...logic apparently was "inescapable" because reality is logical...Usually this is described logic being part of the "fabric" of reality (whatever that means). — MindForged
But then I suppose this gets us back to the issue with there being all sorts of different algebraic logics (Boolean algebra, Heytin algebra, etc.), and we even know that some Non-Classical Logics can be constructed purely within their own meta-theory (e.g. Paraconsistent semantics). — MindForged
In what sense is logic supposed to be fundamental to reality? — MindForged
In what sense is logic supposed to be fundamental to reality? Obviously it's not supposed to be some purely empirical matter (e.g. go find a logical object), since while logic can be thought of in several ways (norms of argumentation, study of formal languages, theories of logical consequence, etc.) it's not supposed to be about anything in particular. — MindForged
Is Logic "Fundamental" to Reality?
A good observation. You must be referring to a hyper-classical school of thought. I'm not sure if they necessarily wanted to mechanize reality. Their tendency is towards determinism but, perhaps, with exuberance (and here now I am sympathetic) logic was thrown in for good measure.logic apparently was "inescapable" because reality is logical. — MindForged
But I should add that, though logic isn't fundamental to Reality, it's fundamental to metaphysical-reality, and is what what-metaphysically-is is constructed of. — Michael Ossipoff
I'm a logical pluralist of some sort — MindForged
The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve. We should be grateful for it and hope that it will remain valid in future research and that it will extend, for better or for worse, to our pleasure, even though perhaps also to our bafflement, to wide branches of learning. — Eugene Wigner
Logic (and mathematics) sets out how we can use words and other symbols. It's groups of grammatical rules. Yep, there are lots of different logics. It should not be a surprise that the one we worked out first works well in our everyday experience.
Geometry started with Euclid; that's the geometry best for building and dividing blocks of land. Non-Euclidian geometries were a fun exercise for mathematicians until General Relativity. Now we use it to make our GPS work.
We choose the grammar for the job at hand, just like we choose an axe or a saw.
In another sense there seems to be something built into the universe that lends itself to logic or mathematics. I would think that any possible universe is governed by rules, and by rules that have some consistency, at least generally. I would say that for any possible universe there are fundamental rules or laws that allow us to use logic to describe that universe. One could also argue that the fundamental rules or laws that govern any universe, IS the logic that's part of the reality of that universe. So maybe in that sense one could argue that logic is fundamental to any possible universe. It's hard to see how this wouldn't be the case.
Logic is fundamental to reality in the sense that every object in reality is what it is and is not what it is not. In other words, every object in reality is identical to itself and different from other objects. And when the identity and difference of objects is established, all propositions about them are logically consistent. This is basically the law of identity or non-contradiction. Without this law, reality would be absurd and even the difference between existence and non-existence would be erazed. I have no idea what that would mean.
Even the logic systems that relax the law of non-contradiction in certain situations, like the paraconsistent logic, would not work without the law of non-contradiction - because they need to specify - non-contradictorily! - how the law of non-contradiction is relaxed. They just seem to block the spreading of contradictions to other parts of an information system to save the whole system from becoming worthless. If they completely abandoned the law of non-contradiction they would be worthless because they would automatically negate whatever claim they would make.
There are known systems of logic which lack the Principle of Identity or even change the law itself. — MindForged
Well this is just false.The way that (dialetheic) paraconsistent logics deny the Law of Non-contradiction is simple. They merely give a case wherein there is a proposition which is true and its negation is true. — MindForged
Do they say that an object is not what it is? That an object is not identical to itself?
(I can forward this paper if you can't get it from sci-hub)"Quantum mechanics raises some ontological issues which are hard to deal with in simple terms. More than one of those issues concern the relationship between quantum mechanics and logic, and here we shall be dealing with a particular aspect of one such logical problem. We begin by recalling the infamous Problem of the Identical Particles. According to a widely held interpretation of non-relativistic quantum mechanics, there are many situations in which one cannot distinguish particles of the same kind; they seem to be absolutely indiscernible and that is not simply a reflection of epistemological deficiencies. That is, the problem, according to this interpretation, is seen as an ontological one, and the mentioned indiscernibility prompted some physicists and philosophers alike to claim that quantum particles had "lost their identity", in the precise sense that quantum entities would not be individuals: they would have no identity. Entities without identity such as quantum particles (under this hypothesis) were claimed to be non-individuals."
-"Classical Logic or Non-Reflexive Logic? A case of Semantic Underdetermination" — Krause & da Costa
And do they say that it is true that there is such a case? If so, then they are employing the law of non-contradiction.
Personally, I think this sentence sums up the confusion perfectly. Logic is reified into "something" as a class itself, then applied to another class of things which then act as properties of "reality".In what sense is logic supposed to be fundamental to reality? — MindForged
"Reality", as I take it to mean here, is the sum total of what there is and how it all interacts. To state there is something "fundamental to reality" creates a false distinction - for how can one part of "reality" be fundamental and another part be secondary for "reality"?
That is not the principle of identity. The POI says that for every "x", x stands in a symmetrical, transitive and reflexive relation with itself. — MindForged
To restrict the domain of application of the POI means that the objects is question are metaphysically (not epistemically) indistinguishable. — MindForged
"This sentence is false." — MindForged
By the principle of identity I mean that an object is identical to itself: that it is what it is. That's what this principle has meant since ancient Greece:
https://en.wikipedia.org/wiki/Law_of_identity
When you violate this principle of identity you also automatically commit a contradiction and when you commit a contradiction you automatically violate this principle of identity: you say that object X is not object X, or: "Object X has property P" AND "Object X does not have property P".
If two objects are metaphysically indistinguishable then they are one and the same object. Can two electrons in quantum mechanics be distinguished? Well it seems they can; they can be distinguished by at least one of their properties - by their position in space. It also depends on how you define "electron".
I don't claim you can't utter contradictions like this one. But contradictory sentences don't correspond to any object in reality. They are just a string of words that doesn't correspond to anything in reality. They have no meaning.
And do they say that it is true that there is such a case? If so, then they are employing the law of non-contradiction. — litewave
Ah, well I'm not much of a one for either of them as stylists.Well, if Harry Potter were written well...
My taste leans towards Tolkien — Banno
contradictory sentences don't correspond to any object in reality. — litewave
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