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.

Saying that analytic truth can be wrong it like saying that kittens can be 15 story office buildings it cannot possibly ever happen. — PL Olcott

Analytic truth can be wrong, when it contradicts the reality. The reality has potential possibility to be otherwise from status quo at any moment of time. Therefore AT has potential possibility of being wrong.

Untrue unless provable from Facts does seem to be the correct model for the entire body of analytic truth. — PL Olcott

Analytic truth can be true, but wrong. Can "wrong" be "true", and "right" be "false"?

So, do you agree that some concepts are absolutely simple, and thusly unanalyzable and incapable of non-circular definitions, but yet still valid; or do these so-called, alleged, primitive concepts need to be either (1) capable of non-circular definition or (2) thrown out? — Bob Ross

What does a brick mean on its own lying on the ground apart from being a brick? Nothing. Many bricks must be piled with the cement mix into a shape to form a barbecue, a wall, workshop or a house to be meaningful for its manifestation.

Likewise what does "being" or "exist" mean on its own in a grammatically incomplete utterance? Nothing apart from being an object of inference, intuition or poetry, which must be thrown out in philosophical discussions as nonsense.

"To be or not to be" means "should something exist, or should it not?" — Bob Ross

But Hamlet doesn't exist. Hence "Exist" on its own, is vague and obscure. It is said to indicate things that doesn't exist as if it exists. When a claim is made "X exists", it must be supplied with more information on where, how and when. Without the info, it is a meaningless utterance such as "I think therefore I am."

:brow: — Bob Ross

It is the most famous and quoted phrase in English language.

This is not an example of a valid analysis of 'to be': 'to be or not to be?' ungrammatical, old english for "should something exist, or not?". — Bob Ross

What would be your valid analysis of "To be or not to be"? Why is it ungrammatical? What do you suggest for grammatically correct sentence for it?

I have the classic Clocksin and Mellish. — PL Olcott

The ones I ordered are,
PROLOG ++: The Power of Object-oriented and Logic Programming" by C. Moss.
Prolog Programming for Artificial Intelligence by Bratko.

All my Computer Programming Logic books have a chapter or two on ProLog.

I see your point. I was seeing HOL from totally different point of view. In programming languages HOL enables them more flexible and powerful in building rules and operational logics based on the real world applications requirements. Hence, any statements can be assigned into available variables for getting assigned as preset TF values for required operations. In the programming environment, the only source of truths is the external world, not truth tables. New logics get built in the system according to the specs.

I am waiting for a couple of cheap old Prolog books which are on my way. Prolog seems to be the system for Logic programming. It seems to be a PL which has a long history, but seems to be still very much popular even now especially for AI applications.

I am not talking about anything like that. I am referring to the (non-existent truth value of the) actual semantic meaning of the English sentence: What time is it? — PL Olcott

I see. But my point was, isn't the main point of using HOL (as also mentioned in the OP title) is being able to set TF values to the non-existent truth value sentences or word such as "What time is it?", and make use of them in the real world applications?

For example, in algorithmic language
Set S = "What time is it?"
Read External Data Q
If Q = S then
S = True
If S = True then Read Time from the System Clock
Write{"Time is 09:00.")
If Q <> S then
S = False
If S = False then
Write("Please type your question again."
End. => Can be translated into any other PL such as C, C++, java, Python or Pascal ..etc

Saying "What time is it?" has no TF value sounds like ignoring the flexibility and applicability of the program languages and also armchair linguistic philosophy of 1950s. :D

Tarski never noticed that "This sentence is not true" is not a truth bearer thus the same ask asking is this sentence true or false — PL Olcott

I am not sure how Prolog works in Boolean value settings and execution operations. I have ordered a couple cheap Prolog books by the way. But in Pascal, C and other HLPLs, they have no problems dealing with the paradox cases in the sentence for the operations due to ability to assign the sentences into either Constants or variables. Then the constants or variables can be initialised with boolean values at the start-up of procedures or functions, which sets the variable or constant values to either True or False.

And then operations for checking the constants or variables with the input data or external condition or states, which generate further TF values, in which case then further process of operations could be written depending on the TF values of the checked out variable or constants.

The paradox problems were only problem or paradox because the TF values were reflected from the semantic values in the word "true" or "false" in the sentence rather than the TF values on the whole sentence.

In PASCAL or C, "What time is it?" can be set as True or False in a variable, and can be used to check the condition of the input data for comparing and generating another TF value from the checking operation. I presumed that was what HOL was all about. Being able to assign any sentence or type of data into the vast different type of variables, and manipulate the TF conditions by controlling them. I am not sure how Prolog would do it, yet.

:blush: :pray:

This eliminates this terrible mistake by Gödel: — PL Olcott

Yes, it would be good if you could present the Tarski's and Godel's theorems in connection with HOL with your own explanations (the proofs and refutations) in clear English with added formulas too (if needed).

Why does our brain have limited capacity? Why aren't all living things all-loving, all-knowing and all-powerful? How do you know that someone could have done something else at the time and place of the doing instead of what was done? I am not convinced that anyone could have done something else but I could be wrong as I am not all-knowing. — Truth Seeker

Good question. I wish I know the answers for the questions. Only thing I know is that there are things we know, and there are things we don't know. Most of the unknowability can never be cleared I presume. Humans are critically and sorely limited existence in time of life on the earth, knowing and thinking capabilities due to them having the biological bodies, and thinkings and knowings that rely on the biological brain.

There is no substitute for actual experience. No amount of reading will help you comprehend how painful pain is. — Truth Seeker

I have no knowledge or experience in the field of pains and clinical psychology. I am sorry that I cannot offer any info or advice on the situation. I hope that you will feel better and get back to your normal emotional state and physical health as soon as possible.

I will read Hume and Kant if I ever get to either 0 or +1 on the mood scale. Thank you for the recommendations. — Truth Seeker

You are very welcome Truth Seeker. Please take your time. If you open new threads with Hume or Kant topics later on when you feel better, I will definitely try to join and engage in discussions with you then. Take care, and thank you for engaging discussions with me for the interesting OP.

All I can say, is that ‘being’ is ‘to be’, ‘to exist’, ‘existence’, etc.; but this does not afford any real analysis into what ‘to be’ really is itself but, rather, is just a reiteration, in different words, of the same meaning. — Bob Ross

If an actor says on the stage "To be, or not to be: that is the question.", is it about himself, or Hamlet?

It's not possible to think freely. Can you think up everything there is to know about dark matter and dark energy? No, you can't. Can you think of a trillion thoughts per second? No, you can't. Our thoughts are determined and constrained by our genes, environments, nutrients, and experiences. — Truth Seeker

The reason we can not do those is because of lack of data to us, and our brain has limited capacity in thinking, not because anything is determined.

We are all prisoners of causality - doomed to suffer and die. I am all-loving but I am not all-knowing and all-powerful. I am so sad. I wish I never existed. — Truth Seeker

These comments are not factual objective descriptions of anything in the world, but just reflection of your psychology. You can change your beliefs and emotions by changing your reasoning and reading some philosophical textbooks. No one else can change your beliefs apart from yourself.

Hume and Kant were dualists. They are both wrong. You are also wrong about having free will. I am a materialist monist hard determinist because I am convinced by evidence. — Truth Seeker

Hume and Kant were dualists? There are different interpretations about them. It is not that simple. They are not wrong. They present us with deep and rich arguments on our mind and the world. You should try reading them first, and try to understand them. I am sure you will enjoy.

HOL is simply a bridge so that people that don't have a clue what knowledge ontologies are can think of them using the simpler isomorphism of what they do know. — PL Olcott

Isn't HOL the expanded logical system from the other simpler ones with the relation and operation variables in the formulas? Most modern programming languages seem to be based on HOL. How about Prolog? My computer logic book has a chapter on Prolog with its syntax. It says it is a declarative language rather than procedural like PASCAL, and it always has to refer to a database for the facts and rules.

Sounds good idea. Only problem with the PLs handling the paradox cases could be the program crash, when the contradicting variables with TF values were encountered during the execution. But being HOL with the expanded variable availabilities, the inner sentence could be assigned to the next variable for the different boolean values. HOL being arithmetic oriented structure, not sure how they would be in handling the text or sentence based data handling. It would be great help in understanding the operational side of it if the real program testing sessions would be available to see with the paradox cases.

Suffice to say you are not an honest interlocutor. — AmadeusD

:roll: :rofl:

"Do you accept that all events have prior causes?" If so, that syllogism holds and defeats your position. — AmadeusD

It appears that you haven't read any Hume at all. It is not matter of all events have prior causes or not. But the matter is that causes exist in your mind, not in the external world. Hence all causes are psychological judgement. In other words you have been talking about something which is your mental state, rather than objective existence or facts.

I can see why you were upset, and being defensive calling trolling and changing goal posts etc. The logical argument you presented is not logical at all. It just is reasserting your belief on determinism.

I am glad that you declared the end of discussion. I have nothing more to add apart from the points I made in the last posts. All the very best.

that is, they will allow you to match a term against an uninstantiated
subterm of itself. — PL Olcott

From your coding, it seems no problem for HOL dealing with the Liars paradox and also Tarksi's undefinability.

I am sure you can. First of all, try reading Hume and Kant, focusing on Cause and Effect theory. Then you can decide on what you feel and convince as correct. It is totally up to your free thinking what you decide as truth.

Finally, a note about how Prolog matching sometimes differs from the
unification used in Resolution. Most Prolog systems will allow you to
satisfy goals like: — PL Olcott

:up: :pray: I have not used Prolog, but it gives a rough idea to go about and trying it in the other PLs such as C, C++ or Java. Thanks Olcott.