Except I'm not religious at all.

Except I'm not religious at all. — Sam26

OK, no fancy schmancy tea then. Just regular tea.

"But I should add that, though logic isn't fundamental to Reality, it's fundamental to metaphysical-reality, and is what what-metaphysically-is is constructed of". — Michael Ossipoff

Word salad. — StreetlightX

Not finding "word salad" in a dictionary, I'll just guess that it means words that don't constitute a sentence, or maybe a sentence that doesn't have a meaning, or a large collection of sentences that doesn't say anything.

But my words were a sentence, one sentence. And each of its clauses has an explicit declarative meaning.

Shall I separate the statements in the clauses?

1. Logic isn't fundamental to Reality.

Many agree with that.

2. Logic is fundamental to metaphysical-reality.

Not everyone believes that metaphysical reality is all of Reality. The statement that logic is fundamental to metaphysical reality is explicit. I didn't explain it or justify it, The OP didn't ask for that. He asked a yes or no question.

3. Logic is what what-metaphysically-is is constructed of.

You could replace "constructed of" with "consists of", if that would be clearer.

As I said, I didn't explain or justify that statement, because explanations and justifications weren't asked for.

But it's a clause with a straighforward declarative meaning.

Maybe what StreetlightX was confusedly trying to say was that i didn't explain what I meant, or make any effort to justify it. As stated above, explanations and justifications hadn't been asked for.

Then I'll briefly here give a bit of explanation, in case StreetlightX has seen any of my posts about that:

I suggest the following:

Any fact about this physical world implies and corresponds to an if-then fact.

For example:

"There's a traffic roundabout at the intersection of 34th & Vine."

"If you go to 34th & Vine, then you'll encounter a traffic roundabout."

Additionally, any fact in this physical world is at least part of the "if " premise of some if-then statements, and is the "then" conclusion of other if-then facts.

For example:

A set of hypothetical physical-quantity values, and a hypothetical relation among them (called a "physical law") are parts of the "if " premise of an if-then fact.

...except that one of those quantity-values can be taken as the "then" conclusion of that if-then fact.

Obviously, a quantity-value can be part of the "if " premise of some if-then facts, and the "then" conclusion of other if-then facts.

There are infinitely-many complex systems of such inter-referring if-then facts.about hypotheticals.

Inevitably, there's one system, among those infinitely-many logical systems, that has the same events and relations as your experience. There's no reason to believe that your experience is other than that.

I call that your life-experience possibility-story.

I can't prove that the objectively, fundamentally, existent physical world that Materialists believe in doesn't superfluously exist, as an unverifiable, unfalsifiable brute-fact alongside of, and duplicating the events and relations of, the if-then system that I've described.

We're used to declarative, indicative grammar, and it's convenient. But, as described here, this physical world can be described entirely by conditional grammar. Maybe we're too willing to believe in the grammar that we use..

Instead of one world of "is", infinitely-many worlds of "if".

This suggestion (but maybe referring to mathematical/logical structure, but not explicitly about if-thens, and not stated from the subjective point-of-view) was apparently first made (in the West at least) by the physicist Michael Faraday, in 1844.

Michael Ossipoff

Logic is fundamental to reality in the sense that every object in reality is what it is and is not what it is not. In other words, every object in reality is identical to itself and different from other objects. — litewave

Actually, the Platonic analysis of this apparently obvious point, was that no object truly is, on account of it being an appearance only, without inherent reality (following Parmenides.) But this is not so with 'ideal objects' such as numbers, which really are what they are; so A=A is certain, but when it comes to the sensory or phenomenal domain, there are actually no 'A's as such, but only representations in material form. That in a nutshell is the difference between phenomenal and noumenal objects.

What is confusing is that having generally rejected the kind of critical realism that the Platonist tradition offered, we start nowadays from an assumption of naive or scientific realism, which is to accept that the 'objects of perception' have real or inherent existence in their own right. We hardly even know what it would mean to question that sense. Whereas the Platonist tradition actually provided a perspective within which the apparent certainty of sensory perception might be critically questioned.

I don't have anything elegant to add to this but if the world were capricious, mostly random and unpredictable, reason, logic and math would be of little use so are we not "putting the cart before the horse" so to speak. The order of the universe is what makes the evolution of reason useful, not vice versa.

I know what identity is, I was spelling out the properties of the identity relation, which is what the principle is. To "violate" the law of identity does not entail violating the Law of Non-contradiction. The LNC asserts that a proposition cannot be true and its negation be true as well. The Law of Identity tells you how to know when a seemingly distinct objects are in fact identical (when they share all their properties). That is why one can remove the law of identity from their formal logic and yet retain the LNC. — MindForged

When you claim that object X has property P and object X does not have property P, you violate LNC by holding both the proposition "object X has property P" and its negation as true. And you simultaneously violate Law of Identity because you claim that object X is something it is not - that it has a property that it doesn't have. Such an object is absurd and cannot exist in reality. In this sense, reality is logical (logically consistent). Or do you think that reality contains objects that have and simultaneously don't have the same property?

That's an assumption (one which I would share), but it's not obviously the case given certain possibilities in quantum mechanics. I already quoted the relevant paper explaining this up above, but thus far you seem to have avoided acknowledging anything I've linked. — MindForged

I am sorry but your quote didn't explain why the authors believe that particles don't have identity. It just says that they don't have identity and that in many situations one cannot distinguish particles of the same kind. And I am not sure what they mean by "cannot distinguish particles of the same kind". Do they mean that the particles are exactly the same? But if the particles have different positions at the same time then they can be distinguished by their position, so position is a property that gives them distinct identities, even though all of their other properties are the same.

Well that's a silly view. Lots of things don't correspond to reality, yet they are true. There are an infinite number of mathematical truths that don't correspond to anything in reality yet I doubt you'd deny them or claim they were meaningless. — MindForged

Actually, reality or existence in the most general sense includes all consistently defined objects - that is objects that have an identity. Objects that don't have an identity - objects that are not what they are, that don't have properties they have - are nonsense, so these are not included in reality.

You asserted that if Dialetheists argue there is a true contradiction (that the LNC is not true) then they are thereby employing the LNC. This could only be the case if the notion of a "contradiction" assumed the LNC, which doesn't make any sense. Rejecting the LNC simply means you believe there is at least one true proposition which also has a true negation. — MindForged

Completely rejecting LNC means that you believe not only that there is at least one true proposition which also has a true negation, but that you also believe the opposite: that there is no true proposition which also has a true negation. As you see, such a belief is absurd and self-defeating. Even as you try to get rid of LNC, you still have to hold on to it. You can utter a contradictory statement, such as "there is a triangle that is not a triangle" (and at the same time hold on to LNC by regarding the statement as true rather than true and false), but I don't think you can find such a triangle in reality. I see no reason to admit such absurd objects in ontology.

Being contradictory isn't sufficient for meaninglessness. A meaningful sentence is meaningful if it's components are meaningful. — MindForged

A contradictory sentence is meaningless in that it doesn't correspond to any object with an identity. And an object without an identity is an absurdity. I don't even think it's an object; it's nothing.

And besides, the sentence "This sentence is false" seems perfectly meaningful and it has a referent in reality (the very sentence itself, as that's what it specifies). — MindForged

This sentence says that it has the property of falsehood and simultaneously says (implicitely) that it doesn't have the property of falsehood. Even though a part of it ("This sentence") refers to itself, the sentence as a whole (with the predicate "is false") doesn't refer to anything; it doesn't correspond to itself because it characterizes itself as both false and true when in fact it is just false (like any contradiction).

The phenomenon is known as 'ambiguous loss': it seems that the most balanced human reaction is to embrace the contradiction, i.e. to accept that the missing person is both alive and dead, like Schrodinger's cat. — mcdoodle

I can imagine that a person is unsure whether someone is dead or alive but I haven't met a person who believed that someone is both dead and alive.

Actually, the Platonic analysis of this apparently obvious point, was that no object truly is, on account of it being an appearance only, without inherent reality (following Parmenides.) But this is not so with 'ideal objects' such as numbers, which really are what they are; so A=A is always certain, but when it comes to the sensory or phenomenal domain, there are actually no 'A's as such, but only representations. — Wayfarer

But an appearance or representation is still identical to itself, no? An appearance of a triangle is an appearance of a triangle, not an appearance of a circle.

We call 'reality' what makes sense to us, what else? Logic is the formalization of that 'making sense'. Beyond that, it's not clear to me what you are asking about.

When you claim that object X has property P and object X does not have property P, you violate LNC by holding both the proposition "object X has property P" and its negation as true. And you simultaneously violate Law of Identity because you claim that object X is something it is not - that it has a property that it doesn't have. Such an object is absurd and cannot exist in reality. In this sense, reality is logical (logically consistent). Or do you think that reality contains objects that have and simultaneously don't have the same property?

Quantifying over the properties of an object is a second-order task, it's not relevant to the LNC which requires only 3 things: negation, conjunction and variables. Identity is not bound up with it. Again, you're equating equality with 3 separate notions. A contradiction is not the assertion that an object has a property "X" and lacks that property, it's the assertion that a proposition holds and it's negation holds. Again, FOL without identity exists while retaining the LNC, because equality is not defined in the language. I don't think this is disputable unless we pretend that logic doesn't exist. I believe Wittgenstein writes about it (but doesn't develop it further, thankfully Hintikka did) in the Tractatus.

I am sorry but your quote didn't explain why the authors believe that particles don't have identity. It just says that they don't have identity and that in many situations one cannot distinguish particles of the same kind. And I am not sure what they mean by "cannot distinguish particles of the same kind". Do they mean that the particles are exactly the same? But if the particles have different positions at the same time then they can be distinguished by their position, so position is a property that gives them distinct identities, even though all of their other properties are the same.

Well yea bro, I'm not gonna quote the entire paper. I named the paper at the end of the quote and offered to send to the PDF of the paper in question if you couldn't access Sci-Hub (it's having issues right now). And the quote I gave stated what it meant: the particles are, under this view, *metaphysically* indistinguishable and yet they are not identical. Reading the paper would really help, it goes over this in greater detail than appropriate in a forum post.

Actually, reality or existence in the most general sense includes all consistently defined objects - that is objects that have an identity. Objects that don't have an identity - objects that are not what they are, that don't have properties they have - are nonsense, so these are not included in reality.

"objects that are not what they are"
That's not what a contradiction is, why do you keep saying that? You could probably *derive* a contradiction from the assertion that "X !== X" but that's not the Law of Non-contradiction. Further, your original objection on this point was that because it does not "correspond to reality", which I assumed was physical reality since that was what I asked about in the OP.


You asserted that if Dialetheists argue there is a true contradiction (that the LNC is not true) then they are thereby employing the LNC. This could only be the case if the notion of a "contradiction" assumed the LNC, which doesn't make any sense. Rejecting the LNC simply means you believe there is at least one true proposition which also has a true negation.
— MindForged

Completely rejecting LNC means that you believe not only that there is at least one true proposition which also has a true negation, but that you also believe the opposite: that there is no true proposition which also has a true negation. As you see, such a belief is absurd and self-defeating. Even as you try to get rid of LNC, you still have to hold on to it. You can utter a contradictory statement, such as "there is a triangle that is not a triangle" (and at the same time hold on to LNC by regarding the statement as true rather than true and false), but I don't think you can find such a triangle in reality. I see no reason to admit such absurd objects in ontology.

Well this is the easiest thing in the world. I did not mention "completely rejecting the LNC" because Dialetheists don't completely reject it. They don't believe ALL contradictions are true, only some. So you were simply misreading what was said (I did, after all, specify that only one exception was a requirement for dialetheism). And also, to call the belief therefore "absurd and self-defeating" is either a meaningless designation or else it's question begging. If "absurd" or "self-defeating" simply mean "contradictory" then that's a bad way to argue for one's position.

A contradictory sentence is meaningless in that it doesn't correspond to any object with an identity. And an object without an identity is an absurdity. I don't even think it's an object; it's nothing.

This doesn't follow and it ignores the compositionality of meaning. If "It is raining" has meaning, and it's negation "It's not case that it's raining" are meaningful, then "It's raining and it's not the case that it's raining" is meaningful. Confusing "meaningless" and "false" (or even "necessarily false") is an error. Meaningless statements, by and large (if not always), are not truth-apt, they cannot be false. Identity has nothing to do with this.

I mean let's just demonstrate this. Take an open question in mathematics; I'll be unoriginal and use Golbach's Conjecture (GC). Either GC is the case or it's not the case (for the sake of argument). So if tomorrow we discover the GC is true, surely it must be necessarily true and those saying it was false were necessarily incorrect. Were those who were wrong about the GC uttering a meaningless assertion just because the GC turned out to be necessarily true? Of course not, because a meaningless proposition cannot even e given a truth-value, because it cannot even be interpreted. Contradictions can be interpreted, and that's precisely the reason they are necessarily false.

This sentence says that it has the property of falsehood and simultaneously says (implicitely) that it doesn't have the property of falsehood. Even though a part of it ("This sentence") refers to itself, the sentence as a whole (with the predicate "is false") doesn't refer to anything; it doesn't correspond to itself because it characterizes itself as both false and true when in fact it is just false (like any contradiction).

That's not the case. Just take relational semantics. There is a proposition "P such that "P" relates to truth and "P" relates to falsity. This is perfectly coherent and understandable in modern mathematics. Also, properties of objects don't "correspond to themselves". "This sentence" refers to the ENTIRE sentence, not to the phrase "this sentence". To not understand what sentence it refers to is to be blind, because there's only one such sentence there. It can even be made more explicit:

[The sentence in brackets is false.]

Now there's no way to avoid recognizing the referent. We can even do this purely formally like Tarski did:

~True(x) <=> T

The predicate "is false" is part of the sentence being referred to here. If your issue is with self-reference, well, I think you're up a creek there. Even classic and groundbreaking work in mathematics treats self-reference as a coherent concept (such as Godel numbering used in Godel's Incompleteness Theorems). I mean, "This sentence has five words" is equally self-referential and yet the predicate "has five words" is clearly the case about the sentence. Or "This sentence is an English sentence", etc. Heck self-reference crops up in everyday dialogue as well (Kripke has some classic examples of this phenomena) and few treat these as incoherent.

But an appearance or representation is still identical to itself, no? An appearance of a triangle is an appearance of a triangle, not an appearance of a circle. — litewave

It is - but when we say that 'one triangle is the same as another' that is an intellectual operation - we're able to say 'this shape is the same as that one' because of the rational ability to abstract and compare types. In fact we're able to categorise it as 'a triangle' on the basis of the same ability. So in this case, it is ideas that are being compared, not objects as such. So again, what is 'a triangle'? It is not an object per se - an object is this or that triangle, a particular - but what a triangle really is is a plane surface bounded by three straight lines.

The reason I mention it, is that according to this analysis, objects, per se, only have real identity as instances of forms. That is what enables reason to operate on them.

Your Platonism is showing.

Still labouring away....

And I am not sure what they mean by "cannot distinguish particles of the same kind". Do they mean that the particles are exactly the same? — litewave

It means that there are scenarios where you can have two (or more) particles that can't be physically distinguished, even in principle.

To see this, have a look at the Hong–Ou–Mandel effect. Figure 1 shows the four quantum states in superposition when two photons enter a beam splitter at the same time, one photon entering from above and one photon entering from below. (The minus sign for states 3 and 4 represents the phase shift for the lower photon reflecting from the lower side of the beam splitter.)

On a classical analysis, it would seem that on repeated runs of the experiment, each state should be observed a quarter of the time. However under quantum mechanics when (and only when) two states in superposition are physically identical, they interfere. What is actually observed is that the two photons always emerge together on either the upper or lower side of the beam splitter (i.e., either state 1 or 4). This means that states 2 and 3 always destructively interfere and so must therefore be physically identical, in principle. Which means there is no physical information identifying each emerging photon uniquely with one or the other of the entering photons. Thus raising an issue about our understanding of identity.

Thanks for that, you explained it quite well. My education at uni didn't require me to learn any physics more complicated (annoying) than relativity, so I generally bow out of QM discussions. xD

Even if identity is eventually determined to be preserved, I find considering such possible objections and potential revisions to be useful for a number of reasons. I never find arguments to the effect of "axiom X is inescapable and even denying it affirms it" compelling. Most of the time such arguments just assume the axiom in the metalanguage and use that assumption to claim the axiom will appear in any language whatsoever, even though it only appears in the corresponding object language because it's being assumed in the first place...

That logic could improve so much with the advent of Classical Logic via Frege, and improve over the prior Aristotelian Logic, motivates me to try not to assume that whatever logic is dominant at present is infallible or some such. That said, I'm mostly satisfied with some of the answers I got in this thread, thanks~

A contradiction is not the assertion that an object has a property "X" and lacks that property, it's the assertion that a proposition holds and it's negation holds. — MindForged

So please give me an example of a contradiction, and we'll see if it violates the identity of some object.

Well yea bro, I'm not gonna quote the entire paper. I named the paper at the end of the quote and offered to send to the PDF of the paper in question if you couldn't access Sci-Hub (it's having issues right now). — MindForged

It might help if you explained the reason why you think quantum particles don't have identity to someone who is a layman in physics. For me, two objects (particles or whatever) are identical (metaphysically indistinguishable, that is, one and the same object) iff all of their properties are the same (including e.g. their position in space). This is just the principle of identity of indiscernibles or indiscernibility of identicals. So how is this violated in QM?

Well this is the easiest thing in the world. I did not mention "completely rejecting the LNC" because Dialetheists don't completely reject it. They don't believe ALL contradictions are true, only some. — MindForged

That's why I said that they still need LNC even though they relax it in certain situations. In ontology I wouldn't relax LNC at all because it would mean to accept the existence of objects without identity (with violated identity.)

If "It is raining" has meaning, and it's negation "It's not case that it's raining" are meaningful, then "It's raining and it's not the case that it's raining" is meaningful. — MindForged

I clarified that by "meaningless" I meant that the sentence doesn't correspond to any object with identity. What object does the sentence "It's raining and it's not the case that it's raining" (as a whole) correspond to? There exists no such state of weather; it would be an absurd state of weather.

There is a proposition "P such that "P" relates to truth and "P" relates to falsity. — MindForged

What do you mean by "relates to truth"? Simply that it "is true"? Your above proposition seems to mean that something is true and not true, which is a contradiction.

"This sentence" refers to the ENTIRE sentence, not to the phrase "this sentence". — MindForged

I agree. The phrase "this sentence" refers to the entire sentence. But the entire sentence as a whole doesn't refer to anything, because there is no sentence that is both false and true. The entire sentence says it is both false and true, but in fact it is just false (like any contradiction).

I mean, "This sentence has five words" is equally self-referential and yet the predicate "has five words" is clearly the case about the sentence. — MindForged

This sentence as a whole refers to itself because it indeed has five words.

So again, what is 'a triangle'? It is not an object per se - an object is this or that triangle, a particular - but what a triangle really is is a plane surface bounded by three straight lines. — Wayfarer

Both particulars and universals are objects because they are identical to themselves and different from what they are not.

Well, I suppose so. I admit I was trying to make a point which was somewhat tangential to yours. (Although universals are not actually 'objects' except for in a metaphorical sense.

To see this, have a look at the Hong–Ou–Mandel effect. Figure 1 shows the four quantum states in superposition when two photons enter a beam splitter at the same time, one photon entering from above and one photon entering from below. — Andrew M

So at the beginning of the experiment the two photons are not identical because they have at least one different property - position in space: one is above the beam splitter, the other is below.

What is actually observed is that the two photons always emerge together on either the upper or lower side of the beam splitter (i.e., either state 1 or 4). — Andrew M

So at the end of the experiment both photons have the same position in space? If so, can we say they are just one photon? I guess not, because there is energy of two photons there, not of one. So the two photons must be numerically different. But what is their distinguishing property then? I think their distinguishing property is their different position in an abstract space where even photons with all the same physical properties are distinguished. I don't know how to call it, perhaps primitive particularity or "thisness".

Whether the two photons at the end of the experiment can be distinguished by physicists seems to be an empirical problem, not ontological. Also, whether each photon at the end of the experiment is the same photon as it was at the beginning of the experiment is a question of the preservation of identity through time. Identity doesn't have to be preserved in time; an object can be annihilated, or merged with another object, or separated from another object at some point in time. But at each point in time an object is identical to itself and different from other objects.

So please give me an example of a contradiction, and we'll see if it violates the identity of some object.

It's raining and it's not the case that it's raining. I'm sserting a proposition and its negation both hold, not that there is some object which has and lacks a property (that *is* a contradiction).

It might help if you explained the reason why you think quantum particles don't have identity to someone who is a layman in physics. For me, two objects (particles or whatever) are identical (metaphysically indistinguishable, that is, one and the same object) iff all of their properties are the same (including e.g. their position in space). This is just the principle of identity of indiscernibles or indiscernibility of identicals. So how is this violated in QM?

Because particles can share all their physical properties, yes, including what space they occupy (see the link to a relevant effect that a previous user posted). And come on, just gesturing at Leibniz's Law does nothing different than gesturing at the Law of Identity. The Indiscernability of Identicals will fail if identity is not part of the language or if it fails to be applicable to some class of objects (see the paper I mentioned, it goes over this in a way physics laymen are more likely to understand, even giving an analogy IIRC)

Well this is the easiest thing in the world. I did not mention "completely rejecting the LNC" because Dialetheists don't completely reject it. They don't believe ALL contradictions are true, only some.
— MindForged

That's why I said that they still need LNC even though they relax it in certain situations. In ontology I wouldn't relax LNC at all because it would mean to accept the existence of objects without identity (with violated identity.)

I don't think you understood me. Accepting that not all contradictions are true is *not* the LNC, that's simply a rejection of Trvialism. That's not using the LNC, because rejecting the LNC does not entail accepting all contradictions.

I clarified that by "meaningless" I meant that the sentence doesn't correspond to any object with identity. What object does the sentence "It's raining and it's not the case that it's raining" (as a whole) correspond to? There exists no such state of weather; it would be an absurd state of weather.

Well that doesn't make sense then since each conjuct does have a referent. If you don't mean "meaningless" just use a different word. Heck, we even have a proper term for this in logic: False. Of course the situation is false, but you were going beyond that for some strange reason. Contradicions are false, not meaningless (lacking a *physical* referent is irrelevant).

What do you mean by "relates to truth"? Simply that it "is true"? Your above proposition seems to mean that something is true and not true, which is a contradiction.

Truth assignment in logic is a relation (usually a function, but not in this case) between a proposition and a semantic value. In other words, a proposition is true when some proposition (or whatever truth bearer you have in mind) relates to the value "true" (pRt), and it's false if it relates to the value "false" (pRf). I'm aware it's a contradiction, that's the whole point. One can give a perfectly coherent semantics for how a contradiction holds, using the techniques of modern math.

"This sentence" refers to the ENTIRE sentence, not to the phrase "this sentence".
— MindForged

I agree. The phrase "this sentence" refers to the entire sentence. But the entire sentence as a whole doesn't refer to anything, because there is no sentence that is both false and true. The entire sentence says it is both false and true, but in fact it is just false (like any contradiction).

That's ridiculous. The sentence clearly has a reference: itself. If it didn't have a reference it couldn't have a truth-value. Both Classical Logicians and Dialetheists agree that contradictions have the proeprty of being false (Dialetheists believe they are also true, as explained above). Saying that "the sentence doesn't refer to anything because there is no sentence which is true and false" entails rejecting that a contradiction is even a thing at all, which is ludicrous. The contradictory sentence exists. If on your view it is simply false, the sentence exists so saying the sentence lacks a referent is gobbldygook (non-existent things cannot have a proeprty like falsehood.)

This sentence as a whole refers to itself because it indeed has five words.

That is completely ad hoc. Self-reference doesn't prevent a sentence from having a truth-value, being contradictory doesn'r stop it from having a truth-value (a contradictory sentence is a false sentence after all) and both the Liar sentence and "This sentence has five words" have clear referents.

Whether the two photons at the end of the experiment can be distinguished by physicists seems to be an empirical problem, not ontological. Also, whether each photon at the end of the experiment is the same photon as it was at the beginning of the experiment is a question of the preservation of identity through time. Identity doesn't have to be preserved in time; an object can be annihilated, or merged with another object, or separated from another object at some point in time. But at each point in time an object is identical to itself and different from other objects.

It's an ontological issue bearing on identity, not an empirical (epsitemic) one. As per the article linked, the photons are completely physically indistinguishable.

We assume now that the two photons are identical in their physical properties (i.e., polarization, spatio-temporal mode structure, and frequency).
[...]
Since the two photons are identical, we cannot distinguish between the output states of possibilities 2 and 3 in figure 1, and their relative minus sign ensures that these two terms cancel. This can be interpreted as destructive interference.

I can imagine that a person is unsure whether someone is dead or alive but I haven't met a person who believed that someone is both dead and alive. — litewave

My proposal is just an emotional equivalent to the logical argument: that there are many situations in life where one holds two possibilities to have equal weight, and must live with that fact, which to a logician is 'contradictory'.

To me the issue also happens in some supposedly binary choices in ethical dilemmas, where there is no right answer: there the important thing is to commit, one way or the other, and live with the consequences. I think many consequentialist thought-games are like that, where one is supposed to add up likely deaths from this action and compare with likely deaths from an alternative: that isn't how ethical choices happen, it's just a logician's game empty of serious human meaning.

It's raining and it's not the case that it's raining. I'm sserting a proposition and its negation both hold, not that there is some object which has and lacks a property (that *is* a contradiction). — MindForged

By asserting this contradiction you are also asserting an object ("it"/weather) has the property of raining and does not have the property of raining. Since the identity of every object is determined by its properties, you are asserting that the object is not identical to itself. By asserting a contradiction, you violate the identity of an object.

I don't think you understood me. Accepting that not all contradictions are true is *not* the LNC, that's simply a rejection of Trvialism. That's not using the LNC, because rejecting the LNC does not entail accepting all contradictions. — MindForged

Ok, I automatically also assumed the principle of explosion. So, you can reject LNC and accept only some contradictions as long as you block the principle of explosion in some way and thus prevent contradictions from spreading to all other statements. Blocking the principle of explosion seems an arbitrary act but I guess it can be useful in some situations like where you don't want contradictions to contaminate a whole information system - it's a pragmatic solution designed to prevent spreading of false information but with no implications for ontology (reality). In ontology I reject all contradictions because contradictions refer to absurd objects without identity.

The contradictory sentence exists. If on your view it is simply false, the sentence exists so saying the sentence lacks a referent is gobbldygook (non-existent things cannot have a proeprty like falsehood.) — MindForged

The sentence "This sentence is false." exists but it doesn't refer to itself. Only a part of it ("This sentence") refers to the sentence. Compare with the sentence "My dog is not a dog.": a part of the sentence ("My dog") refers to my dog but the sentence as a whole doesn't refer to anything because there is no dog that is not a dog.

I think this has to do with uncertainty of knowledge, not with ontological contradictions.

By asserting this contradiction you are also asserting an object ("it"/weather) has the property of raining and does not have the property of raining. Since the identity of every object is determined by its properties, you are asserting that the object is not identical to itself. By asserting a contradiction, you violate the identity of an object.

Identity regards the properties of an object, LNC regards whether some proposition is the case or is not the case. Again, if you drop equality out of classical logic, you get First-Order Classical Logic without Identity, which still retains LNC. You keep switching between metaphysics and logic without recognizing the difference. LNC doesn't make reference to identity at all, nor does Identity entail LNC (otherwise such a logic could not exist, yet it does).

Ok, I automatically also assumed the principle of explosion. So, you can reject LNC and accept only some contradictions as long as you block the principle of explosion in some way and thus prevent contradictions from spreading to all other statements. Blocking the principle of explosion seems an arbitrary act but I guess it can be useful in some situations like where you don't want contradictions to contaminate a whole information system - it's a pragmatic solution designed to prevent spreading of false information but with no implications for ontology (reality). In ontology I reject all contradictions because contradictions refer to absurd objects without identity.

Well I mentioned Paraconsistency in the OP so it didn't come out of nowhere (there'd be no reason to advocate for a true contradiction unless you dropped explosion). And it's not arbitrary to do this; if you accept the Liar as a sound argument you need to eliminate or restrict an inference rule that generates explosion.

The sentence "This sentence is false." exists but it doesn't refer to itself. Only a part of it ("This sentence") refers to the sentence. Compare with the sentence "My dog is not a dog.": a part of the sentence ("My dog") refers to my dog but the sentence as a whole doesn't refer to anything because there is no dog that is not a dog.

I don't know what you're trying to say here. Only the phrase "this sentence" has a referent, the entirety of a sentence can't have a referent. The sentence you gave is simply a contradiction, it's not false because it lacks a referent, and besides which that sentence isn't even self-referential. It's false because it's a contradiction, all of which are necessarily false (even under Dialetheism). "This sentence is false" has a referent in any way that one defines what a referent is. Your argument would entail that "This is an English sentence" either lacks a referent or is false, which seems ridiculous.

Identity regards the properties of an object, LNC regards whether some proposition is the case or is not the case. — MindForged

But what is a proposition? It is a statement that assigns a property to an object. So when you deal with propositions you can't avoid dealing with objects and their properties and thus with identity of objects. So tell me an example of a contradictory proposition that doesn't violate the identity of some object.

Well I mentioned Paraconsistency in the OP so it didn't come out of nowhere (there'd be no reason to advocate for a true contradiction unless you dropped explosion). And it's not arbitrary to do this; if you accept the Liar as a sound argument you need to eliminate or restrict an inference rule that generates explosion. — MindForged

Liar is a contradiction so I regard it as false.

I don't know what you're trying to say here. Only the phrase "this sentence" has a referent, the entirety of a sentence can't have a referent. — MindForged

Take the sentence "My dog is black". This sentence as a whole has a referent in reality. The referent is the fact that my dog is black.

But what is a proposition? It is a statement that assigns a property to an object. So when you deal with propositions you can't avoid dealing with objects and their properties and thus with identity of objects. So tell me an example of a contradictory proposition that doesn't violate the identity of some object.

Um, that's incorrect. A proposition is just an object, whose ontological status will depend on what view you adopt about abstract objects. A statement is not the same thing as a proposition, though they are related.

As for a contradiction that doesn't violate identity, well, just post any arbitrary contradiction. I'll stipulate, for my example, that it's in a language which lacks equality, and therefore the semantics required for identity. "P & ~P". A contradiction and therefore false to be sure, but identity isn't required.

Liar is a contradiction so I regard it as false.

Well even dialetheists agree with that.

I don't know what you're trying to say here. Only the phrase "this sentence" has a referent, the entirety of a sentence can't have a referent.
— MindForged

Take the sentence "My dog is black". This sentence as a whole has a referent in reality. The referent is the fact that my dog is black.

No, that's not what a referent is. A referent is what the sentence is about. The referent of "My dog is black" is the dog in question, not "reality". In exactly the same way, "This sentence is false" has a referent: itself. That's what "This sentence" is pointing at, so to speak.

Um, that's incorrect. A proposition is just an object, whose ontological status will depend on what view you adopt about abstract objects. A statement is not the same thing as a proposition, though they are related. — MindForged

A proposition, whatever its exact nature, assigns a property to an object. So propositions are inseparable from identities of objects.

As for a contradiction that doesn't violate identity, well, just post any arbitrary contradiction. I'll stipulate, for my example, that it's in a language which lacks equality, and therefore the semantics required for identity. "P & ~P". A contradiction and therefore false to be sure, but identity isn't required. — MindForged

You still haven't given an example of a contradictory proposition that doesn't violate the identity of some object. "P & ~P" is not an example; it's a general symbol for a contradictory proposition.

No, that's not what a referent is. A referent is what the sentence is about. The referent of "My dog is black" is the dog in question, not "reality". — MindForged

The sentence "My dog is black" is not just about the dog but also about the dog's relation to black color.

A proposition, whatever its exact nature, assigns a property to an object. So propositions are inseparable from identities of objects.

No, a proposition is just an object. An object doesn't assign properties to itself, an object is just something with properties.

As for a contradiction that doesn't violate identity, well, just post any arbitrary contradiction. I'll stipulate, for my example, that it's in a language which lacks equality, and therefore the semantics required for identity. "P & ~P". A contradiction and therefore false to be sure, but identity isn't required.
— MindForged

You still haven't given an example of a contradictory proposition that doesn't violate the identity of some object. "P & ~P" is not an example; it's a general symbol for a contradictory proposition.

I said the contradiction can be arbitrary, so it doesn't matter what you substitute for "P". The Golbach Conjecture is true and it isn't true.

The sentence "My dog is black" is not just about the dog but also about the dog's relation to black color.

You are shifting the goal post. The referent is what the sentence is about, the predicate tells us that the object in question is related to black. Your initial objection here was the claim the Liars lack a referent in reality. The Liar sentences have a referent (themselves) and that's just the way it is. It doesn't commit you to dialetheism so I don't see the issue acknowledging that. The Liar paradoxes are notoriously difficult to solve; even logicians (who study this phenomenon) don't have a standard resolution. The only agreement seems to be that no one has done a proper solution, and whatever the solution ends up being will necessarily be rather strange since all the non-strange/obvious "solutions" have failed.

No, a proposition is just an object. An object doesn't assign properties to itself, an object is just something with properties. — MindForged

When you say "The dog is black" you assign the property of blackness to the dog.

I said the contradiction can be arbitrary, so it doesn't matter what you substitute for "P". The Golbach Conjecture is true and it isn't true. — MindForged

Well, you have just said that an object (Goldbach Conjecture) both has the property of being true and doesn't have the property of being true. Again, you have violated the identity of an object.

The referent is what the sentence is about, the predicate tells us that the object in question is related to black. — MindForged

The sentence "The dog is black" is about the situation of a dog having the property of blackness. Its referent is not just the dog, and not just blackness, but the whole situation.

Your initial objection here was the claim the Liars lack a referent in reality. The Liar sentences have a referent (themselves) and that's just the way it is. — MindForged

The Liar sentence "This sentence is false" says that the sentence is both false and not false, so its referent is a situation where the sentence is both false and not false. But such a situation doesn't exist, because the Liar sentence is just false (like any contradiction). So the Liar sentence has no referent.