Law of excluded middle

[Cirion Spellbinder]

It isn't consistent, since it violates non-contradiction. Everything is true and everything is false. If you want to call that consistent by another definition (of sameness) sure, but it also has no reliable output. That makes it essentially a non-system. It can not differentiate truth from falsity, validity from invalidity.

My friend suggested that systems like this boil down to two valued systems. Here's what he said:

Tripartite systems in the real world eventually reduce to true and false issues. Take the integers: to any two pair of numbers can be assigned a "truth value", < if the first number is less than the other, > if the opposite is true, and = if they are equal. But that reduces to asking whether, for (a,b), a < b is true or false, a = b is true or false, and a > b is true or false

Tell me what you think.

[brimstoneSalad]

@Cirion Spellbinder Sure, as I said, if the statement is precise enough and represents something that actually can exist you can get down to true or false

[Cirion Spellbinder]

@brimstoneSalad
So if every tripartite problem can be boiled down to multiple bipartite parts, wouldn’t all bipartite systems be at least as broad as tripartite systems?

[brimstoneSalad]

@brimstoneSalad
So if every tripartite problem can be boiled down to multiple bipartite parts, wouldn’t all bipartite systems be at least as broad as tripartite systems?

I suppose, just with limited application in cases where there's empirical ignorance. If they're consistent, they probably end up being comparable to each other once you get enough information.

[Cirion Spellbinder]

@carnap, is what I said to @brimstoneSaladcorrect (at least in the tripartite case)? It contradicts what you said early about systems with more truth values being broader.

[brimstoneSalad]

@carnap, is what I said to @brimstoneSaladcorrect (at least in the tripartite case)? It contradicts what you said early about systems with more truth values being broader.

Somewhat of a metaphysical question contingent on the answer to whether or not you would ultimately arrive at solid truth values once you have more information/eliminate the ambiguity of the claim.

[mkm]

Tell me what you think.

I would ask for the reason why should we think, that the reality is as simple as the theory of integers. And even if it is, if we want our theories to be consistent and they include the arithmetic, then necessarily there are statements that are true, but unprovable. For such statements the comment of your friend is meaningless.

[Cirion Spellbinder]

I would ask for the reason why should we think, that the reality is as simple as the theory of integers.

It was meant as an analogy for tripartite systems. If it is a false analogy, tell me (and why) so I can tell him.

And even if it is, if we want our theories to be consistent and they include the arithmetic, then necessarily there are statements that are true, but unprovable.

Is this incompleteness theorem?

[carnap]

Quite the anthropocentric definition.

When talking about human reasoning, yes, its going to be an anthropocentric definition. Again "reason" shouldn't be mistaken for a logical system, human thinking doesn't represent a logical system. Human reasoning isn't the application of a set of inference rules, its much more than that.

See, that's not how I define reason; bias and emotion have no place in reason, that's something else.

While you can argue that bias represents a sort unavoidable deviation from rational decision making you cannot say the same about emotion. Emotions are a critical component to our ability to reason. Reasoning about the real world is typically done with imperfect information where conclusions, in the deductive sense, cannot easily be made. To restrict "reason" to just clear cases of deductive reasoning would exclude most of our reasoning abilities.

The other comments you made in your post make the mistake of assuming that logical operators have a semantic independently of some logical system. The meaning of the "or" operator hinges on a specific logic.

[carnap]

@carnap, is what I said to @brimstoneSaladcorrect (at least in the tripartite case)? It contradicts what you said early about systems with more truth values being broader.

I'm not sure what brimstone is trying to say because they don't appear to be using the common mathematical definitions of notions like "consistent", etc. Many-valued logics can be consistent, a logical system is concerned "consistent" so long is that there isn't any statement that can be both proved and disproved.

In terms of metaphysics, there is no obvious reason why every statement should be either true or false. In fact quantum mechanics seems to show that there are statements that are neither true or false. So it would seem that classical logic is more a representation of how we think about the world rather than reality itself. I think this is an interesting issue that often gets ignored, namely, the limitation to human thought. Our ability of reason was crafted evolutionary to solve real world problems....not research the nature of the universe. It may very well be that our modes of thought will limit what we can discover about the world. Our entire system of science may just be set of useful anthropocentric notions that has no connection with "reality".