Logic, Logical Principles, and Proof

[Demojen]

Suppose in law of identity "A" includes the object and also all the coordinates of the object (including time). Two otherwise identical objects, but at different coordinates, wouldn't qualify A=A. When A is fully and exactly defined, there's no problem(?) (other than with how we in ordinary language understand identity as a continuum, but that's a different question)

Objectively, it might include its coordinates but subjectively? Do you define yourself by where you are or where you're going (not metaphysically or metaphorically)?

I ask because, there is no position on this planet for which we can stand and mark the space-time coordinates of any individual. The more accurately you measure one variable, the less accurate you can measure others.

Matter Wave Interpretation of the Heisenberg uncertainty principle states:
According to the de Broglie hypothesis, every object in our Universe is a wave, a situation which gives rise to this phenomenon. Consider the measurement of the position of a particle. The particle's wave packet has non-zero amplitude, meaning that the position is uncertain, it could be almost anywhere along the wave packet. To obtain an accurate reading of position, this wave packet must be 'compressed' as much as possible, meaning it must be made up of increasing numbers of sine waves added together. The momentum of the particle is proportional to the wavenumber of one of these waves, but it could be any of them. So a more precise position measurement, by adding together more waves, means that the momentum measurement becomes less precise (and vice versa).

The only kind of wave with a definite position is concentrated at one point, and such a wave has an indefinite wavelength (and therefore an indefinite momentum). Conversely, the only kind of wave with a definite wavelength is an infinite regular periodic oscillation over all space, which has no definite position. So in quantum mechanics, there can be no states that describe a particle with both a definite position and a definite momentum. The more precise the position, the less precise the momentum.

 

[Kelly Jones]

Truth and logic are one and the same.

How do you know?

Because truth means that which is, and not that which is not. It's the same as logic.

Just because logic creates a formula for us to interpret arguments in a progressive way, does not make logic inherently truth.

Logic actually creates the structure of any truth. You need to understand the law of identity to see this.

The Paradox was born out of logic and uses basic logic arguments.

A paradox actually boils down to a mistake in reasoning, such as equivocation, or poorly defined propositions. There aren't any paradoxes.

 

[Kelly Jones]

Sorry for the mispelling of your username, Squawk.

Logic and truth may not exist at all, but it's an idiotic position to take because to even postulate it, you have already assumed them to be true.

What's an idiotic position to take? Assuming truth is true? Yes, it is. But if one defines truth to be truth (which is rational, since what else could it be?), then no assumption is made.

I'm still not 100% on the whole identity thing though, since it requires a more thorough understanding of time. Without actually knowing what time is,

No, any definition of time rests on the law of identity. Any definition of anything, for that matter. Surely this is obvious.

I'm not saying the law of identity exists objectively, out there beyond the mind. Just that it's fundamental in a logical process.

 

[Kelly Jones]

[quoting Heisenberg] ... the only kind of wave with a definite wavelength is an infinite regular periodic oscillation over all space, which has no definite position. So in quantum mechanics, there can be no states that describe a particle with both a definite position and a definite momentum. The more precise the position, the less precise the momentum.

This is a very precise identity for subatomic particles, and relies on A=A all the way.

"A" in this case is given the label, "a quantum particle", with the meaning "having states that are either precisely located or precisely measured in velocity, but never both to human knowledge." It's a very clear description, but like all scientific statements needs to be considered as contingent on empirical data and therefore not absolutely conclusive.