Tractatus Logico-Philosophicus (English): Difference between revisions

If this work has a value it consists in two things. First that in it thoughts are expressed, and this value will be the greater the better the thoughts are expressed. The more the nail has been hit on the head.— Here I am conscious that I have fallen far short of the possible. Simply because my powers are insufficient to cope with the task.—May others come and do it better.

(If I introduce by an equation a new sign “''b''”, by determining that it shall replace a previously known sign “''a''”, I write the equation—definition —(like Russell) in the form “''a=b'' Def.”. A definition is a symbolic rule.)

In the tautology the conditions of agreement with the world — the presenting relations — cancel one another, so that it stands in no presenting relation to reality.

It is clear that in the description of the most general form of proposition ''only'' what is essential to it may be described — otherwise it would not be the most general form.

Laws of inference, which — as in Frege and Russell — are to justify the conclusions, are senseless and would be superfluous.

5.1362 The freedom of the will consists in the fact that future actions cannot be known now. We could only know them if causality were an ''inner'' necessity, like that of logical deduction. — The connexion of knowledge and what is known is that of logical necessity.

5.151 Suppose in a schema like that above in No. 5.101 ''T_r'' is the number of the "T"'s in the proposition ''r'', ''T_rs'' the number of those "T"'s in the proposition ''s'', which stand in the same columns as "T"'s of the proposition ''r''; then the proposition ''r'' gives to the proposition ''s'' the probability {{nowrap|''T_rs : T_r''}}.

If then, I say, It is equally probable that I should draw a white and a black ball, this means, All the circumstances known to me (including the natural laws hypothetically assumed) give to the occurrence of the one event no more probability than to the occurrence of the other. That is they give — as can easily be understood from the above explanations — to each the probability ½.

5.155 The unit of the probability proposition is: The circumstances — with which I am not further acquainted — give to the occurrence of a definite event such and such a degree of probability.

5.31 The Schemata No. 4.31 are also significant, if "''p''", "''q''", "''r''", etc. are not elementary propositions.

And it is easy to see that the propositional sign in No. 4.42 expresses one truth-function of elementary propositions even when "''p''" and "''q''" are truth-functions of elementary propositions.

If ''e.g.'' an affirmation can be produced by repeated denial, is the denial — in any sense — contained in the affirmation?

5.452 The introduction of a new expedient in the symbolism of logic must always be an event full of consequences. No new symbol may be introduced in logic in brackets or in the margin — with, so to speak, an entirely innocent face. (Thus in the "Principia Mathematica" of Russell and Whitehead there occur definitions and primitive propositions in words. Why suddenly words here? This would need a justification. There was none, and can be none for the process is actually not allowed.)

Men have always thought that there must be a sphere of questions whose answers — a priori — are symmetrical and united into a closed regular structure.

5.461 The apparently unimportant fact that the apparent relations like ∨ and ⊃ need brackets — unlike real relations — is of great importance.

Thus "Socrates is identical" says nothing, because we have given ''no'' meaning to the word "identical" as ''adjective''. For when it occurs as the sign of equality it symbolizes in an entirely different way — the symbolizing relation is another — therefore the symbol is in the two cases entirely different; the two symbols have the sign in common with one another only by accident.

5.475 It is only a question of constructing a system of signs of a definite number of dimensions — of a definite mathematical multiplicity.

5.501 An expression in brackets whose terms are propositions I indicate — if the order of the terms in the bracket is indifferent — by a sign of the form "<math>( \bar{\xi} )</math>". "''ξ''" is a variable whose values are the terms of the expression in brackets, and the line over the variable indicates that it stands for all its values in the bracket.

5.525 It is not correct to render the proposition "(∃''x'') . ''f x''" — as Russell does — in words "''f x'' is ''possible''".

5.5352 Similarly it was proposed to express "There are no things" by "(∃''x'') . ''x'' = ''x''" But even if this were a proposition — would it not be true if indeed "There were things", but these were not identical with themselves?

5.5421 This shows that there is no such thing as the soul — the subject, etc. — as it is conceived in contemporary superficial psychology.

Logic ''precedes'' every experience — that something is ''so''.

5.553 Russell said that there were simple relations between different numbers of things (individuals). But between what numbers? And how should this be decided — by experience?

the form "''ξ . η''" thus: —