True Contradictions and The Liar
The notion itself, "true contradictions" mistakenly presupposes that a contradiction is capable of being true.
It does not make much sense to think and/or believe that a contradiction is even capable of being true. Contradictions are the result of a plurality of assertions; statements; propositions. In particular, those that negate one another and/or are mutually exclusive. By definition, contradictions are not even capable of being true or false. They consist of mutually exclusive propositions, contradictory belief, irreconcilable assertions, etc.
So, "this sentence is false" does not even have what it takes to be a contradiction. Being a true contradiction requires being a contradiction. The liar is not.
Besides that...
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.
It does not make much sense to think and/or believe that a contradiction is even capable of being true. Contradictions are the result of a plurality of assertions; statements; propositions. In particular, those that negate one another and/or are mutually exclusive. By definition, contradictions are not even capable of being true or false. They consist of mutually exclusive propositions, contradictory belief, irreconcilable assertions, etc.
So, "this sentence is false" does not even have what it takes to be a contradiction. Being a true contradiction requires being a contradiction. The liar is not.
Besides that...
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.
Comments (73)
You are correct. it's not a contradiction, but rather, an unresolved paradox. Any self-referential statement represents the un-computable in nature. It stems from self-awareness/consciousness. It's also found in mathematics (Godels theorem).
Another example would be:
Socrates: What Plato is about to say is false.
Plato: Socrates has just spoken truly.
How about the statement: 'I saw your brother today' and you reply my brother died yesterday. Wouldn't that be a true contradiction?
In my opinion, the Godel sentence used in the proof of the incompleteness theorem is best understood in an analogous fashion, since the proof is purely syntactical. Its semantic interpretation as a sentence asserting it's own lack of provability is a heuristic argument that isn't formally acceptable, because the Godel number supposedly referred to by the Godel sentence is infinitely long when the sentence is recursively unpacked by substituting the sentence into itself.
On the other hand, if 'this sentence is false' is interpreted semantically as being a pair of sentences, each sentence belonging to a different language whose meaning is the negation of the sentence in the other language, then we get the traditional semantic understanding of the sentence as a contradiction.
However, since the liar paradox is a paradox of natural language that is it's own meta-language, as opposed to being a paradox of formal language, my preferred resolution is to consider the liar paradox as being a meaningful sentence (since we can understanding the paradox), that isn't a contradiction, rather it is a self-negating sentence with alternating truth value. This interpretation best describes our use of the paradox. i.e. "It is true - hence it is false - hence it is true... etc"
Put those together and you get:
If it's false it's true which makes it false which makes it true which makes it false........
I think that's what he meant
That depends on your notion of truth. Classically, you're right; for truth is not traditionally considered to be the property of a sentence or of it's construction, but of a timeless matter of fact referred to by the sentence that is existentially independent of, and external to, the sentence. From that perspective, the notion of 'alternating truth' i have sketched should be interpreted as referring to 'alternating belief' in the truth of a sentence, where a sentence is said to be 'true' merely if one accepts it and 'false' otherwise.
I don't see the direct link between The Liar and Godel's proof that there is always an assumption buried somewhere within an inductive system of logic that cannot be proven by any means within that system. Nevertheless, I'll attend to the other example you've offered for consideration...
Quoting 3017amen
How is this a true contradiction? This reminds me of an amended Liar, or reinforced, or whatever they call it. It is a contradiction, but it is neither true nor false. The two claims are about one another, and are in direct conflict with one another. The same lack of truth conditions of the Liar, but with an improvement on the referents. There is nothing that can make either one true/false.
It's a confused way to speak. It's a contradiction, but contradictions aren't able to be true/false.
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...
No. It would be a false statement followed by a true one about the same referent. It is a contradiction, but only the latter half of it is true(assuming the brother died). Or, if the brother did not die, and was seen by the speaker, it would be a true statement followed by a false about the same referent, with the first half of the contradiction true.
Or, to simplify matters, alternating assertion and denial of a sentence.
Or, to simplify further, production or selection of sentence tokens (utterances/inscriptions) that successively contradict each other.
Without a frame of reference (context) most sentences are meaningless.
Practically every statement is referential.
That would be like a math formula without an =.
We can then consider each of these:
"this sentence does not correspond to a fact" corresponds to a fact
"this sentence does not correspond to a fact" does not correspond to a fact
I'm unsure about the first, but there's a way to interpret the second as reasserting the liar sentence rather than contradicting it.
Is this sentence/statement true or false?
Neither of them are contradictions. I said they were paradox's; not contradictions.
Godel's theorem speaks to the un-computable, undecidable, middle ground or gray area in logical deduction. Another axiom in life that is illogical, if you will.
https://en.wikipedia.org/wiki/G%C3%B6del's_incompleteness_theorems#Truth_of_the Gödel_sentence
Otherwise, a contradiction is A and-A. This ball is red and not red. But there are also conscious phenomena that breaks that rule, including the limitations of language/descriptions about a thing, thus:
https://en.wikipedia.org/wiki/Principle_of_bivalence
Read 'Vagueness" halfway down.
So let's say the sentence is A:
If I believe A is true, then I believe A is false.
It's still a paradox. If/then isn't describing a sequence of events.
The syntax is correct, but the true meaning is indeterminant. You could say it's 50% true. It wouldn't make it a contradiction or paradox though.
(But, Godel' would say: It is not syntactically complete, since there are sentences expressible in the language of first order logic that can be neither proved nor disproved from the axioms of logic alone. )
To make it a paradox you would re-word to say: This statement is a lie.
'I am a liar.'
is already a paradox. Tell me if you know I am a liar or not?
Godel' would say: It is not 'syntactically complete', since there are sentences expressible in the language of first order logic that can be neither proved nor disproved from the axioms of logic alone.
'I am a liar' then is considered incomplete or indeterminant.
Kind of like : The girl ran. The girl is a liar. (Or otherwise a simple sentence structure of subject-verb, which is actually syntactically correct, but not according to Godel's incompleteness rules.)
In either case, one does not know whether the girl ran, or whether she or you are a liar. It's indeterminant or incomplete. It cannot be proved or disproved.
Again, to make it a paradox you would have to change it to: This statement is a lie. Because if it's true, it's a lie. But if it's a lie, it's not true.
I think the more practical implication here is the fact that deductive logic (formal logic/mathematics) has inherent limitations in the world of experience. To that end, one could argue that 'I am a liar' is a synthetic proposition. It would require empirical evidence/experience to determine it's truth value.
All we can say about these sentences is that they contain no information.
This statement is false.
Everything I say is a lie.
'I am a liar'
Don't believe anything I say..... etc....
I am crazy
These all contain the same paradox.
Ever read Catch 22? That novel is all about being caught up in a paradoxical situation you can't escape from.
The strengthened liar paradox – “this very sentence is false” - is an abstraction obtained from either “I am a liar” or “I am lying”.
A liar: a) someone who tells lies (not “someone who never tells truths”), b) someone with a propensity to lie, such that they are attracted to lying, or c) someone whose propensity to lie is greater than average.
A lie: an intentionally (or, less commonly, unintentionally) told statement known to the speaker to be untrue whose contents are intended to be believed true by those to whom the statement is told. (If the speaker believes her statement to be true, the statement would not be a lie.)
“I am a liar” (or “all people are liars”, etc.) cannot then feasibly be a contradiction, for it intends to correlate to the fact that the individual (or that all people, etc.) has told lies or, else, has some propensity to lie in certain contexts. Or, in some contexts, it would be the momentarily honest expression that one or all of one’s cohort has a greater than average propensity to lie. In all such cases the statement would be unequivocally true.
It is not feasible that a human never utters a true sentence in the entirety of their lives. If for no other reason, no such person could tell successful lies, for no trust would be imparted upon such person and, so, none of their false statements would be believed true by others. Hence, the equivalence of a liar to someone that never tells truths – something that appears required for the liar paradox to obtain - is a product of mistaken reasoning.
“I am lying,” on the other hand, is in real world application made in reference to sentences that have already been spoken or, less commonly, that have yet to be spoken. This, again, is not a contradiction. The statement of “I am lying” would itself be unequivocally true in these cases.
The liar paradox is then always abstracted from mistaken reasoning applied to the significance of real world cases in which “I am a liar” or “I am lying” is spoken. Given the verity of this, the liar paradox – both strengthened and non-strengthened – is the product of faulty reasoning. And, if the product of faulty reasoning, then the contradiction it presents is itself as specious as would be any other contradictory outcome of reasoning.
I still don't know what your answer is when I say, 'I am a liar'. This statement is either true or false. Which one is it?
The only way it's truth-value would be problematic is *if* you have never told a lie in your life *and* you know this to be true *and* you speak what you know to be untrue. You find this scenario feasible in real-world applications?
Assume X is true, then X is false.
Assume X is false, then X is true.
Y = This sentence is false and this sentence is true.
Assume Y is true, then Y is false (and true, but we knew that already)
Assume Y is false, then Y is true (and false, but we knew that already)
X and Y are equivalent.
But Y evaluates as:
Y is True and False.
True and False evaluates as False.
Y is false.
Y and X are equivalent.
X is false.
X is just false. No contradiction here.
Problems?
...thanks. No, but I remember it was popular even a few decades after its release, both in movie and book form.
Back to the topic, generally speaking, all anyone has to remember about liar's paradox is the common theme of self-reference and negation of same... . I think there is only one exception outside of self-reference where paradox appears, but can't remember right now....maybe fdrake knows
Neither X nor Y are capable of being true or false.
Why?
That's how conjunction works. Look at its truth table.
This sentence is short.
This sentence is false.
Why is the first truth apt but not the second?
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.
Nice.
It has truth conditions.
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.
So not a sophist. LOL.
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?
Quoting frank
You have only a fried egg for breakfast.
Did you have a fried egg and beans?
No.
Ultimately, definition of conjunction.
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.
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.
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:
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 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.
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.
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.
Correct.
Having truth value is the result of following the rules of correct inference.
Quoting 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.
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.
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?
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?
Contradictions are not meaningless. Rather, contradiction requires a plurality of meaningful statements.
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.
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.
Quoting creativesoul
Which is the same as saying it is meaningless.
Quoting 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.
Quoting 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?
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
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.
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
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.
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.
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?
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?
Sound like you just claimed the apple has no color at all.
The apple has a color. It is red. If it were a different color, I'd say so.
If words are vague then that most likely means that you havent established some context for your use of words.
As far as i'm concerned, I'm a married-bachelor until the ink of the registrars signature is dry.
It seems to me that you are a bachelor until the ink dries, if the state of the ink is what determines whether you are a bachelor or married.
That begs another question (viz being and becoming/the paradox of time); here's another limitation of language a priori:
Jack is a newlywed.
Oh really? Was Jack a newlywed in the past, present or future?
So are you saying 'Jack is a newlywed' is a false statement?
"Is" refers to the present tense. Can Jack claim to be a newlywed a year from now? That depends on what a newlywed is. This is like asking, when do we stop saying, "Happy New Year"? When is the year no longer "new"? It seems to me that all we need to solve these problems are more specific definitions.
Time is a measurement of change. The measurement uses change to measure change, like the change of the second hand across the face of the clock relative to the change in the location of your body across the track during a race. So, in talking about past, present, and future, we are talking about relative change. This change occurred prior to this change, while this change occurred after that change. Simultaneous change would qualify as the "present", while prior and subsequent changes would qualify as "past" and "future".
How the guy seems to conflate "existence" with the "present" is interesting. He says that what is in the past existed but no longer does and the future will exist but doesn't yet - as if what exists qualifies as the present. Something must exist, and that is the present.
Did exist = the past. Will exist = the future. Exists = the present.
Not what I wrote, nor does it follow from what I wrote.
Yeah, I thought it was interesting too!
One takeaway is the question of what does existence mean (verb v. noun)? The act or condition of existing. Very circular.
Generally speaking, I think of time as another abstract.