Logic and language

#1
Logic derives from language to the extent that all logic is about propositions and the relationships between propositions. Seems like a harmless and obvious enough fact. But if logic is a construct of language, much as say grammar or rhetoric or belief is too, how does it apply to the real physical world of non-logically related components? I mean really. Do we seriously think the mere existence of objects in a universe have anything like a logical necessity to them? No. Innumerable universes are conceivable without the existence of any given physical object. There is no inherent logic to reality. It just happens as it does, and even if it happens according to laws and principles, that still doesn't mean it is logical. There is iow no imperative that naturalistically ordered events occur in all possible universes. The laws of nature that apply to our own particular universe do not necessarily apply to all possible universes. How then does this order between propositions and statements called logic pertain to the physical world, to the extent that we can infer facts and events before we even know about them? More specifically, how do the rules for what follow from given statements pertain to what follows from given facts and events. Unless...facts and events are also language constructs?
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#2
(Feb 21, 2016 12:51 AM)Magical Realist Wrote: Logic derives from language to the extent that all logic is about propositions and the relationships between propositions.


In that succinct generic placeholders can replace word / statement examples expressing a proper template for reasoning, the classic "language" version of logic can be reduced to symbol manipulation systems (as happened in the 20th century, and mathematics far earlier). If there are multiple "games" of logic [quote at very bottom], then the common property they would still have is adherence to the rules of each particular approach and maintaining throughout its usage the correct identities of the invariant elements, conventions and relationships. [Consistency; coherence.]

Quote:Seems like a harmless and obvious enough fact. But if logic is a construct of language, much as say grammar or rhetoric or belief is too, how does it apply to the real physical world of non-logically related components? I mean really. Do we seriously think the mere existence of objects in a universe have anything like a logical necessity to them? No. Innumerable universes are conceivable without the existence of any given physical object. There is no inherent logic to reality. It just happens as it does, and even if it happens according to laws and principles, that still doesn't mean it is logical. There is iow no imperative that naturalistically ordered events occur in all possible universes. The laws of nature that apply to our own particular universe do not necessarily apply to all possible universes. How then does this order between propositions and statements called logic pertain to the physical world, to the extent that we can infer facts and events before we even know about them? More specifically, how do the rules for what follow from given statements pertain to what follows from given facts and events. Unless...facts and events are also language constructs?

Perfectly true conclusions require the input of perfectly true / accurate premises, which we don't have except for those defined or set as true (those given a strict, immutable identity by an invented system). Thus the Einstein clichè: "Insofar as mathematics is exact, it does not apply to reality; and insofar as mathematics applies to reality, it is not exact."

Deductive logic only repackages the information contained in the premises. It doesn't introduce new knowledge about the world, apart from maybe exhuming something already contained in the existing knowledge or suggesting new applications via the reformulation of the original content.

Scientists output proximate or potentially mutable truths by several creative processes grouped under "induction". Though attempts have been made to express induction as a consensus-accepted set of rules (make it a fully non-ambiguous type of inference), the efforts have long been criticized, doubted, rejected. But the practices are by no means non-useful, as ably demonstrated by science.

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Topos theory may be able to incorporate this murky quantum logic. It underlies the laws of mathematics and logic that we use, and is more fundamental than either, the physicists argue. Each topos describes a different "mathematical universe," with its own mathematical constructions and logic. And each topos can be used as a different lens through which to view the world, depending on requirements.

Isham and colleagues have identified a topos in which quantum theory appears to make logical sense—as long as you embrace a new type of logic, in which "true" and "false" are no longer your only options. There are now multiple shades in between. A different topos recreates classical reality with its firm "yes" and "no" answers. Isham and Döring believe that every physical system, from atomic particles to the universe as a whole, can be viewed through different topoi.

"In a sense, using a topos is changing the whole of mathematics," says Döring. "One chooses a ’mathematical universe’ in which to argue."
http://fqxi.org/community/articles/display/125
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#3
Quote:In that succinct generic placeholders can replace word / statement examples expressing a proper template for reasoning, the classic "language" version of logic can be reduced to symbol manipulation systems (as happened in the 20th century, and mathematics far earlier). If there are multiple "games" of logic [quote at very bottom], then the common property they would still have is adherence to the rules of each particular approach and maintaining throughout its usage the correct identities of the invariant elements, conventions and relationships. [Consistency; coherence.]

That symbols can be structured according to set rules that somehow apply to physical reality seems nothing short of magic to me. These rules are surely nothing we learned from experience. Their self-evidence is grasped thru their coherence in a self-referring system, much as mathematics is, not thru any correspondence to an empiricle state of affairs.
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#4
(Feb 21, 2016 12:51 AM)Magical Realist Wrote: Logic derives from language to the extent that all logic is about propositions and the relationships between propositions.

Or at least propositional logic is. I'm less confident that predicate, tense or modal logics are.

Quote:Seems like a harmless and obvious enough fact. But if logic is a construct of language, much as say grammar or rhetoric or belief is too, how does it apply to the real physical world of non-logically related components?

Nobody knows. It's one of the outstanding problems of metaphysics.

I'm inclined to say that there's an isomorphism (a similarity or identity of form) between the logic of human language and concepts, and the logic displayed by the physical world.  

Quote:Do we seriously think the mere existence of objects in a universe have anything like a logical necessity to them?

That's part of what motivates my minor skepticism about theoretical physics. Why are we be so certain that a proof scrawled on a physics classroom chalkboard corresponds to necessary relationships in the real world?

Quote:There is no inherent logic to reality. It just happens as it does, and even if it happens according to laws and principles, that still doesn't mean it is logical.

I'm not sure what you mean by that. If things happen in accordance with laws and principles that seem to adhere to logic, then reality would seem to be logical in some sense. So I would say that reality does display an inherent logic.

But... if you are saying that there needn't be any necessity to it, of the sort that we attribute to logic, I'm more inclined to entertain that idea. (My skepticism expressed above.)

Quote:There is iow no imperative that naturalistically ordered events occur in all possible universes.

I'm inclined to agree.

Quote:The laws of nature that apply to our own particular universe do not necessarily apply to all possible universes.

Ok.

Quote:How then does this order between propositions and statements called logic pertain to the physical world, to the extent that we can infer facts and events before we even know about them?

Because the patterns of thinking that human beings (and other animals) presumably emerged from the logical behavior of neurons in this particular universe. Not only that, our modes of thinking presumably evolved so as to model (however imperfectly) the behavior of that universe. The better we can do that, the more survival value it has.

Quote:More specifically, how do the rules for what follow from given statements pertain to what follows from given facts and events. Unless...facts and events are also language constructs?

I don't want to embrace that strong idealist conclusion. No, no, no.

I'm more inclined to see us as biological organisms, and hence as parts of the physical world. So whatever principles apply in the physical world apply to us too. It only makes sense (to me anyway) that our cognition would have some relationship to how the physical world behaves. That doesn't mean that it's the only way that things could possibly be, in all possible worlds.
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#5
Quote:Because the patterns of thinking that human beings (and other animals) presumably emerged from the logical behavior of neurons in this particular universe. Not only that, our modes of thinking presumably evolved so as to model (however imperfectly) the behavior of that universe. The better we can do that, the more survival value it has.

Very plausible. It might also explain why reality is so..."languagable"..Language arose in the reality matrix, incorporating its rules of spacetime and acoustics and vision and atomicity and composite being and hierarchal order and life itself, into its own blood and sinew. It leaps up flopping on dry land, dripping and soaked in the cold lifegiving river water of physicality.
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