Law of excluded middle

[brimstoneSalad]

That's a question of metaphysics and epistemology.

That is precisely the point, its not a question of logic but rather metaphysics.

Incidentally also a subject where we apply logic.

An or operator would probably be the correct way to do so.

In what sense? Also the meaning of the "or" operator itself differs from logic to logic.

In the sense of how it's typically used. I'm not defining every term and then defining every term in the definition of that term.

Look into computer logic gates. If one or other other is valid, consider it valid.

But since logical systems can be arbitrary, it wouldn't be difficult to build two that were consistent with themselves but conflicting with each other.

I'm skeptical of that claim.
If it's not difficult, then please demonstrate.

And bear in mind a system which just says all invalid things are valid and all valid things are invalid (just to contradict classical logic) isn't consistent since multiple invalid propositions can contradict each other.
Likewise proposed "systems" like dialetheism aren't even systems because they have no means to differentiate validity from invalidity at all.

It means more statements are provable in classical logic but that it comes at a cost, namely, you no longer have the existence property.

That's worth discussing, but nothing in that should make us think that classical logic is at any disadvantage in describing reality.

I've brought up alternate logics because there is no obvious reason to favor one as the one true logic or better somehow at describing "reality".

Because classical logic is broader and where there is no justifiable reason to narrow it, that's the one we default to.

[Cirion Spellbinder]

The core of the problem is that in reality there may not be dichotomy "everything is eaither true or false".

What indicates that to us?

Is it the sentence? Negating a sentence in the natural language means putting a “not” before the verb right? The negation of “I am running” is “I am not running.”

Applaying classical logic to the reality results in logical determinism, because there is no "maybe" between 1 and 0.

Isn’t the issue of maybe an issue of observation? If we have a “full picture” of reality, won’t the notion of maybe be redundant?

[brimstoneSalad]

The core of the problem is that in reality there may not be dichotomy "everything is eaither true or false".

What indicates that to us?

The issue is that only certain very precise statements are true or false. But that's also a metaphysical question.

Classical logic isn't really built to deal with gradations or probability, but that doesn't mean that it can't do it if we import some rules to handle that as premises.

Isn’t the issue of maybe an issue of observation? If we have a “full picture” of reality, won’t the notion of maybe be redundant?

Mostly, although there are issues of quantum indeterminism; this, however, is not an issue of "maybe", but rather an issue of wave mechanics.

This only becomes a problem if you subscribe to something like the Copenhagen interpretation as metaphysical truth and you believe that represents actual reality.
If you subscribe to something like MWI you don't have a problem with this, since the universe(multiverse) as a whole is only perceptually random. Abstract logical truths are still true in an absolute sense.

[Cirion Spellbinder]

Classical logic isn't really built to deal with gradations or probability, but that doesn't mean that it can't do it if we import some rules to handle that as premises.

But can’t we formulate a mathematical description of probability and gradients based on classical logic?

Mostly, although there are issues of quantum indeterminism; this, however, is not an issue of "maybe", but rather an issue of wave mechanics.

Given that I don’t have a background in physics, am not pursuing a career in physics, but value this issue, will my general education be enough to understand your response if I try to fulfill what I can with physics courses?

[brimstoneSalad]

Classical logic isn't really built to deal with gradations or probability, but that doesn't mean that it can't do it if we import some rules to handle that as premises.

But can’t we formulate a mathematical description of probability and gradients based on classical logic?

Maybe.

Mostly, although there are issues of quantum indeterminism; this, however, is not an issue of "maybe", but rather an issue of wave mechanics.

Given that I don’t have a background in physics, am not pursuing a career in physics, but value this issue, will my general education be enough to understand your response if I try to fulfill what I can with physics courses?

You might need second year university level courses. BUT you could research and learn about it yourself. I think there are some good lectures on it, but I don't have any on hand.

I've talked about MWI and Copenhagen a bit here, you might be able to dig up an old rant on interpretations of quantum mechanics (and some tangents complaining about string theory).

It's usually not important to know about unless you're deep into debating a very educated theist.

[carnap]

Incidentally also a subject where we apply logic.

We reason about metaphysics which isn't the same as applying some formal logical system. Which logic best models how we think about the world (that would probably be classical or constructive logic) isn't necessarily the same as the logic that best describes "reality".

But we have a certain limitation, while we can analyze other logical systems we cannot readily reason with them. The logical structure of our thinking is fairly fixed (a fuzzy system of classical/constructive logic).

In the sense of how it's typically used. I

The "or" operator is typically used within a logic, not to aggregate numerous logics. So one would have to define the operator in this context. "Logic gates" are based on classical operators.

And bear in mind a system which just says all invalid things are valid and all valid things are invalid (just to contradict classical logic) isn't consistent since multiple invalid propositions can contradict each other.

A logical system defines what is and isn't valid so defining a logical system that says "all invalid things is valid" makes no sense. A logic doesn't even need to be consistent, in fact, people have worked on inconsistent logics as a way to model belief revision. Human reasoning doesn't represent a consistent system, that is, people often hold contradictory points of view.

but nothing in that should make us think that classical logic is at any disadvantage in describing reality.

The lack of the existence-property puts it at a disadvantage, part of "describing reality" would be the ability to construct objects that exist in the "reality".

And classical logic is broader than constructive logic, its not broader than all other logics.

[Cirion Spellbinder]

And classical logic is broader than constructive logic, its not broader than all other logics.

What is broader than classical logic?

[mkm]

What indicates that to us?

Quantum mechanics again, and things like Young's experiment. Statements like "given two holes, electron will go through the first one" are undetermined, at least in the view of the most popular interpretation, so you can't really assign 0 or 1 to these statements.

Isn’t the issue of maybe an issue of observation? If we have a “full picture” of reality, won’t the notion of maybe be redundant?

Even if things are determined for some reasons, we will never know, so the notion of "possibilities" and indeterminism won't be redundant anytime soon

Even without modern physics, you could argue that any statements about future events are undetermined until they happen, otherwise you tacitly assume determinism just by logic you use. Check "problem of future contingents".

[Cirion Spellbinder]

Quantum mechanics again, and things like Young's experiment. Statements like "given two holes, electron will go through the first one" are undetermined, at least in the view of the most popular interpretation, so you can't really assign 0 or 1 to these statements.

But isn’t all science formulated based on classical logic, as in it used math which was formulated with classical logic?

Even if things are determined for some reasons, we will never know, so the notion of "possibilities" and indeterminism won't be redundant anytime soon

I agree with this.

Even without modern physics, you could argue that any statements about future events are undetermined until they happen, otherwise you tacitly assume determinism just by logic you use.

But we could also create an approximation of the probability of such an event given other observed criteria, no? And like I mentioned before, I believe the math of physics is all based on classical logic.

Check "problem of future contingents".

How does constructive logic solve this problem?

[Cirion Spellbinder]

But can’t we formulate a mathematical description of probability and gradients based on classical logic?

Maybe.

Could you elaborate? Doesn’t probability based on mathematics based on classical logic already exist?

I’ll check out what you’ve said otherwise.