Ok, no one is advocating the same sort of materialism as in the 17th century. There's a reason a few people have mentioned "physicalism". You are simply choosing to overreact rather than try to understand what was said. Also, how is materialism (physicalism) goal-oriented??? I honestly can't tell if you are just messing around.

The first thing to note is that questions aren't true or false, plausible or implausible. Only propositions are, as I've always understood the words 'true' and 'plausible'. Second, the question I raise is hardly ridiculous. Is there any reliable way to tell that things exist when unperceived? If there isn't, then the belief that things exist unperceived is sheer guess work. The question itself isn't the idle speculation. Rather, a failure to answer the question shows that the belief in unperceived existence is idle speculation.

You're being too pedantic. Obviously questions aren't truth-apt, I was referring to the proposition to which your question was about: Objects either existing when unperceived or failing to exist when unperceived.

It isn't guesswork. I'll repeat: Do you think objects exist when perceived? Your next bit indicates you do so I'll continue after quoting it, because I may not have been clear what I've been driving at:

Lastly, yes, I agree that some objects exist when perceived. Hold up a piece of paper in front of your face. There is something that exists at the moment when you are perceiving it. But that doesn't settle the question of whether it exists unperceived.

Ok, so you agree objects exist when perceived and your question is if they exist unperceived. The only way this question can be interesting beyond idle speculation is if there is a relation between "perceiving a thing" and "that thing exists". Now why is this the case? Well, if you agree it exists when perceived, we have justification for believing the thing exists. After all, as you said, we perceived the thing in question. If I then ask "But does it exist when I'm not perceiving it?", I have to be making the following assumption:

"There is a relationship (causal presumably) between perception and existence. Perception brings a thing into existence."

Because otherwise what is the connection between not being perceived and not existing? No one says "Oh you weren't considering that maths problem so the conclusion of the problem doesn't exist", because that seems like a non sequitur. What do those 2 things have to do with each other. To just state it plainly: Why should I think objects don't exist when not perceived given that I accept they exist when I do perceive them? Perceiving them gives evidence that the objects at least existed at that time. But does it therefore mean that not perceiving them lends justification to the idea that they don't exist otherwise?

If you say that we need a reason to think they continue to exist, I don't know how we require further justification than that they did exist when we perceived them unless you think perception brings objects into being. Maybe I'm missing something, because this seems like pure speculation.

But I never attempted to prove that things don't exist unperceived, so I don't need to establish any causal relation between perception and existence. I asked whether there is any way that I can know that things do exist when unperceived. I haven't speculated at all. Simply raised a question.

Well I can raise a question about any old thing I want. Perhaps mathematical truths are only true when a conscious being considers their truth value. But as with your "simple question", unless there is a reason to motivate considering the question as being true or at least plausible, it seems like idle speculation. And that you seem to accept that objects exist when perceive would entail some kind of relationship between existence and perception if we wish to raise a question about if they exist unperceived.

A state isn't an object, it cannot be physical. If one equates brain states with consciousness, one is not saying a "state" is a physical thing nor does it entail your favorite quantum woo.

A "state" in this case can be understood as the way the world is, some particular arrangement that you pick out in a proposition or sentence or something of that sort.. No one said the states are physical, because one need not assume a state is a thing in and of itself.

When you're doing logic, you're using these rules and axioms to derive other truths. That's what logical consequence is, no? Like, if I have "A & B" then I can deduce that "A".

I already answered this. Even if I assume time is relative in the way you suggest, the LNC forbids a proposition and its negation from being true in the same sense. That does not exclusively mean "at the same time" (though it can mean that). Example:

"2+2=4 & it's not the case that 2+2=4"

There is no concept of time imported here, it's just the conjunction of a proposition with its negation and regards a formal, time-independent matter. And yet, it's a contradiction. Ergo the concept of a contradiction does not require the concept of time to be assumed.

So? Lacking a reason to think that Not-P is not a reliable means of establishing that P. It isn't a reliable method of establishing anything.

From your OP I assumed you accepted that objects that we perceive exist. If that is the case, to give any reason to believe they do not exist when unperceived, don't you need to establish some causal relation between perception on one hand, and existence (or at least persistence) on the other? Otherwise it just looks like an arbitrary speculation.

But without identity there is not really an object. I don't know what it would mean that an object has no identity or what it would mean that the law of excluded middle does not hold. Paraconsistent logic and intuitionistic logic seem to characterize imperfect knowledge rather than objects in reality.

So you say, and yet the entire point of this view (non-reflexive logics and the referenced view in QM) is that it might be the case that you can have an object without an identity. That just makes your post question begging against an opposing view. I've told you what it could mean: That identity only holds for some objects and not others, which is sketched out via a restriction in the logic as to what identity applies to. If you're looking for an in-depth semantics as to how this can work, well, I already reference the papers. Here, I'll even link them:

Classical Logic or Non-Reflexive Logic? A case of Semantic Underdetermination

The Received View on Quantum Non-Individuality: Formal and Metaphysical Analysis

Otherwise just responding by importing Identity into the metalanguage is just ignoring how the objection is formulated and I'm not interested in that.

As for Paraconsistent Logic and Intuitionistic logic, I think you're incorrect. Or rather, your view about them is not what their proponents believe about those logics. Intuitionists certainly don't believe that their formalism is simply about "imperfect knowledge" or something. Michael Dummett certainly didn't believe that, and Graham Priest definitely believes true contradictions exist (even in the world itself).

So there is a language in which an object can have and not have the same property?

One can construct a language (easily in fact) where equality is not part of the language, ergo identity isn't. Your forumlation of identity is incorrect; that is simply a contradiction.

The Wiki quote just says that the referent of the word "Mary" is Mary and the referent of the word "me" is me, with which I agree. But the whole sentence "Mary saw me" is a linguistic expression too, and its referent (meaning) is the situation that Mary saw me.

"Black" is not a referent though, it's a predicate, a proeprty an object may have or lack. In your sentence, the "dog" is the only referent in the sentence.

The referent of the word "Dog" is the dog, the referent of the word "black" is black (color), and the referent of the sentence "The dog is black" is the situation that the dog is black.

You're confusing a predicate with a referent, and you're mistaking a state of affairs (or "a situation") with a referent. A referent can obtain in some state of affairs, but the sentence you typed had only one referent.

That's why I said in an earlier post that the Liar sentence says "implicitely" that it is true. But that doesn't matter. The meaning of the sentence is that it is both false and true, and that's what matters. That's why it is a contradiction.

That's certainly an implication of it. That said, it's referent is itself, it's not a situation. "false" is not a referent, so I don't know how your comparison with "My dog is black" is even relevant here, seeing as it's neither self-referential nor does the Liar lack a referent. What do you think self-reference even means? That a situation refers to itself? That's nonsense. Sentence can have references to themselves, not situations.

Because you haven't given a reason to motivate believing existence or persistence is dependent upon perception.

An interesting quote from a paper I had saved on my laptop might be of interest here with the discussio of identity in QM and how one can give an understanding of the law of identity not applying:

This is also connected with a second point. What exactly is meant when
we say that we deny a tautology (or a logical law, or a logical necessity)? In
denying that an axiom of classical logic is valid in general, don’t we have to
accept that this ‘axiom’ is false in at least one interpretation of an alternative
system in which the same formula may be expressed? Consider, for instance,
intuitionistic logic. In denying the validity of some instances of the law of
excluded middle, it is not the case that intuitionists accept its negation in its
place. However, they do accept that the law may be false sometimes (mostly
when we deal with infinite collections). For another example, consider some
paraconsistent logics, like those in da Costa’s Cn hierarchy. In denying the
Explosion Law, it is certainly not accepted as an axiom (or as logically valid
in the system) the negation of the Explosion Law, but some of its instances
must be false in some valuations. So, the argument could go, in denying the
universal validity of the reflexive law of identity in non-reflexive logics, are we
not committed to accepting that it may be false sometimes?
As we have said in the previous section, in non-reflexive logics we do not
accept the negation of the reflexive law of identity. Also, we don’t have to accept
that it must fail in at least some interpretations. Rather, we adopt its restriction
in the form of its inapplicability. Here, ‘inapplicability’ is couched in terms of
identity not making sense, not being a formula, for some kinds of terms. — The Received View on Quantum Non-Individuality: Formal and Metaphysical Analysis

In other words, Identity (arguably) not applying to a certain class of objects is not the same as saying "An object has a property and does not have that property".

Fair enough.

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'm aware. What you said, however, was that objects assign properties,; objects don't do anything. Objects have properties. If that's what you meant then there was a typo somewhere in your post.

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.

That's a contradiction, not an identity violation. Without equality in the language identity isn't present within the language.

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.

No it isn't that's not what a referent is. I hate to quote Wiki of all places but it states it plainly:

"A referent (/ˈrɛfərənt/) is a person or thing to which a name – a linguistic expression or other symbol – refers. For example, in the sentence 'Mary saw me', the referent of the word 'Mary' is the particular person called Mary who is being spoken of, while the referent of the word 'me' is the person uttering the sentence."

The referent of "The dog is black" is the dog in question, not "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.

The Liar sentence does not say it is both true and false. The Liar claims, of itself, that it is false. That the Liar is also true is entailed by it being false. Further, you are again confused about what a referent is. A referent is not the situation to which a proposition refers unless that's explicitly what some proposition refers to. I'll repeat an obvious example to demonstrate this:

[The sentence in brackets is false.]

The referent is itself, the only sentence in brackets. It's not referencing a "situation". The Liar has a referent, being a contradiction does not change that.

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.

Please read my OP. I've given the references. I don't see how there can be a contradiction when time isn't absolute.

??? I said there isn't a contradiction. Also, what @Rich said.

I was not referring to any "particular set of axioms" as being indispensable, although it is arguable that there are some axioms that seem to be fundamental to human experience; and that consequently seem self-evident, and anyone can intuitively 'get' them. The axioms of Euclidean geometry would seem to fall into this category. Of course, non-Euclidean geometries exist, but they are not intuitive in the 'direct' way that Euclidean geometry is.

But doesn't that show the weakness of this view (relying on intuition to settle the matter)? Intuition doesn't really seem to lend much justification to accept what we are "getting" via it, and worse, intuition can cause us to dismiss truths which conflict with them. You mention Euclidean Geometry as being direct and intuitive, but some of our best scientific theories suggest we have to understand the space of the universe as being Non-Euclidean (Relativity comes to mind).

That's not to say intuitions aren't important, but I'd probably not hold them in too high a regard when discussing "deeper" issues.

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.

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.

No it's not, that's the thing. An axiom would be something presupposed as true, or assumed as true, or necessarily implied as true. But the LNC is not a presupposition or assumption or a necessary implication of anything, it just has the form of such, which is what's misleading. But because it's not a truth claim, it's not for refuting.

Um, what? It literally is an axiom. That's how it's introduced within a logic, it's presupposed as true in all models. It is a truth claim. Specifically, it is the claim (assumption) that either a proposition "P" is true or the negation of "P" is true, but not both. So if one wants to attempt to refute it, one merely (if possible) has to show that some propositions is true and its negation is true as well.

For example "A = A" (which is the root of the others, which are just "corollaries" IMHO, although even saying that could be misleading) looks like you're making a truth claim about reality, like this is an assumed fact, or a discovery about reality or the world. But it's actually just setting out the rules of the game: "We will use "A" consistently."

Well I didn't say these had to be assertions about reality. These can be understood purely formally and syntactically. And if you read some previous stuff in the thread, it's not clear identity is universally applicable.

What on earth would it mean to say that "a thing is identical with itself"? Is that an informative statement

I dislike that rendering because it doesn't tell you much. A better definition is that identity is a reflexive, transitive and symmetric relation.

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.

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.

You can refute an example of inconsistency, but how do you "refute" the very commitment to remain consistent that defines reason?

Didn't I answer that? We are committed to *trying* to remain consistent, but that doesn't mean we can actually meet that commitment. Nor, do I think the commitment (surely this is normative) to remain consistent is what defines reason. We can be perfectly reasonable in holding contradictory beliefs or separate beliefs that contradict each other. If we have good reason to hold these conflicting beliefs, but no way to resolve the contradiction (if resolution is possible), then the reasonable thing to do is to maintain the contradiction until you are able to resolve it.

(Not trying to be flip here, this is really how I see it. The LNC is on a different level from things that use the LNC. The form of it makes it look like an object-language statement - which could be consistent or inconsistent - but I think it's really a statement of intent.)

It's an axiom and it's generally reasonable, even to the Dialetheist. Even granting that we ought to remain consistent (as possible), what we intend to do might not be identical to what we are able to do in practice.

I'm just here to say the title of this thread is hilarious. Props~

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~

Well I missed where the disagreement was then, we both said that Godel showed a limitation on the ability to give proofs in mathematics. Sooo, eh, whatever.

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.

By the principle of identity I mean that an object is identical to itself: that it is what it is. That's what this principle has meant since ancient Greece:
https://en.wikipedia.org/wiki/Law_of_identity

When you violate this principle of identity you also automatically commit a contradiction and when you commit a contradiction you automatically violate this principle of identity: you say that object X is not object X, or: "Object X has property P" AND "Object X does not have property P".

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. Again, there is a version of *classical* logic which ditches identity and yet the LNC is still provable. Identity and LNC are not bound together, that's some weird Aristotelian view, not a view in modern logic.

If two objects are metaphysically indistinguishable then they are one and the same object. Can two electrons in quantum mechanics be distinguished? Well it seems they can; they can be distinguished by at least one of their properties - by their position in space. It also depends on how you define "electron".

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.

I don't claim you can't utter contradictions like this one. But contradictory sentences don't correspond to any object in reality. They are just a string of words that doesn't correspond to anything in reality. They have no meaning.

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. And you *did* say you can't utter contradictions. Just look:

And do they say that it is true that there is such a case? If so, then they are employing the law of non-contradiction. — litewave

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. Nothing in the prior sentence assumes the LNC, it is literally in direct violation of it, because it's proposing that a contradiction holds.

The sort of argument you're trying to make is just question-begging; you're trying to sneak the LNC into the meta-language as a means of claiming it's inescapable in the object language.


Also, it's just false to say contradictions have no meaning. Even in Classical Logic, contradictions do have a meaning. The thing is that their meaning is such that they cannot be true in such a logic (or indeed, in any logic besides a dialetheic logic). Being contradictory isn't sufficient for meaninglessness. A meaningful sentence is meaningful if it's components are meaningful. If "P" is meaningful, and "Not-P" is meaningful, "P & Not-P" will be meaningful. The conjunction will simply be false though, not meaningless.

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). After all, an equally self-referential sentence like "This sentence has five words" is meaningful. These questions aren't easy, but besides that, I've taken us on a tangent from the OP. Dear lord, lol.

"Reality", as I take it to mean here, is the sum total of what there is and how it all interacts. To state there is something "fundamental to reality" creates a false distinction - for how can one part of "reality" be fundamental and another part be secondary for "reality"?

I can mostly jive with what you're saying. However, here I think there's something one might argue. To say that something is reality is "more fundamental" than something else would, I suppose, mean that the "less fundamental" thing is ontologically dependent on the more fundamental thing. So I suppose the argument could be that "logic is fundamental to reality" means that logic (of some sort) forms the final ground upon which everything else in reality is dependent on in order to be.

Whether this works or not, I don't know. It just came to mind as the possible intended interpretation of this sort of argument. Though I don't think it flies for reasons I gave in the OP.

Do they say that an object is not what it is? That an object is not identical to itself?

The POI says that for every "x", x stands in a symmetrical, transitive and reflexive relation with itself. I think stating the the way you have is somewhat misleading because it ignores how exactly identity is understood and how it is applied. In the case of Non-reflexive logics and quasi-set theory as they relate to quantum mechanics, you misunderstand. To restrict the domain of application of the POI means that the objects is question are metaphysically (not epistemically) indistinguishable. Or to quote the paper in question:

"Quantum mechanics raises some ontological issues which are hard to deal with in simple terms. More than one of those issues concern the relationship between quantum mechanics and logic, and here we shall be dealing with a particular aspect of one such logical problem. We begin by recalling the infamous Problem of the Identical Particles. According to a widely held interpretation of non-relativistic quantum mechanics, there are many situations in which one cannot distinguish particles of the same kind; they seem to be absolutely indiscernible and that is not simply a reflection of epistemological deficiencies. That is, the problem, according to this interpretation, is seen as an ontological one, and the mentioned indiscernibility prompted some physicists and philosophers alike to claim that quantum particles had "lost their identity", in the precise sense that quantum entities would not be individuals: they would have no identity. Entities without identity such as quantum particles (under this hypothesis) were claimed to be non-individuals."

-"Classical Logic or Non-Reflexive Logic? A case of Semantic Underdetermination" — Krause & da Costa

(I can forward this paper if you can't get it from sci-hub)

And do they say that it is true that there is such a case? If so, then they are employing the law of non-contradiction.

You don't seem to understand what the Law of Non-contradiction is. The LNC says that either a proposition "P" is the case or the negation of "P" is the case, not both. Merely using the concept of truth and saying there is a case where the LNC fails does not employ the LNC. Let's make this simple with the example I mentioned (don't debate the example here if you wish to contest it; there is already a thread on this is the logic section):

"This sentence is false."

There's not question of what the referent here is. It specifies an object (itself), a sentence, and asserts that the sentence is not the case. But if the sentence is not the case, then what the sentence says is not the case. But the sentence says, of itself, that it isn't the case. So it's true. But it's truth entails its own falsity as well. Yes it's a contradiction, but it follows from relatively simple principles that are not obviously incorrect.

Your argument would hold that contradictions cannot even be uttered, which is patently silly otherwise we wouldn't even know what the LNC is. You need not accept the Liar sentences as counter-examples to the LNC, but your own argument about the LNC does not work. Accepting at least one violation to the LNC does not commit one to the view that every contradiction is true (that's why these proponents suggest using a paraconsistent logic).

Again, the following paper is quite thorough and is relatively easy to understand, even for those with little to no background in formal logic: "What is an Inconsistent Truth Table?"

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. And when the identity and difference of objects is established, all propositions about them are logically consistent. This is basically the law of identity or non-contradiction. Without this law, reality would be absurd and even the difference between existence and non-existence would be erazed. I have no idea what that would mean.

This is not an obvious truth. Take Identity. There are known systems of logic which lack the Principle of Identity or even change the law itself. Namely, take a look a Non-Reflexive logics and quasi-set theory, mostly associated with Newton da Costa. The stated point of these formal systems is the claim that issues in quantum mechanics may require changing identity or else what we think it applies to. You can have the Law of Non-contradiction without the Law of Identity, as these logics have the LNC without identity. Or heck, there's a version of classical logic without identity; aptly called "first-order classical logic without identity".

I'd recommend Graham Priest's book which has some discussions about other potential issues where identity may come into question (issues regarding the nature of instantiation, from what I recall): One. That said, Identity is fine with me. I just mean to say you can work without it, or at least work with an altered or restricted version of it

Even the logic systems that relax the law of non-contradiction in certain situations, like the paraconsistent logic, would not work without the law of non-contradiction - because they need to specify - non-contradictorily! - how the law of non-contradiction is relaxed. They just seem to block the spreading of contradictions to other parts of an information system to save the whole system from becoming worthless. If they completely abandoned the law of non-contradiction they would be worthless because they would automatically negate whatever claim they would make.

Well this is just false.The way that (dialetheic) paraconsistent logics deny the Law of Non-contradiction is simple. They merely give a case wherein (according to them) there is a proposition which is true and its negation is true as well. A typical case is the Liar sentence. Denying the LNC as a tautology does not "automatically negate whatever claim they would make", they simple give an example they (dialetheists) believe shows the LNC to fail to be a tautology. For the dialetheist, the whole point of removing the principle of explosion is that it prevents the true contradiction from trivializing the logic, so what you say here seems incorrect.

Heck, paraconsistent logics have even been done within their own meta-theory (meaning consistency is not a requirement), such as here: "What is an Inconsistent Truth Table?"

In another sense there seems to be something built into the universe that lends itself to logic or mathematics. I would think that any possible universe is governed by rules, and by rules that have some consistency, at least generally. I would say that for any possible universe there are fundamental rules or laws that allow us to use logic to describe that universe. One could also argue that the fundamental rules or laws that govern any universe, IS the logic that's part of the reality of that universe. So maybe in that sense one could argue that logic is fundamental to any possible universe. It's hard to see how this wouldn't be the case.

But I think, as I say in the OP, my issue with this is: Is the suggestion that the same rules apply to every possible world? In other words, even though we know there are all sorts of algebras for different logics, what's the rationale for saying only one of these systems can be mapped onto a possible world?

Logic (and mathematics) sets out how we can use words and other symbols. It's groups of grammatical rules. Yep, there are lots of different logics. It should not be a surprise that the one we worked out first works well in our everyday experience.

That's not quite right. Classical logic is not the logic we first worked out, classical logic is the logic created by people like Frege and Boole in the late 19th century. At best one might say that about Aristotelian Logic or whatever work the Indian grammarian Panini was doing, but it's practically universally accepted that Classical Logic was a definite improvement over prior logical systems. That said, I agree when you say,

Geometry started with Euclid; that's the geometry best for building and dividing blocks of land. Non-Euclidian geometries were a fun exercise for mathematicians until General Relativity. Now we use it to make our GPS work.

We choose the grammar for the job at hand, just like we choose an axe or a saw.

That's basically the view I mentioned that I hold when I think about logic.

Gödel shows how limited is our ability to give direct proofs. (Just like, well, Turing did also.) Gödel's theorems simply show how tricky self-reference (which with Gödel doesn't end up in a Paradox) is and thus the idea of there being a way to prove everything that is true to be so is simply false. That doesn't at all make Mathematics unlogical.

...yea? I didn't say Godel's results made math "unlogical", I said his Incompleteness theorems entail that any sufficiently expressive formal system (i.e. one capable of arithmetic) must be either incomplete or inconsistent. In other words, there's a limitation of what sorts of desirable properties such an enterprise can have. Paraconsistent Mathematics allows one to (non-trivially) maintain Completeness, but it's inconsistent (this is too far for some people). Standard mathematics retains consistency (well, no known inconsistencies anyway), and as such is necessarily incomplete. That's all I said, so I don't think we disagree.

I don't think you can refute the LNC, because it's not a "law," it's not a thing for refuting; it's a reflection of our commitment to speak consistently (e.g. to interpret "dead" identically for A and B). What would be the sense in refuting our own commitment? How do you refute a commitment? It doesn't make sense.

I don't really understand this. The LNC is an axiom in reasoning, there's no reason why it cannot be subject to refutation. That we wish to remain consistent does not entail that we can remain consistent. It's not [merely] a commitment.

Like take Tarski's undefinability theorem. Any language which contains its own truth predicate must be either inconsistent or incomplete. Natural languages most assuredly do contain their own truth predicate (even Tarski had to admit this was clearly the case). So natural languages are inconsistent because they can produce Liar-type sentences; this was why Tarski advocated for a hierarchy of formal languages, and why Wittgenstein eventually just suggested we avoid making Liar paradoxes.

If a Liar-type sentence holds, then the LNC does not hold because there is a counter-example. It's no different than when Intuitionists say that the Law of the Excluded Middle is not a tautology. A Dialetheist would say that not all contradictions are truth and false, but that some of them are. Not because they are violating some commitment, but because they believed it is entailed by features in our language or semantics.

Ah, my mistake then.

That axioms are not proveable does not entail that they are not rationally warranted. They are rationally warranted because without them there can be no discourse. The irrational demand for absolute proof is the whole source of these kinds of humean errors of thought.

I think I was mostly with you until you said this (depending on what you meant). If by this you meant a particular set of axioms are rationally warranted because without them discourse is impossible, I would find that dubious (people disagree about what axioms should be adopted in math and logic, and they do so intelligibly). But if you meant there needed to be some set of axioms to get thing s rolling, then I would agree.

We can draw a parallel between Hume and Godel.

In the early 20th century mathematicians, led by Hilbert, were engaged in a program of proving the soundness of mathematics. Godel proved that that was impossible. Did that mean that Godel claimed we shouldn't use mathematics? Of course not! He thought we should, but just that we should not waste our time trying to prove its foundations were sound.

Ehh, that's not it. Early 20th century mathematicians weren't trying to prove the soundness of mathematics, they were trying to prove its completeness and consistency of it. But as it turned out, you could only have incompleteness or inconsistency. I don't think the analogy holds since the Incompleteness of formalisms capable of expressing number theory doesn't make mathematics rationally unjustifiable. It just means you have to accept that, unless you go with Paraconsistent Mathematics, your mathematical enterprise will be incomplete.

As long as you insist on confusing math with physics, people are compelled to push back. Contemporary physics does not allow for infinite divisibility of matter or time. The question isn't even meaningful since there's a certain point past which we can't measure space or time. Math does allow infinite divisibility, but math isn't physics. I suspect you know this, and I'm not sure why you are pushing this line of argument.

Um, that's incorrect. There's nothing impermissible about time being infinitely divisible. Whether anything can be infinitely divided, well, I don't know. Space probably is infinitely divisible.

I have a number of issues here so bear with me please.

Logic should be used in circumstances of uncertainty. In order to have a formal deductive logic, axioms must be set. These axioms should be ideally be grounded in the scientific method. It is fair to claim that the scientific method is itself, grounded in its own axioms, but the reproducibility and outside application of its results is reason enough to believe in its merit.

Um, no. Science uses mathematics, which is constructed via axioms which seem plausible and useful in mathematics. Mathematicians reason according to particular formal systems which they choose to use. The dominant such system of the day is Zermelo-Frankel set theory + Classical Logic (despite the name, Classical Logic was invented in the late 1800s, not the classical period, lol). And I assure you, science did not play a role in why this system rose to prominence (although there are a number of competing systems worth study). ZFC & CL gained prominence due to issues in *mathematics*, not science. Such as (with ZFC) the attempt to regiment mathematics axiomatically (ended up failing but the system is useful), such as understanding infinity and number theory etc. Classical Logic was the result of trying to find what rules for reasoning would be needed to overcome the inability of Aristotlean Logic to account for how mathematicians actually reasoned.

Science had nothing to do with it and it's difficult to see how it could itself determine the rules for reasoning when you have to use reasoning (and math) in science. The situation is more complicated than I've made out so far, but I'll get to that soon.

The same argument can be applied to the concept of logic as well. In situations where an axiom is not grounded in scientific reasoning, for my personal use, the best option is to create arguments and attempt to decide what is more probable based on said arguments. This is a process that can only be done with intuition. The merit of those arguments, if not eventually supported by scientific progress, can be measured through the durability of those claims due to public scrutiny. Logic is only useful in determining future behavior. When trying to determine what the best course of action is, the first step is to make observations, based on those observations, you ask yourself questions. Once you have your questions, you create a set of axioms that are logically consistent with each other and use deductive reasoning in order to determine the best outcome. Finally, if things do not go as planned, you come back and question those initial axioms and go back and change them as necessary. Then repeat the cycle.

How on earth are you doing probability without reasoning? What is the axiom in question that you are questioning? Arguments need to be constructed in particular ways (the correct rules for reasoning) to be valid. Now one *can* disagree about which rules are correct for reasoning (Classical Logic, Intuitionistic Logic, Paraconsistent Logic, etc.), but to settle logical disagreements one has to appeal to a model of theory choice and decide based which theory of logic is the best theory of reasoning (determined by the usual criterion of theory choice).


Intuition is a terrible idea here since people's intuitions aren't all the same, nor is there any inherent reason why intuition allows one to reach a true conclusion better than anything else. And isn't this kind of odd? You say science must do X Y & Z and yet you say we have to resort to intuition?

And besides, what observations are going to bear on logic? Look, logic isn't about the world, the world isn't logical. A logic is a formal system that maps out a particular consequence relation. The world is... whatever the heck it is, I don't know (ask a metaphysician). Outside a formalism, one simply reasons. If there is a relationship between logic and reality, it's not obvious what that relationship is.

Also, you made an assumption here. Axioms don't have to be "logically consistent with each other", as then you're simply assuming a particular axiom already (the Law of Non-Contradiction). There are formal systems where that law is not a tautology. Namely, dialetheic logics, a type of Paraconsistent Logic.

The problem with this though is where I state that the axioms should be grounded in the scientific method. Correct me if I'm wrong, but I basically just re-transcribed the scientific method. It seems like the scientific method is just the application of logic, reduced to 'scientific' axioms. My question is this, is there any knowledge worth knowing, that cannot be learned through this cycle? Is there any reason not to just follow the scientific method and adjust based on the pragmatic maxim when in times of doubt?

1) There's no such thing a "the" scientific method.
2) Science is basically useless (because it's inapplicable) in formal disciplines like mathematics and logic. And surely we've gained knowledge from mathematics and logic.

This thread makes no sense to me. Logic is not science and science is not rebranded logic. "Pragamtism" is not logic either.

You're right. Propositions are ''about'' the world but doesn't that require that they concur with the actual goings on in the world? If I say ''God exists'' or ''I should do good'' etc. am I not making claims of this world. The facts of the world apply to propositions do they not?

Of course not. Propositions can be false and so fail to describe something about the world (if it's a claim about the world anyway). However, the facts of the world do not apply to propositions, propositions are not a physical object. How would facts about the world apply to a proposition? Propositions (OK, this isn't quite right since these are sentences but for simplicity's sake) are true or false statements. Like if I say "Mars exists" that's either true or false. But the proposition itself isn't part of the world, the content of the proposition does contain references to a real object though.

It has to be. If it weren't then everything would be a contradiction. I'm hungry at noon and not hungry in the afternoon. This isn't a contradiction because the two occur at different times.

Well you can say it is, but I can just look at a formalism of a logic and simply note that the system contains no concept of time in it. You are moving between "logic" (theories of what follows from what) to reality (the domain of physics). As I said, if you want to legitimately add time as part of the LNC you'd have to use a temporal logic, which makes the appropriate adjustments.

Relativity is understood in the standard mathematical lens (ZFC & CL), which most assuredly DOES have the Law of Non-Contradiction as an axiom.