Syntactically: P v ~P
Semantically: Every sentence in the language is either true in the model or it is false in the model (where 'or' is the inclusive or; while the 'but not both' clause for exclusive or is demanded by the law of non-contradiction: ~(P & ~P)). — TonesInDeepFreeze
And how would you write down Wittgenstein's proposal that we should happily welcome contradictions in mathematics, syntactically and semantically? What sort of axiom would that translate into, in your opinion? — Olivier5
The question is, what kind of existence conceptual information has. — Wayfarer
But, the rationalist’s claims appear incompatible with an understanding of human beings as physical creatures whose capacities for learning are exhausted by our physical bodies.' — Wayfarer
What kind of existence does a material object have? A material existence. What kind of existence does conceptual information have? A conceptual existence. This is all just a matter of words as I see it. — Janus
The interesting thing is that materiality is already ‘conceptual’ through and through in that the very notion of an empirical object is a complex perceptual construction , an idealization. Furthermore , it is this idealizing abstraction at the heart of our ideas of the spatial object that makes the mathematical
possible. They are parasitic on and presuppose each other. — Joshs
The math involved in structural engineering have changed overtime. If in one of these changes, them engineers postulated that anything mathematical is both true and false at the same time, as Wittgenstein was effectively (though unwittingly) suggesting, they might have ended building quite a few failed bridges. — Olivier5
Things are the case or not the case within this wider sense-making space, which is context-sensitive. — Joshs
The bottom line is that the meaningful
sense of S is P is a moving target , and what the LEM does is delimit how much the sense of the meaning of the proposition can vary before it becomes incoherent. At that point we blame each other for misunderstanding the definitions. — Joshs
material things are sensed, even animals find themselves in an environment comprised of material entities which, judging from their behavior, they must see much as we do (although obviously they don't conceive of them as material entities). — Janus
What animals ( and humans) ‘sense’ , once we have removed all the higher level constructions that make phenomena appear for us as self-persisting things in a geometric space-time, is a constantly changing, chaotic flux of impressions. Out of this steaming flux we discern regularities and correlations, not just in the changes happening in our environment, but in the relation between these changes and the movements of our body. An ‘object’ is the product of all these correlations and regularities. Most of what we see at any moment ina spatial object is provided by our own expectations based on previous experience with something similar. We mostly construct the object from memory and anticipation. So the idea of spatial objects is an idealization based on actual experience which is contingent and relative.
It is not a fact that objects persist in time , it is a presupposition, and one which is necessary in order for there to be naturalistic empirical science and mathematical calculation. — Joshs
Which empiricism generally resists, on the grounds that humans are born 'tabula rasa', a blank slate, on which ideas are inscribed by experience. — Wayfarer
All the math involved in structural engineering requires is that it works; that it can effectively model things like tensive and compressive forces and the hardness, strength and flexibility of construction materials. — Janus
This is where you lose me. I do not understand what you mean. That the LEM is not universally applicable, that it has a clear domain of applicability here but not there? If yes then ok, it's consistent with the above about propositions being true in certain contexts and not others.
3h — Olivier5
You made a general statement about it. You made your own claim about mathematics and mathematical logic. And your claim is incorrect. — TonesInDeepFreeze
[...] allowing contradictions in math is equivalent to dropping the law of the excluded middle from mathematical logic [...] — Olivier5
When I throw the ball for my dog he can obviously see the ball, he tracks it as it flies through the air and usually manages to be within a meter or two of it when it hits the ground. — Janus
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