Asserting determinism, or at least what is often referred to as "hard" or "rigid" determinism consists in claiming that from any set of conditions there can arise only one outcome at any subsequent time. An often cited "thought experiment" is that if it were possible to restart the evolution of the universe from the initial moment it came into being it would again unfold exactly, down to the minutest detail, as it has actually done this time.

This is an entirely groundless assumption. Under the aegis of Newtonian mechanics this may have seemed obviously true, but in the light of QM it seems not only vanishingly unlikely, but even just plain impossible. — Janus

Simplest interpretation is that he doesn't understand a measurement's being accurate to within a certain error. — Banno

Married men don't need to wear a wedding band and bachelors can if they like. And neither needs to be doing "married" or "bachelor" things to be married or a bachelor. A married man and a bachelor can be sitting in a Jacuzzi together wearing nothing but swimming trunks. How do I draw that one is a married man and one is a bachelor? — Michael

So again, you're just denying dialetheism rather than refuting it, and what you said earlier about not being able to picture certain things in the mind is an irrelevant comment that does nothing to further your case (and has been shown false by my example of the number of stars in the universe, or the existence of dark matter). — Michael

Then you're just begging the question by asserting that contradictions are impossible. That's not a refutation of dialetheism, it's just a denial of it. — Michael

You may have missed my edit, and it may be redundant now that you're backtracking from your talk about being able to draw stars, but how would drawings of a married man, a bachelor, and a married bachelor even differ? They'll just be drawings of a man that I say is married, a bachelor, or a married bachelor. — Michael

So now you're saying that things can only be the case if they can be drawn? What about dark matter? — Michael

Right. And so the word "contradiction" doesn't mean zero information, for that is nonsensical, but refers to conflicting sources of information, actions, intentions, judgements and so on. A "true" contradiction can be taken to refer to an unresolved conflict that is logically implied.

For example, conflicts of judgement that are present in discrete borderline categorisation problems, as in being in the kitchen and not in the kitchen, are not resolvable by introducing more linguistic precision, for the same borderline problem resurfaces on a finer level of semantic granularity; here the "true" contradiction refers to the fact that the concept of discreteness cannot be reconciled with the existence of borderline cases. It's all well and good hoping that the conflict is potentially resolvable, but there is no reason to believe that all such conflicts are resolvable. — sime

You seem to be saying that married bachelors and square-circles can't be the case because I can't picture them in my mind, and yet there are 10²¹ stars in the universe even though I can't picture that many stars in my mind.

You then say that this doesn't matter because I can symbolize the fact that there are 10²¹ stars in the universe with scribbles on the screen, but I can also symbolize married bachelors and square-circles with scribbles on the screen.

So which is it? Must I be able to picture things in my mind for them to be the case, in which case there can't be 1021 stars in the universe, or is it enough that I can symbolize things with scribbles on the screen, in which case there could be married bachelors and square-circles? — Michael

What do you mean by symbolize? How does it differ from picturing? It's not just about being able to say the words is it? As you said before "the fact that you can put two scribbles or sounds that refer to opposite things together in space and time doesn't make what those scribbles refer to real, or true." — Michael

And on the other side I can picture impossible objects like a Penrose triangle, so looking to what we can or can't imagine just doesn't seem like the appropriate way to determine what can or can't be the case. — Michael

There are more stars in the universe than I can picture at any one time, yet presumably they still exist. — Michael

Would it be better if I had said that things can't be the case if we can't represent, symbolize, or simulate them in our mind? — Harry Hindu

Here you claimed that things can't be the case if we can't picture them in our mind, and now you're saying that the innate nature of cups can't be pictured in our mind; only their appearances can. — Michael

Yes in the sense of contradictory propositions. Nobody of course, experiences contradictory propositions - which goes to show that the general meaning of "contradiction" isn't to refer to propositions but to conflicts, such as the conflict between the definition of a language and it's application, or the rules of a sport and the moral notion of fair-play etc. — sime

Then you're contradicting yourself. Here you claimed that things can't be the case if we can't picture them in our mind, and now you're saying that the innate nature of cups can't be pictured in our mind; only their appearances can.

You need to drop one of these claims. Either only appearances are the case or things can be the case that can't be pictured in our mind. — Michael

This doesn't answer my question. — Michael

Can you picture a cup without just picturing how a cup appears to us? — Michael

Can you picture just the innate nature of the cup? — Michael

Can you picture a cup without picturing the look of a cup, or the feel of a cup, i.e. how a cup is experienced? — Michael

Or are you saying that cups have some innate appearance, irrespective of what they look and feel like to us? — Michael

i) Self-negating universal imperatives, i.e. hypocritical statements such as "Don't live by rules!". — sime

ii) When a semantic distinction is more fined grained than is expressible in the language used, such as when standing in a doorway and thereby "being in the kitchen but not in the kitchen". — sime

iii) When a semantic distinction is vague or uncertain, such as "a heap of sand" that isn't defined in terms of a particular numeric range of sand grains Hence "heaps of sand" exist, but no particular collection of sand grains constitutes a heap. — sime

ii + iii are contradictions that programmers have to deal with, but they also present challenges for self-learning autonomous agents, that like human beings must somehow internalise a truth-language distinction.

I suspect that like humans, AI agents will also behave in a logically inconsistent fashion relative to their self-knowledge. — sime

It's a wonder that them physicist get anything right. — Banno

Priest (and other dialetheists) would obviously disagree. They present arguments. You should study them sometime. — Theorem

And while I find them fascinating and worth learning about, I wouldn't say that I endorse them. — Theorem

Are you saying that things can only be the case if we can picture them in our mind? — Michael

It's also worth noting that if our measurements of initial position and velocity are inherently imperfect, so will any subsequent measurements of position and velocity also be imperfect. — Janus

The whole thing reminds me of the political entity we so fondly call "government" of, say, the USA. At the end of every term, the entire team that is the government is changed (barring the times when a party gets re-elected) - the president is different, the vice president is different, and so on, and yet, we still refer to every one of these disparate entities as the government of the USA. Likewise, every little essential detail of the LNC has been altered and all that remains of the real LNC is just the label - the law of noncontradiction. It's an empty word if you ask me. — TheMadFool

More precisely, he argues that there are actual situations containing statements that are both true and false, namely, those situations that fit the semantics of the enclosure schema. These situations involve self-reference and/or reference to absolute limits. — Theorem

One compelling example of an alleged true contradiction is, of course, the Liar sentence. It is surprisingly difficult to develop a classical account of the Liar that satisfies everyone and that is not prey to revenge paradoxes. Dialetheism provides a very straightforward solution to this and related paradoxes. — Nagase

Second, paraconsistent logics in general are concerned with controlling the trivialization that follows from the principle of explosion. That is, such logics provide a workaround for when we find contradictions in our belief set or in our model. Now, you may say, why would we want such a workaround? Shouldn't we just jettison the contradiction and be done with it? Well, yes, but the problem is, how do we do this? Suppose I have beliefs A1,…,AnA1,…,An, and from these beliefs I eventually derive a contradiction, say B&¬BB&¬B. This means that I should give up one of the AiAi's, but which one? There may be no obvious way of selecting such an AiAi, since there may be equal evidence for each of them. In that case, a reasonable course of action would be to investigate further into the source of the contradiction so that I can eventually revise my beliefs. In the meantime, however, do I need to act irrationally, as if I believed everything (which would follow from the explosion)? Of course not. But this means that I will need to employ a paraconsistent logic, since I will need to ignore explosion. So paraconsistency may be a useful tool in "controlling" a contradiction during belief revision. — Nagase

And per ↪Nagase regarding belief revision, dialetheism could also have practical applications within the field(s) of artificial intelligence and machine learning. In fact, now that I look at it, the SEP article linked in the OP actually contains a short section devoted to this topic. — Theorem

Since the law of noncontradiction (LNC), expressed as ~(p & ~p), is critically dependent on the definitions of negation and the AND logical connective, it follows that paraconsistent logic or dialetheism has different definitions for both of them. — TheMadFool

Taking subjective to mean "influenced by or based on personal beliefs or feelings", it's a simple matter to find such statements:

Banno likes vanilla ice cream.
Trump is a poor excuse for a president
Being cold is unpleasant

Each of these is based on personal beliefs or feelings. Each is true. — Banno

The standard philosophical prejudice is that given an accurate enough account of the position of the box and a given ball, a competent physicist will be able to tell us which of the bins across the bottom the ball will land in.

And in this sense the path of the ball is determined.

But of course no one could determine the final resting place of the ball. Even the smallest error in the initial positions will be magnified until it throws out the calculations. — Banno

wrote this in a time of only nascent chaos theory, which could only serve to amplify her point.

The notion that the universe is determined fails. — Banno

And it's with the "exact," it seems to me, that dialetheism fails. And this because with exactness it must affirm and then deny what it affirms. — tim wood

Vagueness — bongo fury

Physics has shown us the universe has many laws or rules by which it operates; gravitational constant, conservation laws, uncertainty principle, thermodynamics etc.

But why? Why have any consistency to anything? Why not have a gravitational force that changes constantly or a conservation law that works "most" of the time. — Benj96

Aren't their truths about individuals? I can say I'm angry, you can say that I don't look angry. I can reply that I'm holding it in. Surely there is a truth about whether I feel angry — Marchesk

Which metaphysical and epistemological problems need to be solved prior to understanding, or being able to use, logic? Tell me how you answer that question without using logic. — Harry Hindu

Which logical axioms should we accept? — 83nt0n

I think that depends on what you mean by some element of truth. Newtonian mechanics is wrong but useful. — 83nt0n

Picturing an entire galaxy in your mind is impossible. — 83nt0n

Is this statement about logic true? If logic isn't used to "establish logic", how do we "establish truth" about logic without "using logic"? — 180 Proof

This is why I am not outright saying one of these fields should be first. It seems like metaphysics/epistemology depend on logic, but logic depends on metaphysics/epistemology. Analogous to the problem of the criterion. — 83nt0n

What do you mean by useful? If you mean how is it relevant to the discussion, well dialetheism goes to show that the foundations of logic are disputed, so how do we find a 'correct' logic? If we use logic to establish logic, this would be circular. — 83nt0n

Are you implying that because something habitually works that it is true/correct? — 83nt0n

Let's just say I don't necessarily agree that logic is first. It seems that if we want our logical system to be justified/true we will need to employ epistemology or ontology/metaphysics, otherwise we're in danger of arbitrarily picking axioms. — 83nt0n

This question is already assuming that the law of non-contradiction to be the case, so I'd imagine a dialetheist would answer by saying that the question is not well formed. — 83nt0n

Yes of course you can't escape the classical laws of logic if you assume the classical laws of logic. Just like if you wore red sunglasses you wouldn't be able to escape seeing everything as red until you take the glasses off. The reason why I personally find it hard to escape classical logic is probably because it is habitual. — 83nt0n

Sure -- but it wasn't "science" or "logic" in the sense that was meant above. Hunter-gathers weren't conducting controlled experiments, nor were they doing syllogisms. Again, this is why I said the equating of "logic" to "thinking" is misleading. Thinking has gone on for millennia, just as language has. Logic and grammar are not that. — Xtrix

To say thinking is "correct" because it conforms to the rules of logic just doesn't tell you much. — Xtrix

There are several conflicting systems of logic. For example, dialetheism denies the law of non-contradiction. https://plato.stanford.edu/entries/dialetheism/ Even the axioms of logic are disputed. So how do we know which system to use? — 83nt0n

So you agree with me that "true" and "objective" are synonyms
— Harry Hindu

No, I said that you used "objective" to take on the sense of "true". — Banno

I'll agree with you that "objective" can take on the sense of "true"; hence, when it replaces "true" in the OP it does so without replacing the meaning. — Banno