Frank P. Ramsey: Proposition

Frank P. Ramsey was British mathematician, philosopher. Explore interesting quotes on proposition.
Frank P. Ramsey: 20   quotes 2   likes

“[T]he formalist school, of whom the most eminent representative is Hilbert, have concentrated on the propositions of mathematics, such as '2 + 2 = 4'. They have pronounced these to be meaningless formulae to be manipulated according to arbitrary rules, and they hold that mathematical knowledge consists in knowing what formulae can be derived from what others consistently with the rules…. for example…'2' is a meaningless mark occurring in these meaningless formulae. But… '2' occurs not only in '2 + 2 = 4', but also in 'It is 2 miles to the station', which is not a meaningless formulae, but a significant proposition, in which '2' cannot conceivably be a meaningless mark.”

Frank P. Ramsey

The Foundations of Mathematics (1925)

School , Mathematics , Knowledge

“The assimilation of tautologies and contradictions with true and false propositions respectively results from the fact that tautologies and contradictions can be taken as truth-functions just like ordinary propositions, and for determining the truth of falsity of the truth-function, tautologies and contradictions among its arguments must be counted as true or false respectively. …Are the propositions of symbolic logic and mathematics tautologies in Mr Wittgenstein's sense?”

Frank P. Ramsey

The Foundations of Mathematics (1925)

Truth , Mathematics , Sense , Falseness

“Philosophy must be of some use and we must take it seriously; it must clear our thoughts and so our actions. Or else it is a disposition that we have to check, and an inquiry to see that this is so; i. e. the chief proposition of philosophy is that philosophy is nonsense. And again we must then take seriously that it is nonsense, and not pretend, as Wittgenstein does, that it is important nonsense!”

Frank P. Ramsey

"Philosophy" (1929) as quoted by Nils-Eric Sahlin, The Philosophy of F. P. Ramsey (1990)

“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.”

Frank P. Ramsey

The Foundations of Mathematics (1925)

Reality

“[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.”

Frank P. Ramsey

Footnote: In the future by 'mathematics' will always be meant 'pure mathematics'.
The Foundations of Mathematics (1925)

Mathematics , Idea , Nature , Science