To conclude: there are two well-known minor ways in which language has mattered to philosophy. On the one hand there is a belief that if only we produce good definitions, often marking out different senses of words that are confused in common speech, we will avoid the conceptual traps that ensnared our forefathers. On the other hand is a belief that if only we attend sufficiently closely to our mother tongue and make explicit the distinctions there implicit, we shall avoid the conceptual traps. One or the other of these curiously contrary beliefs may nowadays be most often thought of as an answer to the question Why does language matter to philosophy? Neither seems to me enough.

From any vocabulary of ideas we can build other ideas by formal combinations of signs. But not any set of ideas will be instructive. One must have the right ideas.

Probability fractions arise from our knowledge and from our ignorance.

When land and its tillage are the basis of taxation, one need not care exactly how many people there are.

Statistics began as the systematic study of quantitative facts about the state.

Much early alchemy seems to have been adventure. You heated and mixed and burnt and pounded and to see what would happen. An adventure might suggest an hypothesis that can subsequently be tested, but adventure is prior to theory.

A single observation that is inconsistent with some generalization points to the falsehood of the generalization, and thereby 'points to itself'.

Until the seventeenth century there was no concept of evidence with which to pose the problem of induction!

Many modern philosophers claim that probability is relation between an hypothesis and the evidence for it.

Opinion is the companion of probability within the medieval epistemology.

Pascal is called the founder of modern probability theory. He earns this title not only for the familiar correspondence with Fermat on games of chance, but also for his conception of decision theory, and because he was an instrument in the demolition of probabilism, a doctrine which would have precluded rational probability theory.

There are two ways in which a science develops; in response to problems which is itself creates, and in response to problems that are forced on it from the outside.

Well, he wasn't a relativist. There's a long and complicated story of the rise of a desire for scientific relativism. Part of it may well be simply sort of rage against reason, the fear of the sciences and a kind of total dislike of the arrogance of a great many scientists who say we're finding out the truth about everything-and here [with Kuhn] there was a way to undermine that arrogance.

We favor hypotheses for their simplicity and explanatory power, much as the architect of the world might have done in choosing which possibility to create.