Mathematics, in its widest significance, is the development of all types of formal, necessary, deductive reasoning.
Necessity is the mother of invention” is a silly proverb. “Necessity is the mother of futile dodges” is much nearer the truth.
Philosophers can never hope finally to formulate these metaphysical first principles. Weakness of insight and deficiencies of language stand in the way inexorably. Words and phrases must be stretched towards a generality foreign to their ordinary usage; and however such elements of language be stabilized as technicalities, they remain metaphors mutely appealing for an imaginative leap.
Russell is a Platonic dialogue in himself.
God is the unlimited conceptual realization of the absolute wealth of potentiality.
A student should not be taught more than he can think about.
Science only deals with half the evidence provided by human experience. It divides the seamless coat – or, to change the metaphor into a happier form, it examines the coat, which is superficial, and neglects the body which is fundamental.
Philosophy is an attempt to express the infinity of the universe in terms of the limitations of language.
The certainty of mathematics depends on its complete abstract generality.
This doctrine of necessity in universality means that there is an essence to the universe which forbids relationships beyond itself, as a violation of its rationality. Speculative philosophy seeks that essence.
Panic of error is the death of progress, and love of truth is its safeguard.
It is a false dichotomy to think of Nature and Man. Mankind is a factor in Nature which exhibits in its most intense form the plasticity of Nature.
The purpose of thinking is to let the ideas die instead of us dying.
Science is a river with two sources, the practical source and the theoretical source.
A duration is a concrete slab of nature limited by simultaneity which is an essential factor disclosed in sense-awareness.
It is the ideal of speculative philosophy that its fundamental notions shall not seem capable of abstraction from each other. In other words, it is presupposed that no entity can be conceived in complete abstraction from the system of the universe, and that it is the business of speculative philosophy to exhibit this truth. This character is its coherence.
But the purpose of philosophy is to rationalize mysticism: not by explaining it away, but by the introduction of novel verbal characterizations, rationally coordinated.
As soon as high consciousness is reached, the enjoyment of existence is entwined with pain, frustration, loss, tragedy. Amid the passing of so much beauty, so much heroism, so much daring, Peace is then the intuition of permanence. It keeps vivid the sensitiveness to the tragedy; and it sees the fineness beyond the faded level of surrounding fact. Each tragedy is the disclosure of an ideal: What might have been, and was not; What can be. The tragedy was not in vain.
In so far as your metaphysical beliefs are implicit, you vaguely interpret the past on the lines of the present. But when it comes to the primary metaphysical data, the world of which you are immediately conscious is the whole datum.
Only the adventurous can understand the greatness of the past. In its day, the literature of the past was an adventure. Aischylus, Sophocles, Euripides were adventurers in the world of thought. To read their plays without any sense of new ways of understanding the world and of savouring its emotions is to miss the vividness which constitutes their whole value. But adventures are to the adventurous. Thus a passive knowledge of the past loses the whole value of its message.
In this sense, God is the great companion – the fellow-sufferer who understands.