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" "The first problem I propose to tackle is this: how much of its income should a nation save? To answer this a simple rule is obtained valid under conditions of surprising generality; the rule, which will be further elucidated later, runs as follows. The rate of saving multiplied by the marginal utility of money should always be equal to the amount by which the total net rate of enjoyment of utility falls short of the maximum possible rate of enjoyment.
Frank Plumpton Ramsey (22 February 1903 – 19 January 1930) was a precocious British philosopher, mathematician and economist who died at the age of 26. He was a close friend of Ludwig Wittgenstein and was instrumental in translating Wittgenstein's into English, as well as persuading Wittgenstein to return to philosophy and Cambridge. Like Wittgenstein, he was a member of the , the intellectual secret society, from 1921.
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[W]e shall be concerned with the general nature of pure mathematics, and how it is distinguished from other sciences. Here there are... two distinct categories of things of which an account must be given—the ideas or concepts of mathematics, and the propositions of mathematics. ...the great majority of writers on the subject have concentrated their attention on the explanation of one or the other... and erroneously supposed that a satisfactory explanation of the other would immediately follow.
The formalists neglected the content altogether and made mathematics meaningless, the logicians neglected the form and made mathematics consist of any true generalizations; only by taking account of both sides and regarding it as composed of tautologous generalizations can we obtain an adequate theory.
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Tautologies and contradictions are not real propositions, but degenerate cases. ...Clearly, by negating a contradiction we get a tautology, and by negating a tautology a contradiction. ...A genuine proposition asserts something about reality, and it is true if reality is as it is asserted to be. But a tautology is a symbol constructed so as to say nothing whatever about reality, but to express total ignorance by agreeing with every possibility.