can be used to test Induction by taking the inductive conclusion and applying it elsewhere deductively.
In general, Deduction uses accepted truth’s for the premises, while Induction uses possibles as premises and only requires the inferred conclusion to be true so that the confirmed conclusion remains probable.
If, however, the inferred conclusion is false, then the inductive confirmed conclusion is exactly false.
Given that the common Inductive inferred conclusion is borrowed from something that has already been deduced or tested by deduction (even if after being inferred), it’s not directly wrong to say that deduction provides proofs and induction provides probabilities.
That would be relevant if the thread wasn’t about science and was about logical reasoning. I think some people in this forum may wish to examine the difference between discursive logic and empirical method.
Proofs require axioms. I’m not aware of many “scientific axioms.”
It doesn’t affect the usefulness of science at all. Science is as useful as it’s always been. It does affect our understanding of science’s usefulness though (which is probably what you mean). It use to be thought that science is useful for uncovering the nature of our world and the manner (or the laws) by which it works. Hume showed that science couldn’t possibly do this (at least not deductively). It only provides the data. An extra step is needed to draw conclusions about the way the world works, and that is human inference, and even then, this inference is necessarily inductive. This doesn’t mean such inferences are doomed to falsehood, nor that science is absolutely useless - only that we’re making a subtle leap of faith when we invest in it. Science, in other words, may still be invaluably useful, but we can’t prove it conclusively.
I believe the latter (depending on what the ‘two propositions’ are - induction and deduction?). Of course, if we don’t have infallible reason to invest absolute trust in science, this may seem a major blow to its reasonableness. But it’s really a blow to our faith in deductive reasoning - at least, to our faith that the scope of deductive reasoning covers science and the objects of its study. There is still reason in using science, but we have to face the implications of Hume’s philosophy: that these reasons are not that science is a deductive method of inquiry. What other reasons are there? For one thing, Hume’s skepticism is not a proof that causation is only a fabrication of our making, nor that a good statistical track record can’t be extrapolated into the future. It would be foolhearty to deny such possibilities just because we can’t prove them. That would be like saying that one can feel free to jump off a 10 story building because he can’t prove that he’ll fall despite the lack of evidence that anything ever defied gravity in the past.
As far as I’m concerned, deductive reasoning has only proven useful (that is, guaranteed to work) in the realm of abstract thinking, and even then only in mathematics and formal logic. You don’t get quite the same absolute guarantee when applying it to the real world.
That last point is a monumental insight (I think) on Hume’s part. Before Hume, it was quite fashionable in philosophy to take human reason to be the gateway into the discovery of truths about the actual world - as if one could take his observations and deductively conclude far-reaching implication also about the actual world. Hume showed that regardless of the state of the world at any point in time - that is, regardless of one’s observations - nothing can be deduced about past, future, or co-present states. This was a major blow to the rationalists who thought ‘first principles’ had priority in the persuit of truth over empirical methods. Hume still left them their abstract endeavors, such as math and logic, but these now seemed all the more useless if they couldn’t be applied deductively to the real world.
But science, math, logic, and even certain themes in philosophy got on with the job anyway. Is this a testamony to some other use, some other rational, underlying their application? Or is it a testamony to human nature? That is, do we carry on with these enterprises despite Hume’s skepticism only because that’s just what we do? And if it is, could that be reason enough to suppose there is some use to it after all? Isn’t our nature useful for something? For our survival?
Let me retry this. Hume’s entire point about the induction problem is pure reasoning, especially via inductive method, can lead one to false conclusions. Hume is the one who is indicting this form of “pure reasoning.”
And no, science is not a fan of discursive logic, its a fan of sensory experience which is why Hume is considered the founder of empiricism and gave Kant a hissy fit about uniting logical reasoning with physical / perceived / experienced reality.
Science may infer in its logic with regards to data from time to time, but I’m not aware of any valid argument that the modern form of the method or the arguments based from empirical research as for being inductive.
If you do, I’d like for you to tell me why Karl Popper is incorrect.
Whether or not deductive logic works in math is irrelevant to sensory experience.
It’s actually uncontroversially correct. You don’t even have to have read Hume to know this. I’ll betcha a zillion bucks that something like this can be found in any enclyclopedia.
I accept your bet, show me the empirical evidence of your claim. I have a zillion dollars in my pocket and I’ll happily forward it to you if you can support your claim.
And then I’ll probably still have to explain to you the difference between a necessary and sufficient connection… lol