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April 6 - April 20, 2023
The propositional sign consists in the fact that its elements, the words, are combined in it in a definite way. The propositional sign is a fact.
Only facts can express a sense, a class of names cannot.
The essential nature of the propositional sign becomes very clear when we imagine it made up of spatial objects (such as tables, chairs, books) instead of written signs.
Objects I can only name. Signs represent them. I can only speak of them. I cannot assert them. A proposition can only say how a thing is, not what it is.
A proposition about a complex stands in internal relation to the proposition about its constituent part.
The proposition in which there is mention of a complex, if this does not exist, becomes not nonsense but simply false.
The proposition expresses what it expresses in a definite and clearly specifiable way: the proposition is articulate.
3.3 Only the proposition has sense; only in the context of a proposition has a name meaning.
And in this form the expression is constant and everything else variable.
What values the propositional variable can assume is determined. The determination of the values is the variable.
I conceive the proposition—like Frege and Russell—as a function of the expressions contained in it.
Thus there easily arise the most fundamental confusions (of which the whole of philosophy is full).
If a sign is not necessary then it is meaningless. That is the meaning of Occam’s razor. (If everything in the symbolism works as though a sign had meaning, then it has meaning.)
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 “∼p” (“not p”) and “p ∨ q” (“p or q”).
The thought is the significant proposition. 4.001 The totality of propositions is the language.
Language disguises the thought; so that from the external form of the clothes one cannot infer the form of the thought they clothe, because the external form of the clothes is constructed with quite another object than to let the form of the body be recognized.
Most propositions and questions, that have been written about philosophical matters, are not false, but senseless. We cannot, therefore, answer questions of this kind at all, but only state their senselessness. Most questions and propositions of the philosophers result from the fact that we do not understand the logic of our language. (They are of the same kind as the question whether the Good is more or less identical than the Beautiful.) And so it is not to be wondered at that the deepest problems are really no problems.
The proposition is a picture of reality. The proposition is a model of the reality as we think it is.
The gramophone record, the musical thought, the score, the waves of sound, all stand to one another in that pictorial internal relation, which holds between language and the world. To all of them the logical structure is common.
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.
The proposition determines reality to this extent, that one only needs to say “Yes” or “No” to it to make it agree with reality. It must therefore be completely described by the proposition. A proposition is the description of a fact. As the description of an object describes it by its external properties so propositions describe reality by its internal properties.
By means of propositions we explain ourselves.
A proposition must communicate a new sense with old words.
One name stands for one thing, and another for another thing, and they are connected together. And so the whole, like a living picture, presents the atomic fact.
Reality is compared with the proposition.
Propositions can be true or false only by being pictures of the reality.
The propositions “p” and “∼p” have opposite senses, but to them corresponds one and the same reality.
A proposition presents the existence and non-existence of atomic facts.
The totality of true propositions is the total natural science (or the totality of the natural sciences).
Philosophy is not one of the natural sciences. (The word “philosophy” must mean something which stands above or below, but not beside the natural sciences.)
The object of philosophy is the logical clarification of thoughts.
Philosophy is not a theory but an activity. A philosophical work consists essentially of elucidations. The result of philosophy is not a number of “philosophical propositions”, but to make propositions clear.
Philosophy should make clear and delimit sharply the thoughts which otherwise are, as it were, opaque and blurred.
The theory of knowledge is the philosophy of psychology.
The Darwinian theory has no more to do with philosophy than has any other hypothesis of natural science.
Everything that can be thought at all can be thought clearly. Everything that can be said can be said clearly.
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.
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.
What can be shown cannot be said.
An internal property of a fact we also call a feature of this fact.
A property is internal if it is unthinkable that its object does not possess it.
One cannot distinguish forms from one another by saying that one has this property but the other that: for this assumes that there is a sense in asserting either property of either form.
Series which are ordered by internal relations I call formal series.
Similarly the series of propositions “aRb”, “(∃x) : aRx . xRb”, “(∃x, y) : aRx . aRy . yRb”, etc. (If b stands in one of these relations to a, I call b a successor of a.)
Formal concepts cannot, like proper concepts, be presented by a function.
They all signify formal concepts and are presented in logical symbolism by variables, not by functions or classes (as Frege and Russell thought).
The logical forms are anumerical. Therefore there are in logic no pre-eminent numbers, and therefore there is no philosophical monism or dualism, etc.
Even if the world is infinitely complex, so that every fact consists of an infinite number of atomic facts and every atomic fact is composed of an infinite number of objects, even then there must be objects and atomic facts.
If the elementary proposition is true, the atomic fact exists; if it is false the atomic fact does not exist.
A proposition is the expression of agreement and disagreement with the truth-possibilities of the elementary propositions.
