Wittgenstein: Fool or Wise Man?

In the first proposition of his Logical-Philosophical Treatise, Wittgenstein says “the world is everything that is the case.” And ‘the case’ refers to ‘facts’. And ‘facts’ refer to ‘atomic facts’ [Sachverhalten, “actual situations”]. And ‘atomic facts’ in turn refer to ‘objects (entities, things)’. ‘Objects’, however, are ‘simple’ [einfach, “onefold”], because they “form the substance of the world”. And “If the world had no substance, then” it would “be impossible to form a picture of the world (true or false).”

This is all very well, perhaps; but then he says:

“Two objects of the same logical form are – apart from their external properties – only differentiated from one another in that they are different.”

This is the point at which he seems to have stopped thinking. Thus in his elaboration of this proposition (which is itself an elaboration), he says: “there are several things which have the totality of their properties in common”. But this cannot be ‘the case’…

It seems to me that Wittgenstein was still an Aristotelian and thereby a complete fool. Aristotle would be an idiot in our time.

I’m not even going to explain myself. I’ll just say Wittgenstein was a mathematician, not a philosopher. He believed in mathematics. But mathematics is not ‘true’. Philosophy begins where Wittgenstein halted:

“Whereof one cannot speak, thereof one must be silent.”

This statement, which I suspect the easily impressed consider the most profound statement ever made, defines Wittgenstein as unphilosophical: for philosophy is precisely the attempt to express the inexpressible.

Wittgenstein himself agreed with some of what you’ve said about his Tractatus, and you’re right that it’s the philosophical treatise of a mathemagician.

I think he has his brilliant moments, and I do find him an engaging philosopher, but some of the time his mind is so technically concerned that there’s nothing much of interest to anyone else.

Trying to express the inexpressable?

How about trying not to use such outdated metaphors? Christ knows if philosophy can answer any big questions. At the least it can be entertaining.

Wittgenstein was brilliant, but he was not particularly wise.

A better way of saying it is: expressing the unexpressed.

"Of late did I gaze into thine eye, O Life! And into the unfathomable did I there seem to sink.
But thou pulledst me out with a golden angle; derisively didst thou laugh when I called thee unfathomable.
“Such is the language of all fish,” saidst thou; “what they do not fathom is unfathomable.”
[Thus Spake Zarathustra, The Dance-Song.]

I prefer to think of my philosophising as an over-coming rather than an enter-tainment.

Hi to All,

I can not say much about Wittgenstein in general, other than Wiki reports that he was hailed as a philosophical genius, they write:

“Return to Cambridge
In 1929 he decided, at the urging of Ramsey and others, to return to Cambridge. He was met at the railway station by a crowd of England’s greatest intellectuals, discovering rather to his horror that he was one of the most famed philosophers in the world. In a letter to his wife, Lydia Lopokova, John Maynard Keynes wrote: ‘Well, God has arrived. I met him on the 5.15 train.’”

However, I can say that despite the fact that he was also considered a mathematical genius, he made at least one major flawed assertion about mathematics.

He claimed that all mathematics was a tautology, which meant, by his unique and misleading definition of the word, that the axioms of a mathematical system determine all the true or false statements in that system.

Godel’s Incompleteness Theorem, which has two apparently independent proofs, shows that this is not the case.

mathematics is a tautology… it is a series of definitions that play off of each other, nothing more…

mathematics is purely analytical and a priori…

two apparent independent (non)mathematical proofs that prove mathematics as independent of mathematics? please demonstrate these proofs…

-Imp

Hi Imp,

I had posted a more complete explanation on the attached link.

viewtopic.php?f=1&t=160077

If you disagree with anything here, or don’t understand it, or simply think that it does not apply, please let me know.

By the way, how do you think that Kant would classify the following mathematical statement?

5 + 7 = 12.

You might be surprised. I was.

The Incompleteness Theorem says that there exists true statements in mathematical systems, as rich as arithmetic, that can not be proved by that mathematical system. This is the critical statement here.

The consistency theorem says that mathematics, as rich as arithmetic, can not prove, using the axioms of the system, the consistency of that particular system.

I think that this second theorem is your point, but I don’t see how it applies.

You don’t actually want me to reproduce the proofs do you? The Godel proof, which is not actually a real proof, just a sketch of one, is 72 pages in the English translation, but Peter Smith’s proof, which I prefer, is over a 100 pages long.

Thanks for responding.

Ed

P.S. from personal experience in constructing novel theorems in mathematics, I think that Wittgenstein’s comments fail in a far simpler way, than having to resort to the Godel Theorems. Additionally I strongly agree with Aporia’s assertion that some mathematical statements are synthetic.

I like Witty’s works. I’ve read his last book all the way through and skimmed through some of his others in book stores. I don’t pay much attention to his mathematics, but he’s logically minded. His style of writing is repetitive, convincing. Moreso, he thinks in terms of language and used math as an example for how versatile communication is. He was about colors, sounds, and visualization.

I hear he liked it in the butt.
Here nor there…

Saully, Wittgenstein was definitely hinting on the things in and of themselves, but that despite similarities, there is an identity unseen that defines them as their own bodies. Saying Aristotle was an idiot is a harsh judgement, I’d say, and for math vs philosophy: philosophy can be spoken by word or number…it’s just the barrier of learning to comprehend it.

agreement is not proof. there is no empirical evidence of mathematical statements… there are statements, terms, names, labels, linguistic devices of whatever name and then there are things in themselves and never the two shall meet…

-Imp

Yes, he seems to think that an “essence” remains when you strip things from all their properties, all their relations. Do you?

Hi Imp,

I’m out of town until the weekend.

Just a simple response for now.

I agree about Kant’s classification, but it should be noted that a small percent of mathematicians take Kant’s definition of numbers to heart. They are called Intuitionists, and are lead by a guy named L. E. J. Brouwer.

When I have more time, I would like to explore some of your comments in more detail

Thanks Ed

It’s possible. The ‘substance’ he refers to is a true oneness within the web of evolution, I think; how everything is connected, but if it is always changing, it cannot be defined.

Imp always has good things to say on identity, perception, and the like.
I’ve also seen people argue that full consciousness is not a phenomena of the brain but is present in plants and microscopic organisms. This can always twist the outlook of ‘in itself’.

Hi Imp,

The truth of the Godel statement is derived. i.e. it is predicated from the base assumptions. It is not a posteriori.

What I am curious about, in general, is philosophical classification systems and, in this particular case, a priori and a posteriori.

I have become very skeptical of these systems, and would like to get your input.

The little I know is that Quine attacked this system (though I am not familiar with the detail), and that from an anthropomorphic point of view it seems to me that mathematics should vary from person to person and not from group to group (as evidence appears to show), if it were exclusively a priori.

The concept that I thought I would be challenged on is this:

Without recourse to the Godel’s Incompleteness theorem, can I show that some mathematical systems are a priori synthetic?

Anyway, I am curious about your input.

Thanks Ed

it varies from person to person and from group to group in exactly the same method and degree as any other language system…

a priori- before experience, based upon definition
a posterori after experience, based upon experience itself

where does your skepticism lie? in the circle of definitions before or the complication of memory and future prediction after the fact of experience?

-Imp

Hi Imp,

I was struck a few months ago by a report that Australian aborigines do not know of the concept of 2. This seems so fundamental to me that I questioned my assumptions about the nature of mathematics.

My assumption was that mathematics was an intellectual construct (where the definitions come from) based on a human’s innate ability to abstract certain concepts. It never occurred to me that any normal human being might not be able to abstract the concept of 2.

If forced to classify mathematics, it’s against my nature to classify things in the first place - it’s kind of like submitting to authority - I would have said that mathematics was strictly a priori.

But now I think that there must be an environmental component in our ability to make these constructs.

If there is an environmental component then mathematics, at least in part, is dependent on environment and I would think that our a priori classifications are at least partially dependent on a posteriori events.

On the other side of the curtin.

Both from what I think of as common sense, and from reading “What is this thing called science” by Chalmers our a posteriori experiences can be literally determined by our world view/beliefs (complications of memory?).

In short it appears to me that, in part, a priori depends on a posteriori AND a posteriori depends on a priori.

If I understand your questions properly, I think both the definitions and the complications are problems.

Thanks Ed

P.S. I am curious if there is any anecdotal evidence that logic is dependent on environment.

logic depends on environment as not all systems of logic are the same…

mathematics is a language

language is a priori

do a posteriori “things” appear that we categorize into our pre-established definitions? yes… but the definitions came first…

-Imp

But real logic, i.e. foundation logic, which comprises all existing things is prior to language, I assert that a full understanding of boolean logic is apriori and built into reality itself, because physical structure is true logic itself (i.e. energy), i.e. you have to be able to know this is not that, that something is there, yes or no. Before you can construct logical statements (spoken or written language, or even moving your hand right or left (yes or no again)), 1 or 0. Logic has to be apriori because of how senses function empiraclly, you can’t even have a thought, or even a single perception. Personally I think your problem is trust in what you think you know. Maybe it’s time to take Ibn Al-Haytham’s advice?

“Therefore, the seeker after the truth is not one who studies the writings of the ancients and, following his natural disposition, puts his trust in them, but rather the one who suspects his faith in them and questions what he gathers from them, the one who submits to argument and demonstration, and not to the sayings of a human being whose nature is fraught with all kinds of imperfection and deficiency. Thus the duty of the man who investigates the writings of scientists, if learning the truth is his goal, is to make himself an enemy of all that he reads, and, applying his mind to the core and margins of its content, attack it from every side. He should also suspect himself as he performs his critical examination of it, so that he may avoid falling into either prejudice or leniency.”

That’s because you’re not gaspin the logic here, he’s talking about the geometry of stuff in the world, all of the stuff in the world is made of universal form of logic - energy, everything that exists is merely a different aspect of the same energy in a different form, there are no “different energies” per se, at bottom there is one universal substance, and all the other distinctions in that substance are merely different subdivided parts of that same universal surface energy.

You’d need to get a background in physics and need a very visual mode of thinking to grasp what he is saying.