Thanks. Dialetheism it is then.

Hah, it's not that simple but I confess I find the view persuasive.

Just give up like I did. It's easier than thinking about this kind of depressing stuff (although the thread title is a bit silly).

Similarly, the expansion of the universe was an unintended bit of behavior, but once they found it, it became a feature rather than a bug. ;-)

That seems false. Just take the Liar and it gives you a grounded truth value to start with (namely falsity). Of course, that value will entail the contrary value and voila, a contradiction. It does not require infinite recursion at all; The T-schema for instance uses the diagonal lemma and so can produce the Liar.

I had assumed we were discussing within that context, along with the inconsistencies and explosions that inevitably flow from that. Why do you think that involves denying the possibility of self-reference? My expansion of the sentence to the more formal version above is following how Russell expands 'The present king of France is bald' in his theory of definite descriptions, not seeking to forbid self-reference. The aim is to make explicit the implicit assertions hidden within a definite description.

The fact that my expanded sentence still contains the word 'this sentence' should be sufficient to demonstrate that the operation did not banish self-reference.

Ah my mistake, I must have misread something during my last response. When I read this:

I understood it as saying that "false" was not part of the sentence being referred to ("should not be connected by the word 'is' "). So if we're going with Russell's theory of descriptions (not sure I accept it), I think an initial issue is that there is not quantifier in the Liar sentence. Note the argument I gave prior was just a propositional logic (where it is usually studied IIRC). What is actually used is predication, so the recourse to quantification seems suspect to me, if not simply misrepresentative of how the paradox is formed.

It also seems like you're conjunction is a bit odd.

'there exists x that is the truth value of this sentence and x = False'

Is what is referred to by "this sentence" is the entire conjunction or just the first conjunct? (I think it's the latter) And does this actually dissolve the paradox? I mean, if 'x' is "false" it seems like the following happens:

"False is the truth value of this sentence and false=false"

Which just seems like the Liar paradox put in a conjunction. Of course the conjunction comes out as necessarily false because the Liar paradox (a contradiction) is the first conjunct.

I'm afraid I don't know what you are referring to with the words 'the Liar'. And also, I'm afraid I can't make anything of your first sentence. In my understanding, a sentence does not have a referent, it is names or symbols that have referents.

Basically I was saying that the Liar is making a predicate of falsity of itself. And I meant to say the "subject" of the sentence, not the referent.

I think all you're really doing is denying the possibility of self-reference, because the Liar is constructed within a semantically closed language unless you work in a metalanguage, e.g. "This sentence" is true, which is not even truth-apt. That's how Tarski attempted to resolve the Liar but this sort of approach isn't in vogue anymore (for a number of reasons, so I'll just gesture at them over on the SEP).

If you are being "excruciatingly literal minded" then you wouldn't substitute the truth value in for the referent of the sentence. The truth-value is part of the sentence that's being referred to, that's the Liar. X is not defined as the value "false", X is defined as asserting that "~True(X)".

Isn't it just Tarski's undefinability theorem and why he advocated the metalanguage hierarchy? If the language has negation, self-reference and the diagonal lemma holds, you can produce the Liar sentence:

x <=> ¬True(x)

To be fair, I just enjoy reading about dialetheism because it gets at a lot of intuitions we take as plausible and shows that we have to either accept the consequences of those intuitions (T-schema leading to a true contradiction) or we have to drop some rule that really seems like it ought to be a correct rule. Or maybe I just like being insufferable. :)

Well yea it's using the T-schema to pull out the Liar. If you think the unrestricted catch and release rules are correct, it entails a contradiction. Naturally if you think the argument is sound you'd better be dropping the explosion principle. :-)

I'm confused, why are you substituting the value in for the self-reference? The liar isn't "False is false". Like the point of my "This sentence is true" example was to object to the claim that self-referential interpretations are visciously circular. "This sentence is true" does self-refer to its own truth-value but there's no problem assigning it as "true" or "false". If "This sentence is true" is itself true, then it's true. If it's false then it's false.

But that seems to suggest that we can't immediately say there's a flaw in this sort of thing, otherwise it seems a bit unprincipled (it has all the same features as the Liar). So when you say you can't guess a solution, well, the Dialetheist is liable to just say you can guess a solution, but the solution is that it's both true and false (pick whatever semantics your prefer in order to spell out how this is this case).

Ugh, look I'm assuming this is a word salad because it reads as if it's trying too hard to be profound, but if I must:

"Before becoming" it isn't a thing at all, so it is neither what what it will become nor what it will be, nor is it even itself because it isn't a thing, it has no properties because there is no "it" there.

Nope.

Michael said:

So T(x) ≔ x and x ≔ ¬T(x). Therefore, T(x) ≔ ¬T(x). Your definitions are contradictory.

My objection was that he was incorrect, because that's not how they were defined. I took the T-schema and so said that "True(x)" has the same truth-value as just asserting that "x". And so the Liar (as per Tarski) can be expressed as "~True(x) <=> x" (The truth of x's negation has the same truth value as asserting that x)
I mean, if "~True(x) <=>x" then "x <=> ~True(x)" (it's a biconditional after all)

Not as Michael rendered: "True(x) <=> ~True(x) (that's not how the T-schema is defined, x and True(x) are inter-derivable).

Ah so you were objecting to the T-schema, in which case my formulation of the argument for the paradox isn't available. I think Tarksi's hierarchy of metalanguages has its own problems, but Kripke's solution has a more straightforward issue with the Revenge paradoxes which call into question if it really solves anything. Namely:

"This sentence is valueless"/"This sentence is neither true nor false"/"This sentence is either false or neither".

...Noted, but the problem is that if referring to its own interpretation were actually inherently problematic then the following ought to produce a similar paradox (but clearly it doesn't):

"This sentence is true".

It's odd I guess, since nothing really happens if you attribute truth or falsity to it.

But truth (and falsity) is just another predicate, I don't see the principle difference between self-referring to that and self-referring to some other property (save for the contradiction it entails). Unless we're going to stipulate that referring to interpretations is a no-no.

Which is what? Certainly not self-reference because, as you mention, there are self-referential sentences which don't pose a problem. Something else about the liar paradox (in conjunction with self-reference) causes the problem, but it isn't a given that this "something else" is the same thing for both "this sentence is false" and "this sentence is meaningless" (or "this sentence is either false or meaningless.").

It is the same thing, specifically asserting its own untruth (or if you want to go deeper, both versions of the paradox I gave make use of what Graham Priest calls the "Enclosure Schema"). Both "false" and "meaningless" are untrue, and it is that untruth which the sentence asserts of itself, which causes the paradox.

I'm not saying that the T-schema defines itself as a contradiction. I'm saying that the T-schema defines T(x) as x and that this definition of T(x) is inconsistent with the liar paradox's definition of x as ¬T(x).

What you said earlier was:

The T-schema defines T(x) as x. The liar paradox defines x as ¬T(x). These are contradictory definitions.

This is a mistake, The T-schema (if accepted) just says the to predicate truth on 'x' is just to say that 'x' is the case; it's a biconditional, not equality, so they have the same truth-value. The liar simply takes a proposition which self-refers regarding some property of itself, and that entails the contradiction. Just take a look at the fuller argument I gave earlier. The proposition "L" is defined as asserting it's own untruth, but never is "L" defined as asserting its own truth.

It can't both be the case that T(x) means x and that x means ¬T(x).

T(x) has the same truth-value as 'x' under the T-schema, so either one an derive the other. The Liar in the format is that "~T(x)<=>x". I think if we went with your response we couldn't even accept Tarski's undefinability theorem.

This title is great, lmao

Yes the universe is a mathematical/logical system

Wouldn't it be better to say something like "The universe can be modeled by a mathematical or logical system"? Because reality and formal systems (or abstract objects if you swing that way) have properties the other cannot. Although to be honest, I've never found that to be a very profound discovery. There are an infinite number of mathematical and logical systems so it almost seems inevitable that at least one could be isomorphic with reality in some sense (while other such systems would map onto different possible realities).

Why? They're different sentences.

Because it's the same type of paradox caused by the same feature. If a purported solution dissolves one version but not another it simply isn't a solution. Problems with the same apparent flaw should be solved the same way, otherwise the answer is completely ad hoc. Or heck, we can just use:

"This sentence is either false or meaningless."

Which forces the contradiction again.

The T-schema defines T(x) as x. The liar paradox defines x as ¬T(x). These are contradictory definitions.

No, T-schema defines a true proposition as being such just if x is the case. It's not defining itself as a contradiction, it's deriving a contradiction by taking the "capture and release" rules and other basic principles and applying them to a proposition that asserts its own falsity. This isn't the only way to run the argument, but here it is again:

1) True(L) ∨ ¬True(L) (Excluded Middle)
2) True(L)
3) L (release)
4) ¬True(L) (definition of L)
5) ¬Tr⁡ue(L) ∧ True⁡(L) (adjunction)

L is simply defined as asserting its own falsity, which produces the liar as above.

I didn't define x as contradictory, I took x and applied the T-schema to produce the Liar.

From what axioms and definitions can one derive "this sentence is false"? Can you set out the proof that concludes with the liar sentence?

Just take the T-schema. 'x' is true just if it is the case that 'x'. So if you have some proposition as follows:

¬True(x) <=> x

You get a liar. To expand it to a more proper argument, we have to recognize the use of "Capture" and "Release" (there are other rules involved of course) as constituting the T-schema:

1) True(L) ∨ ¬True(L) (Excluded Middle)
2) True(L)
3) L (release)
4) ¬True(L) (definition of L)
5) ¬Tr⁡ue(L) ∧ True⁡(L) (adjunction)

There are other ways of course.

I don't understand how this relates to the liar paradox. "this sentence is false" and "this sentence is meaningless" are two different sentences. I'm saying that the former cannot have a truth value because it having a truth value doesn't mean anything. I'm not saying anything about the latter. It, too, might be a problematic sentence, but there's no prima facie reason to believe that a solution to one must also be a solution to the other.

"This sentence is meaningless" is just another Liar paradox, I'm aware they're different sentences. The point is if your solution works for "This sentence is false" then it should dispel "This sentence is meaningless", but it doesn't. So at best, if it does work, it's incomplete and can't really be a general strategy for eliminating Liar paradoxes. Prima facie, if the problem is the same (the contradiction) and the features that give rise to it are the same (the self-reference and certain properties predicating to give rise to a contradiction) then the solution ought to be the same. Otherwise the solutions look ad hoc at best.

How is it not in the realm of a deductive truth? It's taking bivalence and using it to derive a contradiction when applied to a certain kind of self-referential sentence. There doesn't seem to be anything about truth predication that makes it different than properties like those in the other self-referential sentences. This would seem to require abandoning Tarski's Undecidability Theorem if you really can't make this move.

And besides which, isn't your solution subject to the same revenge, e.g.

"This sentence is meaningless"

I don't think meaninglessness is really truth predication, so it seems immune to that objection. But it obviously just generates the paradox again since that new Liar is meaningless, and because it says of itself that it's meaningless, it's also true.

@OP I just go with Dialetheism, personally. Also, there is no official position on the Liars. The only agreement among logicians seems to be that no one has a proper solution yet, so if there is a solution it must be a strange one because all the obvious responses have been tried and they failed (e.g. Kripke's solution doesn't work, Tarski's infinite hierarchy of metalanguages doesn't work, etc.)

I don't think that really works. There's nothing about the liar which is any different than any other self-referential sentence. E.g. "This is an English sentence", "This sentence has five words", etc. For your solution, it seems to generate another Liar, e.g.

"This sentence is incapable of interpretation"

Which, as with the Liar, must be the case of itself. Meaning it's true and it's incapable of interpretation. These Revenge Paradoxes incline me to think such solutions as this, or to call the Liars "meaningless" (or else "neither true or false", like Kripkke's) can't work. They either eat themselves (so to speak) or their solution seems to indicate that perfectly sensible sentences are lacking propositions. On the face of it, nothing seems wrong with saying the Liar is truth-apt. After all, even to me the Liars are contradictions, meaning they have to at least be false.

As @Pseudonym said, the OP just begs the question.

Show an error in reality. Computers have scores of errors all the time, and it's not really hard to find them. Where are the equivalent of crashes in people, for example? Where are the infinite loops? Doesn't entail that we don't live in a simulation or aren't a simulation, but it does show that the the question "Are we in a CG simulation?" cannot be operating under the same understanding of how computers work as we have for our computers. Which seems to be evidence against this since the key term is too vague.

ironic since they never get married. ;)

What problem are you having with it?

I disagree with the silly argument made in the OP.

Yep, "min()" would definitely be conjunction then, since if the values of both conjuncts isn't 1, the conjunction comes out as false (as it should). So min() will just take the lowest value. No problem!

Huh? By accepting my math example you've already conceded the point. The concept of a contradiction does not require time. That doesn't mean no contradictions make use of the concept. In fact, that is demonstrably not the case as I showed. Also, your God example doesn't work. There is a contradiction in:
A: God exists
~A: It's not the case that God exists

Even ignoring time, that's a contradiction if both are asserted.

1) is just saying that the truth-value of the disjunction will be the largest number of the respective values of the disjuncts, I suppose. the "max()" function I assume returns the value of the largest of its arguments (it will return either the value of "a" (v(a)) or the value of "b" (v(b)). So if in #1 a=1 and b=0, v(aVb) will return 1. Maybe I missing something, I don;t have that text.

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.

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".

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.

I really don't know how to get through to you. We know that in a certain sense, Newtonian physics is wrong (even if close enough to true below light speed), but the materialist worldview of that time has been dead for a long time. Seriously, just peruse the SEP article on physicalism:

https://plato.stanford.edu/entries/physicalism/#Ter

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.

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.

Yes, it is exactly the same only minor contortionist tweaks like "selfish genes" and "Thermodynamic Imperative". There is no such thing as "material" for 100 years. Materialism doesn't exist (as the Daoists observed).

But academia keeps it alive.

Oh bullshit man. The current view of the nature of the universe, even just from the standpoint of physics, has radically changed since the 17th century. Few are suggesting we live in a Newtonian universe anymore. Also, "materialism doesn't exist" seems like a really silly sentence. Possibly, materialism is false, but that aside, no one is advocating for the same view of the universe. You are just being thick headed for reasons I cannot grasp.

No it doesn't, and I would never make this inference. That is, the fact that an object, O, exists when perceived by me does not entail that O does not exist when unperceived. The former does not even make it likely that O does not exist when unperceived. So, I am not assuming that 'perception brings a thing into existence'. I am not assuming the opposite either.

You'd have to be assuming that because otherwise there's no reason to suggest they do not exist when not perceived. If we know an object, O, exists when perceived, we know it at least existed. If you question its persistence sans-perception, the only way that can be the case is if perception causes existence. I don't see how you're not assuming that; it's the only possible way for the contrary to be true (unless things just happen randomly, I suppose).

But even given this, there is still a further question about whether O exists unperceived or not. Either it does or it doesn't, and the fact that it exists when perceived doesn't entail that it also exists unperceived. It might be, for all we have said so far, that O exists when I perceive it but the moment I stop perceiving it, it ceases to exist. I am not assuming that this is true, and so I am not 'idly speculating'. What I am saying is that this has not been ruled out by anything we have said so far. You have not suggested any reliable method by which we could determine whether something exists when unperceived. You have suggested that some things exist while they are being perceived, and I have agreed with you on that. You then seem to think that somehow it just follows that they exist when unperceived as well. It does not follow, unless there is some reliable way to establish that these things don't just disappear from the world when unperceived.

My point is as follows. Take the following statements:

1) X is perceived, so X exists
2) X is no longer perceived
3) X either continues to exist or it fails to continue existing

If perceiving it is grounds for saying it exists, good. Why should one question if it exists otherwise? Even if you're just asking a question, it doesn't matter. Questions can import false assumptions as much as a direct statement can. In this case, why should the notion that it stops existing when unperceived be taken seriously? After all, if perception does not cause existence, and we know the thing exists because we perceived it, there seems to be no grounds from which to raise the idea that the object stops existing when unperceived. We justified believing "O" exists by our perception, we didn't justify the notion that "O" exists only when we perceived it.

I just mean to say, it doesn't see m like we require a reason to answer "they exist independent of perception" unless we are already assuming that perception plays a role in an object existing or persisting in its existence. And many many people would likely dispute that notion (for many objects, anyway).