Americans and Englishmen, when they become acquainted with the Balkans, feel an astonished contempt when they study the mutual enmities of Bulgarians and Serbs, of Hungarians and Rumanians. It is evident to them that these enmities are absurd and that the belief of each little nation in its own superiority has no objective basis. But most of them are quite unable to see that the national pride of a Great Power is essentially as unjustifiable as that of a little Balkan country.
To teach how to live without certainty and yet without being paralysed by hesitation is perhaps the chief thing that philosophy, in our age, can do for those who study it.
When you are studying any matter or considering any philosophy, ask yourself only: what are the facts, and what is the truth that the facts bear out. Never let yourself be diverted by what you wish to believe, but look only and surely at what are the facts.
Formality Thus the absence of all mention of particular things or properties in logic or pure mathematics is a necessary result of the fact that this study is, as we say, "purely formal".
All traditional logic habitually assumes that precise symbols are being employed. It is therefore not applicable to this terrestial life but only to an imagined celestial existence... logic takes us nearer to heaven than other studies.
In astronomy, the law of gravitation is plainly better worth knowing than the position of a particular planet on a particular night, or even on every night throughout a year. There are in the law a splendour and simplicity and sense of mastery which illuminate a mass of otherwise uninteresting details. But in history the matter is far otherwise. Historical facts, many of them, have an intrinsic value, a profound interest on their own account, which makes them worthy of study, quite apart from any possibility of linking them together by means of causal laws.
Of these austerer virtues the love of truth is the chief, and in mathematics, more than elsewhere, the love of truth may find encouragement for waning faith. Every great study is not only an end in itself, but also a means of creating and sustaining a lofty habit of mind; and this purpose should be kept always in view throughout the teaching and learning of mathematics.
A priori Logical propositions are such as can be known a priori without study of the actual world.
BERTRAND RUSSELL, The Philosophy of Logical Atomism We've associated that word philosophy with academic study that in its own way has gotten so far beyond the layman that if you read contemporary philosophy you've no clue, because it's almost become math. And it's odd that if you don't do that and you call yourself a philosopher that you always get 'homespun' attached to it.
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