Brunschvicg, Léon

« this, Brunschvicg devotes a long chapter to the development of modern logical theory - to Boole, Peano, Frege and, above all, Russell. The final chapters are devoted to drawing the moral of this long historical inquiry.

Brunschvicg here clarifies his own point of view, and presents a qualified form of 'intellectualism' in his final chapter on 'The reaction against "mathematism": the sense of intellectualism in mathematics' .

Up to now, he claims, the philosophy of mathematics has lacked a proper appreciation of the nature of truth in mathematics.

In accepting that the logical order of exposition reverses the direction of the psychological order of discovery, philosophers of mathematics admit implicitly that the concern for rigour that is characteristic of reasoning is foreign to, indeed opposed to, the discovery of mathematical truth.

Thus their conclusion should be that the logical formalization of mathematics makes no difference to its truth.

So even in mathematics one should bear in mind the two distinctive marks of the intellect - 'an indefinite capacity for progress' joined with 'a perpetual disquiet about verification' .

As such, mathematics represents one of the most powerful and lasting achievements of the human genius; it reveals to us the capacities of the human intellect, and should be as much a foundation for our knowledge of the mind as it is for the natural sciences.

' The activity of the mind has been free and productive only since the epoch when mathematics brought to mankind the true standard of truth ' ([1912] 1972: 577 ). 3 Other works Brunschvicg's numerous writings are diverse.

One area of interest was the history of philosophy, especially seventeenth-century French philosophy.

He produced the standard edition of Pascal 's Pensées et opuscules (1897 ); wrote Spinoza et ses contemporains (Spinoza and His Contemporaries) (1923 ); and in 1942 completed Descartes et Pascal: lecteurs de Montaigne (Descartes and Pascal: Readers of Montaigne) (1944 ).

In an earlier work on a much grander historical scale, entitled Le Progrés de la conscience dans la philosophie occidentale (The Progress of Consciousness in Western Philosophy) (1927 ), he had opened up wider and bolder lines of thought. Brunschvicg also wrote on the philosophy of science.

He took the view that the development of science was not autonomous: philosophy is not to be separated from science and should not pretend to a superior or distinctive kind of truth.

This line of thought, which continues that of Les étapes de la philosophie mathématique , is presented in L'expérience humaine et la causalité physique (Human Experience and Physical Causality) (1922 ) and La physique du vingtième siècle et la philosophie (Philosophy and Twentieth-Century Physics) (1936 ).

For Brunschvicg, the development of science reveals the work of the human intellect and shows reason at work; as Plato held, the philosopher or the scientist should be able to concern himself with truth in a completely disinterested spirit, following to the limit the movement of commitment which, from Copernicus to Einstein, has manifested the character of the human intellect.

In the same spirit, the philosopher and scientist should seek to bring together the pursuit of truth with that of beauty and the good.

Grasped in its essence, science should aim to. »