Formal logic is mathematics, and there are philosophers like Wittgenstein that are very mathematical, but what they're really doing is mathematics - it's not talking about things that have affected computer science; it's mathematical logic.
It is undesirable to believe a proposition when there is no ground whatsoever for supposing it is true.
3rd Earl Russell of Kingston
A tautology's truth is certain, a proposition's possible, a contradiction's impossible.
A pair of statements may be taken conjunctively or disjunctively; for example, "It lightens and it thunders ," is conjunctive, "It lightens or it thunders" is disjunctive. Each such individual act of connecting a pair of statements is a new monad for the mathematician .
To reason logically is so to link one's propositions that each should contain the reason for the one succeeding it, and should itself be demonstrated by the one preceding it. Or at any rate, whatever the order adopted in the construction of one's own exposition, it is to demonstrate judgments by each other.
The mathematician starts with a few propositions, the proof of which is so obvious that they are called self-evident, and the rest of his work consists of subtle deductions from them. The teaching of languages, at any rate as ordinarily practiced, is of the same general nature authority and tradition furnish the data, and the mental operations are deductive.
Mathematics is a logical method. . . . Mathematical propositions express no thoughts. In 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.
Elementary propositions consist of names.
Pure mathematics consists entirely of assertions to the effect that, if such and such a proposition is true of anything, then suchand such another proposition is true of that thing.... Thus mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true.
If pressed to supplement Tweedledee's ostensive definition of logic with a discursive definition of the same subject, I would say that logic is the systematic study of the logical truths. Pressed further, I would say that a sentence is logically true if all sentences with its grammatical structure are true. Pressed further still, I would say to read this book.
Truth and falsity is something that concerns language, it's a property of language.
Sentences are not as such either true or false.
Reversing a proposition rearranges its terms, but still keeps out new terms.
Some philosophers fail to distinguish propositions from judgements; ... But in the real world it is more important that a proposition be interesting than that it be true. The importance of truth is that it adds to interest.
Mathematics is purely hypothetical: it produces nothing but conditional propositions.
The system becomes logically closed when each of the logical implications which can be derived from any one proposition within the system finds its statement in another proposition in the same system.
The Syllogism consists of propositions, propositions consist of words, words are symbols of notions. Therefore if the notions themselves (which is the root of the matter) are confused and over-hastily abstracted from the facts, there can be no firmness in the superstructure. Our only hope therefore lies in a true induction.
