Re: Is It Possible To Think Without Language?
Posted: Mon Nov 05, 2018 3:20 am
The whole point of language is to articulate pre-existing thoughts.
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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!
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:
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!!TimeSeeker wrote: ↑Sat Nov 03, 2018 1:50 pm 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
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.TimeSeeker wrote: ↑Mon Nov 05, 2018 12:52 amOne can simply point to Godel's incompleteness theorems as point of departure that that all logic (language) is incomplete.
Furthermore, these theorems are about provability and not expression (with which we are concerned).Wikipedia wrote: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
Moreover, Godel’s incompleteness theorems does not concern First Order Logic which is both complete and consistent.Wikipedia wrote: 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
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 gamesAverroes wrote: ↑Mon Nov 05, 2018 6:54 am 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!
Ok. That is a definition - not an example.creativesoul wrote: ↑Mon Nov 05, 2018 1:05 amWhen 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.TimeSeeker wrote: ↑Mon Nov 05, 2018 12:32 am
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.
Alright. It was nice exchanging with you.TimeSeeker wrote: ↑Mon Nov 05, 2018 7:12 amIndeed. Running up.Averroes wrote: ↑Mon Nov 05, 2018 6:54 am 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!
It’s alright, don’t worry about it.TimeSeeker wrote: ↑Mon Nov 05, 2018 7:12 amTo things like type theory/lambda calculus which contains no contradictions in any classical sense - only syntactic/semantic errors (mea culpa!).
_____________________________Wikipedia wrote: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
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!TimeSeeker wrote: ↑Mon Nov 05, 2018 7:12 am 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".
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.TimeSeeker wrote: ↑Mon Nov 05, 2018 7:12 am 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.
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.TimeSeeker wrote: ↑Mon Nov 05, 2018 7:12 am 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
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.Averroes wrote: ↑Tue Nov 06, 2018 9:21 am 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:
So my thoughts are language now? And yet you keep drawing a distinction between 'thoughts' and 'language' throughout our interaction. Why?Averroes wrote: ↑Tue Nov 06, 2018 9:21 am 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 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.Averroes wrote: ↑Tue Nov 06, 2018 9:21 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.
Of course.
Contradictions occur by upholding contradictory statements, whether these statements are precise or not.
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.TimeSeeker wrote: ↑Tue Nov 06, 2018 11:33 am So my thoughts are language now? And yet you keep drawing a distinction between 'thoughts' and 'language' throughout our interaction. Why?
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!TimeSeeker wrote: ↑Tue Nov 06, 2018 11:33 am You are getting closer and closer to either moving the goal posts or admitting that there were none.
You do! In fact, you now not only have just one proposition but three! This is what you wrote:TimeSeeker wrote: ↑Tue Nov 06, 2018 11:33 amI don't have a proposition!Averroes wrote: ↑Tue Nov 06, 2018 9:21 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.
So, your propositions are:TimeSeeker wrote: ↑Tue Nov 06, 2018 11:33 am 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.
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!!TimeSeeker wrote: ↑Tue Nov 06, 2018 11:33 am You have pre-supposed that a word for the tastes in my mouth already exists.
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:TimeSeeker wrote: ↑Tue Nov 06, 2018 11:33 am 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.
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!TimeSeeker wrote: ↑Sat Nov 03, 2018 1:50 pm 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
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??TimeSeeker wrote: ↑Tue Nov 06, 2018 11:33 amIf all propositions are already in the English language, then how can any idea be 'original'?
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.Averroes wrote: ↑Wed Nov 07, 2018 7:43 amOf course.
Contradictions occur by upholding contradictory statements, whether these statements are precise or not.
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.TimeSeeker wrote: ↑Tue Nov 06, 2018 11:33 am So my thoughts are language now? And yet you keep drawing a distinction between 'thoughts' and 'language' throughout our interaction. Why?
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!TimeSeeker wrote: ↑Tue Nov 06, 2018 11:33 am You are getting closer and closer to either moving the goal posts or admitting that there were none.
_______________________________
You do! In fact, you now not only have just one proposition but three! This is what you wrote:TimeSeeker wrote: ↑Tue Nov 06, 2018 11:33 amI don't have a proposition!Averroes wrote: ↑Tue Nov 06, 2018 9:21 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.
So, your propositions are:TimeSeeker wrote: ↑Tue Nov 06, 2018 11:33 am 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.
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!
____________________________
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!!TimeSeeker wrote: ↑Tue Nov 06, 2018 11:33 am You have pre-supposed that a word for the tastes in my mouth already exists.
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:TimeSeeker wrote: ↑Tue Nov 06, 2018 11:33 am 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.
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!TimeSeeker wrote: ↑Sat Nov 03, 2018 1:50 pm 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
______________________________
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??TimeSeeker wrote: ↑Tue Nov 06, 2018 11:33 amIf all propositions are already in the English language, then how can any idea be 'original'?
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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Yes.TimeSeeker wrote: ↑Wed Nov 07, 2018 8:50 am Ohhhhhh! MENTIONING a thought (e.g the unidentifiable taste) is sufficient for expression?
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.TimeSeeker wrote: ↑Wed Nov 07, 2018 8:50 am 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 still have to comply with the standards of logic though, i.e. you cannot make a contradictory statement in you discourse or exposition.
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!!!TimeSeeker wrote: ↑Wed Nov 07, 2018 8:50 am 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.
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!TimeSeeker wrote: ↑Wed Nov 07, 2018 8:50 am So. Is that evidence for or against the claim that “There are some thoughts which cannot be expressed in language"?
This is an interesting claim.
How can that be a contradiction if contradictions don't exist? I thought it's a law?
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 wrote: ↑Wed Nov 07, 2018 1:35 pm Once you handle the above challenge then we can focus on this lie:
But you said "any language". Now you INSIST on doing it on this platform? Why?
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.TimeSeeker wrote: ↑Wed Nov 07, 2018 1:35 pm
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.