by Ludwig Wittgenstein, read in 2016
The basic propositions of the Tractatus:
1. The world is everything that is the case.
2. What is the case, the fact, is the existence of atomic facts.
3. The logical picture of the facts is the thought.
4. The thought is the significant proposition.
5. Propositions are truth-functions of elementary propositions.
6. The general form of truth-functions is: [p,ξ,N(ξ)].
7. Whereof one cannot speak, thereof one must be silent.
Loc 373: "3.5 The applied, thought, propositional sign is the thought." How is this to be parsed as a sentence? Is it meant to be the definition of 'thought'?
Loc 379: "4.003 Most propositions and questions, that have been written about philosophical matters, are not false, but senseless"
Loc 399: "4.021 The proposition is a picture of reality, for I know the state of affairs presented by it, if I understand the proposition. And I understand the proposition, without its sense having been explained to me." And exactly how, do you suppose, does that happen?
Loc 401: "4.023 The proposition determines reality to this extent, that one only needs to say "Yes" or " No" to it to make it agree with reality. Reality must therefore be completely described by the proposition." I think it is a stretch to use the term 'completely' here. Some context is certainly implied, but all of reality?!
Loc 454: "4.12 Propositions can represent the whole reality, but they cannot represent what they must have in common with reality in order to be able to represent it-the logical form." We need to be careful in using the term 'whole reality'.
Loc 455: "To be able to represent the logical form, we should have to be able to put ourselves with the propositions outside logic, that is outside the world." Yes! Exactly! And when we "put ourselves...outside the world" the term 'whole reality' cannot include us.
Loc 458: "4.1212 What can be shown cannot be said."
Loc 495: "4.1273 If we want to express in logical symbolism the general proposition "b is a successor of a" we need for this an expression for the general term of the formal series : aRb, (gx) : aRx . xRb, (gx,y) : aRx . xRy . yRb, . . . The general term of a formal series can only be expressed by a variable, for the concept symbolized by "term of this formal series" is a formal concept. (This Frege and Russell overlooked ; the way in which they express general propositions like the above is, therefore, false ; it contains a vicious circle.)" Yes, and it is that falsehood upon which they base their erroneous acceptance of the infinitude of the integers.
Loc 496: "We can determine the general term of the formal series by giving its first term and the general form of the operation, which generates the following term out of the preceding proposition." Really? *Which generates"? How does that happen? Does the thinker "generate" an infinity of terms? Or is there a machine that was built and which did the job to completion? Both are preposterous ideas. We need to abandon our naive acceptance of the notion of infinity.
Loc 497: "4.1274 The question about the existence of a formal concept is senseless. For no proposition can answer such a question. (For example, one cannot ask: "Are there unanalysable subject-predicate propositions? ")" That is too strong. You have only shown that "The question about the existence of a formal concept of "infinity "is senseless." Other explicitly defined and declared concepts are legitimate and useful. We need not give them up.
Loc 498: "4.128 The logical forms are anumerical. Therefore there are in logic no pre-eminent numbers, and therefore there is no philosophical monism or dualism, etc." Again, this is too strong and for the same reason. Defining the numbers 'one', 'two', etc. up to 'one million' is perfectly legitimate as long as an unambiguous definition of each number has been made by some thinker or by some machine, e.g. by the construction of an abacus with six wires and the explicit description of how each configuration of the beads is to be interpreted and named. So it is perfectly legitimate to entertain the notions of monism, dualism, treblism, etc.
Loc 508: "A definition is a symbolic rule.)"
Loc 514: "4.25 If the elementary proposition is true, the atomic fact exists ; if it is false the atomic fact does not exist." It seems to me that this is the definition of 'truth' and 'falsity'. It would be better stated as, If the atomic fact exists, the elementary proposition is said to be true. If not, the proposition is said to be false.
Loc 514: "4.26 The specification of all true elementary propositions describes the world completely" This is fine as long as we acknowledge the fact that we thinkers are not to be considered to be in, or part of the world. (See my note responding to 4.12)
Loc 578: "5.101 The truth-functions of every number of elementary propositions can be written in a schema of the following kind:
(T T T T) (p, q) Tautology (if p then p, and if q then q) [ p→p. q → q]
(FTTT)(p,q) in words: Not both p and q. [-(p.q))
(T F T T) (p, q) If q then p. [q→p]
(TTFT)(p,q)„ „ If p then q. [p→ q]
(TTTF)(p,q)„ „ p or q. [pvq]
(FFTT)(p,q)„ „ Not q. [-q]
(FTFT)(p,q)„ „ Not p. [-pJ
(F T T F) or q, but not both. [p. q : v : q. p]
(T F F T) (p, q) „ „ If p, then q; and if q, then p. [ p=q]
(T FTF)(p,q),, „ p
(TTFF)(p,q),, „ q
(FFFT)(p,q)„ „ Neither p nor q. [-p. -q or plq]
(FFTF)(p,q),, p and not q. [p.-q]
(FTFF)(p,q),, „ q and not p. [q.-p]
(TFFF)(p,q)„ „ p and q. [p. q]
("FFFF)(p,q) Contradiction (p and not p, and q and not q ([p.-p.q.-q]
Loc 743: "5.53 Identity of the object I express by identity of the sign and not by means of a sign of identity. Difference of the objects by difference of the signs."
Loc 748: "5.5303 Roughly speaking : to say of two things that they are identical is nonsense, and to say of one thing that it is identical with itself is to say nothing."
Loc 756: "5.535 So all problems disappear which are connected with such pseudo-propositions. This is the place to solve all the problems which arise through Russell's "Axiom of Infinity". What the axiom of infinity is meant to say would be expressed in language by the fact that there is an infinite number of names with different meanings" This IMHO indeed the root of the problem. I am eager to see how he "so!ves all" of them.
Loc 797: "What we cannot think, that we cannot think: we cannot therefore say what we cannot think. 5.62 This remark provides a key to the question, to what extent solipsism is a truth."
Loc 799: "In fact what solipsism means, is quite correct, only it cannot be said, but it shows itself. That the world is my world, shows itself in the fact that the limits of the language (the language which I understand) mean the limits of my world."
Loc 802: "5.632 The subject does not belong to the world but it is a limit of the world."
Loc 808: "Everything we can describe at all could also be otherwise. There is no order of things a priori. 5.64 Here we see that solipsism strictly carried out coincides with pure realism. The I in solipsism shrinks to an extensionless point and there remains the reality co-ordinated with it."
Loc 810: "5.641 There is therefore really a sense in which in philosophy we can talk of a non-psychological I. The I occurs in philosophy through the fact that the " world is my world ". The philosophical I is not the man, not the human body or the human soul of which psychology treats, but the metaphysical subject, the limit-not a part of the world." This seems to imply a hierarchical structure to reality with the world at one level and the "I" outside and one level higher.
Loc 815: "6.02 And thus we come to numbers: I define x..." This is an error IMHO: the plus sign in the superscript has not been defined, so at this point it is simply a meaningless notation mark.
Loc 816: "According, then, to these symbolic rules we write the series x, S2'x, S2' S2' x, f2' S2' S2' x .... . as : Q `x, no+,, x," Similarly here, the ellipses have not been defined.
Loc 818: "And I define: o+I=I Def. 0+1+1 =2 Def. 0 + I + I + I = 3 Def. and so on. " And here the "and so on" has not been defined. His "definition" hides the implicit assumption that some thinker, or some process has at some time in the "past" proceeded with the process to its conclusion in order to produce a countably infinite set of numbers. That is a preposterous and unwarranted assumption, IMHO."
Loc 820: "6.031 The theory of classes is altogether superfluous in mathematics." It would be superfluous if we did not accept and admit the notion of infinity into mathematics. The theory of classes is a vain attempt to remove the consequent antinomies.
Loc 876: "6.13 Logic is not a theory but a reflexion of the world. Logic is transcendental." Hmmmm.
Loc 975: "7 Whereof one cannot speak, thereof one must be silent."
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