The premise is "if not A then B". Conclusion: not A, so B

Does this necessarily require "everything is A or B?" — Edmund

I think that if something is not true, that means it is false. At least if you frame it the way you do in the OP.

However, I don't think it is a requirement that something, or everything as you say, must necessarily be false if not true - at least in the context of belief.

The OP is obviously a reference to belief in God - must God not exist if we cannot prove he exists? No, but it is likely he doesn't. Or at the very least we don't have to cite evidence for dismissing his existence. And saying you don't believe in him doesn't mean you think he cannot exist.

Question: If something is not true is it false? — Edmund

Search "Law of excluded middle".

But consider "The present king of France is bald". There isn't a present king of France. Is "The present king of France is bald" true, or is it false? Or is it something else?

So if not A then B — Edmund

Only if B is (not A). But if (A and not A), then B, regardless of what B is.

Does this necessarily require "everything is A or B?" — Edmund

No. "everything is a pancake or a bus" is not true. But "everything is a pancake or not a pancake" is true.

But having said all that, one might adopt a non-classical logic, and do as one likes with the Law of Excluded Middle.

The premise is "if not A then B". Conclusion: not A, so B — Gregory

Indeed; from not A implies B, we can validly conclude that not A implies B.

I think that if something is not true, that means it is false... However, I don't think it is a requirement that something, or everything as you say, must necessarily be false if not true — ToothyMaw

So if it's not true, that means it's false, but it might be true if it's not true...?

The OP is obviously a reference to belief in God — ToothyMaw

No it isn't.

What if not A, A, and B were all the same thing. This would be nonclassical logic wherein each presupposes the other. This example seems like the Trinity to me. Does the law of explosion apply to faith?

But consider "The present king of France is bald". There isn't a present king of France. Is "The present king of France is bald" true, or is it false? Or is it something else? — Banno

Are there any logical systems dealing with indexicals?

What if not A, A, and B were all the same thing. — Gregory

A and not A are inconsistent. One point of logic is to determine what can be concluded from given premises. But we know from basic logic that a contradicting implies anything, and hence from a contradiction we can conclude anything. Accepting a contradiction undermines classical logic. Search "Principle of explosion". If A and not A are true for some sentence, then anything goes.

There are two direct ways to respond to this. It is somewhat important in this context to understand the difference between the two. The first is to say that the contradiction is neither true nor false. That is, to introduce a third truth value, usually thought of as something like "unknown". This leads to paraconsistent logic.

The second is to accept that there are true contradictions, a view called dialetheism. This is sometimes proposed as a way of solving some paradoxes, such as The Liar Paradox.

Graham Priest is the man to read, should you like to examine these further. He argues that we might have some true contradictions, and yet avoid explosion. His approach is interesting but often considered somewhat arbitrary. While it solves some philosophical issues, there are other approaches that do not rely on such a radical departure from classical reasoning.

Note that A and not A are sentences, presumably setting out how things are. If we find ourselves in a situation where two sentences are contradictory, is it more reasonable to suppose that we have found a contradiction that exists in the actual world, or that we have misdescribed what is going on? Should we throw out classical logic or check that we are seeing what we think we are seeing?

If we find an apparent contradiction, it would seem at least advisable to look again.

So if some theology sets out a contradiction as fact, the first reasonable approach is to suppose that the theology is wrong.

Faith is, at it's core, believing things not because of the evidence but despite the evidence. Faith begins by denying reason.

But again, there is nothing in the OP that indicates is interested in issues of theology.

Sure. It's in the parsing. Kaplan has a subtle system for dealing with them. Are you thinking of treating "present king of France" as an indexical? It's more that the expression has no referent that is the issue.

It's more that the expression has no referent that is the issue — Banno

Right but isn't the fact that it has no referent due to the context-sensitive nature of the proposition? 'Present king of france' seems to be a temporal indexical-phrase to me. I am aware of Kaplan but haven't yet looked into his work.

isn't the fact that it has no referent due to the context-sensitive nature of the proposition? — Heracloitus

Perhaps. It doesn't follow that all such cases are cases of the use of indexicals.

One's environment is an example A being true, however there are consciousnesses that exist in that environment who disagree with you on fundamental questions, so from a purely material perspective things are in contradiction. Maybe contradiction looks just like being to us

, logic generally deals in what is true and what is false, not what is believed or disbelieve. That’s partially because folk often believe things that are not true.

So generally speaking if someone disagrees with you it is because one of you is wrong.

That’s not a contradiction.

Logic cannot justify its methods. I am Muslim, Catholic, Hindu, and Buddhist. All faiths can be true for me. How am I in contradiction?

Logic cannot justify its methods. — Gregory

If someone does not accept logic, then it is not possible to convince them by rational discussion.

So i guess that ends that discussion.

My point was that I can say Jesus rose and didn't rise at the same time because these truths are under a higher truth. That reality doesn't bow to logic. Have fun with symbols

That reality doesn't bow to logic. — Gregory

If someone does not accept logic, then it is not possible to convince them by rational discussion. — Banno

If that is the rule you wish to use, yes. If not then maybe not.

Convention exists because it appears to be functional for us not because it is some underlying principle of nature or because it is not. What is might be and what might be might be what it is.

Applying abstractions to multiple singular instances and expecting to hold fast is likely stupidity veiled as something many call ‘knowledge’. Whereas ‘wisdom’ is more obsessed with not excepting such knowledge as an unquestionable effigy.

If something is not true is it false? — Edmund

Principle of bivalence: There are only 2 truth values (true and false; a proposition is either true or false, but neither both nor neither)

So if not A then B. Does this necessarily require "everything is A or B? — Edmund

1. ~A $\rightarrow$ B
2. ~~A v B [1 Imp]
3. A v B [2 DN]

The letters A and B are being used sensibly but not consistently.

Compare Everything is (A)rt or not (A)rt to Everything is (A)rt or (B)ald. :wink: @Banno

Principle of bivalence: There are only 2 truth values (true and false; a proposition is either true or false, but neither both nor neither) — Agent Smith

Tertium non datur

Question: If something is not true is it false? So if not A then B. Does this necessarily require "everything is A or B?" — Edmund

What is true to A is not true to B. What is true to B is not true to A. But the greater truth i would say is that A and B both exist (are true) but that truth is defined (limited/given strict parameters) by their individual perspective (assumptions).

Paradox, like argument, like contradiction, can only exist when two opposimg assumptions can be logically considered as true and battle one another for supremacy.

Positive and negative poles of any spectrum, any duo of opposites, any two faces of a coin, exist in direct contradiction of one another such that they cancel one another out.

0 can = 0, but 0 can also = - 1 + 1

Tertium non datur — Heracloitus

Yep! What do you make of trivalent logic? True, false, and ... ?

I'm still learning about normal logic systems, but yep interesting stuff. Has been applied in computer science (true, false and undefined).

Another example is Lukasiewicz's 'future contingent':

I can assume without contradiction that my presence in Warsaw at a certain moment of next year, e.g., at noon on 21 December, is at the present time determined neither positively nor negatively. Hence it is possible, but not necessary, that I shall be present in Warsaw at the given time. On this assumption the proposition “I shall be in Warsaw at noon on 21 December of next year,” can at the present time be neither true nor false. For if it were true now,
my future presence in Warsaw would have to be necessary, which is contradictory to the assumption. If it were false now, on the other hand, my future presence in Warsaw would have to be impossible,
which is also contradictory to the assumption. Therefore the proposition considered is at the moment neither true nor false and must possess a third value, different from “0” or falsity and “1” or truth. This value we can designate by “1/2.” It represents “the possible,” and joins “the true” and “the false” as a third value. — Lukasiewicz

What is true to A is not true to B. — Benj96

Let A be New York and B be London. Both are cities of over a million folk. So what is true of A is true of B.

But the greater truth i would say is that A and B both exist (are true) — Benj96

Shoes exits, but are not true. Sentences are true. Truth and existence are different things.

but that truth is defined (limited/given strict parameters) by their individual perspective (assumptions). — Benj96

An individual perspective can be wrong. Indeed, we only need speak of individual perspectives because they are sometimes wrong.

And so on.

There's gotta be a workaround for future claims.

Seems to me the obvious response, should you want to keep bivalence, is the block universe. It is true, or it is false, that “I shall be in Warsaw at noon on 21 December of next year,” but we don't know which.

Seems to me the obvious response, should you want to keep bivalence, is the block universe. It is true, or it is false, that “I shall be in Warsaw at noon on 21 December of next year,” but we don't know which. — Banno

What do you make of the statement, spoken by Brown to Jones, "I'll call you tomorrow at 9:00 AM" when

1. Jones does get a call from Brown at 9:00 AM (tomorrow)
2. Jones' phone doesn't ring at all from 8:00 AM to 10:00 AM (tomorrow)

?

(1) is true, (2) unknown, since Brown may have called but not gotten through, no?

Objection sustained!

I think yes, in literal, absoulute terms. Something is either true or false. There's no intermediate state. We cannot say partly or partially true in absolute terms. E.g. We can say "This is partially true", "This is half the truth, "This is not the whole truth", etc. but this will influence the outcome of a case, in favor or against it. But these are not decisive statements if we are to establish the truth of the case, e.g. in a court.

As for your example "If not A then B", it cannot stand by itself, in general. A context is needed. And even then it may true or false (Here we are! :smile:). E.g. the statement "If am not native, I am foreing" stands (it is correct, true). The statement "If am not American, I am Greek" does not stand (for obvious reasons).

Why do you ask if you don't really care about replies?