After struggling with a few sections of the Tractatus, as well as the explanations of said sections is Monk's How to Read Wittgenstein and Glock's A Wittgenstein's Dictionary, I've come to a certain interpretation, or at least analogy, of the Tractatus that draws from axiomatic systems.
In short, what I wish to ask with the current post is: do any passages from the Tractatus or other of (early) Wittgenstein's writings contradict this interpretation?
Pseudo- and Formal-talking
The semantic meaning of the constants of the language of Peano Arithmetic (PA) or Zermelo-Fraenkel set theory (ZF) are natural numbers and sets respectively. Thus, we can make the claims
PA speaks of natural numbers alone. (p1)
ZF speaks of sets alone. (p2)
Yet neither of these sentences is a formal sentence, a well-formed formula in the lingo, of PA or ZF. They are what I will call pseudo-statements, while statements that can be expressed within PA (or ZF, or whatever formal system is at play) are formal-statements; examples include
1 + 2 = 3 + 2 [in PA] (f1)
∀X (Ø∈X) [in ZF] (f2)
Note that formal-statements (or pseudo-statements) need not be true.
If someone expresses (p1) out loud, they are pseudo-talking, and when they express (f1) they are formal-talking. The same distinction applies to the verbs say, write, express, etc. and the nouns expression, sentence, etc.
The Goal of Tractatus
The interpretation runs as follows:
- What Wittgenstein means when he says a sentence is meaningless or nonsense, is that such sentence is not formal, yet it may be a pseudo-sentence or something else, and as such, it may convey meaning (in the ordinary use of the word).
- Tractatus pseudo-states truths about the collection of all formal-statements; think of how (p2) states a truth about all formal-statements in ZF.
- Hence, in Wittgenstein's own lingo, much of the Tractatus is itself non-sense.
These, together with Wittgenstein's almost-absolute (the Tractatus itself being an exception) refusal to engage in pseudo-talk, seem to explain the goal of Tractatus.
What such interpretation explains
In the preface, Wittgenstein writes
The book will, therefore, draw a limit to thinking, or rather — not to thinking, but to the expression of thoughts; for in order to draw a limit to thinking we should have to be able to think both sides of this limit (we should therefore have to be able to think what cannot be thought). The limit can, therefore, only be drawn in language and what lies on the other side of the limit will be simply nonsense.
This begs the question: for the limit to be drawn in language, do we not need to express what cannot be expressed? Wittgenstein's answer (in the Tractatus itself) is `yes':
My propositions serve as elucidations in the following way: anyone who understands me eventually recognizes them as nonsensical, when he has used them — as steps — to climb up beyond them. (He must, so to speak, throw away the ladder after he has climbed up it.) He must transcend these propositions, and then he will see the world aright.
Wittgenstein pseudo-expressed the limits of what can be formal-said in the Tractatus, and asks us to stop attempting to formal-talk about things which cannot be formal-expressed i.e. asks us to drop the ladder. If one was to think of ZF as the 'perfect' or 'correct' language, then explaining that we can only formal-talk about sets would require us to engage in pseudo-talk, after which the listener/reader should, in the belief that hey ought not pseudo-talk, stop talking about anything but sets.
Russell's Issue
In the introduction, Russell wrote
What causes hesitation is the fact that, after all, Mr Wittgenstein manages to say a good deal about what cannot be said.
The confusion arises when we do not differentiate between pseudo-say and formal-say. What Wittgenstein does in the Tractatus is to pseudo-say things about what cannot be formal-said (similar to how we can pseudo-say (p1), which is itself a statement about what can be formal-said in PA, and of where the limits of what can be formal-said lie).
Monk speaks of Frank Ramsey who, defending the Tractatus, wrote "What can’t be said, can't be said". I believe the meaning of such phrase is "What can't be formal-said, can't be formal-said", or, more bluntly: "The collection of all formal-sentences cannot be described in a formal-sentence itself", just as the collection of all sets is not a set in ZF, or how the collection of all numbers ℕ is not in the semantics of PA.
Ramsey further added "and it can't be whistled either", which seems to mean "and it can't be pseudo-said either", which I disagree with. Monk, after mentioning Ramsey's phrases, explains that some (James Conant, Cora Diamonds) have argued that Tractatus does not attempt show deep truths, and of how such defense runs into trouble. I here agree with Monk: Wittegenstein was trying to show deep truths in the Tractatus.
The main issue with Conant and Diamonds' argument is their belief that "a nonsensical proposition lacks any meaning, so it cannot possibly express a truth, unassailable or otherwise. Nonsense, according to them, can neither say nor show anything." As I mentioned, if Wittgenstein used words such as 'meaning' and 'sensical' to refer to formal-sentences, then non-sensical statements such as (p1) still provide meaning in the usual use of the word (not Wittgenstein's use).
Monk writes
Russell [tried] to persuade Wittgenstein that the sentence "There are at least three things in the world" was both meaningful and true. Russell later recollected that during the discussion he took a sheet of white paper and made three blobs of ink on it, urging Wittgenstein to admit that, since there were three blobs, there must be at least three things in the world, 'but he refused resolutely ... He would admit there were three blobs on the page, because that was a finite assertion, but he would not admit that anything at all could be said about the world as a whole. That the world contains at least three things is shown by there being three blobs, but "the world contains at least three things" is, for Wittgenstein, no more a meaningful proposition than "the world contains objects, properties and relations".
What Wittgenstein meant was that "There are three blobs on the page" was a formal-sentence, and thus had meaning and could, morally, be uttered, while "There are at least three things in the world" was a pseudo-sentence, thus lacking meaning and not to be uttered.
