Is It Possible To Think Without Language?

[Greta]

The whole point of language is to articulate pre-existing thoughts.

[A_Seagull]

Is it possible to think with language? If so how?

For there is nothing within language itself that suggests how thinking can be effected.

[Averroes]

The interesting thing in all this is that I have already imposed a necessary condition for the existence of a thought that it be expressible in language, exactly complying with the demands of intuitionistic logic. I am already done in intuitionistic logic!

A condition which I reject,

That condition is imposed by intuitionistic logic itself! You cannot reject that condition in intuitionistic logic, while it is you who wanted to go in intuitionistic logic!! That was your own choice, no one forced you. So, are you running away from intuitionistic logic now? Remark, I am still ALSO happy in classical logic. Whatever you chose, it’s all the same for me!
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so the rest of your post doesn't matter

Does that mean you are running away from your claim that you can prove the existence of thoughts that cannot be expressed in language in intuitionistic logic? For I clearly remember you saying that you had the capacity to do something really great!! So, the following is what you said:

You have set yourself up for disappointment. You have contrived an impossible challenge. A game that cannot be won given the rules you seem to be playing by. You are asking me to prove a negative while at the same time it appears you are holding me accountable to the laws of Aristotelian/Classical logic.

The only way I know how to prove a negative is to abandon Aristotelian logic and embrace constructive/intuitionistic logic. Which necessarily means abandoning the laws of excluded middle AND the laws of non-contradiction!

It is only in that framework where proof-by-contradiction becomes a viable strategy: https://en.wikipedia.org/wiki/Proof_by_contradiction

So, lets embrace constructive logic and ASSUME that all thought can be expressed in language and see what absurdities/paradoxes this leads to.

Of course, now the game is rigged in my favour because I KNOW you have no empirical/ontological/scientific grounding for what a 'thought' is and isn't

I can wait some more if you are not giving up so easily after having made such an eloquent speech about your capacities to prove "a negative" in intuitionistic logic!!
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One can simply point to Godel's incompleteness theorems as point of departure that that all logic (language) is incomplete.

Absolutely not! Not all logic is incomplete! Godel’s incompleteness theorems is about axiomatic systems with arithmetic, in that such systems cannot be both complete and consistent.

Wikipedia:

The incompleteness theorems apply to formal systems that are of sufficient complexity to express the basic arithmetic of the natural numbers and which are consistent, and effectively axiomatized, these concepts being detailed below. https://en.wikipedia.org/wiki/G%C3%B6de ... s_theorems

Furthermore, these theorems are about provability and not expression (with which we are concerned).

In general, a formal system is a deductive apparatus that consists of a particular set of axioms along with rules of symbolic manipulation (or rules of inference) that allow for the derivation of new theorems from the axioms. One example of such a system is first-order Peano arithmetic, a system in which all variables are intended to denote natural numbers. In other systems, such as set theory, only some sentences of the formal system express statements about the natural numbers. The incompleteness theorems are about formal provability within these systems, rather than about "provability" in an informal sense. Site: https://en.wikipedia.org/wiki/G%C3%B6de ... s_theorems

Moreover, Godel’s incompleteness theorems does not concern First Order Logic which is both complete and consistent.

So, Godel’s incompleteness theorem is of no relevance to our discussion, where you freely took the responsibility of proving your own claim not involving arithmetic in a formal system of your own choice which was intuitionistic logic. Nevertheless, if you are still worried about completeness, then here is a proof that intuitionistic logic is complete: http://www.math.unipd.it/~silvio/papers ... opComp.pdf

So now, the only thing to do is for you to get to work and prove what you said you could easily prove in intuitionistic logic! How much time do you need for that task? Or do you give up?

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[TimeSeeker]

That condition is imposed by intuitionistic logic itself! You cannot reject that condition in intuitionistic logic, while it is you who wanted to go in intuitionistic logic!! That was your own choice, no one forced you. So, are you running away from intuitionistic logic now? Remark, I am still ALSO happy in classical logic. Whatever you chose, it’s all the same for me!

Indeed. Running up. Into the realms of higher order logic. To things like type theory/lambda calculus which contains no contradictions in any classical sense - only syntactic/semantic errors (mea culpa!). I have no interest in playing philosophical word games

But for the sake of conclusion and using the broadest definition of "language" that I am familiar with - the Chomsky Type-3 Grammars then anything in the RE complexity class can be expressed in language (Kleene's theorem). Which is basically the universe (or multiverse) itself. The philosophising then is not whether it can or cannot be expressed, but rather expressed by whom? Language is a red herring. The reference frame and the quantity of available information to construct a testable model is the key to the puzzle.

I could agree to a proposition that in principle all thoughts can be DESCRIBED in language by an entity observing and interacting with the thinker - and particularly the thinker's brain.
Whether all thoughts can be EXPRESSED in language by the thinker themselves. Still going with "No".

I have no idea what this taste in my mouth is right now. I don't have a word to describe it or express it, so no matter how much I think about it I can't tell you what it is, but you are welcome to provide a falsifier. Alternatively (and since you are only concerned with expression) I guess I could say that it tastes like rafnobaks. I just made that word up, but I guess I never bothered to ask how low your bar for 'expression' is? If there is no bar then inventing words whose meaning cannot be shared with anybody else is par for the course. Art!

P.S Type systems are a superset of first order logic. And they are algebraic. And they are axiomatic - so Godel applies, but only as a corollary to Turing's halting problem ( https://www.scottaaronson.com/blog/?p=710 ) since everything is a subset of the RE complexity class then every problem reduces to decidability (Hilbert's Entscheidungsproblem). So I think the onus is on you to present the constructive models for "thought" and "language" that YOU have in mind before we can decide (or decide that it is undecidable) whether they are isomorphic, or whether one is a subset of the other. That is - I am invoking Newton's flaming laser sword

But I suspect it will be soon revealed that by "thinking" you mean "Turing machine" and by "language" you mean Type 3 Chomski grammar then is there any sense in debating the Curry–Howard–Lambek correspondence?

[TimeSeeker]

I don't remember us discussing meaning which is prior to expression. I remember us discussing meaning that is a posteriori language to which you are yet to give me an example.

When it is the case that language already exists, correlations can be drawn between the language, it's use, and other things. This is meaning that is existentially dependent upon language:When part of the correlation is language, it is existentially dependent upon language.

Ok. That is a definition - not an example.

Can you be more particular?

Drawing correlations is about inference. So we are definitely in the realm of interpretation. And so it seems to me that you are talking about Lesk’s algorithm ( https://en.wikipedia.org/wiki/Lesk_algorithm )

Or more broadly the field of automated disambiguation: https://en.wikipedia.org/wiki/Word-sense_disambiguation

[Averroes]

That condition is imposed by intuitionistic logic itself! You cannot reject that condition in intuitionistic logic, while it is you who wanted to go in intuitionistic logic!! That was your own choice, no one forced you. So, are you running away from intuitionistic logic now? Remark, I am still ALSO happy in classical logic. Whatever you chose, it’s all the same for me!

Indeed. Running up.

Alright. It was nice exchanging with you.

To things like type theory/lambda calculus which contains no contradictions in any classical sense - only syntactic/semantic errors (mea culpa!).

It’s alright, don’t worry about it.

There is no logic and hence no mathematics without the law of non-contradiction. Just consider Type theory itself, which was devised to address the Russell paradox by Russell himself. And the Russell paradox as you already know is a statement that violated the law of non-contradiction. So, for Type Theory to be addressing the Russell paradox, it cannot in turn be possible for it to violate the law of non-contradiction! Here are some information I found in Wikipedia for others who might be reading this:

Wikipedia:

Between 1902 and 1908 Bertrand Russell proposed various "theories of type" in response to his discovery that Gottlob Frege's version of naive set theory was afflicted with Russell's paradox. By 1908 Russell arrived at a "ramified" theory of types together with an "axiom of reducibility" both of which featured prominently in Whitehead and Russell's Principia Mathematica published between 1910 and 1913. They attempted to resolve Russell's paradox by first creating a hierarchy of types, then assigning each concrete mathematical (and possibly other) entity to a type. Entities of a given type are built exclusively from entities of those types that are lower in their hierarchy, thus preventing an entity from being assigned to itself. In the 1920s, Leon Chwistek and Frank P. Ramsey proposed a simpler theory, now known as the "theory of simple types" or "simple type theory", that collapsed the complicated hierarchy of the "ramified theory" and did not require the axiom of reducibility. https://en.wikipedia.org/wiki/Type_theory

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I could agree to a proposition that in principle all thoughts can be DESCRIBED in language by an entity observing and interacting with the thinker - and particularly the thinker's brain.
Whether all thoughts can be EXPRESSED in language by the thinker themselves. Still going with "No".

There is a subtlety here that you must appreciate. That which you are expressing with the expression "all thoughts can be DESCRIBED in language," is in fact merely a translation! And we translate from one language to another! So, whether a thought is expressed or not in the English language (or whatever other language such as French etc.), it is already a proposition! If it is now expressed in the English language (for example), then it is merely a translation that has occurred from one language to another!

I have no idea what this taste in my mouth is right now. I don't have a word to describe it or express it, so no matter how much I think about it I can't tell you what it is, but you are welcome to provide a falsifier.

If you feel a taste in your mouth, then you already have a thought and hence you already have a proposition! Now, that you cannot express that thought in the English language is another matter which is due to your limited knowledge of the English language, which is nothing peculiar/specific to you but can happen to every English speaker.

So I think the onus is on you to present the constructive models for "thought" and "language" that YOU have in mind before we can decide (or decide that it is undecidable) whether they are isomorphic, or whether one is a subset of the other. That is - I am invoking Newton's flaming laser sword

A set is a subset of itself and isomorphic to itself something called automorphism, if I am not mistaken. If you are going from the premise that you can separate thought from language, then it's not my point of view. What I am arguing is that this is itself impossible. So you can only talk of isomorphism or subset relations between thoughts and language as you would of a set with respect to itself, but this is trivial.

So that's it. It was interesting exchanging with you.
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[TimeSeeker]

There is no logic and hence no mathematics without the law of non-contradiction. Just consider Type theory itself, which was devised to address the Russell paradox by Russell himself. And the Russell paradox as you already know is a statement that violated the law of non-contradiction. So, for Type Theory to be addressing the Russell paradox, it cannot in turn be possible for it to violate the law of non-contradiction! Here are some information I found in Wikipedia for others who might be reading this:

Then allow me to rephrase. By having a sufficiently expressive and descriptive grammar and semantics Type theory addresses the root causes of contradictions - ambiguity and synonym mixups, insufficient individuation/distinction of terms. Contradiction stems from lack of precision.

And so if the grammar is followed and if your types are clearly individuated and defined then a contradiction cannot occur. This is what software compilers (strongly typed) and interpreters (weakly typed) do. They make sure that the statement is interpretable e.g meaningful. They detect semantic and syntactic errors. If the software still doesn't work - your model is wrong.It's a bug, not a contradiction. Garbage in - garbage out.

https://en.wikipedia.org/wiki/Strong_and_weak_typing

There is a subtlety here that you must appreciate. That which you are expressing with the expression "all thoughts can be DESCRIBED in language," is in fact merely a translation! And we translate from one language to another! So, whether a thought is expressed or not in the English language (or whatever other language such as French etc.), it is already a proposition! If it is now expressed in the English language (for example), then it is merely a translation that has occurred from one language to another!

So my thoughts are language now? And yet you keep drawing a distinction between 'thoughts' and 'language' throughout our interaction. Why?
You are getting closer and closer to either moving the goal posts or admitting that there were none.

All human experience and expression is language. A tautology I pointed out as early as my 2nd response to you when I recognized you scoping language far more broadly than I am.

If you feel a taste in your mouth, then you already have a thought and hence you already have a proposition! Now, that you cannot express that thought in the English language is another matter which is due to your limited knowledge of the English language, which is nothing peculiar/specific to you but can happen to every English speaker.

I don't have a proposition! By virtue of now knowing what this taste of my mouth is and lacking an ostensive definition - I cannot propose anything. I have an unidentified taste in my mouth! It is different from the unidentified taste in my mouth I had yesterday. So I have two unidentified tastes in my mouth. So it is not so much my knowledge of English that is lacking. It is prior knowledge of these tastes! I have no point of reference for them.

You have pre-supposed that a word for the tastes in my mouth already exists. Which is as per my original criticism - you take language, and in particular English, for granted and you assume it to be complete in terms of expressiveness. Which necessarily means that the full spectrum of human experiences is already captured in the English language. While at the same time you also claim that original ideas are expressed in English. If all propositions are already in the English language, then how can any idea be 'original'?

What a silly, point of view!

New language comes AFTER new thought. All human experiences and expression are information. As per Shannon, 1948 (but that is just my preferred axiomatic truth).

[Atla]

Some people, usually categorized as savants, have a rare ability: they can voluntarily use their subconscious (I guess? or is it the unconscious part?) to "think". They just know things, often instantly. They can't really explain how they do it, they just do it. The end result of the "thinking" process just appears in their minds, often almost instantly, and they usually can't recall how they got there. It all may be somehow, some way, silently parallel processed in their subconscious (/unconscious).

There are many kinds of savants, my favourite candidate for this is Capablanca the third world chess champion, who arguably had the biggest natural chess talent in history (but I suspect that Tal and Carlsen have some of this ability too).

Fine on Capablanca:
"What others could not see in a month's study, he saw at a glance."

Kasparov on Tal:
"We calculate: he does this then I do that. And Tal, through all the thick layers of variants, saw that around the 8th move, it will be so and so. Some people can see the mathematical formulae, they can imagine the whole picture instantly. An ordinary man has to calculate, to think this through, but they just see it all. It occurs in great musicians, great scientists. Tal was absolutely unique. His playing style was of course unrepeatable. I calculated the variants quickly enough, but these Tal insights were unique. He was a man in whose presence others sensed their mediocrity."

I guess an example of a savant scientist would be Tesla.

So the arguably highest form of human cognition is not only not done in language, it's not even done in what we would normally call "thoughts".

[Averroes]

Then allow me to rephrase.

Of course.

Contradiction stems from lack of precision.

Contradictions occur by upholding contradictory statements, whether these statements are precise or not.

So my thoughts are language now? And yet you keep drawing a distinction between 'thoughts' and 'language' throughout our interaction. Why?

I have been saying all along several times that thoughts are propositions! I also quoted Kant and Wittgenstein on that! You are not paying attention.

You are getting closer and closer to either moving the goal posts or admitting that there were none.

The goal post is not being moved, it is still there, but you ran away from it! Did you forget that already? We can go there again if you want, there is no problem on my side!

_______________________________

If you feel a taste in your mouth, then you already have a thought and hence you already have a proposition! Now, that you cannot express that thought in the English language is another matter which is due to your limited knowledge of the English language, which is nothing peculiar/specific to you but can happen to every English speaker.

I don't have a proposition!

You do! In fact, you now not only have just one proposition but three! This is what you wrote:

I have an unidentified taste in my mouth! It is different from the unidentified taste in my mouth I had yesterday. So I have two unidentified tastes in my mouth.

So, your propositions are:
1. I have an unidentified taste in my mouth!
2. It is different from the unidentified taste in my mouth I had yesterday.
3. So I have two unidentified tastes in my mouth.

These are three meaningful English language propositions that every English speaker can understand!

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You have pre-supposed that a word for the tastes in my mouth already exists.

I do not need to presuppose, because it is a fact that an expression already exists as you already used it! With the English expression “an unidentified taste in my mouth” and the English expression “the unidentified taste in my mouth I had yesterday” you already referred to those tastes in your mouth with English expressions!!

Which is as per my original criticism - you take language, and in particular English, for granted and you assume it to be complete in terms of expressiveness.

Indeed there is no thought that cannot be expressed in language. Which thought cannot be expressed in language?! I remember that you had set out to prove in intuitionistic logic that there can be thoughts which cannot be expressed in language. I remember you said the following:

You have set yourself up for disappointment. You have contrived an impossible challenge. A game that cannot be won given the rules you seem to be playing by. You are asking me to prove a negative while at the same time it appears you are holding me accountable to the laws of Aristotelian/Classical logic.

The only way I know how to prove a negative is to abandon Aristotelian logic and embrace constructive/intuitionistic logic. Which necessarily means abandoning the laws of excluded middle AND the laws of non-contradiction!

It is only in that framework where proof-by-contradiction becomes a viable strategy: https://en.wikipedia.org/wiki/Proof_by_contradiction

So, lets embrace constructive logic and ASSUME that all thought can be expressed in language and see what absurdities/paradoxes this leads to.

Of course, now the game is rigged in my favour because I KNOW you have no empirical/ontological/scientific grounding for what a 'thought' is and isn't

So what happened to that great project of yours, which was rigged in your favor?! Do you want to give it another try? I can wait some more, I am not in a hurry!
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If all propositions are already in the English language, then how can any idea be 'original'?

All propositions are expressible in language. Original thoughts have been and are being expressed in the English language. Now, you ask: How can there be any original thought in the English language? We already addressed that many times already on this thread! So again, if the English language cannot be used to express original thoughts nowadays, then why is the UK authorities, for example, cracking down on plagiarism??
I have raised this issue a couple of times already, but you have consistently evaded providing an answer! Will you give it a try this time? I doubt it!

So that’s it. I will now be waiting for your demonstration of the possibility of thoughts that cannot be expressed in language! That is the goal post that you have been evading, after being so close to attaining in intuitionistic logic!!
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[TimeSeeker]

Then allow me to rephrase.

Of course.

Contradiction stems from lack of precision.

Contradictions occur by upholding contradictory statements, whether these statements are precise or not.

So my thoughts are language now? And yet you keep drawing a distinction between 'thoughts' and 'language' throughout our interaction. Why?

I have been saying all along several times that thoughts are propositions! I also quoted Kant and Wittgenstein on that! You are not paying attention.

You are getting closer and closer to either moving the goal posts or admitting that there were none.

The goal post is not being moved, it is still there, but you ran away from it! Did you forget that already? We can go there again if you want, there is no problem on my side!

_______________________________

If you feel a taste in your mouth, then you already have a thought and hence you already have a proposition! Now, that you cannot express that thought in the English language is another matter which is due to your limited knowledge of the English language, which is nothing peculiar/specific to you but can happen to every English speaker.

I don't have a proposition!

You do! In fact, you now not only have just one proposition but three! This is what you wrote:

I have an unidentified taste in my mouth! It is different from the unidentified taste in my mouth I had yesterday. So I have two unidentified tastes in my mouth.

So, your propositions are:
1. I have an unidentified taste in my mouth!
2. It is different from the unidentified taste in my mouth I had yesterday.
3. So I have two unidentified tastes in my mouth.

These are three meaningful English language propositions that every English speaker can understand!

____________________________

You have pre-supposed that a word for the tastes in my mouth already exists.

I do not need to presuppose, because it is a fact that an expression already exists as you already used it! With the English expression “an unidentified taste in my mouth” and the English expression “the unidentified taste in my mouth I had yesterday” you already referred to those tastes in your mouth with English expressions!!

Which is as per my original criticism - you take language, and in particular English, for granted and you assume it to be complete in terms of expressiveness.

Indeed there is no thought that cannot be expressed in language. Which thought cannot be expressed in language?! I remember that you had set out to prove in intuitionistic logic that there can be thoughts which cannot be expressed in language. I remember you said the following:

You have set yourself up for disappointment. You have contrived an impossible challenge. A game that cannot be won given the rules you seem to be playing by. You are asking me to prove a negative while at the same time it appears you are holding me accountable to the laws of Aristotelian/Classical logic.

The only way I know how to prove a negative is to abandon Aristotelian logic and embrace constructive/intuitionistic logic. Which necessarily means abandoning the laws of excluded middle AND the laws of non-contradiction!

It is only in that framework where proof-by-contradiction becomes a viable strategy: https://en.wikipedia.org/wiki/Proof_by_contradiction

So, lets embrace constructive logic and ASSUME that all thought can be expressed in language and see what absurdities/paradoxes this leads to.

Of course, now the game is rigged in my favour because I KNOW you have no empirical/ontological/scientific grounding for what a 'thought' is and isn't

So what happened to that great project of yours, which was rigged in your favor?! Do you want to give it another try? I can wait some more, I am not in a hurry!
______________________________

If all propositions are already in the English language, then how can any idea be 'original'?

All propositions are expressible in language. Original thoughts have been and are being expressed in the English language. Now, you ask: How can there be any original thought in the English language? We already addressed that many times already on this thread! So again, if the English language cannot be used to express original thoughts nowadays, then why is the UK authorities, for example, cracking down on plagiarism??
I have raised this issue a couple of times already, but you have consistently evaded providing an answer! Will you give it a try this time? I doubt it!

So that’s it. I will now be waiting for your demonstration of the possibility of thoughts that cannot be expressed in language! That is the goal post that you have been evading, after being so close to attaining in intuitionistic logic!!
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Ohhhhhh! MENTIONING a thought (e.g the unidentifiable taste) is sufficient for expression? The CONTENTS of a thought are of no consequence? I don’t have to describe the taste or elucidate it so that it is communicable to; and resonates with others? I thought I was being held to a higher standard.

Well in THAT case!

The proof I promised is in my head. And I am mentioning it, but I have no idea how to translate it into English or formal logic.

So. Is that evidence for or against the claim that “There are some thoughts which cannot be expressed in language"?

[Averroes]

Ohhhhhh! MENTIONING a thought (e.g the unidentifiable taste) is sufficient for expression?

Yes.
An important correction though, “the unidentifiable taste” is not yet a thought but just an expression and in a sentence it called a noun phrase. The thought was: “I have an unidentified taste in my mouth!” This is basic grammar anyway, you should already know all this.

The CONTENTS of a thought are of no consequence? I don’t have to describe the taste or elucidate it so that it is communicable to; and resonates with others?

You have already described the taste, you said it was “unidentifiable.” And it “resonated” (i.e. I understood) when I read it. So, we are good here.

I thought I was being held to a higher standard.

You still have to comply with the standards of logic though, i.e. you cannot make a contradictory statement in you discourse or exposition.

The proof I promised is in my head. And I am mentioning it, but I have no idea how to translate it into English or formal logic.

So now you have mentioned the expression “the proof I promised,” and that expression is intended to refer to the proof in your head that there are thoughts which cannot be expressed in language. Alright!!!

So. Is that evidence for or against the claim that “There are some thoughts which cannot be expressed in language"?

Against! Because now, the expression “thoughts which cannot be expressed in language,” is referring to thoughts that cannot be expressed in language!! And we have a contradiction!

Do you want to give it another try?

[TimeSeeker]

Contradictions occur by upholding contradictory statements, whether these statements are precise or not.

This is an interesting claim.

Could you demonstrate perhaps? Please go ahead and type two contradictory statements in any programming language of your choosing.

You are welcome to use this platform: https://repl.it/languages

Once you handle the above challenge then we can focus on this lie:

Against! Because now, the expression “thoughts which cannot be expressed in language,” is referring to thoughts that cannot be expressed in language!! And we have a contradiction!

How can that be a contradiction if contradictions don't exist? I thought it's a law?
Now you are asserting a contradiction? So contradictions DO exist?

What kind of a 'law' is this?!?

I told you all of classical logic is in my trash can - you don't believe me.

[Averroes]

Once you handle the above challenge then we can focus on this lie:

Against! Because now, the expression “thoughts which cannot be expressed in language,” is referring to thoughts that cannot be expressed in language!! And we have a contradiction!

No. We started here, and we will have to end it here. Don't try to run away again from the "goal post." Either you give up or you prove what you promised, there is no escape.

[TimeSeeker]

No. We started here, and we will have to end it here. Don't try to run away again from the "goal post." Either you give up or you prove what you promised, there is no escape.

But you said "any language". Now you INSIST on doing it on this platform? Why?

Lets do it in Python.

And in Python there are no contradictions. So I reject the LNC until you can demonstrate or provide some evidence that contradictions exist.

[Averroes]

How can that be a contradiction if contradictions don't exist? I thought it's a law?
Now you are asserting a contradiction? So contradictions DO exist?

What kind of a 'law' is this?!?

I told you all of classical logic is in my trash can - you don't believe me.

You have chosen intuitionistic logic, I am fine with that. But in intuitionistic logic, there is still the law of non-contradiction. If you cannot provide a proof by upholding the law of non-contradiction, then you have not fulfilled your "promise" (as you say). Take your time. I am not in a hurry.