# Four Propositions to End Logical Thinking



## Dodecaplex (Oct 14, 2011)

*I.* All logical propositions are tautologies. In other words, _logical thinking_ does not tell us _what is the case_; in reality, _what is the case_ tells us how to _think logically_ (i.e. saying "the cat is on the mat" does not mean that a cat is sitting on a mat, but, rather, a cat sitting on a mat means we can say that "the cat is on the mat"). Thus, logical thinking by itself is entirely useless. It is neither right nor wrong.

*II.* From the above, it follows that one cannot actually say whether logical thinking is right or wrong. Indeed, if logical thinking was wrong, then by what standards is it wrong? Surely, not by the standards of logical thinking itself. Yet, at the same time, as demonstrated by Propostition *I*, logical thinking also can't be right.

*III.* From the paradox of Proposition *II*, it follows that logical thinking has no foundation. It cannot be argued for or against. For instance, we cannot prove that A --> B and B --> C means that A -->C. We can only 'see' it by virtue of simply 'seeing' it.

*IV.* Thus, logic is inexpressible. It is transcendental.

Q.E.D.


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## Philip (Mar 22, 2011)

Sorry, this has already been thought through... by Poincaré, a century ago, by Leibniz, centuries before that, and so on...

--------------------------------
Henri Poincaré

La Science et l'hypothèse

_Sur la nature du raisonnement mathématique

--- I ---

La possibilité même de la science mathématique semble une contradiction insoluble. Si cette science n'est déductive qu'en apparence, d'où lui vient cette parfaite rigueur que personne ne songe à mettre en doute ? Si, au contraire, toutes les propositions qu'elle énonce peuvent se tirer les unes des autres par les règles de la logique formelle, comment la mathématique ne se réduit-elle pas à une immense tautologie ? Le syllogisme ne peut rien nous apprendre d'essentiellement nouveau et, si tout devait sortir du principe d'identité, tout devrait aussi pouvoir s'y ramener. Admettra-t-on donc que les énoncés de tous ces théorèmes qui remplissent tant de volumes ne soient que des manières détournées de dire que "A" est "A" ?

Sans doute, on peut remonter aux axiomes qui sont à la source de tous les raisonnements. Si on juge qu'on ne peut les réduire au principe de contradiction, si on ne veut pas non plus y voir des faits expérimentaux qui ne pourraient participer à la nécessité mathématique, on a encore la ressource de les classer parmi les jugements synthétiques à _priori_. Ce n'est pas résoudre la difficulté, c'est seulement la baptiser ; et lors même que la nature des jugements synthétiques n'aurait plus pour nous de mystère, la contradiction ne se serait pas évanouie, elle n'aurait fait que reculer ; le raisonnement syllogistique reste incapable de rien ajouter aux données qu'on lui fournit ; ces données se réduisent à quelques axiomes et on ne devrait pas retrouver autre chose dans les conclusions.

Aucun théorème ne devrait être nouveau si dans sa démonstration n'intervenait un axiome nouveau ; le raisonnement ne pourrait nous rendre que les vérités immédiatement évidentes empruntées à l'intuition directe ; il ne serait plus qu'un intermédiaire parasite et dès lors n'aurait-on pas lieu de se demander si tout l'appareil syllogistique ne sert pas uniquement à dissimuler notre emprunt ? La contradiction nous frappera davantage si nous ouvrons un livre quelconque de mathématiques ; à chaque page l'auteur annoncera l'intention de généraliser une proposition déjà connue. Est-ce donc que la méthode mathématique procède du particulier au général et comment alors peut-on l'appeler déductive ?

Si enfin la science du nombre était purement analytique, ou pouvait sortir analytiquement d'un petit nombre de jugements synthétiques, il semble qu'un esprit assez puissant pourrait d'un seul coup d'oeil en apercevoir toutes les vérités ; que dis-je ! on pourrait même espérer qu'un jour on inventera pour les exprimer un langage assez simple pour qu'elles apparaissent ainsi immédiatement à une intelligence ordinaire.

Si l'on se refuse à admettre ces conséquences, il faut bien concéder que le raisonnement mathématique a par lui-même une sorte de vertu créatrice et par conséquent qu'il se distingue du syllogisme.

La différence doit même être profonde. Nous ne trouverons pas par exemple la clef du mystère dans l'usage fréquent de cette règle d'après laquelle une même opération uniforme appliquée à deux nombres égaux donnera des résultats identiques.

Tous ces modes de raisonnement, qu'ils soient ou non réductibles au syllogisme proprement dit, conservent le caractère analytique et sont par cela même impuissants._

[...]
--------------------------------

But you are welcome to revisit the question!


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## Dodecaplex (Oct 14, 2011)

I'm not revisiting the question actually. I'm simply restating Wittgenstein's argument in the Tractatus, which was published after Poincare's death, so I believe whatever Poincare is trying to say there (which I haven't read) has been demolished by Wittgy already.


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## Philip (Mar 22, 2011)

I'll take the rigour of a mathematician over that of a philosopher any day of the week.


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## Polednice (Sep 13, 2009)

Philip said:


> I'll take the rigour of a mathematician over that of a philosopher any day of the week.


Indeed, old Wittgy's proposition seems a bit bogus to me. I thought this thread was a joke, actually. I think Dodeca may be a little bit blinded by Wittgy love.


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## Dodecaplex (Oct 14, 2011)

Philip said:


> I'll take the rigour of a mathematician over that of a philosopher any day of the week.


What you take is of no importance. Poincare is a has-been anyway, and he didn't have a quarter of Wittgy's genius.


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## Dodecaplex (Oct 14, 2011)

Polednice said:


> Indeed, old Wittgy's proposition seems a bit bogus to me. I thought this thread was a joke, actually. I think Dodeca may be a little bit blinded by Wittgy love.


You're welcome to argue against Wittgy's propositions any time you want. Until then, everything you say is meaningless.

That last sentence is true though.


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## Philip (Mar 22, 2011)

Dodecaplex said:


> What you take is of no importance. Poincare is a has-been anyway, and he didn't have a quarter of Wittgy's genius.


Hahahaha... say what? i guess i'll have to do some reading before i completely destroy your first post in most concise and educated way, but for now all i can say is that the first sentence of the first proposition makes absolutely no sense:

Please explain to me how the logical proposition called a "contradiction" can be a tautology as well?


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## Dodecaplex (Oct 14, 2011)

Philip said:


> Hahahaha... say what? i guess i'll have to do some reading before i completely destroy your first post in most concise and educated way, but for now all i can say is that the first sentence of the first proposition makes absolutely no sense:
> 
> Please explain to me how the logical proposition called a "contradiction" can be a tautology as well?


Obvious:


Wittgy said:


> *Tractatus 4.2* The sense of a proposition is its agreement and disagreement with the possibilities of the existence and non-existence of the atomic facts.


So, if it's neither in agreement or disagreement with the possibilities of the existence or non-existence of atomic facts, then it's a nonsensical proposition. Thus:



Uncle Ludwig said:


> *Tractatus 4.463* Tautology leaves to reality the whole infinite logical space; contradiction fills the whole logical space and leaves no point to reality. Neither of them, therefore, can in any way determine reality.


As such, the entirety of logic amounts to nothing but tautological statements that have no bearing on reality.


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## Polednice (Sep 13, 2009)

Humour me by making all the jargon mean something by putting this in the context of how it might have a real-world effect.


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## Kopachris (May 31, 2010)

Language has its limits. As with the scientific method, it is merely the best tool we have for its task. Logic is a means by which we hone that tool. Even tautology has its purpose.


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## Dodecaplex (Oct 14, 2011)

Polednice said:


> Humour me by making all the jargon mean something by putting this in the context of how it might have a real-world effect.


It doesn't. Its only purpose is to stop you from speaking jargon in the first place, and thereby return you to the real world.

It might be useful here if I point out that the Tractatus was a response to the works of the philosophers and logicians who came before Wittgy. So, essentially, it was jargon that attempted to put an end to jargon. Hence why Wittgy says near the end:


> *Tractatus 6.54* My propositions are elucidatory in this way: he who understands me finally recognizes them as senseless, when he has climbed out through them, on them, over them. (He must so to speak throw away the ladder, after he has climbed up on it.)
> He must surmount these propositions; then he sees the world rightly.


Does that make it clearer or is it just more confusing now?


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## ComposerOfAvantGarde (Dec 2, 2011)

Philip said:


> Sorry, this has already been thought through... by Poincaré, a century ago, by Leibniz, centuries before that, and so on...
> 
> --------------------------------
> Henri Poincaré
> ...


Je ne comprends pas.


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## Crudblud (Dec 29, 2011)

Vous êtes stupide! Hahaha! En toute sincérité, je ne comprends pas non plus.

What little I remember of the French probably showing itself very plainly, ladies and gentlemen.


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## ComposerOfAvantGarde (Dec 2, 2011)

Crudblud said:


> Vous êtes stupide! Hahaha!


Je ne suis pas stupide.



> En toute sincérité, je ne comprends pas non plus.


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## brianwalker (Dec 9, 2011)

http://plato.stanford.edu/entries/logic-free/

http://plato.stanford.edu/entries/kant-transcendental/

http://plato.stanford.edu/entries/heidegger/

More specifically.

http://plato.stanford.edu/entries/analytic-synthetic/#ProDis

But the analytic/synthetic distinction is a false one.

Q.E.D.


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## science (Oct 14, 2010)

Ten, maybe twelve years ago, this would have mattered to me so much. I was really putting the work in, trying to understand Kant, Heidegger, Wittgenstein. Going to be one of the great minds, figure it all out for everyone and receive grateful applause from humankind. 

Now I say, just sit back and wait a generation or so, and the psychologists will figure it out for us.


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## Dodecaplex (Oct 14, 2011)

science said:


> Ten, maybe twelve years ago, this would have mattered to me so much. I was really putting the work in, trying to understand Kant, Heidegger, Wittgenstein. Going to be one of the great minds, figure it all out for everyone and receive grateful applause from humankind.
> 
> Now I say, just sit back and wait a generation or so, and the psychologists will figure it out for us.


Funny thing is: all you're saying here is that you agree with Wittgy's false sentiment that these philosophical discussions achieve nothing whatsoever, and that one should simply leave these questions to the scientists. It would be interesting to know what route you took to reach this conclusion.


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## Dodecaplex (Oct 14, 2011)

brianwalker said:


> But the analytic/synthetic distinction is a false one.


Indeed, it is. Thank you for finally pointing that out. (Not being sarcastic. 'Onest)


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## brianwalker (Dec 9, 2011)

science said:


> Ten, maybe twelve years ago, this would have mattered to me so much. I was really putting the work in, trying to understand Kant, Heidegger, Wittgenstein. Going to be one of the great minds, figure it all out for everyone and receive grateful applause from humankind.
> 
> Now I say, just sit back and wait a generation or so, and the psychologists will figure it out for us.


You really think the psychologists will figure it out?

Because science already has had the capability to study the particles at the sub-atomic level for many years now, and if the totality of human experience is reducible to the human brain and the interaction of things at the atomic or supra-atomic level, then why haven't they figured everything out by now?

http://www.bryanappleyard.com/wagner-madness/

http://blogs.wsj.com/ideas-market/2011/11/11/neuroscience-cant-explain-wagner-or-b-b-king/

The neuroscience of music is APPALLINGLY bad.

If the scientists ever claim to figure out "music" and the "human mind" then the proof will have to be in the pudding.

They will have to compose an opera greater than Parsifal, and write a novel greater than The Wings of Dove, and make a film more stimulating than Andrei Rublev.

http://en.wikipedia.org/wiki/Hubert_Dreyfus's_views_on_artificial_intelligence

This guy chastised the AI community in the 60s and 70s. They dismissed him. 30 years later, most of his predictions were right.


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## Fsharpmajor (Dec 14, 2008)

brianwalker said:


> If the scientists ever claim to figure out "music" and the "human mind" then the proof will have to be in the pudding.
> 
> They will have to compose an opera greater than Parsifal.


Well, what if they don't happen to think, based on the results of their research, that Parsifal is any good? Would they then produce a better opera than Parsifal, or a worse one?


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## brianwalker (Dec 9, 2011)

Fsharpmajor said:


> Well, what if they don't happen to think, based on the results of their research, that Parsifal is any good? Would they then produce a better opera than Parsifal, or a worse one?


Parisfal's greatness is an axiom. Parsifal is one of the most sublime and noble work in all of art. If there was any conclusive study that "proved" that Parsifal wasn't any good, that study would be wrong.

If their "metric" for evaluating musical greatness, does not measure Parsifal any good, their metric is wrong.

Why do you presume that anything that hasn't yet been validated by science is wrong? Or that science is the measure of all things?

http://plato.stanford.edu/entries/kant-aesthetics/

http://plato.stanford.edu/entries/heidegger-aesthetics/



> In the late 1930s, Heidegger understood such technological optimization as an all-encompassing attempt to derive the maximal output from the minimal input, a quantification of quality that threatens to dissolve quality in the same way that the objectification of the subject threatens to dissolve subjectivity. Heidegger seems first to have recognized this objectification of the subject in the Nazis' coldly calculating eugenics programs for "breeding" a master race, but (as he predicted) that underlying impulse to objectively master the human subject continues unabated in more scientifically plausible and less overtly horrifying forms of contemporary genetic engineering.[25] Most importantly for us here, Heidegger also recognized this ongoing objectification of the subject in the seemingly innocuous way that aesthetics "somersaults beyond itself" into neuroscientific attempts to understand and control the material substrate of the mind. For, once aesthetics reduces art to intense subjective experience, such experiences can be studied objectively through the use of EEGs, fMRIs, MEG and PET scans (and the like), and in fact aesthetic experiences are increasingly being studied in this way. At the University of New Mexico's MIND Institute, to mention just one telling example, subjects were given "beautiful" images to look at and the resulting neuronal activity in their brains was studied empirically using one of the world's most powerful functional Magnetic Resonance Imaging machines. In this way, as Heidegger predicted in 1937:
> 
> Aesthetics becomes a psychology that proceeds in the manner of the natural sciences; that is, states of feeling become self-evident facts to be subjected to experiments, observation, and measurement. (N1 89/GA43 106)
> "Here," Heidegger writes, "the final consequences of the aesthetic inquiry into art are thought through to the end" (N1 91/GA43 108). Aesthetics reaches its logical conclusion-the "fulfillment or consummation" (Vollendung) which completes it and so brings it to its end-when it thus "somersaults beyond itself" into enframing.
> ...


The notion that science could "prove" that Parsifal isn't any good is a philosophical confusion.

The only thing that could be put into question is my taste in music. The argument that Parsifal isn't any good could only be an extension of the argument that the things I hold in the highest regard isn't very good, that I have bad taste, but that is a different discussion altogether.

It is not the duty of the Classics, be it literature, music, painting, etc, to conform to the stilted instruments of science, but the reverse.

So far science has failed to measure up.

If you were to make another claim, the claim that Parsifal's magnificence (in the Kantian sense) is "an illusion", then that's a philosophical confusion of the term "illusion".


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## Philip (Mar 22, 2011)

brianwalker said:


> Parisfal's greatness is an axiom. Parsifal is one of the most sublime and noble work in all of art. If there was any conclusive study that "proved" that Parsifal wasn't any good, that study would be wrong.
> 
> If their "metric" for evaluating musical greatness, does not measure Parsifal any good, their metric is wrong.
> 
> ...


science doesn't "prove", it falsifies, says Popper. anything unfalsifiable is thus metaphysical.

science has no pretension.


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## Fsharpmajor (Dec 14, 2008)

brianwalker said:


> Parisfal's greatness is an axiom. Parsifal is one of the most sublime and noble work in all of art. If there was any conclusive study that "proved" that Parsifal wasn't any good, that study would be wrong.



I would have thought that it goes without saying that one's opinion of a work of art is only that--an opinion. But I could be wrong.


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## brianwalker (Dec 9, 2011)

Philip said:


> science doesn't "prove", it falsifies, says Popper. anything unfalsifiable is thus metaphysical.
> 
> science has no pretension.


There are too many claims in the social sciences, not to mention evolution, which are totally unfalsifiable. The neuroscientific claims made about music are utterly unfalsifiable. By the standards of falsifiabilty the present neuroscientific commentary on music would not qualify as science.


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## brianwalker (Dec 9, 2011)

Fsharpmajor said:


> I would have thought that it goes without saying that one's opinion of a work of art is only that--an opinion. But I could be wrong.


Opinion in contradistinction to what? Fact?

What would be a "fact" about the relative merits of a work of art? A fact that is beyond all opinion?

Is the claim "Bach is a great composer" an opinion, on the same level as "this cheesecake is OK"?

If all judgments w/r/t to music are mere "opinions", then how is any scientific investigation of music possible, since in the end our appraisal of music is dependent on our own subjective responses to it, and thus, "opinion"?


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## Philip (Mar 22, 2011)

brianwalker said:


> There are too many claims in the social sciences, not to mention evolution, which are totally unfalsifiable. The neuroscientific claims made about music are utterly unfalsifiable. By the standards of falsifiabilty the present neuroscientific commentary on music would not qualify as science.


oh but there's corroboration...


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## Fsharpmajor (Dec 14, 2008)

brianwalker said:


> If you were to make another claim, the claim that Parsifal's magnificence (in the Kantian sense) is "an illusion", then that's a philosophical confusion of the term "illusion".


That's not exactly the kind of claim that I tend to make.

(Trying to add a friendly wink here--honestly I am--but I can't get the smileys to work on my browser ever since the site's software was upgraded a couple of weeks ago).


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## science (Oct 14, 2010)

I am with the skeptics on the objective qualities of art; the most I'd be able to concede there is that perhaps in principle some art would appeal to all psychologically normal people, but that would surprise me. 

As to the philosophy/neuroscience question, we'll see. I don't expect a detailed explanation of why a particular individual likes a particular work of art, and that seems off topic to me. But an account of the nature of human reasoning is, I think, going to come about. The idea that we should understand everything made of particles be quad we understand the particles does not seem compelling. For instance, understanding traffic flow is not a matter of understanding how vehicles and roads are made.


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## brianwalker (Dec 9, 2011)

Philip said:


> oh but there's corroboration...


"Corroboration" can't be falsified since there are always multiple logically coherent just-so stories for corroborative evidence; corroboration is just "proof" through a side door.


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## Philip (Mar 22, 2011)

hence the term corroboration


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## LordBlackudder (Nov 13, 2010)

but logic accounts for human failure and emotions. the best outcome or what you want whether good or bad.

why should there only be one logical conclusion.

i don't know why you say logic must have a god-like certainty. that would hold back evolution.


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## Acervehes (Jun 5, 2012)

*Tres instructif*

pourquoi pas


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## Roberto (Jul 17, 2010)

Dodecaplex said:


> *I.* All logical propositions are tautologies.


a) you did not even attempt to prove this first point - you merely assert it
b) you employ a kind of rough logic to reach your conclusion - your propositions are therefore (as you imply) meaningless indeed.


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