Perhaps in poetry but more formally something either is the case, or it is not the case.

Do Brussels sprouts taste good? True or false?

If x is a cat, it can't be not a cat. [law of noncontradiction, law of the exclused middle, XOR].

For any proposition p,

Either p is true OR p is false [principle of bivalence]

Either p is true OR p is false [principle of bivalence] — TheMadFool

Didn't you read my question?

“I stole this from Zen Master Suzuki Roshi: If it's not paradoxical it's not true!”
― C.B. Murphy

The law of non-contradiction appears to work "opposite" when applied to relative vs essential truth. An apparent thing must be one thing or the other. Do I turn left or right to get to this specific destination?

But if we are talking about the "ultimate" "destination", as it were, its not confined to left, right, up or down, forward or backward. Above or beneath. Its not everywhere, nor is it nowhere, nor is it both, neither, nor both and neither, nor neither both nor neither?

Any answer that is limited is limited. It can't be a complete answer, and thus falls short. The answer must be infinite to be fully true. Yet no answer is truly infinite, is it? Or is everything complete?

So we are limited to saying what the absolute truth is not? Or is there no real limitation?

In summary? Because the absolute truth is one, not two (any two must share a single reality or else each could not be grouped together), therefor any statement which says 'two' would contradict the truth of 'one'. Therefor all dualistic 'this, not that' statements are ultimately not true. Even though they may be pragmatically true. Eg, we may have to turn left.

Didn't you read my question? — SolarWind

I did. I gave it some thought and decided we should start from the basics.

A proposition being both true and false is a contradiction. I gave the example of how if x is a cat, it's impossible that x is not a cat (x is cat is true and x is a cat is false). There are three important principles at play here:

1. The law of noncontradiction. (can a proposition p be both true and false i.e. not true)

2. The law of the excluded middle (a proposition or its negation is true)

3. Principle of bivalence (a propositions can be either true or false and nothing else)

So,

If a proposition can be true and false, we have to look at 1 and 2

If a proposition can be neither true nor false, we have to examine 3

Is it possible for things to be both true and false at the same time or neither true or false at the same time? Or must things be either true or false at any given time? — TiredThinker

My coffee is neither true nor false. The word "hello" is neither true nor false.

Only claims(premises) and arguments can be true or not true in our world.
So a true claim is the one that is in agreement with current facts (describes them accurately).
An implication of this is that a claim may be true according to the current available facts but missing facts might mean it can ultimately be a false claim.
Since we have no access to all facts or Ultimate or Absolute claims...we only can work on what is currently available.
So a claim can never be true or not true at the same time because it is a judgment based on facts at that specific moment.
Hindsight is just a meta analysis of a claim with facts that do not belong at the same temporal point.

A proposition being both true and false is a contradiction. I gave the example of how if x is a cat, it's impossible that x is not a cat (x is cat is true and x is a cat is false). — TheMadFool

What if you talk about the evolutionary ancestors of cats? One researcher says that's already a cat, another says that's not a cat yet.

Do Brussels sprouts taste good? True or false? — SolarWind

Love Brussels sprouts. So - true, true, true.

Is it possible for things to be both true and false at the same time or neither true or false at the same time? Or must things be either true or false at any given time? — TiredThinker

This is my old refrain. Most things that get people, at least philosophers, excited are neither true nor false. Examples:

• Free will vs. determinism
• Realism vs. idealism vs. materialism vs. pragmatism
• The nature of reality
• The nature of truth

Is it possible for things to be both true and false at the same time or neither true or false at the same time? Or must things be either true or false at any given time? — TiredThinker
This is my old refrain. Most things that get people, at least philosophers, excited are neither true nor false. Examples:
Free will vs. determinism
The nature of reality
The nature of truth — T Clark

This is also the old Reductive versus Holistic refrain. If you look at particular things or events, each can be evaluated as Good or Bad, in the specified context : relative to me, to you, to everybody. But if you look at everything-in-general, the values are not so Black & White.

That's why my personal Holistic philosophy is summarized in the BothAnd Principle. From that perspective, it's hard to get too excited about any single example of the duality of reality. It's characterized by neither of the extremes (all-good or all-bad), but a moderate mixture of both. Otherwise life in the real world would be heavenly or hellish. So, the job of Philosophy (Wisdom) is to evaluate in terms of relative values : more-or-less Good or Bad ; True or False ; Real or Ideal. The Middle Path, the Way of Tao. :smile:

Both/And Principle :
My coinage for the holistic principle of Complementarity, as illustrated in the Yin/Yang symbol. Opposing or contrasting concepts are always part of a greater whole. Conflicts between parts can be reconciled or harmonized by putting them into the context of a whole system.
http://blog-glossary.enformationism.info/page10.html

So, the job of Philosophy (Wisdom) is to evaluate in terms of relative values : more-or-less Good or Bad ; True or False ; Real or Ideal. The Middle Path, the Way of Tao. — Gnomon

I posted this in the Knowledge of Good and Evil thread earlier today:

The belief of the existence of evil, at all, is what allows for the infinite manifestations of evil that we experience daily.
— PseudoB

Or as Lao Tzu wrote:

Recognize beauty and ugliness is born.
Recognize good and evil is born.
Is and Isn't produce each other. Hard depends on easy, Long is tested by short,
High is determined by low, Sound is harmonized by voice, After is followed by before.

Tao Te Ching, Verse 2. Addiss and Lombardo translation. — T Clark

But this is a bit different from the point I was trying to make in my post in this thread. I have a broken record refrain, for those who remember what that means. It goes like this - Most of the difficult issues we discuss in philosophy are metaphysical issues - they relate to the underlying assumptions we bring to the discussion. Metaphysical issues; like free will vs. determinism and the nature of reality, do not have true or false answers. They have no truth value. They are merely more or less useful for dealing with particular issues.

A proposition being both true and false is a contradiction. I gave the example of how if x is a cat, it's impossible that x is not a cat (x is cat is true and x is a cat is false).
— TheMadFool

What if you talk about the evolutionary ancestors of cats? One researcher says that's already a cat, another says that's not a cat yet. — SolarWind

It's the sorites paradox.

Between each ancestor-descendant pair there really is not much of a difference to deserve separate species categories but in the long run, over many generations, differences accumulate and amplify and a point is reached when species distinction becomes necessary.

The researcher who claims that the forbears of cats are cats and the other researcher who makes the opposite claim are talking past each other - their meaning of "ancestor" is not the same. In the case of the former, the ancestor is exactly like the modern cat in physical and behavioral characteristics but in the latter's case, the ancestor is something else entirely.

Not a true contradiction - a definitional issue at best, confusion at worst.

People are angry.
Trusting people is a problem.

Are those binarily True or False?

Look before you leap is a good heuristic.
He who hesitates is lost is a good heuristic.

Are those simply true or false?

Viruses are not life forms.
True or false?

So a claim can never be true or not true at the same time because it is a judgment based on facts at that specific moment. — Nickolasgaspar

Here also:
Viruses are lifeforms.
Facts and expert opinion currently are mixed.

Not a true contradiction - a definitional issue at best, confusion at worst. — TheMadFool

But everything depends on definitions. You wrote it yourself with Sorite's paradox. What is the use of insisting on binary logic if I cannot apply it in many cases? In politics there are many questions where binary logic is of no use. Is the pay of a particular worker fair? Yes or no?

or neither true or false at the same time? — TiredThinker

If x is a cat, it can't be not a cat. [law of noncontradiction, law of the exclused middle, XOR].
For any proposition p,
Either p is true OR p is false [principle of bivalence] — TheMadFool

1. Item number 2 is true
2. The number of true statements in this list is not 2.
3. Puppies are evil co-conspirators with aliens from Haley's comet secretly scheming to steal your precious bodily fluids.

3 cannot be false; because if it is, 2 can neither be true nor false, and 1 be neither true nor false. That violates the principle of bivalence. Therefore, beware the puppies.

1. Item number 2 is true
2. The number of true statements in this list is not 3.
3. Puppies are evil co-conspirators with aliens from Haley's comet secretly scheming to steal your precious bodily fluids.

3 cannot be false; because if it is, 2 can neither be true nor false, and 1 be neither true nor false. That violates the principle of bivalence. Therefore, beware the puppies. — InPitzotl

1. True
2. True
3. False

1. True
2. True
3. False — TheMadFool

Corrected.

What is the use of insisting on binary logic if I cannot apply it in many cases? In politics there are many questions where binary logic is of no use. — SolarWind

You have a bit of a misconception here. Boolean logic is not used to answer questions but to validify statements - the answers to the questions. Epistemology of course plays a role in this and so - knowledge being something subjective and personal - whether a statement is true or false may differ from person to person.

A system of logic mustn't contradict itself within it's own framework. There's no need to be consistent across different frameworks though.

The statement "It's 12pm in the USA" doesn't contradict "It's 12am in China" because the logic systems use a different framework (in this case being the timezone).

Person A may say "Trump is an asshole" but can not say "Trump is a nice guy" at the same time because that would be a contradiction within the framework.

Person B may say "Trump is a nice guy" regardless of Person A because their opinions are different frameworks.

Person A may say "Trump is an asshole" but can not say "Trump is a nice guy" at the same time because that would be a contradiction within the framework. — Hermeticus

That's not a great example. Let's say person A does indeed say:
"Trump is an asshole, and is a nice guy."

Does that mean Person A said something contractory? Nope, and that's SolarWind's point. Ah, but he did make a contradiction, in some framework. Okay, but is Person A using that framework? All you can say is essentially, Person A contradicted himself, if he was in a framework where that's a contradiction.

All you can say is essentially, Person A contradicted himself, if he was in a framework where that's a contradiction. — InPitzotl

And that is, as @TheMadFool pointed out an issue of definition. Language is a framework shared amongst all humans. Somewhere humanity agreed upon some arbitrary sequences of noises/signs to have a certain meaning. There are also rules of how these words need to be ordered and structured to make any sense. It's defined as such:

"the principal method of human communication, consisting of words used in a structured and conventional way and conveyed by speech, writing, or gesture."

And if I do not adhere to this framework of language, then I am simply not using language.
You may say, nothing is stopping me from saying something like "The Am philoso I I am you philosoph I the you the".
But this doesn't make any sense. It doesn't pertain to structure and convention. It's not language. I'm just making random noises which happen to have a meaning in the framework of language (which I'm not using).

Likewise, in the framework of language, as per definition of the words "Trump is an asshole and is a nice guy" doesn't make any sense. So this too, isn't even language. It's just a sequence of signs that seems to convey meaning - but doesn't.

What I am actually saying is that there are issues that are not subject to binary logic like opinions of different people. But there are also problems with it in logic like the liar paradox.

In the end, all that remains to be said is that binary logic can be applied where it can be applied and cannot be applied where it cannot be applied.

Truly binary. :lol:

Most of the difficult issues we discuss in philosophy are metaphysical issues - they relate to the underlying assumptions we bring to the discussion. Metaphysical issues; like free will vs. determinism and the nature of reality, do not have true or false answers. They have no truth value. They are merely more or less useful for dealing with particular issues. — T Clark

Yes. That's why theoretical Philosophy, as contrasted with empirical Science, has not made much measurable progress over the centuries.

We still debate some of the same questions that Plato addressed in his writings. What progress we find in the evolution of Philosophy results mostly from the discoveries of Science, which gives us new technical terms, with which to discuss the same old mysteries, such as Body/Soul. Today, we can use theories of Information to find commonalities of Mind & Body ; freewill & determinism, etc. Those topics are still "difficult" and mysterious, but with our modern understanding of how reality works on a fundamental level, we can look at those ancient topics from new perspectives.

Our conclusions from such observations, still have no absolute True/False values, but they do offer some relative values in specified contexts, especially situations that are unique to modern times, and that would have sounded like fairy tales to the ancient Greeks. To me, that's philosophical progress. :smile:

Yes. That's why theoretical Philosophy, as contrasted with empirical Science, has not made much measurable progress over the centuries...We still debate some of the same questions that Plato addressed in his writings. — Gnomon

I don't think that making progress is the point. Philosophical, metaphysical, issues are intended to be basic, foundational. What's to progress? It's the application of those principles that needs to progress to address changes in the world, e.g. science. That's the problem, as I see it, not that metaphysics hasn't advanced, but that people continue to mistake it for concrete, universal, irreducible, eternal, unchangeable reality.

Those topics are still "difficult" and mysterious, but with our modern understanding of how reality works on a fundamental level, we can look at those ancient topics from new perspectives. — Gnomon

Maybe... Sort of... Wait, no. I changed my mind. Free will vs. determinism was never difficult and mysterious. Philosophers made it so. Science has changed. The fundamentals of metaphysics have not. Which is a good thing. Hmm... Do I believe that? Not sure.

People are angry.
Trusting people is a problem.

Are those binarily True or False?

Look before you leap is a good heuristic.
He who hesitates is lost is a good heuristic.

Are those simply true or false?

Viruses are not life forms.
True or false? — Bylaw

If any of these is the case then they are true. If they are not the case they are false. 'Look before you leap' is a saying and does not have this kind of truth value. I don't know what 'trusting people is a problem' means.

I don't know if I'd call this "logic" as is understood technically.

The weather may be cold for me but hot for you. This is a fine book for me but meaningless to you.

On to more weighty topics:

Over 5 million people have died during Covid.

One view, which is accurate, would say that this is quite a high number of people. And more are dying.

On another view, this is actually not that many, compared to other viruses which are much more lethal.

And so on.

So I wasn't going to comment, but then this article kept showing up in my suggested reading. I happen to be a fan of Graham Priest and once upon a time he briefly participated in the old forums as a guest philosopher. This particular article is super accessible.

Graham Priest on Beyond True and False

On a less approachable note, see paraconsistent logic and dialethia.

In short form, there are lots of truth values out there besides true and false (some of which are useful in specific applications such as data analysis). Here is a discussion of some of it SEP on Truth Values. A major issue with rejecting the LNC is something called explosion. This objection is as simple as "anything can be proven from a contradiction" and is demonstrated by "negation introduction" and similar forms of indirect proofs. Based on logic as traditionally conceived, permitting something to be both true and false at the same time is a major no no.

As a historical aside, the problem of future contingents has been around since Aristotle and serves as an easy demonstration that our thinking is impoverished by imagining that any proposition must be true or false, but not both, at every moment.

I can add more if anyone wants.

Our statements are always being judged by their truth. And when we say truth, we obviously mean "human truth". Which is by nature - definition limited.
So every judgment based in such criteria should be limited too.
So yeah it is possible something to be true or false at the same time, since we can never be sure about the absolute Truth!
But these misunderstandings-problems, imo, can be crucial reduced by using the proper and careful wording in each statement we make.