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I'm wondering if deduction is in the end based on induction.

The problem of induction discovered by the Scottish philosopher David Hume is quite well known. On the other hand, it's commonly supported that deduction can't be falsified by a set of facts in the same way as induction can.

Let's use as an induction example (A):

1) All the crows I've seen so far are black, 2) Mark is a crow, 3) Mark is black.

Even if (1) and (2) are true, (A) can be falsified by a not-black crow.

Let's use as a deduction example (B):

1) All the crows are black, 2) Mark is a crow, 3) Mark is black.

If (1) and (2) are true, theres' no fact that can falsify (3), a conclusion that we deduce from the first two premises.

Now let's suppose a very strange fact: in the whole universe the logic laws start to fail. For instance, the principle of non-contradiction doesn't work anymore, and in B Mark is and is not black. This fact is way more weirder than a white crow (that would invalidate A), but being weird or even unimaginable doesn't mean that it can't happen.

The (inconceivable) failure of the laws of logic can be considered like a fact that would invalidate any deduction? Or it's considered like an a priori impossibility (but why, since we can't foresee the future)?

(This question is related to this one).

  • This has already happened with Quantum Mech. See Double-slit experiment – Mauro ALLEGRANZA Jan 3 at 15:42
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    If we follow this approach, we can sat that logic is empirical; see H.Putnam, Is Logic Empirical?. But I do not think that this means that logic is "induction based"... – Mauro ALLEGRANZA Jan 3 at 15:56
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    The issue is tricky; you can consider Quine's holism : logic is the "core" of our complex network of theories and thus it is hard to imagine that we change logic in order to account for facts. Maybe we prefer to change out "theory of colors" and - under suitable circumstances - adopt the view that there is a peculiar species of ravens that is both black and not-black at the same time. – Mauro ALLEGRANZA Jan 3 at 17:31
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    I cannot grasp what's being asked. Are you suggesting that we use induction to determine that the laws of logic cannot break-down? – PeterJ Jan 4 at 10:53
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    @FrancescoD'Isa - Ah. Interesting question. You might have a point. Perhaps the answer depends on our world-view. If the universe is mind-created then it would never contravene the law of non-contradiction or the laws of mathematics, and this might be called deduction without induction. Not sure. I don't have a clear answer to suggest and might agree with you on this one. – PeterJ Jan 4 at 13:55
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Only if what genes do is induction...

There is a long history from theological arguments to Kant, of considering human logic an absolute limit on our thinking, perhaps inferior to the logic that may actually control the world, but the best we can relate to.

On a more modern level, logic does not appear to result from observation. Babies are given pause by a certain level of illogic -- they stare at anomalies longer than views that confirm deductions. It is an inborn emotional response.

Taking those seriously, it is quite possible that logic does not really work, but that the ways in which it fails are hidden from us. At a certain level of focus, we already know this, as Mauro points out above, quantum dynamics violates things like the Law of the Excluded Middle -- the photon shot at a double slit does not go through the left slot and it does not go through the right slot, yet it gets to the other side and acts as if it went through both.

Yet logic works in our everyday lives. Potentially this is only because we evolved to take advantage of the rules in our part of the universe, at our scale of expression. The reason that what is inconceivable doesn't happen may just be because we refuse to perceive what we cannot conceive.

This is not just a goofy 'deepity'. It is something that we need to take seriously at the quantum level and that may be quite relevant if we venture far from our original place in the universe.

If we really cannot make sense out of a world we are not born to, we may need to develop extremely complex coping mechanisms to explore far from home. It also questions things like astrophysics and the study of cosmology. If logic, and thus math, is local, why would we not expect our science to mislead us endlessly about a lot of things?

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The problem of induction discovered by the Scottish philosopher David Hume is quite well known.

Induction is allegedly a process that starts with observations, uses them to derive a theory and then shows the theory is true or probable or good or something similarly vague. The problem of induction is that such a process is impossible. Any set of observations is compatible with an infinite set of possible relationships between them. For example, if your first three observations of some quantity are 1,2,3 that series could continue as 4,5,6... or 3220145,12,-100... and there are many other possibilities. As such, no set of observations implies the truth of any particular theory about how the world works or about what you will observe in the future. If you had some observations and a particular theory of how the world works that might imply what will happen in the future, but that's what induction is supposed to give us. There are many other problems with induction as pointed out by Karl Popper, see the reading list here:

http://fallibleideas.com/books#popper

Popper provided an alternative to induction that can be used in reality. Knowledge is created by noticing problems, guessing solutions and eliminating solutions using criticism. Solutions aren't shown to be true or probably or good or anything like that. A solution is a guess that has either been refuted or not.

The laws of logic and mathematics, like all other knowledge, consist of guesses that have survived criticism. See "The Fabric of Reality" by David Deutsch chapter 10 for an explanation of this issue.

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