The Fallacy of Logic

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• 323
I'd rather put it this way. One modern view of logic boils down to: logic is really just using symbols consistently in some symbol-shuffling game (or algorithm: recipe for symbol-shuffling). In this sense, logic is thought of as pure syntax, intrinsically detached from semantics (or the "interpretation" of those symbols, which makes the symbols stand for things in the world).

In that case, it's just happenstance that some dreamed-up algorithm happens to fit reality.

But then a lot of people go an illegitimate further step, and think that means logic isn't inherent in nature, isn't bundled into semantics.

But if a dreamed-up algorithm fits reality,it really fits. i.e. nature really, objectively hasthat particular pattern. So in fact, the syntax of logical statements that do happen to actually describe the world is derived from semantics (which is another way of saying what the later Wittgenstein was banging on about, the sort of thing Sime talks about above). Even though we can extend logic and play with patterns that are divorced from anything real, the starting point is the logic of the middle-sized furniture of the world that we commonly interact with from birth - just the standard logic. What logically follows from what depends on the nature of the things being symbolized.

The upshot is that you can't demonstrate the validity of logic in general (because logic is just dreamed-up consistent play patterns that may or may not fit some reality). But for any given logic that does fit the world as we find it, the world as we find it necessarily has that logic, that nature, that flow, that grain.

However, of course while that's obvious in principle, in practice, since the scope of our knowledge is limited, there may be any number of unknown factors that could make our deduction wrong, unbeknownst to us.

And this is really what makes the difference between induction and deduction. Induction isn't actually any different from deduction - rather, it's deduction that's aware of knowledge limitations, hence it's expressed in terms of probabilities. Induction is the punting of a specific nature or identity for experience, then the deducing of necessary conclusions (for experience) from that nature or identity. This is the process of science, in essence - we think up a possible character for things, and see if experience bears out the logical implications of the character we've posited for the things. But because of knowledge limitations, we have to hedge our bets ("all things being equal", "presuming no confounding factors", "it is probable/possible/likely that ..." etc.).

Just one final thought: it's unproblematic to think of logic as innate to some degree. It's pretty obvious that we bootstrap ourselves all the way from childhood into adult knowledge not from a pure blank slate position, but from an innate understanding of some basic logical primitives. However, that understanding has to be drawn out from us (in the Platonic sense of anamnesis), it's not in front of us reflectively from infancy, rather it's just innate in the way we act from infancy (e.g. reaching out expecting to touch something), and comes to conscious reflection as a result of interaction with the world. (Rather analogous to the way genes are expressed in the phenotype, in fact.)
• 2.7k
Yes, except
...and our intentions...sime
happens too fast.

It's not clear that bringing intent into the discussion helps; why not stop at behaviour?

If I accelerate towards a red light, but my car stalls so that I stop at the light, haven't I obeyed the traffic rule despite my intent?
• 2.3k
n that case, it's just happenstance that some dreamed-up algorithm happens to fit reality.

Speaking for myself, I think logic is derived from the world outside. I've read a few books on logic and all of them make a similar point - that logic is essentially about finding truths about the world. Isn't it obvious then that our logic (its structure) must mirror the structure of reality itself? I don't think this is "just happenstance".

Just one final thought: it's unproblematic to think of logic as innate to some degree.

I agree but here too I believe evolution has played a part. From all the different possible brain structures only those that conform to the rules of the world have been selected. All the other types of brain structures, with logical components that didn't reflect the world's structure, were culled.
• 2.3k
Why not?

Also, where did "mustn't" come from?

It's my understanding that any logical system developed must be useful in the sense that it can find truths about the world. I agree that we can arbitrarily choose the axioms of a logical system BUT the systems with axioms that lead to nothing must be discarded. Right?
• 323
Isn't it obvious then that our logic (its structure) must mirror the structure of reality itself? I don't think this is "just happenstance".

What I'm saying is that even if the fit between our dreamed up logical puzzle games and reality is happenstance, if we find one that fits, then the fact that the puzzle structure came from our side doesn't in and of itself mean that nature doesn't actually have that structure. Indeed, if the structure fits reality, that's prima facie evidence that reality has that structure, that it objectively has it, that the structure is "out there" in the world.
• 2.7k
I don't see why. Logic is just bunches of symbols matched up according to rules. It's a game.

If every now and then a logical system is useful, so much the better.
• 2.3k
I don't see why. Logic is just bunches of symbols matched up according to rules. It's a game.

If every now and then a logical system is useful, so much the better.

But a game can't be played before we've learned the rules.
• 2.7k
Unless the game is inventing the rules.
• 2.3k
Unless the game is inventing the rules.

Yes.
• 269
That said, when we investigate logic itself, we find we're immediately involved in a circular argument. Simply put, we need proof that logic is the best mode of thinking but thinking this way presupposes that logic is the best mode of thinking. Note that we're looking for a deductive proof that logic is the best mode of thinking.

Why would we need to presuppose that? For one, logic is *not* a mode of thinking, that's silly. Logic refers to a theory of logical consequence, that is, a theory of what follows from what. In other words, when some things are true, it appears other truths can be derived from it. E.g. If it's raining, then there are clouds in the sky. It's raining. Therefore there are clouds in the sky. No thinking is needed here, as computers (which are not sentient) operate according to the rules of (essentially) classical propositional logic. And really, if logic were simply a mode of thinking, what logic do we think in accordance with? If anything, it's an extremely weak logic that can hardly derive very much unless we force ourselves to adhere to and specific set of inference rules (because we often have inconsistencies in what we think, meaning we cannot reason via classical logic because of the law of explosion).

So, how does one get out of this predicament, The Fallacy of Logic?

Logic is not innate to the mind. We have to learn it. From where? From the external world. We learn the rules of logic by observing the world. Deductive logic works fine at the macroscopic level. In our everyday lives we never see violations of logical principles and deductive and inductive logic work well.

I've heard that this isn't the case at the quantum level. I believe there are many situations where contradictions (a no-no in logic) arise. For such experiences we need a different kind of logic - something that accomodates the ''strange'' behavior of quantum objects.

This is just wrong and I wish people would stop saying it. Quantum mechanics is a consistent theory, it doesn't portray an inconsistent quantum realm (unless you're Newton da Costa). Quantum physicists use the standard mathematical formalism (ZFC + classical logic) so it's necessarily consistent since otherwise trivialism would follow. Quantum logic is a separate logical system, but that logic only discharges the Distribution Axiom, not the Law of Non-contradiction.

This isn't a logic specific problem at all, it's just a broad epistemological issue. One simply picks their logic in accordance with a model of theory choice (logical systems are competing theories about logical consequence after all) and proceeds to do their work from there. Not everything needs to be justified so this is not an interesting problem to me.
• 2.3k
(Y) Thanks
• 76
Once one starts dictating what constitutes logic one is moving away from rather than towards that which constitutes being logical. That which is logical, first to be considered as being logical,, cannot exist as a state of detached thinking in its own right, it has to be shared by a majority of the population. There is no such thing as independent of perception logic. That which is may fall outside of perception, and then it can demand for more than mere logic to take you there. One can argue logic, prove ones communication skills, and their ability to borrow and steal others thoughts,but none of this is philosophy, either one has good instinct for both producing and recognizing that which is or one does not, its that simple. Brief is always best in philosophy, not in those other areas, but most definitely in philosophy, it is an instinct. Arguments and counter arguments have no place here because they have no end.. Without this instinct and beyond the mental exercise so called philosophy is a total waste of effort, arguments being infinite. The obstacle is big brains, big egos, and big mortgages, but with no natural instinct, and also of course the whole institution around philosophy.
• 38
This is just wrong and I wish people would stop saying it.
But it fits so well with so many, ummm, "theories".
• 269
Once one starts dictating what constitutes logic one is moving away from rather than towards that which constitutes being logical. That which is logical, first to be considered as being logical,, cannot exist as a state of detached thinking in its own right, it has to be shared by a majority of the population. There is no such thing as independent of perception logic. That which is may fall outside of perception, and then it can demand for more than mere logic to take you there. One can argue logic, prove ones communication skills, and their ability to borrow and steal others thoughts,but none of this is philosophy, either one has good instinct for both producing and recognizing that which is or one does not, its that simple. Brief is always best in philosophy, not in those other areas, but most definitely in philosophy, it is an instinct. Arguments and counter arguments have no place here because they have no end.. Without this instinct and beyond the mental exercise so called philosophy is a total waste of effort, arguments being infinite. The obstacle is big brains, big egos, and big mortgages, but with no natural instinct, and also of course the whole institution around philosophy.

I swear you sound like a computer generated message.
• 76
Those furthest from the instinct tend to the longest argument, because the argument is the very next best thing. Those with least natural ability require a degree,.such that their denial can never again see the light of day..
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