Routledge History of Philosophy Volume IV

260 RENAISSANCE AND SEVENTEENTH-CENTURY RATIONALISM
That this is Spinoza’s view of the geometrical method is confirmed by his use
of definitions in the Ethics. 31 These definitions are usually stated in the form,
‘By…I understand…’; and this raises a problem. Spinoza is in effect saying that
he proposes to take a term in such and such a way. Such definitions seem to be
of the kind that is commonly called ‘stipulative’, and it is now usually held that
(in the words of a modern textbook of logic) ‘a stipulative definition is neither
true nor false, but should be regarded as a proposal or resolution to use the
definiendum to mean what is meant by the definiens, or as a request or
command’. 32 Given that that is so, one may ask why one should accept Spinoza’s
definitions. Why should we use words in the way that he tacitly requests or
commands? Why play one particular language game, rather than another?
To answer this question, it will be useful to consider first what Spinoza is
excluding when he states his definitions. The terms that he defines are not words
that he has invented; he uses terms that others had used, but he often uses them in
a new way. So when he says something of the form ‘By…I understand…’, he is
often excluding what some, and perhaps most, philosophers understood by the
term defined. His reason for rejecting such definitions, and for defining terms in
the way that he does, is made clear in the course of the definitions of the
emotions in Part III of the Ethics. Here, Spinoza says that ‘It is my purpose to
explain, not the meanings of words, but the nature of things.’ 33 What he is doing
when he defines terms has a parallel in the practice of scientists, who sometimes
coin completely new terms and sometimes use old terms in a new way—as when
a scientist uses the word Velocity’ to mean, not just speed, but speed in a certain
direction. 34
Definitions form an integral part of the geometrical method, so what has just
been said confirms the view suggested earlier: namely, that Spinoza uses the
geometrical method not just to establish truths, but also to explain, to achieve
understanding. This point will meet us again when we consider the distinctive
way in which Spinoza uses the terms ‘true’ and ‘false’ (see pp. 296–7). At
present, however, there is a further question to be raised. The idea that deductive
reasoning can be used to provide explanations was by no means new with
Spinoza, or indeed in the seventeenth century in general; on the contrary, it can
be traced back as far as Aristotle. In the Posterior Analytics (I 13, 78 a38–b3)
Aristotle explains the fact that all planets shine steadily by presenting it as the
conclusion of a deductive, or more precisely a syllogistic, argument. 35 This raises
the question why Spinoza should have chosen to present his explanatory system
in geometrical, rather than in syllogistic, form. The answer must surely be that he
was influenced by the new science of his time. For this science, mathematics was
the key to the understanding of nature. So, for example, Descartes had declared
in his Principles of Philosophy (Pt II, 64; CSM i, 247) that the only principles
that he required in physics were those of geometry and pure mathematics; to this
one may add Spinoza’s observation, made in the Appendix to Part I of the Ethics
(G i, 79), that truth might have lain hidden from the human race through all eternity
had it not been for mathematics. As to the possibility of an explanatory system