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Correspondence, by Benedict de Spinoza, [1883], at sacred-texts.com
[How can the variety of the universe be shown à priori from the Spinozistic conception of extension?]
Most learned Sir,—I wish you would gratify me in this matter by pointing out how, from the conception of extension, as you give it, the variety of the universe can be shown à priori. You recall the opinion of Descartes, wherein he asserts, that this variety can only be deduced from extension, by supposing that, when motion was started by God, it caused this effect in extension. Now it appears to me, that he does not deduce the existence of bodies from matter at rest, unless, perhaps, you count as nothing the assumption of God as a motive power; you have not shown how such an effect must, à priori, necessarily follow from the nature of God. A difficulty which Descartes professed himself unable to solve as being beyond human understanding. I therefore ask you the question, knowing that you have other thoughts on the matter, unless perhaps there be some weighty cause for your unwillingness hitherto to disclose your opinion. If this, as I suppose, be not expedient, give me some hint of your meaning. You may rest assured, that whether you speak openly with me, or whether you employ reserve, my regard for you will remain unchanged.
My special reasons for making the requests are as follows:—I have always observed in mathematics, that from a given thing considered in itself, that is, from the definition of a given thing, we can only deduce a single property; if, however, we require to find several properties, we are obliged to place the thing defined in relation to other things. Then from the conjunction of the definitions of these things new properties result. For instance, if I regard the circumference of a circle by itself, I can only infer that it is everywhere alike or uniform, in which property it differs essentially from all other curves; I shall
never be able to infer any other properties. But if I place it in relation with other things, such as the radii drawn from the centre, two intersecting lines, or many others, I shall be able hence to deduce many properties; this seems to be in opposition to Prop. xvi. of your Ethics, almost the principal proposition of the first book of your treatise. For it is there assumed as known, that from the given definition of anything several properties can be deduced. This seems to me impossible, unless we bring the thing defined into relation with other things; and further, I am for this reason unable to see, how from any attribute regarded singly, for instance, infinite extension, a variety of bodies can result; if you think that this conclusion cannot be drawn from one attribute considered by itself, but from all taken together, I should like to be instructed by you on the point, and shown how it should be conceived.—Farewell, &c.
Paris, 23 June, 1676.
408:1 Tsehirnhausen.