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Deductive and Inductive Reasoning and Their Connection:
edited 1st Feb '12 11:18:18 AM by abstractematics
Is that cake frosting?I think that you can define probability theory, use a Dutch Book Argument to prove, formally, that, under certain conditions, it is the correct way to estimate the probability of an event given a set of data, and then use deductive reasoning, starting from Kolmogorov's Axioms, to draw conclusions about inductive reasoning. One problem of this is that probability theory does not give you a prior — that is a starting probability estimate. One could "solve" this and use a Solomonoff probability distribution* for that, and prove that this choice will be the best one, up to a multiplicative constant. That's a fun and interesting idea, but up to a multiplicative constant, I am taller than the Empire State Building — unless you can keep this constant down in some way (I personally know of no way of doing that, but I am no specialist), using a Solomonoff distribution is not necessarily the best choice.
But they seem to know where they are going, the ones who walk away from Omelas.
edited 1st Feb '12 11:18:12 AM by abstractematics
I changed accounts.In sociology, we generally consider deductive reason to be more solid, scientifically-speaking, but inductive reason occurs more often because it's easier to look for social patterns and then ask "why" than to look for individual actions and try to say they make up some greater whole...
Inductive reasoning has a more general scope and can do more, but it's not rigorous. But I'm arguing that they're not really two distinct methods after all. I apologize if the essay I just finished is long, but I wanted to get the full explanation across.
I changed accounts.Oh, yeah, no, they're not distinct at all. In Sociology 101 we learned them as a cyclical formation, not different patterns of study. I'm not sure where you got the idea that they're separate in the first place. It's only a matter of where you enter the cycle for study...
They're treated distinctly because one is about arriving at conclusions that must follow from premises, while the other is about probable extrapolation.
I changed accounts.Well, it doesn't have to follow the premises. If it doesn't, you just modify the hypothesis, or, it's been invalidated. I mean, they're distinct in that they're different methodologies, but in the end you will end up using both, so, it's a circle, not a pair of parallel lines...
Just because you use two different things in cooperation doesn't mean they're the same. That was what I was trying to say above. And I'm talking about validity. If the premises are true and the argument is correctly structured, the conclusion follows. The question is of course whether the premises are true.
edited 1st Oct '11 9:37:30 PM by abstractematics
I changed accounts.I guess it's different for math, because there usually aren't so many variables, or at least, not in the theoretical maths. For sociology, there are tons of different things that could be affecting the correlations, so when you finally get to a large theory from the small particulars, you have to go back down again to find more particulars...
I'm not talking about the particular discipline of sociology. Even if you had a thousand factors, if they're true, then a valid argument would lead to a conclusion that follows from those factors. A big if.
I changed accounts.Bleh... in the end, the basics are the same. I guess I should say that I didn't really mean that they're the same, so much as that they're different versions of a similar principle, and, really, reversals of each other. So, basically, Exactly What It Says on the Tin...
DUMBWhat would be a case where the inductive hypothesis was proved in a science? I can't think of any.*
edited 1st Feb '12 11:18:25 AM by abstractematics
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