A Quote by Bertrand Russell
Analytic It is clear that the definition of "logic" or "mathematics" must be sought by trying to give a new definition of the old notion of "analytic" propositions.
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The principles of logic and mathematics are true simply because we never allow them to be anything else. And the reason for this is that we cannot abandon them without contradicting ourselves, without sinning against the rules which govern the use of language, and so making our utterances self-stultifying. In other words, the truths of logic and mathematics are analytic propositions or tautologies.
"We hold these truths to be sacred and undeniable" in a draft of the Declaration of Independence changes it instead into an assertion of rationality. The scientific mind of Franklin drew on the scientific determinism of Isaac Newton and the analytic empiricism of David Hume and Gottfried Leibniz. In what became known as "Hume's Fork" the latters' theory distinguished between synthetic truths that describe matters of fact, and analytic truths that are self-evident by virtue of reason and definition.
'You might think of combinatorics as a machine too', the major says. 'A different sort of machine, though. Have you heard of Babbage's analytic engine? He never built it. ... I have an analytic machine of my own-right here.' He taps his own skull.
A definition is nothing else but an explication of the meaning of a word, by words whose meaning is already known. Hence it is evident that every word cannot be defined; for the definition must consist of words; and there could be no definition, if there were not words previously understood without definition.
Now ... the basic principle of modern mathematics is to achieve a complete fusion [of] 'geometric' and 'analytic' ideas.
It is almost as hard to define mathematics as it is to define economics, and one is tempted to fall back on the famous old definition attributed to Jacob Viner, "Economics is what economists do," and say that mathematics is what mathematicians do. A large part of mathematics deals with the formal relations of quantities or numbers.
I really wanted to give people that tool, that thing, that answer, 'Well, what are you going to do after Katrina? How does New Orleans come back?' And I'm thinking to myself, New Orleans is back. We're the definition of 'back.' We're the definition of 'rebirth,' of 'renaissance.'
It is possible--indeed possible even according to the old conception of logic--to give in advance a description of all 'true' logical propositions. Hence there can never be surprises in logic.
In my view, we ought to replace the notion of analytic philosophy by that of synthetic philosophy.
The very definition of 'blackness' is as broad as that of 'whiteness,' yet we're seemingly always trying to find a specific, limited definition.
...by the time we understand the pattern we are in, the definition we are making for ourselves, it's too late to break out of the box. We can only live in terms of the definition, like the prisoner in the cage in which he cannot lie or stand or sit, hung up in justice to be viewed by the populace. Yet the definition we have made of ourselves is ourselves. To break out of it, we must make a new self. But how can the self make a new self when the selfness which it is, is the only substance from which the new self can be made?
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.
What is a good definition? For the philosopher or the scientist, it is a definition which applies to all the objects to be defined, and applies only to them; it is that which satisfies the rules of logic. But in education it is not that; it is one that can be understood by the pupils.
A definition is death. A definition is the answer to which you must look up the question in the back of your book.
My definition, a definition in the drill books from the time that General Von Steuben wrote the regulations for General George Washington, the definition of the object of military training is success in battle... It wouldn't be any sense to have a military organization on the backs of the American taxpayers with any other definition.
The notion of public service has effectively been abandoned. Every political party now buys into business values, and into the notion that by definition business must run things more efficiently.
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