"But I should add that, though logic isn't fundamental to Reality, it's fundamental to metaphysical-reality, and is what what-metaphysically-is is constructed of". — Michael Ossipoff
Word salad. — StreetlightX
Logic is fundamental to reality in the sense that every object in reality is what it is and is not what it is not. In other words, every object in reality is identical to itself and different from other objects. — litewave
I know what identity is, I was spelling out the properties of the identity relation, which is what the principle is. To "violate" the law of identity does not entail violating the Law of Non-contradiction. The LNC asserts that a proposition cannot be true and its negation be true as well. The Law of Identity tells you how to know when a seemingly distinct objects are in fact identical (when they share all their properties). That is why one can remove the law of identity from their formal logic and yet retain the LNC. — MindForged
That's an assumption (one which I would share), but it's not obviously the case given certain possibilities in quantum mechanics. I already quoted the relevant paper explaining this up above, but thus far you seem to have avoided acknowledging anything I've linked. — MindForged
Well that's a silly view. Lots of things don't correspond to reality, yet they are true. There are an infinite number of mathematical truths that don't correspond to anything in reality yet I doubt you'd deny them or claim they were meaningless. — MindForged
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
Being contradictory isn't sufficient for meaninglessness. A meaningful sentence is meaningful if it's components are meaningful. — MindForged
And besides, the sentence "This sentence is false" seems perfectly meaningful and it has a referent in reality (the very sentence itself, as that's what it specifies). — MindForged
The phenomenon is known as 'ambiguous loss': it seems that the most balanced human reaction is to embrace the contradiction, i.e. to accept that the missing person is both alive and dead, like Schrodinger's cat. — mcdoodle
Actually, the Platonic analysis of this apparently obvious point, was that no object truly is, on account of it being an appearance only, without inherent reality (following Parmenides.) But this is not so with 'ideal objects' such as numbers, which really are what they are; so A=A is always certain, but when it comes to the sensory or phenomenal domain, there are actually no 'A's as such, but only representations. — Wayfarer
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?
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.
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.
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.
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 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).
But an appearance or representation is still identical to itself, no? An appearance of a triangle is an appearance of a triangle, not an appearance of a circle. — litewave
And I am not sure what they mean by "cannot distinguish particles of the same kind". Do they mean that the particles are exactly the same? — litewave
A contradiction is not the assertion that an object has a property "X" and lacks that property, it's the assertion that a proposition holds and it's negation holds. — MindForged
Well yea bro, I'm not gonna quote the entire paper. I named the paper at the end of the quote and offered to send to the PDF of the paper in question if you couldn't access Sci-Hub (it's having issues right now). — MindForged
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
If "It is raining" has meaning, and it's negation "It's not case that it's raining" are meaningful, then "It's raining and it's not the case that it's raining" is meaningful. — MindForged
There is a proposition "P such that "P" relates to truth and "P" relates to falsity. — MindForged
"This sentence" refers to the ENTIRE sentence, not to the phrase "this sentence". — MindForged
I mean, "This sentence has five words" is equally self-referential and yet the predicate "has five words" is clearly the case about the sentence. — MindForged
So again, what is 'a triangle'? It is not an object per se - an object is this or that triangle, a particular - but what a triangle really is is a plane surface bounded by three straight lines. — Wayfarer
To see this, have a look at the Hong–Ou–Mandel effect. Figure 1 shows the four quantum states in superposition when two photons enter a beam splitter at the same time, one photon entering from above and one photon entering from below. — Andrew M
What is actually observed is that the two photons always emerge together on either the upper or lower side of the beam splitter (i.e., either state 1 or 4). — Andrew M
So please give me an example of a contradiction, and we'll see if it violates the identity of some object.
It might help if you explained the reason why you think quantum particles don't have identity to someone who is a layman in physics. For me, two objects (particles or whatever) are identical (metaphysically indistinguishable, that is, one and the same object) iff all of their properties are the same (including e.g. their position in space). This is just the principle of identity of indiscernibles or indiscernibility of identicals. So how is this violated in QM?
Well this is the easiest thing in the world. I did not mention "completely rejecting the LNC" because Dialetheists don't completely reject it. They don't believe ALL contradictions are true, only some.
— MindForged
That's why I said that they still need LNC even though they relax it in certain situations. In ontology I wouldn't relax LNC at all because it would mean to accept the existence of objects without identity (with violated identity.)
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.
What do you mean by "relates to truth"? Simply that it "is true"? Your above proposition seems to mean that something is true and not true, which is a contradiction.
"This sentence" refers to the ENTIRE sentence, not to the phrase "this sentence".
— MindForged
I agree. The phrase "this sentence" refers to the entire sentence. But the entire sentence as a whole doesn't refer to anything, because there is no sentence that is both false and true. The entire sentence says it is both false and true, but in fact it is just false (like any contradiction).
This sentence as a whole refers to itself because it indeed has five words.
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.
We assume now that the two photons are identical in their physical properties (i.e., polarization, spatio-temporal mode structure, and frequency).
[...]
Since the two photons are identical, we cannot distinguish between the output states of possibilities 2 and 3 in figure 1, and their relative minus sign ensures that these two terms cancel. This can be interpreted as destructive interference.
I can imagine that a person is unsure whether someone is dead or alive but I haven't met a person who believed that someone is both dead and alive. — litewave
It's raining and it's not the case that it's raining. I'm sserting a proposition and its negation both hold, not that there is some object which has and lacks a property (that *is* a contradiction). — MindForged
I don't think you understood me. Accepting that not all contradictions are true is *not* the LNC, that's simply a rejection of Trvialism. That's not using the LNC, because rejecting the LNC does not entail accepting all contradictions. — MindForged
The contradictory sentence exists. If on your view it is simply false, the sentence exists so saying the sentence lacks a referent is gobbldygook (non-existent things cannot have a proeprty like falsehood.) — MindForged
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.
Ok, I automatically also assumed the principle of explosion. So, you can reject LNC and accept only some contradictions as long as you block the principle of explosion in some way and thus prevent contradictions from spreading to all other statements. Blocking the principle of explosion seems an arbitrary act but I guess it can be useful in some situations like where you don't want contradictions to contaminate a whole information system - it's a pragmatic solution designed to prevent spreading of false information but with no implications for ontology (reality). In ontology I reject all contradictions because contradictions refer to absurd objects without identity.
The 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.
Identity regards the properties of an object, LNC regards whether some proposition is the case or is not the case. — MindForged
Well I mentioned Paraconsistency in the OP so it didn't come out of nowhere (there'd be no reason to advocate for a true contradiction unless you dropped explosion). And it's not arbitrary to do this; if you accept the Liar as a sound argument you need to eliminate or restrict an inference rule that generates explosion. — MindForged
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
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.
Liar is a contradiction so I regard it as false.
I don't know what you're trying to say here. Only the phrase "this sentence" has a referent, the entirety of a sentence can't have a referent.
— MindForged
Take the sentence "My dog is black". This sentence as a whole has a referent in reality. The referent is the fact that my dog is black.
Um, that's incorrect. A proposition is just an object, whose ontological status will depend on what view you adopt about abstract objects. A statement is not the same thing as a proposition, though they are related. — MindForged
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
No, that's not what a referent is. A referent is what the sentence is about. The referent of "My dog is black" is the dog in question, not "reality". — MindForged
A proposition, whatever its exact nature, assigns a property to an object. So propositions are inseparable from identities of objects.
As for a contradiction that doesn't violate identity, well, just post any arbitrary contradiction. I'll stipulate, for my example, that it's in a language which lacks equality, and therefore the semantics required for identity. "P & ~P". A contradiction and therefore false to be sure, but identity isn't required.
— MindForged
You still haven't given an example of a contradictory proposition that doesn't violate the identity of some object. "P & ~P" is not an example; it's a general symbol for a contradictory proposition.
The sentence "My dog is black" is not just about the dog but also about the dog's relation to black color.
No, a proposition is just an object. An object doesn't assign properties to itself, an object is just something with properties. — MindForged
I said the contradiction can be arbitrary, so it doesn't matter what you substitute for "P". The Golbach Conjecture is true and it isn't true. — MindForged
The referent is what the sentence is about, the predicate tells us that the object in question is related to black. — MindForged
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
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