I disagree. No matter how implausible something is, it is nowhere near the same thing as saying something is objectively impossible. That again partakes of a dangerous misunderstanding of what perfection is. Perfectly impossible is probably just that, as in do not talk about it at all because (re-read this sentence until you get it). — Chet Hawkins

"It is possible that " is based on guessing, illusion, unfounded optimisms of low probability of the cases manifesting in reality. "It is impossible that " is based the empirical experience on the cases backed by the highest probability of something not happening in reality.

They are at the opposite end of the scale in the statements. The point was that "It is impossible that" has far more plausibility than "It is possible that".

Do you think there is some physical space in your imagination or around your understanding? I don't get it.

Hmmm I see what you are saying now, but I don't agree with you. "Beyond" in the example of "It is beyond imagination" has nothing to do with the concept of space. It is just the way people use the word in the context.

If we ask people is this sentence true: "What time is it?" the smartest ones will say type mismatch error. Those that have less insight will simply be confused. — PL Olcott

What time is it? can be true or false depending on what was the criteria of the truth.
If the criteria of truth was whether someone asked the question or not, and someone asked the question, then it was true that the question was asked.

Also it can be inferred and reasoned that the person who asked the question didn't know the time. If the criteria of truth was, if there was anyone who didn't know the time, then it was true that the questioner didn't know the time at the time of asking the question.

If you didn't have the criteria of truth, then you wouldn't have the information regarding true or false on the question, which sounds obvious then you don't know what the context of the question was about, and you had no knowledge of what the criteria of truth of the expression was.

Often the smartest sounding folks can be the dumbest. You have to learn to think differently from others. If you sound the same as the others on these issues, then it wouldn't prove anything apart from that you have spent all your life browsing the internet. If you think differently and come up with different ideas, you may get told that you have a problem in logic by the crowds, but you know that you are thinking with your own mind, not just parroting or agreeing and yearning to be accepted to the group of the crowds.

Basically I am saying that self-contradictory expressions such as the epistemological antinomies that Gödel refers to are not truth bearers (neither true nor false) thus must be excluded from formal systems and never any part of any formal proof. — PL Olcott

Every truth or falsity must be derived from some facts in the world or the known axioms which are self evidently true. The paradox starts with the obscure sentence whose truth falsity value no one knows where or what it was derived from. Therefore there is no point for you progressing into the If then arguments or inferencing. That is my point.

"This sentence is false."

If it is false, then it is true.
If it is true, then it is false.

The If parts need reference (under what ground it is false or true) to claim it is either false or true.
There is no indication of what the reference for presuming it is false or true.
Hence the arguments are invalid.

An expression of language that is both a question and a statement would also have
to be rejected until it is translated into one or the other. — PL Olcott

But people use the expression all the time in daily ordinary communications. Why reject?

The sentence: "Did you lie?"
is not a truth bearer thus would be rejected by a correct Truth Predicate. — PL Olcott

It wasn't "Did you lie?" we were talking about. It was "You lied, didn't you?" That was the original sentence. It cannot be chopped into two sentences. It is one sentence, which is both declarative and questioning form. It means, you lied, and it is true.

"Isn't it a beautiful day?" Another example saying that it is true that it is a beautiful day, but in questioning form.

“it is beyond me” refers to something which is spatially separate from yourself; so, no, this is not an example of a different meaning of ‘beyond’ that is aspatial. — Bob Ross

From your post, it appears that you might not be a native speaker of English language actually. When you said "It is beyond me", it sounds like "It is behind me in space." literally, but it actually means, you are "unable to understand". "Beyond imagination" would mean "unable to imagine". It has nothing to do with physical space in this context.

"Beyond" would only indicate physical space, if you were talking about a placement of a physical object in your sentence.

See my point? Even a simple word, "beyond" has different meanings depending on the context, and how you use it.

No, I am not a Hindu. I am an agnostic atheist materialist monist. — Truth Seeker

For an agnostic atheist materialist monist, having all the

simulation/hallucination/dream/illusion — Truth Seeker

sounds like one's claim that she is a vegetarian, but loves eating beef, pork, chicken, lamb, and enjoys BBQ. :grin:

What do you mean by "So the OP is not the actual case."? — Truth Seeker

It means the OP is under some sort of suppositional or imaginary scenario rather than based on the fact. When you say "It is possible that", it must have some degree of plausibility with the factual evidence for being real life cases. Without it, "It is impossible that" has the same plausibility too.

I did answer the second question by editing my initial answer as I had initially forgotten to answer the second question. — Truth Seeker

Not too worry.

Do you have a religion? — Truth Seeker

If religion is a belief system, then no. No religion is my religion.

I suppose, theoretically, I could have my brain removed and put in a jar that keeps it alive, and is wired to sensory apparatus so I could still perceive what's near me. My guess is I would still be conscious, and still myself. My brain is where my consciousness lies. I can lose any number of body parts, and still be my self. — Patterner

Removing the brain from the body would make them both die immediately. Medically, scientifically and realistically it is unimaginable. Brain can only function properly in the body intact from the birth of the agent, and then naturally having been nurtured by the parents, growing experiencing and interacting with the real world and other members in the society.

The body without a brain is a corpse, a brain without the body is just a biological organ. There have been no cases of brain transplanting in human history, and it is doubtful if it would ever be possible.

I didn't say it was actually the case. — Truth Seeker

I see. So the OP is not the actual case. You have been talking the whole lot under a simulation/hallucination/dream/illusion. Got you. Ok, please carry on. :wink:

Ok fair enough. Two questions.

1. I was not asking you to test the simulation/hallucination/dream/illusion hypothesis. But I was asking you to provide the evidence that your claim is true and real (not guessing and not imagination). That is totally different issue. Would you say so?

2. Are you a Hindu? Because your reply seem to be concretely based on the Hinduism in its principles.

I disagree. I could be a disembodied soul experiencing the simulation or hallucination or dream or illusion that I am in a human body, in a universe where there are other humans and other species. — Truth Seeker

Can you prove that is the case with some evidence? Or is it just your guessing or imagination?

It's possible that my body, the Earth, the universe, and all the other living things including you, are all part of a simulation or a hallucination or dream or illusion that I am experiencing. — Truth Seeker

For you to have been experiencing a simulation, hallucination, dream or illusion, you still need the physical body. No one can have all those experiences without having a biological body and brain. Therefore your reply is not making sense. Would you agree?

The statement: (a) "You lied." and the question: (b) Did you lie? When we break it down to its constituent parts (b) is still not a truth bearer. — PL Olcott

I am not sure if you are allowed to modify the given example sentence under the process of breakdown.
If it is allowed, then virtually all questions can be truth bearers.

For instance, "What time is it now?"
One could modify it into "It is true that she asked what time it is now.", hence one can say it is true.

"How are you doing?" - one can modify it again - "It is true that she asked him how he was doing." Therefore "How are you dong?" is a truth bearer.

Are modifications, inferences and breakdowns on the original sentence allowed for TF values?

questions cannot be {truth bearers} is known by everyone that knows what {truth bearers} are. — PL Olcott

Your statement here sounds nonsense. Some questions can be for true or false. For example, "You lied, didn't you?" This means you lied, and it is true. It is also to mean you should be aware of the fact that you lied.

We are not our body, but we appear to be embodied. I agree about the mind dying when the body dies. — Truth Seeker

What do you mean by "we appear to be embodied"? Can you imagine yourself existing without your body?

What is the true nature of the self? — Truth Seeker

Isn't one's physical body the true nature of the self? The moment the body dies, mind also dies truly and eternally.

Come to think of it, Afterlife sounds life keeps continuing after life ceased. Shouldn't it be called "Afterdeath"? :chin:

You missed the point: my linguistic expression of 'beyond' space is incoherent. 'Beyond' refers to something in space. — Bob Ross

Your keep parroting "You missed the point." in most messages you write wouldn't help you on understanding.

"Beyond" can mean other things too depending on the context. For example, "It is beyond me." - it does't mean something in space.

If your reader didn't understand what you wrote, then it is likely that your writing was not grammatically correct or it was out of context.

Gödel Incompleteness can only be implemented in systems that implement Boolean True(L, x) incorrectly. It cannot exist in systems where True(L, x) means that x is provable from L and False(L, x) means ~x is provable from L and for everything else x is simply untrue in L.

This same reasoning also conquers Tarski Undefinability.
When Tarski anchors his undefinability in the Liar Paradox: — PL Olcott

As I said before, will say again. The whole confusion with the paradox and undefinability have been originated from the single narrow perspective seeing the problems in propositional logic, which only allows a proposition must be either True or False.

If you think about the real world situations and objects, there are cases where things are neutral i.e. neither true nor false such as Number 0. And there are the real world cases where things are both True and False, read on QM or some Metaphysical topics.

If you open up the perspective wide and accept all these possibilities in the real world, it is quite normal for some cases to be either True or False, neither True nor False, or both True and False. If you apply FOL and HOL into your program languages bearing that point in your mind, and design the programs to deal with the particular cases in the real world examples, they deal all the case quite fine (Quine).

No that it not it. He used the term {synonymous} 98 times. — PL Olcott

Really? In which book or article did he do that? I have his Mathematical Logic, Method of Logic, Elementary Logic and The Significance of New Logic, total 4 books. But cannot recall seeing it.

He did not understand that the term {bachelor} is simply assigned the semantic meaning of {unmarried + male + adult}. — PL Olcott

Bachelor is a rather simple term. There are many other words in English which are more abstract to define. Try to define "Self", "Soul" and "Existence". Let's see if analytic truths can define them without contradiction or obscurity.

A person with a 50 million IQ that cannot understand that the term {bachelor} is assigned the semantic meaning of {unmarried + male + adult} is ridiculously stupid about this one point. — PL Olcott

I think Quine did understand what bachelor meant. But his point was that a word can mean different things, the meanings of words can change through time and culture, and for a word to convey clear meanings, it needs the context in the expressions in grammatically correct sentence reflecting the reality situations.

It sounds naive to say that a word means just the simple definitions in a bracket in tautological form, and that is the only truth in all cases under the sun.

Quine objected to true on the basis of meaning trying to get away with saying there is no such thing as meaning. The stupid nitwit could not even begin to understand that bachelors are not married. — PL Olcott

Quine was not a stupid. He was very academic and famous. He wrote many Logic and Philosophy books. I have some Quine books.

Bachelors can mean different things. Bachelor is also "a person who holds a first degree from a university or other academic institution" - Oxford Dictionary

Hence a woman can be a bachelor, so could a man married many times. I am sure there are surnames called "Bachelor", hence some married old folk could be a Bachelor, Mr Bachelor, or if for a woman, Ms Bachelor. They are all B(b)achelors.

For example, we cannot properly express how a non-spatial entity relates to space in english; but this is just a linguistic limitation. I can only say "a non-spatial entity would exist 'beyond' what is in space", but the concept of a non-spatial entity's relation to space as 'beyond' it is perfectly sensible albeit linguistically nonsensical. — Bob Ross

Yeah, it is better I am not clumped with Banno in a thread. From his comment, it is obvious Banno seems to be still in huff or under some sort of psychological trauma from my comments on his Logic in the past. All I said was I didn't agree with him.

Anyway I will make my point short. I can see your point in your last post. But let me say this to you to make the counterfactual point to your point. If you didn't explain your point on the non-spatial objects concepts as clearly as you did, in the grammatical form of standard language, I wouldn't have a clue what you were trying to mean.

A non-spatial entity that exists 'beyond' what is in space cannot be captured by human perception anyway. It can only be described and expressed in logically coherent statements. Concepts get formed via the descriptions using the language. It is a part of language. As you say, some languages don't have certain concepts, but it is not because language in general is unable to form the concepts. It is because no speakers of the language have not tried to form the concepts yet in the language.

The key most important thing about Prolog is that Gödel's incompleteness can not be implemented in Prolog. — PL Olcott

It can be implemented in C or Java in modified form with abstraction and generalisation. It cannot be implemented because you are seeing it in the propositional logic rather than predicate or first-order logic.

That set of facts that comprise the actual model of the real world is the basis.
This includes common sense and also details that almost everyone does not know. — PL Olcott

But your example "cows don't eat house bricks" is neither a fact nor common sense. It is just an irrelevant daft statement, which is based on senseless reasoning. :)

The actual model of the world is the basis. Facts not opinions. — PL Olcott

No one was talking about opinions here apart from yourself. Isn't it a typical case of the strawman?

Again, you are confusing language with concepts. The dictionary doesn't define concepts, it defines words (in a particular language). — Bob Ross

You are misunderstanding concepts as if they are some separate entity from language. Concepts, words, ideas and notions are part of language. Their meanings can only be understood fully in the use of language in some context.

I have the classic Clocksin and Mellish. https://www.amazon.com/Programming-Prolog-Using-ISO-Standard/dp/3540006788 — PL Olcott

I got this book as well. It just arrived. It seems Prolog is a great logic program language which is built on FOL and HOL. An ideal PL for AI applications.

Likewise we can generalize cows eat house bricks into cows eat something.
Any nonsense sentence can be changed into a different sentence that is not nonsense. — PL Olcott

You know the cows eat house bricks is false from common sense.
https://en.wikipedia.org/wiki/Common_sense
You don't need to generalise it to find out it is false. But generalisation and abstraction is what FOL and HOL are for the computability of ordinary language.

That is not true at all. If someone says that a {dog} <is> a fifteen story office building this is ruled as false because there are no {dogs} that <are> fifteen story office buildings in the actual world. — PL Olcott

It sounds a weak argument for your point. Some surly confused guy calling an honest man dishonest doesn't make the honest man dishonest. Likewise some obtuse man making totally irrelevant claims wouldn't have anything to do with the fact that analytic truth is true or false.

You expect your interlocutor try to make the most reasonable inferences for the arguments. If they come with totally irrelevant barmy claims, then you know he is not worth for any discussions on truth or logic.

That would just be ungrammatical. I am unsure, then, what contention you are making with the OP: I am not claiming that ungrammatical sentences make sense. — Bob Ross

It is ungrammatical but also incomplete. If it is incomplete, then listener will add their inference into the sentence trying to make a meaning out of it. The point is that, the axiomatic concepts don't have more meaning than the dictionary meanings on their own. To make meaningful use of them, you must use them in grammatically and contextually correct sentence.

Another point from the OP is that, if "be" is correct to say it means "exist". You could confirm on this. If you say "I am a member.", can it mean, "I exist a member."? It is nonsense.

"Be" is a linking verb. It needs something after it in the form of noun or adjective to make the sentence correct. "I am happy." "I am a member." "She is at the pub."

"I am" or "She is" itself doesn't sound clear or complete, unless it was used to replicate the previous sentence in the meaning, and the objects are inferred or omitted. For example, "Are you happy?" "Yes I am.", or "Is she in the pub now?" "Yes she is."

In other words, using "to be" "be" as same meaning to "to exist" "exist" seems debatable if it is correct in syntax and logic.

So you think that the concept 'triangle' doesn't make any sense in itself? — Bob Ross

Of course it does, but nothing more than it is a triangle with the standard definition. But if you say, something like "I think therefore I triangle", then it would be a poetry. Or if you said out of the blue "Triangle", then one would wonder what you were trying to say or express.

{correct} is an aspect of the meaning of the term {truth} so analytic truth cannot possibly be wrong in any way what-so-ever. If it cannot possibly be wrong in any way what-so-ever then it cannot possibly be wrong in any specific way. — PL Olcott

Your points seem to be confined in the domain of analytic truth only. In a domain where all in the domain is defined as truth regardless of the real world cases, it doesn't seem to be meaningful or productive keep insisting analytic truth is true in all cases. Jump out from the cave of the analytic truth, you can see that there are the real world and possible world with chaotic situations and events, where truth can be wrong, falsity can be right, and lots of possible unknown events, objects and situations. Analytic truths becomes useless in the all possible world.

Another point is that, you have been talking about the Paradox cases in the old propositional logic only. It looks the paradox is problem, and cannot be handled logically, and devoid of truth value from the old restricted logic. But if you look at the paradox from even PL or FOL, it can be handled no problem.

"This sentence is false" can be generalised into "Some sentence is false" which is not a contradiction. Suddenly it is not explicitly self referencing for the truth value. It generalise the sentence into some sentence which is false out there. HOL generalisation and abstraction would be able to handle far more complex cases with its expanded variables for relations, operations and predicates.

Concepts have their own meaning despite how they relate to concepts. The concept of the number 3 is obviously distinct from the number 2, and they don't rely on how they relate to each other to be defined. — Bob Ross

Again the point was the atomic concepts don't tell you much just by themselves apart from being objects of conjectures, confusion, intuition or poetry. They need to be supplied with clear and concrete data in complete and grammatically correct sentences to give you solid meaningful information or ideas about the world.

Hence my suggestion was to throw out the atomic concepts contained in incomplete sentence as meaningless expressions, which was one of your options for conclusion of the OP.

??? — Bob Ross

:roll:

You just tried to prove 'being' is vague because 'to be or not to be' doesn't refer to Hamlet's existence: why would Hamlet not existing have anything to do with it? — Bob Ross

It was not a proof. It was an example, so that you could understand the points better.

That is like saying the integer five may not be any kind of number at all. Everything that is {incorrect} is excluded from the body of {truth}. That people make mistakes has no actual effect what-so-ever on truth itself. If everyone in the universe is certain that X is true and X is not true their incorrect belief does not change this. — PL Olcott

You are not reading what comes after,

Analytic truth can be wrong — Corvus

:)

Analytic truth is a definition fallacy. It is defined as,
1. It is true, even if it is false.
2. Therefore to say it is false, is false even if it is true.

There is always potential possibility of human error in application side of the business due to unknown or changing states of the models in the world, which can make analytic truth wrong.

I am stipulating that analytic truth are only those expressions of language that are a correct model of the actual world. It seems a little nutty to define it any other way. — PL Olcott

Analytic truth can be wrong, if it is wrongly defined, expressed or applied to an incorrect model of the actual world, which is always possible from the human error. Claiming it is absolutely right in all circumstance sounds nutty.