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... — MindForged

Yes, though that objection may not apply if the object language contains its own metalanguage as natural languages do. There presumably are implicit axioms in natural language arguments.

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. — MindForged

Agreed. I don't have any objection to formal logics, including dialetheism, and agree they can be useful. But I also think logic is integral to both ordinary language and empirical investigation and this would be the sense that logic is seen as fundamental to reality. Which is why there is generally assumed to be a principled answer to how the liar sentence should be handled, including by dialetheists.

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.

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. — litewave

Yes, the two photons are initially in different positions. But the reason they are termed "indistinguishable" or "identical" is that if they somehow exchanged positions, this would make no physical difference (i.e., the quantum state would be identical).

Similarly at the end of the experiment they are measured in different positions - see Figure 3 of the earlier link. But at the time that they hit the beam splitter, their positions are also physically indistinguishable. (If they were not, then there wouldn't be interference. This is analogous to distinguishing which slit the photon passes through in the double-slit experiment.)

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. — litewave

So any time that a photon interacts with something (say, the beam splitter or the detector), we could say that it is annihilated and created anew. But sometimes we want to consider the identity to have persisted (as with a photon in the double-slit experiment or things at a macroscopic level, such as humans). Even in the HOM experiment, there is some sort of continuity in that we started with two photons and ended up with two photons. But the history in terms of individual photon identity seems not to physically exist.

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".

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

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

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." — MindForged

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.

The referent of "The dog is black" is the dog in question, not "the whole situation". — MindForged

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.

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. — MindForged

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.

So any time that a photon interacts with something (say, the beam splitter or the detector), we could say that it is annihilated and created anew. But sometimes we want to consider the identity to have persisted (as with a photon in the double-slit experiment or things at a macroscopic level, such as humans). Even in the HOM experiment, there is some sort of continuity in that we started with two photons and ended up with two photons. But the history in terms of individual photon identity seems not to physically exist. — Andrew M

In theory - and also in reality if the theory is correct - there are two photons throughout the experiment, not one photon. They are numerically different, so there must be a property that ensures that they are two photons and not one. I would say that this differentiating property is the position of each photon in an abstract structure of the theory, because it is the abstract structure of the theory (including the definition of energy of a photon as a product of Planck constant and frequency) that differentiates the situation into two photons.

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". — MindForged

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 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.

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).

Easy question? What is real to people is perceptual. Perfect logic only ever exists along side unflawed natural instinct, but since philosophers are spending ninety nine percent of their time in struggling to replace this with intellect logic will never amount to more than yet another intellectual argument, and this shall always be the case whilst philosophy remains an institution owned by the gods. Their only interest is in producing equality for their own members, those with intellect but wanting in genuine philosophical ability. This time is not wasted because all of it and more is required to make a poor job of replacing natural instinctive and genuine philosophers.

"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. — MindForged

Properties are objects too - they are something that is identical to itself and different from other objects. I see no reason why words could not refer to properties.

You're confusing a predicate with a referent, and you're mistaking a state of affairs (or "a situation") with a referent. — MindForged

Situations are objects too - they are identical to themselves and different from other objects. Situations are referents of sentences.

"false" is not a referent — MindForged

"False" is a property, so it can be a referent.

What do you think self-reference even means? That a situation refers to itself? — MindForged

The sentence "This sentence is false" refers to a purported situation that includes the sentence, so in this sense it is a self-referential sentence. The part "This sentence" refers to the sentence itself.

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 — MindForged

Ok, I'll look into it.

Properties are objects too - they are something that is identical to itself and different from other objects. I see no reason why words could not refer to properties.

...What? This seems like an incoherent view. A property is some entity which can be predicated of an object, not objects themselves. In "My dog is black", you are attributing the property of "blackness" to the referent "dog".

Situations are objects too - they are identical to themselves and different from other objects. Situations are referents of sentences.

How are situations objects??? A situation (state of affairs) picks out how things are, it is not itself an object.

"False" is a property, so it can be a referent.

Falsity is a property, so it is not a referent.

The sentence "This sentence is false" refers to a purported situation that includes the sentence, so in this sense it is a self-referential sentence. The part "This sentence" refers to the sentence itself.

You've misunderstood. "Self-reference" regards a sentence which asserts something about itself. My point is that if we agree that's what self-reference is, we have to agree that a referent is not a situation because situation cannot self-refer. That requires some sort of language and operations in the language. "This sentence is false" refers itself, "My dog is black" refers to a dog and then predicates the property of blackness to it.

In "My dog is black", you are attributing the property of "blackness" to the referent "dog". — MindForged

And in so doing I am also referring to the property of blackness. The property of blackness is the referent (meaning) of the word "black".

How are situations objects??? A situation (state of affairs) picks out how things are, it is not itself an object. — MindForged

An object is anything that has an identity. In other words, it is something (as opposed to nothing). In my view "objects" without an identity are nothing (so not really objects).

And in so doing I am also referring to the property of blackness. The property of blackness is the referent (meaning) of the word "black".

No, you are making a *reference* to the property of blackness, the *referent* of the sentence is the dog in question.

An object is anything that has an identity. In other words, it is something (as opposed to nothing). In my view "objects" without an identity are nothing (so not really objects).

Even if it turns out to be the case that "No entity without identity" as the old mantra went, that doesn't entail that the reverse is true. This should be especially true for you given your previous statements about contradictions. Contradictions have properties (they are necessarily false, for instance), and therefore (on your view) they have an identity. So on your view there must be a contradictory situation, and hence, a contradictory object. That's why I think conceiving of a proposition as a "situation" is just a mistake. A state of affairs is not the same thing as a proposition.

No, you are making a *reference* to the property of blackness, the *referent* of the sentence is the dog in question. — MindForged

When I am making a reference to the property of blackness then the referent is the property of blackness, no?

Contradictions have properties (they are necessarily false, for instance), and therefore (on your view) they have an identity. So on your view there must be a contradictory situation, and hence, a contradictory object. — MindForged

A contradiction has an identity as a sentence (a string words) but it does not have a referent. A contradiction refers to a contradictory situation but there is no such situation, so a contradiction has no referent.

When I am making a reference to the property of blackness then the referent is the property of blackness, no?

It's not the referent of the sentence, it's the referent of a word (although that's a bit misleading since "black" or blackness aren't objects). An object is not the same kind of thing as an aspect of the object.

A contradiction has an identity as a sentence (a string words) but it does not have a referent. A contradiction refers to a contradictory situation but there is no such situation, so a contradiction has no referent.

It's not a situation, you can have a contradiction that makes no reference to a state of affairs (contradictions in math, for instance). You said anything with an identity is an object, the latter being something with properties. And it doesn't even have to be a string of words. Propositions aren't strings of words, and yet propositions can be contradictory.

It's not a situation, you can have a contradiction that makes no reference to a state of affairs (contradictions in math, for instance). — MindForged

Example?

Propositions aren't strings of words, and yet propositions can be contradictory. — MindForged

My understanding is that propositions are meanings of strings of words (if the string of words has a subject-predicate structure). In other words, propositions are referents of strings of words, or situations to which the strings of words refer. A contradictory string of words refers to a contradictory proposition/situation but such a proposition/situation would be an object without identity, which would be an absurdity, and therefore such an object doesn't exist and a contradictory string of words has no referent (meaning). We can talk about contradictory propositions or situations but ontologically they are nothing.

In theory - and also in reality if the theory is correct - there are two photons throughout the experiment, not one photon. They are numerically different, so there must be a property that ensures that they are two photons and not one. I would say that this differentiating property is the position of each photon in an abstract structure of the theory, because it is the abstract structure of the theory (including the definition of energy of a photon as a product of Planck constant and frequency) that differentiates the situation into two photons. — litewave

The problem is that quantum mechanics would seem to rule this out. The reason is that if there were a differentiating property such as position while in the beam splitter then, per figure 1, quantum states 2 and 3 would be physically distinct states and therefore would not destructively interfere (cancel out). But, as experiments show, they do.

(BTW, if the photons' positions were tracked to see how they individually traveled through the beam splitter then the interference effect would disappear and quantum states 2 and 3 would then be observed half of the time. This is analogous to the dual-slit experiment.)

So a different explanation is needed. One option is that the photons each have identity but are indistinguishable. A second option is that they don't have identity.

A third option is that the two photons merge into one photon (with higher energy) when they interact with the beam splitter and then subsequently split into two photons again. A fourth option is that the two photons are absorbed by the beam splitter (increasing its energy) which then subsequently emits two photons.

A fifth option is that the two photons actually do retain their individual identities throughout. But instead of the differentiating property being position, it is instead an index to relative branches in a very temporary world branching and merging. So both photons would be in the same spatio-temporal location in their respective branches and their interference effect would appear like the third or fourth options above. A bit like the bent-stick-in-water effect.

Example?

Disjunction introduction is a valid rule of inference and it is not a valid rule of inference. That's a contradiction yet clearly it's not making reference to a state of affairs. This is especially the case if you think logic is fundamental to reality, because then the validity of the inference rules varies in different states of affairs (or at least in different possible worlds), which seems to prevent logic from being fundamental.

My understanding is that propositions are meanings of strings of words (if the string of words has a subject-predicate structure). In other words, propositions are referents of strings of words, or situations to which the strings of words refer. A contradictory string of words refers to a contradictory proposition/situation but such a proposition/situation would be an object without identity, which would be an absurdity, and therefore such an object doesn't exist and a contradictory string of words has no referent (meaning). We can talk about contradictory propositions or situations but ontologically they are nothing.

A proposition is not a situation. The SEP summarizes this well:

Propositions, we shall say, are the sharable objects of the attitudes and the primary bearers of truth and falsity. This stipulation rules out certain candidates for propositions, including thought- and utterance-tokens, which presumably are not sharable, and concrete events or facts, which presumably cannot be false.

[...]
Clearly, not all propositions can be possible states of affairs, because there are propositions that are not possibly true, whereas possible states of affairs must obtain in at least some possible world. We might wish to extend the notion of a state of affairs to include impossible ones.

As I said, a state of affairs is not a truth-bearer on most accounts of what a proposition is. Also, that you refer to a contradiction as an object (I agree it is) would seem to imply that it has properties (it does). But if it has properties, it cannot be "nothing ontologically".

The problem is that quantum mechanics would seem to rule this out. The reason is that if there were a differentiating property such as position while in the beam splitter then, per figure 1, quantum states 2 and 3 would be physically distinct states and therefore would not destructively interfere (cancel out). But, as experiments show, they do. — Andrew M

I am not sure if you understood me. I was saying that the differentiating property of the two photons is their position in the abstract structure of the theory, not in physical space. According to theory (and also in reality if the theory is correct) the energy of one photon is E = hf, where h is Planck constant and f is frequency. So if in an experiment you measure frequency f and total energy 2hf, then theory tells you that there are two photons, not one. So it is the theory, the structure of its definitions and rules, that differentiates the stuff into two photons and thus gives each of them a separate identity. In this theory, in its abstract space or structure (and also in the corresponding abstract structure of reality), the two photons have a different position. But physicists cannot measure this position; it's not a position in physical space.

Disjunction introduction is a valid rule of inference and it is not a valid rule of inference. That's a contradiction yet clearly it's not making reference to a state of affairs. — MindForged

This contradiction is referring to a purported situation where disjunction introduction is a valid rule of inference and not a valid rule of inference.

This is especially the case if you think logic is fundamental to reality, because then the validity of the inference rules varies in different states of affairs (or at least in different possible worlds), which seems to prevent logic from being fundamental. — MindForged

But if an axiom is valid (true) in one possible world and not valid (not true) in a different possible world then it is not a contradiction to say that the axiom is both valid and not valid. A contradiction arises when we affirm and deny something in the same sense, but here we are not doing it: were are saying that the axiom is valid in a possible world and is not valid in a different possible world. It would be a contradiction to say that an axiom is valid and not valid in the same possible world.

A proposition is not a situation. The SEP summarizes this well:

Propositions, we shall say, are the sharable objects of the attitudes and the primary bearers of truth and falsity. This stipulation rules out certain candidates for propositions, including thought- and utterance-tokens, which presumably are not sharable, and concrete events or facts, which presumably cannot be false.

[...]
Clearly, not all propositions can be possible states of affairs, because there are propositions that are not possibly true, whereas possible states of affairs must obtain in at least some possible world. We might wish to extend the notion of a state of affairs to include impossible ones. — MindForged

I mean "situation" not as a fact but as an arrangement of an object and its property. Such an arrangement may hold in some possible world and thus be true in that world, and in another possible world it may not hold and thus not be true.

Also, that you refer to a contradiction as an object (I agree it is) would seem to imply that it has properties (it does). But if it has properties, it cannot be "nothing ontologically". — MindForged

Contradiction in the sense of a string of words without a referent has its identity as a string of words. But contradiction in the sense of the purported referent itself - a contradictory situation/arrangement/proposition - does not have identity (does not have the properties it has) and therefore does not exist in my view; it's ontologically nothing even though we can talk about it as if it were something.

So it is the theory, the structure of its definitions and rules, that differentiates the stuff into two photons and thus gives each of them a separate identity. In this theory, in its abstract space or structure (and also in the corresponding abstract structure of reality), the two photons have a different position. But physicists cannot measure this position; it's not a position in physical space. — litewave

OK, so granting that there are two photons throughout the experiment, are you saying that the property distinguishing the photons would not be physically measurable but still be physically real (a hidden variable)? Or not physically real and just part of the abstract structure (instrumentalist)? Or something else?

OK, so granting that there are two photons throughout the experiment, are you saying that the property distinguishing the photons would not be physically measurable but still be physically real (a hidden variable)? Or not physically real and just part of the abstract structure (instrumentalist)? Or something else? — Andrew M

Depends on what you mean by "physical". Is "imaginary momentum" that a particle has in quantum tunneling "physical"? It cannot be measured, even in principle, but physical theory implies it is there.

This contradiction is referring to a purported situation where disjunction introduction is a valid rule of inference and not a valid rule of inference.

That doesn't make sense. If, as you have said, that logic is fundamental to reality there is no possible situation where disjunction introduction is invalid. Speaking of "situations"/states of affairs in this way is a mistake. They are not the same things as propositions.

But if an axiom is valid (true) in one possible world and not valid (not true) in a different possible world then it is not a contradiction to say that the axiom is both valid and not valid. A contradiction arises when we affirm and deny something in the same sense, but here we are not doing it: were are saying that the axiom is valid in a possible world and is not valid in a different possible world. It would be a contradiction to say that an axiom is valid and not valid in the same possible world.

You already said that you believe logic is fundamental to reality in your first post, on the first page. So this precludes you from dealing with possible worlds where different inference rules hold. That was my point, the only way you could conceivably articulate your position goes against what you previously said. A proposition is distinct from a state of affairs, so you can have a proposition (which is an object) that is a contradiction, yet that doesn't entail there is some state of affairs (or a possible state of affairs) which corresponds to the contradictory proposition. After all, contradictions are necessarily false, even in dialetheism.

A proposition is not a situation. The SEP summarizes this well:

Propositions, we shall say, are the sharable objects of the attitudes and the primary bearers of truth and falsity. This stipulation rules out certain candidates for propositions, including thought- and utterance-tokens, which presumably are not sharable, and concrete events or facts, which presumably cannot be false.

[...]
Clearly, not all propositions can be possible states of affairs, because there are propositions that are not possibly true, whereas possible states of affairs must obtain in at least some possible world. We might wish to extend the notion of a state of affairs to include impossible ones.
— MindForged

I mean "situation" not as a fact but as an arrangement of an object and its property. Such an arrangement may hold in some possible world and thus be true in that world, and in another possible world it may not hold and thus not be true.

A situation (or state of affairs) is some way the world is that makes a given proposition true. It is not the arrangement of an object because objects are part of a state of affairs.

Contradiction in the sense of a string of words without a referent has its identity as a string of words. But contradiction in the sense of the purported referent itself - a contradictory situation/arrangement/proposition - does not have identity (does not have the properties it has) and therefore does not exist in my view; it's ontologically nothing even though we can talk about it as if it were something.

I've already dealt with this. Propositions aren't strings of words (that's a sentence) and yet they can have a referent in reality, and a truth value. Contradictory propositions (under most views) are precisly those propositions which cannot correspond to a possible state of affairs. They are not ontologically nothing, even on your view, because you said that have a property. If you say a contradictory proposition has no properties, that means they don't have the property of falsity. Which is just ridiculous because propositions are necessarily false, which is a property.

That doesn't make sense. If, as you have said, that logic is fundamental to reality there is no possible situation where disjunction introduction is invalid. — MindForged

That's right. But there is also no possible situation where disjunction introduction is valid and invalid. Your contradiction referred to that situation.

Speaking of "situations"/states of affairs in this way is a mistake. They are not the same things as propositions. — MindForged

A situation/arrangement/proposition may be true in some possible world and false in another. And in the world in which it is true it is a fact. I assume that by "state of affairs" you mean a fact, and that is indeed different from situation/arrangement/proposition.

You already said that you believe logic is fundamental to reality in your first post, on the first page. So this precludes you from dealing with possible worlds where different inference rules hold. — MindForged

Unless an axiom itself is self-contradictory (e.g.: "There is a circle that is not a circle"), there is no reason to prefer the axiom or its negation in ontology. They are both true but not in the same possible world (because if they were true in the same possible world they would constitute a contradiction).

A proposition is distinct from a state of affairs, so you can have a proposition (which is an object) that is a contradiction, yet that doesn't entail there is some state of affairs (or a possible state of affairs) which corresponds to the contradictory proposition. — MindForged

I agree that a proposition is distinct from a fact (state of affairs) and that a proposition is an object, but I don't think that a contradictory proposition is an object, because it would be a contradictory object - a referent (meaning) of a contradictory string of words. Contradictory objects lack identity, so they are absurd. And of course there is also no fact that corresponds to a contradictory proposition.

A situation (or state of affairs) is some way the world is that makes a given proposition true. It is not the arrangement of an object because objects are part of a state of affairs. — MindForged

Here is a misunderstanding. By a situation or an arrangement of object and property I don't mean a fact (state of affairs) but simply a proposition.

I've already dealt with this. Propositions aren't strings of words (that's a sentence) and yet they can have a referent in reality, and a truth value. — MindForged

I suppose that by the referent of a proposition you mean a fact. Ok. I'll just add that a proposition that is true in some possible world becomes a fact in that possible world. In other possible worlds this proposition may not be true and then it doesn't become a fact there. I regard a proposition as a kind of property that may be instantiated in some possible worlds (as a fact) and thus be true there and not instantiated in other possible worlds and thus be false there.

And I regard a proposition as a referent (meaning) of a string of words (sentence).

Contradictory propositions (under most views) are precisly those propositions which cannot correspond to a possible state of affairs. They are not ontologically nothing, even on your view, because you said that have a property. If you say a contradictory proposition has no properties, that means they don't have the property of falsity. Which is just ridiculous because propositions are necessarily false, which is a property. — MindForged

Yeah, it's confusing. We can talk about contradictory propositions as if they were objects with a property called falsity but in fact they are not objects, and by characterizing them as (necessarily) false we mean that they cannot be true in any possible world - they cannot be instantiated as a fact in any possible world, which is not surprising, because they are simply nothing.

But a contradictory string of words (sentence) is something, an object with an identity; it just doesn't have a referent (meaning) because its referent is a contradictory proposition, which is nothing. A contradictory string of words is an object that has the property of (necessary) falsity because its meaning (a proposition) cannot be true in any possible world.

Depends on what you mean by "physical". Is "imaginary momentum" that a particle has in quantum tunneling "physical"? It cannot be measured, even in principle, but physical theory implies it is there. — litewave

Yes, I regard it as physical.

The issue I'm thinking about with the HOM experiment is this. Suppose we name the two photons that are measured at the end of the experiment P1 and P2. Can P1 be identified with the photon that was originally above (or, else, below) the beam splitter? Or does that question have no physical meaning (as a question about ontology, not merely the inability to measure it)?

That interference occurs for the "both photons reflecting" and "both photons transmitting" quantum states implies the latter. Would you agree?

The issue I'm thinking about with the HOM experiment is this. Suppose we name the two photons that are measured at the end of the experiment P1 and P2. Can P1 be identified with the photon that was originally above (or, else, below) the beam splitter? — Andrew M

Well, since the two photons have no measurable differentiating property at the end of the experiment, not even a different position in physical space, we cannot find out which one was above the beam splitter at the beginning of the experiment and which one was below the beam splitter.

We might at least measure (if it is technologically feasible) whether their frequency didn't temporarily change during the experiment, to rule out that they temporarily merged into one photon (which would manifest as temporary doubling of frequency, since total energy should be conserved). If they merged into one photon and then separated again it seems that their identities were terminated at the merger and new photons came into existence at the subsequent separation. If there was no merger into one photon then the identity of the particles was preserved but since they have no measurable differentiating property at the end of the experiment we can no longer say which one is which.

Well, since the two photons have no measurable differentiating property at the end of the experiment, not even a different position in physical space, we cannot find out which one was above the beam splitter at the beginning of the experiment and which one was below the beam splitter. — litewave

The photons do have different positions in physical space at the end of the experiment (see figure 3 that shows the distinct photon pairs together either at the top or the bottom of the image).

The issue is only that the two photons could not have any different property while within the beam splitter. The observed destructive interference occurs because the "both photons transmit" and "both photons reflect" quantum states are identical and this entails that the photons are identical.

We might at least measure (if it is technologically feasible) whether their frequency didn't temporarily change during the experiment, to rule out that they temporarily merged into one photon (which would manifest as temporary doubling of frequency, since total energy should be conserved). If they merged into one photon and then separated again it seems that their identities were terminated at the merger and new photons came into existence at the subsequent separation. — litewave

Yes. My guess is that such an experiment would only show evidence of the two photons and also destroy the interference effect in the process. If so, it would neither confirm or rule out the possibility. But it may still be a useful way to think about it. It at least shows how preserving identity can suggest a different physical model or interpretation.

If there was no merger into one photon then the identity of the particles was preserved but since they have no measurable differentiating property at the end of the experiment we can no longer say which one is which. — litewave

Preservation of photon identity is ruled out by the observed destructive interference.