[zkmon]

In general, anything that is observed to be true at a smaller scale or context can't be extended to much larger scales. That involves assumptions on logic and mathematics to be homogenous across all scales. A pure theoretical extrapolation without bounds is quite common in mathematics, such as proof by induction etc.

Also, the foundational axioms of logic themselves could be valid only at a scale that is familiar to humans. For example, the strict bounday between true and false might get blurred and things could be true and false at the same time at other scale.

[red75prime]

> things could be true and false at the same time at other scale.

Being true and false at the same time is a contradiction. But yeah, there is such a thing as mathematical intuitionism that rejects the law of excluded middle (which is not "being true and false at the same time"). It's just one philosophical stance among others though.

[zkmon]

It is a contradiction only because you chose to call it so, or you built a framework that interprets something as a contradiction. Logic and mathematics are built on shaky grounds on larger scale.

Similar to how Earth's tectonic plates are floating on liquid magma, while appearing to be fully solid and fixed at the surface.

[red75prime]

Attempts to formalize dialectics do exist, but it mostly stays at a word-weaving level.

[worldthruword]

Isn't superposition a contradiction for classical physics? Being partly here and there.

[red75prime]

Classical physics doesn't have particles that are simultaneously here and not here. It's a discrepancy between theory and experiment. And there's no point of accepting contradictory statements that are both true to deal with that. You can't fix a wrong description of reality by using some fancy logic that allows (apparent) contradictions.

[vatsachak]

P ^ not P => _|_

The axioms of a logic that are consistent will definitely not let a statement be true and false at the same time.

[zkmon]

Those axioms do not have a basis other than observations at human scale.

[vatsachak]

They have a basis in the formal scale. The cool thing about formal logic is that it's all about physical changes.

Now, the meaning of the statements is definitely human, but the proofs go beyond