Tractatus Logico-Philosophicus by Ludwig Wittgenstein (i want to read a book .txt) ๐
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Ludwig Wittgenstein is considered by many to be one of the most important philosophers of the 20th century. He was born in Vienna to an incredibly rich family, but he gave away his inheritance and spent his life alternating between academia and various other roles, including serving as an officer during World War I and a hospital porter during World War II. When in academia Wittgenstein was taught by Bertrand Russell, and he himself taught at Cambridge.
He began laying the groundwork for Tractatus Logico-Philosophicus while in the trenches, and published it after the end of the war. It has since come to be considered one of the most important works of 20th century philosophy. After publishing it, Wittgenstein concluded that it had solved all philosophical problemsโso he never published another book-length work in his lifetime.
The book itself is divided into a series of short, self-evident statements, followed by sub-statements elucidating on their parent statement, sub-sub-statements, and so on. These statements explore the nature of philosophy, our understanding of the world around us, and how language fits in to it all. These views later came to be known as โLogical Atomism.โ
This translation, while credited to C. K. Ogden, is actually mostly the work of F. P. Ramsey, one of Ogdenโs students. Ramsey completed the translation when he was just 19 years of age. The translation was personally revised and approved by Wittgenstein himself, who, though he was Austrian, had spent much of his life in England.
Much of the Tractatusโ meaning is complex and difficult to unpack. It is still being interpreted and explored to this day.
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- Author: Ludwig Wittgenstein
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To be general is only to be accidentally valid for all things. An ungeneralized proposition can be tautologous just as well as a generalized one.
6.1232Logical general validity, we could call essential as opposed to accidental general validity, e.g. of the proposition โall men are mortal.โ Propositions like Russellโs โaxiom of reducibilityโ are not logical propositions, and this explains our feeling that, if true, they can only be true by a happy chance.
6.1233We can imagine a world in which the axiom of reducibility is not valid. But it is clear that logic has nothing to do with the question whether our world is really of this kind or not.
6.124The logical propositions describe the scaffolding of the world, or rather they present it. They โtreatโ of nothing. They presuppose that names have meaning, and that elementary propositions have sense. And this is their connection with the world. It is clear that it must show something about the world that certain combinations of symbolsโ โwhich essentially have a definite characterโ โare tautologies. Herein lies the decisive point. We said that in the symbols which we use something is arbitrary, something not. In logic only this expresses: but this means that in logic it is not we who express, by means of signs, what we want, but in logic the nature of the essentially necessary signs itself asserts. That is to say, if we know the logical syntax of any sign language, then all the propositions of logic are already given.
6.125It is possible, also with the old conception of logic, to give at the outset a description of all โtrueโ logical propositions.
6.1251Hence there can never be surprises in logic.
6.126Whether a proposition belongs to logic can be calculated by calculating the logical properties of the symbol.
And this we do when we prove a logical proposition. For without troubling ourselves about a sense and a meaning, we form the logical propositions out of others by mere symbolic rules.
We prove a logical proposition by creating it out of other logical propositions by applying in succession certain operations, which again generate tautologies out of the first. (And from a tautology only tautologies follow.)
Naturally this way of showing that its propositions are tautologies is quite unessential to logic. Because the propositions, from which the proof starts, must show without proof that they are tautologies.
6.1261In logic process and result are equivalent. (Therefore no surprises.)
6.1262Proof in logic is only a mechanical expedient to facilitate the recognition of tautology, where it is complicated.
6.1263It would be too remarkable, if one could prove a significant proposition logically from another, and a logical proposition also. It is clear from the beginning that the logical proof of a significant proposition and the proof in logic must be two quite different things.
6.1264The significant proposition asserts something, and its proof shows that it is so; in logic every proposition is the form of a proof.
Every proposition of logic is a modus ponens presented in signs. (And the modus ponens can not be expressed by a proposition.)
6.1265Logic can always be conceived to be such that every proposition is its own proof.
6.127All propositions of logic are of equal rank; there are not some which are essentially primitive and others deduced from there.
Every tautology itself shows that it is a tautology.
6.1271It is clear that the number of โprimitive propositions of logicโ is arbitrary, for we could deduce logic from one primitive proposition by simply forming, for example, the logical produce of Fregeโs primitive propositions. (Frege would perhaps say that this would no longer be immediately self-evident. But it is remarkable that so exact a thinker as Frege should have appealed to the degree of self-evidence as the criterion of a logical proposition.)
6.13Logic is not a theory but a reflection of the world.
Logic is transcendental.
6.2Mathematics is a logical method.
The propositions of mathematics are equations, and therefore pseudo-propositions.
6.21Mathematical propositions express no thoughts.
6.211In life it is never a mathematical proposition which we need, but we use mathematical propositions only in order to infer from propositions which do not belong to mathematics to others which equally do not belong to mathematics.
(In philosophy the question โWhy do we really use that word, that proposition?โ constantly leads to valuable results.)
6.22The logic of the world which the propositions of logic show in tautologies, mathematics shows in equations.
6.23If two expressions are connected by the sign of equality, this means that they can be substituted for one another. But whether this is the case must show itself in the two expressions themselves.
It characterizes the logical form of two expressions, that they can be substituted for one another.
6.231It is a property of affirmation that it can be conceived as double denial.
It is a property of โ1+1+1+1โ that it can be conceived as โ(1+1)+(1+1)โ.
6.232Frege says that these expressions have the same meaning but different senses.
But what is essential about equation is that it is not necessary in order to show that both expressions, which are connected by the sign of equality, have the same meaning: for this can be perceived from the two expressions themselves.
6.2321And, that the propositions of mathematics can be proved means nothing else than that their correctness can be seen without our having to compare what they express with the facts as regards correctness.
6.2322The identity of the meaning of two expressions cannot be asserted. For in order to be able to assert anything about their meaning, I must know their meaning, and if I know their meaning, I know whether they mean the same or something different.
6.2323The equation characterizes only the standpoint from which I consider the two expressions, that is to say the standpoint of their equality of meaning.
6.233To the question
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