OK! Fair enough, I understand what David Pears is about on the very first pages of his book. I really appreciate your commitment to explaining both tautologies and David Pears' commentary. I probably will have some questions while continuing the reading. So, if you don't mind, I would like to share them with you.

Until then. Nice to meet you and welcome to TPF! :up: — javi2541997

I'm glad that I could help, even a little! But, for sure; let's think through it together. ☺️

It is easy to get lost if we don't keep in mind what is at issue:

3.323
In everyday language it very frequently happens that the same word has different modes of signification—and so belongs to different symbols—or that two words that have different
modes of signification are employed in propositions in what is superficially the same way.
...
(In the proposition, ‘Green is green’—where the first word is the proper name of a person
and the last an adjective—these words do not merely have different meanings: they are different symbols.)

3.324
In this way the most fundamental confusions are easily produced (the whole of philosophy is full of them).

3.325
In order to avoid such errors we must make use of a sign-language that excludes them by
not using the same sign for different symbols and by not using in a superficially similar way
signs that have different modes of signification:
that is to say, a sign-language that is governed by logical grammar—by logical syntax.

Put differently, what is important for Wittgenstein in the Tractatus is not what we say, but how we say it.

This sheds light on the following:

4.4611
Tautologies and contradictions are not, however, nonsensical. They are part of the symbolism, much as ‘0’ is part of the symbolism of arithmetic.

4.462
Tautologies and contradictions are not pictures of reality. They do not represent any possible situations. For the former admit all possible situations, and latter none.

In a tautology the conditions of agreement with the world—the representational relations—cancel one another, so that it does not stand in any representational relation to reality.

Tautologies lack sense. They do not represent any one possible situation because they admit all possible situations.

This may leave us wondering why as part of the the symbolism they are not nonsense. Circling back:

3.3421

A particular mode of signifying may be unimportant but it is always important that it is a possible mode of signifying. And that is generally so in philosophy: again and again the individual case turns out to be unimportant, but the possibility of each individual case discloses something about the essence of the world.

And what is this essence? The logical structure that underlies both the world and language. The logical grammar or syntax he advocates is not then simply a matter of saying things in a way so as to avoid error, it is the logic of the world that makes possible saying anything about the world at all.

@013zen @Fooloso4

Hello again, folks. Keeping on the book by David Pears. Chapter three is called 'pictures and logic', and I would like to share some thinking and points with you. Pears states: 'One more step is needed to complete Wittgenstein's task. If the limit of language is to include all factual proposition, the thesis of extensionality must be applied to elementary propositions. For if he applied it to non-elementary propositions, he would leave out some of the possible thruth-functions, because the base to which it was applied would be incompletely analysed. However, it is not this neutrality which proves that he was not a positivist of destruction type.

Thoughts?

Pears also states: Language would be then any language, the metaphysical subject would be the spirit, and Idealism would lie on the route from Solipsism to Realism. Z came from Russell, and X came from Frege. What was the origin of Y, the so-called picture theory of prepositions? Wittgenstein's explanation of logical neccesity, which depends on Y, still to be given.

What does Y is about? To present truths in logical space? Or does David Pears refers to X and Y logical structure?

Without having Pears' book in front of me, there is too little here for me to comment.

@013zen

Finishing today's chapter, David Pears concludes with something pretty interesting. He states: It may seem surprising that logic should reveal the essential structure of reality if the prepositions of logic are tautologies, and lack factual sense. How can something which is empty have content? But Wittgenstein does not suggest that tautologies say anything about reality. He suggests that when certain factual propositions are combined, a tautology is produced.

It reminds me of when you explained to me that tautolgies have their place, and they are not rejected at all. At least Wittgenstein shows respect for this analytical position, but let's see what he thought when he changed his idea after the Tractatus.

OK. I understand, yet I want to thank you for helping me with your explanation of Wittgenstein. O13zen and you were the only ones who actually answered my questions, and I am pleased.

Glad to help. If you have questions about Wittgenstein rather than Pears I will try to help.

What was the origin of Y, the so-called picture theory of prepositions? Wittgenstein's explanation of logical neccesity, which depends on Y, still to be given.

What does Y is about? To present truths in logical space? Or does David Pears refers to X and Y logical structure? — javi2541997

You've touched on a lot and I can't answer it all concisely especially not in regards to Pears, but I can talk a little about this point and see if it helps.

In the Tractatus, Wittgenstein gives a picture theory of language. But, picture theories were not original to Wittgenstein. During the late 1800 early 1900 there was serious debate in science and philosophy regarding what exactly we are up to when we develop a theory, and more importantly to what extent science can give us knowledge about the world.

Do our theories tell us anything about the world, or are they simply useful tools we invent that prove useful (pragmatic).

See, Hume stated we can only have understanding of the world by couching that knowledge on our experiences. I literally can't understand something that is totally unlike anything I've experienced before. The more something resembles past experience, the more I can understand it by developing a theory which explains it.

Consider this:

You have a bag with a random assortment of colored balls.

If I asked what color ball do you think you'll pick out next?

You wouldn't know.

You reach in and take a ball out one at a time, noting the color:

Red, red, red, blue, red, red, blue

Now, if I asked, what would you say?

Perhaps red? Maybe you say about 70% chance red 30% blue?

Hume said we can only describe reality, though and our theories merely call many facts under a single header (like Newton did with gravity). From Hume, Comte developed positivism, which basically said we scientific theories can only describe positive facts about the world, that is those based on experience alone. Any theories using "hidden forces" are to be discard.

This ultimately lead to Ostwald and Mach to deny the existence of Atoms because there was no experience proving their existence. Fictions like Atoms that make up reality might be useful on paper but they don't belong in science.

This lead thinkers like Boltzmann and Hertz to develop a different concept a theory. The picture theory which essentially states that theories are pictures we invent that are based on both experience and logic which are ultimately accepted or rejected based on how successful they are.

Logic determines their validity just as much as experience.

Ultimately these pictures are only one of many ways we can represent reality, as opposed to being constrained by experience.

This flexibility allowed Boltzmann to further develop and utilize the theory of Atoms for explaining the expansion of gasses. But, many scientists rejected the idea because they were positivists.

Wittgenstein develops his own picture theory, but starts from a positivist beginning which he got from Russell and Russell got from Mach. But then he shows how you can introduce logic and arrive at theories like Boltzmann and Hertz.

But, because of the beginning many early thinkers took Wittgenstein to be a positivist. Really he was a picture theory sympathizer. He believed like Boltzmann and Mach that our pictures can always change as more elements are added. And logic coupled with reality leads the way.



"I don't believe I have ever invented a line of thinking, I have always taken one over from someone else. I have simply straightaway seized on it with enthusiasm for my work of clarification. That is how Boltzmann, Hertz, Schopenhauer, Frege, Russell, Kraus, Loos, Weininger, Spengler, Sraffa have influenced me."

-Wittgenstein


Sorry if this was unhelpful or not clear.

but I can talk a little about this point and see if it helps. — 013zen

It was very helpful and pleasant to read. You explain yourself correctly.

I now understand why some states that Wittgenstein was a sympathiser of positivism. You quoted some other authors who appeared in David Pears' book as well. Before joining this thread, I was completely lost. I think that one of the main 'issues' about Wittgenstein and his disciples is how they express themselves. They use a complex vocabulary which seems to only be sent to their 'Vienna' group. They make premises and arguments which are interesting, but nonetheless are difficult to follow if someone - like me - is not used to logical language.

On the other hand, I don't consider Wittgenstein 'senseless' (I read this adjective about him a lot) but complex to follow.

This is where I miss Austin a bit... and his 'ordinary language'

Thanks to you and your example, I can understand what is about his 'pictures and logic'

They use a complex vocabulary which seems to only be sent to their 'Vienna' group. They make premises and arguments which are interesting, but nonetheless are difficult to follow if someone - like me - is not used to logical language.

On the other hand, I don't consider Wittgenstein 'senseless' (I read this adjective about him a lot) but complex to follow. — javi2541997

It's difficult because there is a difference between "nonsense" and "senseless" in Wittgenstein.

Consider:

"Purple vocabulary is very car"

Vs

"A triangle is either a right triangle or not"

The first has no context in which it's meaningful. It's totally meaningless. The second is always true (tautology) and it's simply unclear when you'd utter it.

Wittgenstein calls his own work senseless because he is borrowing Frege's concept of "elucidations".

Frege determined that propositions can feature words which are in the wrong "logical position" but nonetheless aren't totally meaningless.

Consider:

The dog is black

And

The concept horse is a concept that's easily understood

The first example Frege says is an object "dog" connected with a concept "black". Object and concept therefore play different logical roles. An object cannot be used as a concept and a concept cannot be used as an object.

But, in the second example is seems we're using a concept as an object... "The concept horse". Frege says, in fact, "the concept horse" cannot logically be a concept, and must be being used in a different way logically than say:

"Tom understands the concept horse"

Language obfuscates the logical structure. Making it seem like a concept is being used as an object.

Frege thought you could only show this not say it. Just like I've tried to show using different examples. These kinds of examples are elucidations which show how a word is being used even if the proposition itself is incapable of exact analysis.

Frege thought elucidations were a way we could come to understand one another, but ultimately are to be discarded as incorrect.

Like how we explain electricity via water analogy.

Consider:

Watts = Amps x Volts

What's an Amp? What about a volt? A watt??

Well it's like water in a tube:

Amps is like the the rate at which the water flows through the tube

Volts is like the pressure of the water in the tube

Watts is like how much water is passed through the pipe over an hour.

Now, electricity isn't water. What I just said is properly speaking incorrect and not true, but it helps you understand the words "amp" "watt" "volt", and once you understand them you can discard with the elucidations I provided. They only serve the role of acquainting you with the words being used. Ultimately elucidations are to be discarded.

Hence the final lines of the tractatus.

Thank you so much for your instructive response.

Look! Continuing with the reading of Pears, another type of tautology emerges, referred to as 'deep.' David Pears states,'What is reflected in the mirror of language is reflected in the mirror of language,' or more simply, 'there is what there is.' These are deep tautologies because there is something underlying them, attempting to emerge and find a different expression.

It is fascinating; language may be defined or investigated empirically, and according to Pears, the former is a necessary truth, and the latter is a contingent truth.

Before ending this chapter, I would like to quote a beautiful phrase of Wittgenstein:

To be happy is to see the world of facts as a whole with expanding limits, whereas an unhappy man feel that the same limits, enclosing the same facts, were pressing on him.

Enough of tautologies! :grin:

another type of tautology emerges, referred to as 'deep.' — javi2541997

In his notebooks, Wittgenstein referred to a song as "... A kind of tautology, it is complete in itself; it satisfies itself".

This shows that Wittgenstein had a very particular understanding of tautologies. That there could be different kinds. In language and logic, tautologies may have no content, they don't "say" anything, rather they "show" it. They show how symbols an words are to be used (their internal structure), and they show they are complete without relying on any facts to determine them.

But, a beautiful song is itself complete in a way. When you listen to it, it shows itself to be beautiful without any recourse to the facts. I think this is why Wittgenstein compared logical propositions to those of ethical ones. The former is formed of tautologies as we typically refer to them, but Wittgenstein seemed to hold the latter was it's own kind of tautology. That something is important to us shows itself in how we view it, talk about it, regard it without recourse to any facts in the same way a tautology in language and logic does. This is why the happy man can see the same world in a different light than the unhappy man. Just how I can be moved to tears by a song, and regard it as perfectly constructed needing no improvement, while another finds it less than ideal. Ethics and aesthetics are one. And while senseless these are the deepest problems we know.