Comments on Tractatus: 3 The logical picture of the facts is the thought

3 The logical picture of the facts is the thought.

Introduction of the 'think' concept. So now what does 'think', thought' etc mean. Is it the mini-activity of the mind/brain?

3.001 “An atomic fact is thinkable”—means: we can imagine it.

presumably a picture is imaginable too. Who knows...picture, fact, thought,

3.01 The totality of true thoughts is a picture of the world.

Are there other pictures? other pictures of the world?

3.02 The thought contains the possibility of the state of affairs which it thinks.What is thinkable is also possible.

First sentence: empty philosophical blather.Second, untrue.

3.03 We cannot think anything unlogical, for otherwise we should have to think unlogically.

This is patently untrue. Whether by deliberate Lewis Carrollisms, or the veryday drudgery of making mistakes or working with limited knowledge (bounded rationality), or the mixed up conflatino of ideas that is so easy to do, there's all sort s of illogical things we think. viz Whitman (Leaves of Grass 14)

Do I contradict myself?
Very well, then, I contradict myself;
(I am large—I contain multitudes.)

3.031 It used to be said that God could create everything, except what was contrary to the laws of logic. The truth is, we could not say of an “unlogical” world how it would look.

A non sequitur.

3.032 To present in language anything which “contradicts logic” is as impossible as in geometry to present by its co-ordinates a figure which contradicts the laws of space; or to give the co-ordinates of a point which does not exist.

Another non sequitur. One can say all sorts of illogical things. And then (what does not follow) one can describe all sorts of points which have no possibility of existing physically; the laws of physics son't limit what you can say. W seems to have, despite all his interest in philosophizing about mathematics, little understand of how mathematics works.

3.0321 We could present spatially an atomic fact which contradicted the laws of physics, but not one which contradicted the laws of geometry.

Here finally is some real philosophical content: the difference between ... physics and math: experience and thought? no one can think of contradictory things. induction and deduction? This is the closest so far.

3.04 An a priori true thought would be one whose possibility guaranteed its truth.

W is now playing with modal logic. A 'fact' whose possibility implies its truth? That seems a type mismatch. The logic will (or won't) have that as a rule of inference not the fact itself.

3.05 We could only know a priori that a thought is true if its truth was to be recognized from the thought itself (without an object of comparison).

A truth justifies itself? That seems crazy.

3.1 In the proposition the thought is expressed perceptibly through the senses.

What follows is an attempt to explain what propositions and facts and signs and names are. I think inarticulately and unsuccessfully. He is trying to be explicit and articulate about the operation of propositional logic. An elementary text does not go into similar excruciatingly meaningless detail. W should spend time explaining 'variable' (but I'm glad he didn't)

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3.262 What does not get expressed in the sign is shown by its application.What the signs conceal, their application declares.

Finally something metaphorical that holds water: if the form of a proposition doesn't help ecxplain its meaning, the use or manipulation of it does.

More emptiness follows though...

3.313 An expression is thus presented by a variable, whose values are the propositions which contain the expression. (In the limiting case the variables become constants, the expressiona proposition.) I call such a variable a “propositional variable”.

Ah...now a description of 'variable', which sadly is incoherent (at least with a mathematical understanding of 'variable').

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3.318 I conceive the proposition—like Frege and Russell—as a function of the expressions contained in it.

Hm..an actual reference for priority. It sounds like a reference to the idea of 'boolean function'.

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3.321 Two different symbols can therefore have the sign (the written sign or the sound sign) in common—they then signify in different ways.3.322 It can never indicate the common characteristic of two objects  that we symbolize them with the same signs but by different methods of symbolizing. For the sign is arbitrary. We could
therefore equally well choose two different signs and where then would be what was common in the symbolization.
3.323 In the language of everyday life it very often happens that the same word signifies in two different ways—and therefore belongs to two different symbols—or that two words, which signify in different ways, are apparently applied in the same way in the proposition. Thus the word “is” appears as the copula, as the sign of equality, and as the expression of existence; “to exist” as an intransitive verb like “to go”; “identical” as an adjective; we speak
of something but also of the fact of something happening. (In the proposition “Green is green”—where the first word is a proper name and the last an adjective—these words have not
merely different meanings but they are different symbols.)
3.324 Thus there easily arise the most fundamental confusions (of which the whole of philosophy is full).

So W is saying that confusion sometimes comes from polysemy/amphiboly. Genius. Is sarcasm a propositional variable?

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3.325 In order to avoid these errors, we must employ a symbolism which excludes them, by not applying the same sign in different symbols and by not applying signs in the same way which signify in different ways. A symbolism, that is to say, which obeys the rules of logical grammar—of logical syntax. (The logical symbolism of Frege and Russell is such a language, which, however, does still not exclude all errors.)

So symbolism should attempt to be unambiguous. Is W trying to describe math?
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3.33 In logical syntax the meaning of a sign ought never to play a rôle; it must admit of being established without mention being thereby made of the meaning of a sign; it ought to presupposeonly the description of the expressions.

A tenet of formal mathematical thinking.

3.331 From this observation we get a further view—into Russell’s Theory of Types. Russell’s error is shown by the fact that in drawing up his symbolic rules he has to speak of the meaning of the signs.
3.332 No proposition can say anything about itself, because the propositional sign cannot be contained in itself (that is the “whole theory of types”).

Goedel changed all this. I can't blame W for not realizing it; hardly anybody did (except for maybe Tarski and von Neumann).

3.333 A function cannot be its own argument, because the functional sign already contains the prototype of its own argument and it cannot contain itself. If, for example, we suppose that the function F(fx) could be its own argument, then there would be a proposition “F(F(fx))”, and in this the outer function F and the inner function F must have different meanings; for the inner has
the form (fx), the outer the form  ( (fx)). Common to both functions is only the letter “F”, which by itself signifies nothing.
This is at once clear, if instead of “F(F(u))” we write “(9 ) :
F( u) : u = Fu”.
Herewith Russell’s paradox vanishes.

Again, I can't blame W for understanding future logical developments that contradict this.

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3.343 Definitions are rules for the translation of one language into another. Every correct symbolism must be translatable into every other according to such rules. It is this which all have incommon.

This starts to sound like not nonsense.

3.344 What signifies in the symbol is what is common to all those symbols by which it can be replaced according to the rules of logical syntax.
3.3441 We can, for example, express what is common to all notations for the truth-functions as follows: It is common to them that they all, for example, can be replaced by the notations of “sp”
(“not p”) and “p _ q” (“p or q”). (Herewith is indicated the way in which a special possible notation can give us general information.)

This sounds like it should mean something logical, but I can't map it to anything in my (logical) experience.
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