Why is that how conjunction works?

So once again, I'm not sure if you're intending to be a sophist or you actually believe what you're saying.

Row three.

This sentence is short.
This sentence is false.

Why is the first truth apt but not the second? — fdrake

Nice.

It has truth conditions.

Could you continue on to an explanation of what counts as an alternating truth value? Is that what makes it self-negating? If it's true, it is false, etc... — creativesoul

Self-negation, or perhaps to state more accurately, the potential for self-negation, is a common property of negative universal propositions of meta-linguistics, metaphysics and epistemology that declare limits on sense, cognition or knowledge. For example, "All sentences have indeterminate meaning" , "All things are empty of intrinsic existence and nature" , and "Every belief is fallible" are all potentially self-negating propositions. Common coping strategies in the face of such potential contradictions are either to impose an artificial and rigid hierarchy of reference like Bertrand Russell did to avoid Russell's Paradox, or to quit philosophy and declare it to be nonsense as the Early Wittgenstein did, or to accept 'true contradictions' as Hegel did. Accepting alternating truth value is another coping mechanism that understands a person's concept of truth in terms of their present state and rejects the dogma of a static truth concept.

Often self-negation occurs when a conclusion negates it's own arguments, as when Wittgenstein declared that the propositions of the Tractatus are meaningless, after they had served as a 'ladder' to understanding. The later Wittgenstein's "private language arguments" have similarly been interpreted as self-negating "ladder" arguments, and similar remarks have been said about Kant's Critique of Pure Reason. Pure reason certainly can lead to contradictions, yet we don't simultaneously entertain both sides of such philosophical contradictions, rather we use logic to hop from one conclusion to it's opposite and then usually quit philosophising.

I also have a sneaking suspicion that alternating belief states might become a practical problem of artificial intelligence. After all, the human brain is a dynamical system and there is no compelling reason to assume that belief states converge to an equilibrium.

I asked you to explain why the truth table says that.

So not a sophist. LOL.

It has truth conditions. — creativesoul

The two claims you made mean the same thing. Why doesn't "This sentence is false" have truth conditions when "This sentence is short." Does?

I asked you to explain why the truth table says that. — frank

You have only a fried egg for breakfast.

Did you have a fried egg and beans?

No.

Ultimately, definition of conjunction.

You have only a fried egg for breakfast.

Did you have a fried egg and beans?

No.

Ultimately, definition of conjunction. — fdrake

Notice the difference between:

Did you have a fried egg and beans?

and

Did you have a fried egg and not a fried egg?

Look at the truth table again.

Why doesn't "This sentence is false" have truth conditions when "This sentence is short." Does? — fdrake

Because there is nothing that makes the Liar true or false, but there is something that makes the other true. When the truth conditions are met, the sentence is true. When they are not the sentence is false(or not truth apt, in the case of prediction).

"This sentence is short" is falsifiable/verifiable(has truth conditions) because there are standards for what counts as being a short sentence. It's true if it meets those standards. It does, as vague as they may be, four words make for a short sentence. "This sentence is false" is also a short sentence.

Did you have only a fried egg?

Did you have a fried egg and did you have beans?

Sorted. Ultimately not a problem with conjunction, a problem with the awkwardness of rendering sentences conformably with propositional logic.

Ultimately not a problem with conjunction, a problem with the awkwardness of rendering sentences conformably with propositional logic. — fdrake

Oh.

Yeah. Nice addition.

Seems to me that those are examples of incoherence, self-contradiction, equivocation, and/or untenability. Intimately connected to one another via having the very same same elemental constitution... human thought and belief.

I'm working on attempting to account for better explanations of such scenarios in better terms of belief, than history uses... a more universally applicable criterion. Long, involved, very confusing for some... many... but it appeals to my meticulous nature.

:smile:

Ever read Catch 22? — ovdtogt

Can highly recommend it. You'll love it.

A contradiction can't be true and the liar sentence leads to a contradiction meaning that the liar statement has to be false, but that means it is true which means it is false...ad infinitum or ad nauseum, depending on your constitution. The liar statement is a paradox.

I'd like to run the following argument by you and others about a possible "solution":

A = this statement is false
P = A is true
~P = A is false
R = A is a proposition
S = A has a truth value

1. If R then S
2. If S then (P or ~P)
3. If P then ~P...................................the liar paradox in action when A is taken as true
4. If ~P then P...................................the liar paradox in action when A is taken as false
5. R...............................assume for reductio
6. S...................1, 5 MP
7. P or ~P.......2, 6 MP
8.P.........................assume for CP
9. ~P.....................3, 8 MP
10. P & ~P............8, 9 Conj
11. If P then (P & ~P)..................8 to 10 CP
12. ~P.................................assume for CP
13. P....................................4, 12 MP
14. P & ~P...........................12, 13 conj
15. If ~P then (P & ~P)..........12 to 14 CP
16 (P & ~P) or (P & ~P)........7, 11, 15 CD
17. P & ~P..........................16 Taut ( a contradiction)
18. ~R.................................5 to 17 reductio ad absurdum
~R means A is NOT a proposition.
The logical conclusion it seems is that the Liar statement (A) is NOT a proposition.

A contradiction can't be true and the liar sentence leads to a contradiction meaning that the liar statement has to be false, but that means it is true which means it is false...ad infinitum or ad nauseum, depending on your constitution. The liar statement is a paradox.

I'd like to run the following argument by you and others about a possible "solution":

A = this statement is false
P = A is true
~P = A is false
R = A is a proposition
S = A has a truth value

1. If R then S
2. If S then (P or ~P)
3. If P then ~P...................................the liar paradox in action when A is taken as true
4. If ~P then P...................................the liar paradox in action when A is taken as false
5. R...............................assume for reductio
6. S...................1, 5 MP
7. P or ~P.......2, 6 MP
8.P.........................assume for CP
9. ~P.....................3, 8 MP
10. P & ~P............8, 9 Conj
11. If P then (P & ~P)..................8 to 10 CP
12. ~P.................................assume for CP
13. P....................................4, 12 MP
14. P & ~P...........................12, 13 conj
15. If ~P then (P & ~P)..........12 to 14 CP
16 (P & ~P) or (P & ~P)........7, 11, 15 CD
17. P & ~P..........................16 Taut ( a contradiction)
18. ~R.................................5 to 17 reductio ad absurdum
~R means A is NOT a proposition.
The logical conclusion it seems is that the Liar statement (A) is NOT a proposition. — TheMadFool

A has no truth conditions, therefore A is not truth-apt. P neglects this and arrives at nonsense as a result. It makes no sense to say something incapable of being true/false is either.

S = A has a truth value — TheMadFool

That may be correct. I'm unsure. Either way, we need to draw and maintain the distinction between truth conditions and truth value.

Unless I'm working from a misunderstanding of the two, truth value results from following the rules of correct inference. Whereas truth conditions are what makes a belief true. True belief are prior to language acquisition, and definitely during. Being true does not require following the rules of correct inference. Having truth value does. Truth value is not equivalent to truth.

Truth value is shown by truth tables. True belief is long prior to the rules of correct inference. Long before being taken account of and used as a premiss. True belief requires being true. True belief that is prior to language does not - cannot - require truth value.

All of this is just to remind everyone that logic meant to report upo human thought and belief is the classical kind, and it presupposes truth as correspondence(the kind with truth conditions). That's what the "ifs" are all about.

So...

Either truth is prior to truth value or being true doesn't require truth. Of course, I'm going with the former. It also follows that having truth value does not guarantee truth, which we already knew. Coherence does not guarantee truth, it does guarantee truth value. Truth value is not equivalent to truth. The former is earned by following the rules of correct inference, whereas the latter is presupposed - correctly and mistakenly - prior to, during, and long after one's initial language acquisition.

Unless I'm working from a misunderstanding of the two, truth value results from following the rules of correct inference. Whereas truth conditions are what makes a belief true. True belief are prior to language acquisition, and definitely during. Being true does not require following the rules of correct inference. Having truth value does. Truth value is not equivalent to truth. — creativesoul

Truth value is not equivalent to truth.

That would mean things can be true but have no truth value or vice versa.

1. ~(is truth <-> has truth value)
2. ~[(is truth > has truth value) & (has truth value > is truth)]
3. ~(is truth > has truth value) or ~(has truth value > is truth)
4. ~(~is truth or has truth value) or ~(~has truth value or is truth)
5. (~~is truth & ~has truth value) or (~~has truth value & ~is truth)
6. (is truth & ~has truth value) or (has truth value & ~is truth)

Can you give me an example for the first disjunct of line 6 - a truth that doesn't have a truth value.

Truth value is not equivalent to truth.

That would mean things can be true but have no truth value or vice versa. — TheMadFool

Correct.

Having truth value is the result of following the rules of correct inference.

6. (is truth & ~has truth value) or (has truth value & ~is truth)

Can you give me an example for the first disjunct of line 6 - a truth that doesn't have a truth value. — TheMadFool

I do not subscribe to the idea of "a" truth.

The easiest explanation I have to offer is simple. All true belief requires truth. Some true belief is prior to language use. Truth value is what we attribute to that which is said to have followed the rules of correct inference. The rules of correct inference consist of language use. That which consists of something else is existentially dependent upon that something else. The rules of correct inference are existentially dependent upon language use. Truth value is existentially dependent upon language use. Some true belief is not.

Either true belief can exist without truth or truth value is not equivalent(adequate for is probably better) to truth.


To the other...

A completely coherent argument is said to have logically true(valid) conclusions. That is to be given truth value. A coherent argument can have false conclusions, and/or false premisses unbeknownst to the language user. Hence, there are times when truth value is mistakenly assigned to falsehood even though the rules of correct inference are being followed. Truth cannot be false. That which is given a truth value can.

This sentence is short.
This sentence is false.

Why is the first truth apt but not the second? — fdrake

Perhaps because the first has some determinant truth-condition (even if arbitrary, e.g. fewer than 10 letters) whereas the second doesn’t.

I’m partial to Kripke’s take on this. It doesn’t seem to mean anything for the liar sentence to be either true or false. There’s no evaluable fact.

When held up in isolation of all else, "This sentence is false" is incapable of being false. It is also incapable of being true. It is neither coherent nor sensible. Meaningful... Sure. That's what makes it seem so puzzling. It's tempting to say "if it's false, it's true", or "if it's true, it's false"... that's what makes it puzzling... basing subsequent thought on the presupposition that it is even capable of being true or false.

It's not.

It has no empirically verifiable/falsifiable content. It has no truth conditions. There's nothing that can make it true/false.


"This sentence is false" is something often uttered when the speaker is pointing to a specific sentence that they believe contradicts what's happened and/or is happening. Excising "This sentence is false" from the only sensible context to say it in leaves something very important behind. Crucial. The referent of "this sentence".

Sentences that can be false have truth conditions. The Liar does not. Sentences that have referents and truth conditions are meaningful. Sentences that have neither referent nor truth conditions are utterly meaningless.

When properly accounted for - while it's in total isolation from it's normal use - "This sentence is false" is utterly meaningless. — creativesoul

So contradictions and sentences without any clear reference, are meaningless. Contradictions don't have any clear reference either. A contradiction is saying two opposing things about the same thing. One cannot be both a bachelor and a married man. Which one are they? They can't be both and claiming that they are both leaves no room to know which one they actually are until you observe the man wearing a wedding ring or not. Observations resolve contradictions by supplying the truth, and using our definitions, we find the other simply can't be the case when the other is the case.

"This sentence is false", is no different than saying "This sentence is cruel". The sentence is meaningless because it doesn't establish any connection with reality. Which sentence is it pointing to? Which part of it is cruel? Which part of it is false? This is like using words without any context, which makes it meaningless. It doesn't trigger anything meaningful in my mind when I read it. It doesn't give me anything to act on.

It seems to me that if you are saying "This sentence is false" isn't either true or false, then the reason it isn't true or false is because it doesn't actually refer to anything. If something doesn't refer to anything real, does it make that statement automatically false - a lie?

For a statement to be a lie it has to refer to things that aren't the case, or where the statement refers to an idea in the liar's head and not to an actual state-of-affairs that exists outside of their head. Being a victim of a lie means that you confused the idea in the liar's head with a real state-of-affairs outside the liar's head.

If I said that Santa Claus will come visit you in Munchkin Land, is that a true or false statement? Both Santa Claus and Munchkin Land do not exist. There are no references to real things in the sentence. Is it false or true, or neither? Is this a lie, a paradox, a falsehood, a truth, or what?

This sentence is short.
This sentence is false.

Why is the first truth apt but not the second? — fdrake

You need references to say that one is true or not.

This sentence is short. Compared to which other sentences?

This sentence is false. Which sentence and what makes it false?

So contradictions and sentences without any clear reference, are meaningless — Harry Hindu

Contradictions are not meaningless. Rather, contradiction requires a plurality of meaningful statements.

It seems to me that if you are saying "This sentence is false" isn't either true or false, then the reason it isn't true or false is because it doesn't actually refer to anything. — Harry Hindu

There is nothing that can make it true/false. That's the reason that it is neither. It doesn't have what it takes in order to be either.

Contradictions are not meaningless. Rather, contradiction requires a plurality of meaningful statements. — creativesoul

They would only be meaningful if they were seperate statements on their own, not asserting two opposing qualities of the same thing.

"Jack is a married man" and "Jack is a bachelor" are two meaningful statements on their own, but the statement, "Jack is a married bachelor" is meaningless because it doesn't refer to anything real. When you assert two opposing qualities about same entity you arent saying anything meaningful about that entity.

There is nothing that can make it true/false. That's the reason that it is neither. It doesn't have what it takes in order to be either. — creativesoul

Which is the same as saying it is meaningless.

Ultimately, the stakes of the Liar sentence are the consequences it has: if you can formulate it in a language, it does weird shit; has unfavourable inferential consequences for; to the semantics and logic of that language.

Perhaps because the first has some determinant truth-condition (even if arbitrary, e.g. fewer than 10 letters) whereas the second doesn’t. — Michael

Let's press on the "determinant" thing there. One way to look at the conditions under which a statement is true or false is to submit it to a T-sentence and see what happens. At face value, you can T-sentence the Liar:

"This sentence is false" is true if and only if this sentence is false.

The T-sentence (in a deflationary manner) sets out the truth conditions for the statement. Whether it provides a full account of what it means for a sentence to be true doesn't seem too relevant to me here, it's about whether arbitrary sentence interpretation requires the universal applicability of the T-sentence.

Tarski intuited this, and tried to dissolve the paradox by appeal to the idea that the truth predicate "... is true" lives in a higher order meta-language. More precisely, that there are lots of truth predicates we equivocate over in natural language with "...is true", and the contradiction from the Liar arises by mistaking one truth predicate for another; object language and meta language truth predicates. This approach attempts to preserve the universal applicability of the T-sentence (and all statements having truth conditions and being true or false) at the expense of multiplying truth concepts.

In this view, it does not seem to matter whether the sentence is "evaluable" or not as there's always another truth predicate and meta language which can come in to save the day.

So the first approach I detailed here is pretty much Prior's - the liar isn't a paradox, it's just a disguised contradiction, and thus false. It keeps the underlying logic to have 2 truth values (true, false), it seems consistent with the universal applicability of the T-sentence (it just evaluates the statement as false), and there's one truth predicate operative within it.

I’m partial to Kripke’s take on this. It doesn’t seem to mean anything for the liar sentence to be either true or false. There’s no evaluable fact. — Michael

How does the "evaluability" idea block either of the above accounts? At what points does it intervene? And why is it a better response to the Liar?

Jack is a married bachelor" is meaningless because it doesn't refer to anything real. When you assert two opposing qualities about same entity you arent saying anything meaningful about that entity. — Harry Hindu

HH, forgive me for interrupting, but I find the subject fascinating. It's possible, when Creativesoul has said "Contradictions are not meaningless" that it speaks to human phenomena.

For instance, consider the two statements:

Jack is a married bachelor
Jack is sleep-walking

Jack is a married bachelor
Jack is sleep-walking — 3017amen

Married and bachelor are two seperate and opposing qualities.

Sleep-walking are two separate non-opposing qualities. We know from experience that one can both walk, and even talk, while being asleep. One cannot be awake while being asleep. Being asleep doesn't prevent one from walking and talking. It does prevent one from being awake. You cant have both properties of being asleep and being awake at the same time in the same entity. Only at seperate times can these opposing statements about the same entity be meaningful.

Let's press on the "determinant" thing there. One way to look at the conditions under which a statement is true or false is to submit it to a T-sentence and see what happens. At face value, you can T-sentence the Liar:

"This sentence is false" is true if and only if this sentence is false.

The T-sentence (in a deflationary manner) sets out the truth conditions for the statement. Whether it provides a full account of what it means for a sentence to be true doesn't seem too relevant to me here, it's about whether arbitrary sentence interpretation requires the universal applicability of the T-sentence. — fdrake

What determines if the sentence is false? It seems to me that what you find irrelevant is the relevant statement that makes that statement false. The word, "if" implies that another statement is needed to determine if the statement is false.

"IF <this statement> or observation is true, then <this sentence> is false." makes more sense and is meaningful.

You can't determine whether the statement is false on it's own. You need another statement, or an observation to make sense of it.

The sentence, "this sentence is false" isnt a sentence designed for determing whether it is true or not with a T-sentence. It is a claim about some truth in itself. It doesnt make sense to use T-sentence on a statement defing what is already false or true. Using a T-sentence with a statement that already asserts it is false based on some other qualification other than the T-sentence, is nonsensical. You are applying a method for determining the truth of statement that doesnt apply, and claiming that the method the sentence is using to determine its truth value is irrelevant. You can't determine the sentence is false or true because there isnt enough information to go by, and applying the T-sentence is irrelevant.

One cannot be awake while being asleep. — Harry Hindu

Just to break it down slowly, that would not be correct. Because, a person is in-fact awake, while being asleep.

The sleepwalker's eyes are open but may appear as a glassy-eyed stare or blank expression and pupils are dilated. They are often disoriented, consequent to awakening: the sleepwalker may be confused and perplexed, and might not know why or how they got out of bed; however, the disorientation will fade within minutes. They may talk while sleepwalking, but the talk typically does not make sense to the observer.

It occurs during slow wave sleep stage, in a state of low consciousness, with performance of activities that are usually performed during a state of full consciousness. These activities can be as benign as talking, sitting up in bed, walking to a bathroom, and cleaning, or as hazardous as cooking, driving, violent gestures, grabbing at hallucinated objects,or even homicide.

Just to break it down slowly, that would not be correct. Because, a person is in-fact awake, while being asleep. — 3017amen

Then what do you mean by being asleep and being awake? Why use two different terms if they actually mean the same thing? What is the purpose of having two terms to refer to the same event?

Then what do you mean by being asleep and being awake? Why use two different terms if they actually mean the same thing? What is the purpose of having two terms to refer to the same event? — Harry Hindu

Great questions!

My first thought it reminds me of 'Vagueness' in LEM logic or bivalent qualities:

This apple is red.

Upon observation, the apple is an undetermined color between yellow and red, or it is mottled both colors. Thus the color falls into neither category " red " nor " yellow ", but these are the only categories available to us as we sort the apples. We might say it is "50% red". This could be rephrased: it is 50% true that the apple is red. Therefore, P is 50% true, and 50% false. Now consider:

This apple is red and it is not-red.

In other words, P and not-P. This violates the law of noncontradiction and, by extension, bivalence.

So, my first thought is that I think it is partly a result of the limitations of language (a priori), human phenomenon, and natural unresolved paradox (Godel theorems).

In other words, we don't have a term for saying that things are in an indeterminant stage or in a contingent stage or gray area. In the case of the apple though, you could describe it as 'mottled' and get by with resolving the contradiction. But how does one get by with resolving sleepwalking?