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)

...

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').

...

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'.

...

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?

 ...

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?
 ...

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.

...

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.
...

Comments on Tractatus: 7 Whereof one cannot speak, thereof one must be silent.

7 Whereof one cannot speak, thereof one must be silent.

A classic aphorism. Essentially 'Faire et se taire', 'say what you mean and mean what you say, then say nothing else. This I take to be a meaningful aphorism, a truth hidden in it's tautology, that is nothing more than tautologous. I take this as the corollary of Schopenhauer's:

You may also puzzle and bewilder your opponent by mere bombast; and the trick is possible, because a man generally supposes that there must be some meaning in words

So it's not an empty tautology, but a tautology that can be explored. It has real connotations. It can be acted upon. Stop talking about things of which there is nothing to say (there -is- something to say, but nothing worthwhile is the implication).

As to language, I think this works in English as in the original German, that 'to be silent = schweigen' is the logical opposite of 'to not speak = nicht sprechen', making an aphoristic tautology as profundity worthy of Nietzsche.

A large part of the Tractatus could have been treated this way, a lot of blather that doesn't add anything, neither by its direct statement or by the fact that it is said at all. But W is both sincere and humorless. So he must have thought that what I think is empty BS is in fact really useful, but then, you really need to say that out loud: the aphorism denies itself, but a lot of the TLP text really didn't need to be said either implicitly or explicitly. So we don't disagree in principle, just in a large number of the details.

Maimonides: Seven causes of contradiction

Maimonides/Rambam in the Introduction to his "Guide for the Perplexed' gives a noticeably in-your-face immodestly humble disclaimer for the possible confusions that might follow from his text, a list of seven possible causes of contradiction that you may find in his text. (GftP is mostly a collection of short exegeses of word ambiguities and distinctions in the Talmud (among a handful of earth shaking heresies/orthodoxies (and Aristotle))).

What I am particularly impressed with in the list, even beyond the existence of the usefulness of the list, is the attempt at self-judgment. That is, here are the possible problems that you the reader may find (I, the author, have found them in other people's writings) and here is the explanation of why you may misunderstand in my own. Maybe not so humble, rather a pre-justification. Sort of a prepared feint and parry. Or a couple levels deep of Rock Paper Scissors.

Here is my interlinear commenting based on the translation by Friedlander. Maimonides describes a condition where an inconsistency may arise, and an explanation of why it is actually not an inconsistency, just a misunderstanding. I follow with the moral I take to be drawn in order to avoid the inconsistency, even though that doesn't seem to be the intention of Maimonides. It seems he is just trying to say "it's your fault for thinking there's a contradiction, and here's why". Is he talking about his own Talmudic commentaries, or those of others? I don't know.

THERE are seven causes of inconsistencies and contradictions to be met with in a literary work. The first cause arises from the fact that the author collects the opinions of various men, each differing from the other, but neglects to mention the name of the author of any particular opinion. In such a work contradictions or inconsistencies must occur, since any two statements may belong to two different authors.

The reader should distinguish among the multiple sources, that are not the author's own words. This is somewhat difficult if the author doesn't make it obvious. So my advice then should be to the author which would then be: don't plagiarize, make your references obvious, say who said what.

Second cause: The author holds at first one opinion which he subsequently rejects: in his work, however, both his original and altered views are retained.

Again this is more advice to the author. Make your pattern obvious. That is, if you plan on using a reductio ad absurdum, say so, so that it is obvious what your exposition strategy is (this one is possible 'set up something to fail. follow conclusions till a contradiction'). To the reader, don't take things out of context. Maybe the author is saying one thing to then establish its falsehood. Or maybe the author is saying that 'things are complicated', there are two sides from different perspectives and they are both true in their own context.

Third cause: The passages in question are not all to be taken literally: some only are to be understood in their literal sense, while in others figurative language is employed, which includes another meaning besides the literal one: or, in the apparently inconsistent passages, figurative language is employed which, if taken literally, would seem to be contradictories or contraries.

The author should make the metaphors explicit (or watch out for multiple meanings). The reader should not take things so literally.

Fourth cause: The premises are not identical in both statements, but for certain reasons they are not fully stated in these passages: or two propositions with different subjects which are expressed by the same term without having the difference in meaning pointed out, occur in two passages. The contradiction is therefore only apparent, but there is no contradiction in reality.

Make your assumptions explicit. Also, words have more than one meaning. To the reader, don't be so literal or assume that a word must have exactly one meaning.

The fifth cause is traceable to the use of a certain method adopted in teaching and expounding profound problems. Namely, a difficult and obscure theorem must sometimes be mentioned and assumed as known, for the illustration of some elementary and intelligible subject which must be taught beforehand the commencement being always made with the easier thing. The teacher must therefore facilitate, in any manner which he can devise, the explanation of those theorems, which have to be assumed as known, and he must content himself with giving a general though somewhat inaccurate notion on the subject. It is, for the present, explained according to the capacity of the students, that they may comprehend it as far as they are required to understand the subject. Later on, the same subject is thoroughly treated and fully developed in its right place.

This is equivalent to 'lying to children', 'Wittgenstein's ladder' or teaching by approximations, first giving the oversimplified version that is mostly inaccurate but then allowing refinements and nuance later to become more and more accurate. Hey, Einstein didn't show that Newton was wrong just that newtonian mechanics didn't work as well in large scales.

Sixth cause: The contradiction is not apparent, and only becomes evident through a series of premises. The larger the number of premises necessary to prove the contradiction between the two conclusions, the greater is the chance that it will escape detection, and that the author will not perceive his own inconsistency. Only when from each conclusion, by means of suitable premises, an inference is made, and from the enunciation thus inferred, by means of proper arguments, other conclusions are formed, and after that process has been repeated many times, then it becomes clear that the original conclusions are contradictories or contraries. Even able writers are liable to overlook such inconsistencies. If, however, the contradiction between the original statements can at once be discovered, and the author, while writing the second, does not think of the first, he evinces a greater deficiency, and his words deserve no notice whatever.

Some contradictions are actual and not apparent (all the others are about apparent contradictions that really aren't). A long sequence of inferences is problematic: is the moral to shorten it (that seems to be the cause of a true contradiction not appearing) or to fully explicate all the premises and inferences? Is he saying that we find a faulty derivation, then 'his words deserve no notice whatsoever'? That's a bit extreme. Sure it's annoying but there must be something there even if there's a contradiction.

Seventh cause: It is sometimes necessary to introduce such metaphysical matter as may partly be disclosed, but must partly be concealed: while, therefore, on one occasion the object which the author has in view may demand that the metaphysical problem be treated as solved in one way, it may be convenient on another occasion to treat it as solved in the opposite way. The author must endeavour, by concealing the fact as much as possible, to prevent the uneducated reader from perceiving the contradiction.

Things are complex. The moral here is...well sometime to make things understood you have to choose where to stop, at the simple version or after explaining a lot of complexity. Wow, M is really giving a justification for obscurantism, hide the truth from the kids, babies come from storks, gold equals money.


The special thing about these causes is that it is the first place I've ever seen any acknowledgment of other minds. Most entirely, philosophy is narcissistic and autocratic, there is only one voice, there is never even a conception of anything else, there is just voice. These causes allow that there are other minds, other ideas inspired by the text. But, aside from that great perception, these causes are all attempts to lay the blame on the reader for getting it wrong, but at least M is allowing the possibility that the reader has other ideas.