Justify induction through deduction or by making an ampliative inference NOW anon.
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Justify induction through deduction or by making an ampliative inference NOW anon.
Deduction is actually only valid because of induction.
Deduction can be completely formalized in formal logic. Formal logic is just a collection of rules for manipulating symbols. The "validity" a deduction simply means it follows the rules of formal logic. But this is completely meaningless because we have no idea of how those rules relate to reality. So if we want to say anything about reality rather than remaining within merely a hypothetical mathematical realm, we have to extend the concept of validity and say what makes the rules themselves "valid." But a rule is "valid" if it works, and the only domain in which it could work is empirical reality. So we have to empirically infer that the rules work, e.g. if I know something is true, and I manipulate symbols according to rules to produce another statement, and then I later find out that statement is true every time, then I know those rules I used are "valid."
This is obvious if you think about it from another angle. Deductive reasoning is something that goes on in our brain. But at a certain point in evolution we never did deductive reasoning. Evolution occurs through habit formation, induction as the formation of concepts is merely a type of habit formation. So deduction was involved and therefore only exists because of habit. How could deduction be valid but induction invalid?
It sounds like you just cut off a path to justifying induction. If you can't justify induction through deduction, you're left with using induction to demonstrate induction, which is circular.
What deduction has going for it is that the implications appear certain by virtue of considering the relation of ideas, however deduction alone does not get you far.
>If it works, it works. Simple as
It worked in the past, perhaps, but does past success guarantee future success?
Correct, obviously induction cannot be "justified" because justification is a concept of reason and all reason is founded on induction.You're really not saying anything when you say you can't "justify" induction. No system can step outside of itself, there has to be something beyond it, in this case what is beyond induction is simply reality. Reality forces you to use induction because otherwise your brain could not do anything, it could not construct your visual perception or any of your sense perceptions let alone form higher inferences. Induction is simply a fact.
I mean, it's like criticizing Leibniz because he can't "justify" non contradiction. No fricking shit he can't, you have to have non contradiction in the first place.
Problem with this response is that at least with deduction, it is impossible for us to conceive of how a bachelor could be married, because that contradicts the very notion of a bachelor. It is clear and present in the mind that this cannot be the case. On the other hand with induction, we can clearly conceive how induction could be extremely mistaken, and the best we can say is that despite being able to conceive how induction could be totally wrong, we'll persist believing in it anyway. This makes us seem more like irrational creatures of habit and instinct than enlightened beings.
You can conceive of how a bachelor could be married. Simply combine the concepts of "bachelor" and "married" in your mind. You only think it is impossible because you have a closed mind and don't put enough effort into it. You constantly imagine contradictory things in your dreams, you just have to short circuit the normal workings of your mind.
Also, Hume is wrong. Mathematics requires more than merely reasoning from definitions. All foundations of mathematics require existence axioms and other axioms like the axiom of infinity that are not mere definitions. We can suspect that the axiom of infinity in Principia Mathematica can be false, yet if you look at any of the consequences of it you would say that it is "impossible" to conceive of them being false.
Also, if the validity of deduction has induction as a basis, than if it were impossible to imagine deduction being invalid it also follows that it is impossible to imagine induction is invalid, since induction being invalid would imply deduction is invalid.
>You can conceive of how a bachelor could be married. Simply combine the concepts of "bachelor" and "married" in your mind.
I actually can't. If you tell me to imagine a married bachelor, my mind seems to reject this. If I think it makes sense to me, I ask "if being unmarried is a condition for being a bachelor, how does it make sense that this bachelor is married?" And I'm back to having the impression that I am considering nonsense. I could only pretend to apprehend what that means by quieting these mental objections, but then I doubt that I actually assenting to anything I can comprehend. More like a mother who just nods at her child while busy on her phone than someone agreeing with a proposition.
Unusual things happen in dreams, but I never come to believe P & not P in a dream.
This would go beyond Hume. But I am a fictionalist about mathematics. Insofar as it is true, it is true like it is true that Hermoine Granger was born of muggles. It just so happens that mathematics is a very useful fiction that can sometimes correspond to reality.
>Also, if the validity of deduction has induction as a basis, than if it were impossible to imagine deduction being invalid it also follows that it is impossible to imagine induction is invalid, since induction being invalid would imply deduction is invalid.
Experience tells me I can easily doubt induction but I can't easily doubt deduction.
>and as I said, there is something beyond reason, there was a time when reason did not exist. This is called reality. reality itself is irrational. things happen spontaneously and evolve into patterns because of their own arbitrary choices.
I wouldn't call reality rational or irrational. It's a property of thought processes. Reality is what it is.
How would you think about the epistemic validity of induction if it can't be proven and it's so easy to conceive of it being not the case? Are we just going off an instinct/habit we have no clue actually works to get at the truth, or is it probably the case that there's something to our inclination towards induction leading us to increasingly better approximations of the truth?
>Simply combine the concepts of "bachelor" and "married" in your mind.
You can claim to imagine a square circle but one cannot exist based on the definition of a circle.
>This makes us seem more like irrational
and as I said, there is something beyond reason, there was a time when reason did not exist. This is called reality. reality itself is irrational. things happen spontaneously and evolve into patterns because of their own arbitrary choices.
>Problem with this response is that at least with deduction, it is impossible for us to conceive of how a bachelor could be married, because that contradicts the very notion of a bachelor.
There are whole logics built around denying the law of excluded middle. There are even some logics that deny non-contradiction and avoid the principle of explosion in other ways. You lack imagination.
>On the other hand with induction, we can clearly conceive how induction could be extremely mistaken, and the best we can say is that despite being able to conceive how induction could be totally wrong, we'll persist believing in it anyway
Binary truth and falsehood are necessary simplifications, but they are simplifications nevertheless. In reality, it's about being "more true" or "more false" and iterating towards being more true than before.
You just need to look at the entire history of mathematics to understand that. ZFC didn't completely invalidate naive set theory, nor did Lebesgue integration invalidate Riemann. The work before may have been false under a binary standard, but they held true when restricted to relevant areas.
> It worked in the past, perhaps, but does past success guarantee future success?
obviously not. Life is an experiment. The future is unknown. That’s just the way it is
>justify
natural selection justifies everything. If it works, it works. Simple as.
Even if you somehow accepted the form of a deductive argument as objectively true (which is already unjustified as the other anon said) you still have your premises and no premise is absolutely certain to be true.
Even the classic example of "All me are mortal, Socrates is a man, therefore Socrates is mortal" isn't 100% certain, maybe through a freak mutation an immortal man can be born, or maybe Socrates was actually an alien or a demigod.
Am I obliged?
I’d prefer not to
https://www.lesswrong.com/posts/zmSuDDFE4dicqd4Hg/you-only-need-faith-in-two-things
>You only need faith in two things: That "induction works" has a non-super-exponentially-tiny prior probability, and that some single large ordinal is well-ordered. Anything else worth believing in is a deductive consequence of one or both.
>(Because being exposed to ordered sensory data will rapidly promote the hypothesis that induction works, even if you started by assigning it very tiny prior probability, so long as that prior probability is not super-exponentially tiny. Then induction on sensory data gives you all empirical facts worth believing in. Believing that a mathematical system has a model usually corresponds to believing that a certain computable ordinal is well-ordered (the proof-theoretic ordinal of that system), and large ordinals imply the well-orderedness of all smaller ordinals. So if you assign non-tiny prior probability to the idea that induction might work, and you believe in the well-orderedness of a single sufficiently large computable ordinal, all of empirical science, and all of the math you will actually believe in, will follow without any further need for faith.)
>(The reason why you need faith for the first case is that although the fact that induction works can be readily observed, there is also some anti-inductive prior which says, 'Well, but since induction has worked all those previous times, it'll probably fail next time!' and 'Anti-induction is bound to work next time, since it's never worked before!' Since anti-induction objectively gets a far lower Bayes-score on any ordered sequence and is then demoted by the logical operation of Bayesian updating, to favor induction over anti-induction it is not necessary to start out believing that induction works better than anti-induction, it is only necessary *not* to start out by being *perfectly* confident that induction won't work.)
A hypothesis that you might give equal prior credence to the hypothesis that induction works is that induction will work until May 1st, 2024. Applying Bayes rule, P(H|E) = P(E|H)*P(H)/P(E) where H is the hypothesis and E is the evidence. Through every step, the probability of our evidence given our hypothesis was the same as the inductive hypothesis, and the probability of the evidence is a constant factor. So using Bayes rule and just starting with equal priors, we conclude that it's equally likely that induction stops working on May 1st, 2024 as it will always work for all time, because the evidence for both is just as good. So while the probability of induction may go up over time, other alternative hypotheses have also been mounting up the exact same amount of evidence.
This was not to mention that Bayesian epistemology is controversial and suffers from problems like the problem of old evidence and the problem of new theories, and that there's no clear reason to suppose that your beliefs making you susceptible to a dutch should provide a generalized basis for conforming to the laws of probability generality for subjective degrees of confidence.
susceptible to a dutch book*
I'm afraid there are no necessary connexions, Mr Hume