Free A Short History of Modern Philosophy: From Descartes to Wittgenstein, Second Edition by Unknown Author Page B

above preoccupation with our own limited experience and mentality, and learn to see things from the impartial point of view of the rational observer to whom things appear ‘under the aspect of eternity’ (sub specie aeternitatis).
    The geometrical method
    Spinoza took as his model of objective rational enquiry the geometry of Euclid. This, he believed, began from axioms, the truth of which could be seen to be necessary, and from definitions which clarified the concepts used to formulate them. Furthermore it advanced by indubitable logical steps to theorems which, by virtue of the deductive method, must be as certain and free from error as the axioms from which they were derived. In setting up the geometrical method as his philosophical ideal, Spinoza expressly laid aside ordinary conceptions and everyday language. He argued that his definitions were not arbitrary plays on words, but the instruments whereby certain antecedent ideas may be formulated in a language more precise than that made available by the vernacular.
    One of the few works published in his lifetime was The Principles of Cartesian Philosophy (1663), in which he tried to lay down all the fundamental axioms to which Descartes’ metaphysics could be reduced, and then to deduce from those axioms the actual content of Descartes’ philosophy. The work is a brilliant summary, and of great interest in being written from outside the artificial standpoint of Descartes’ Meditations, in which metaphysical doubt is cured only by the invocation of a highly specific contingent premise. But the principal exemplification of Spinoza’s geometric method is in the Ethics, where Spinoza’s own philosophy is set out in axiomatic form. Beginning from what he took to be correct definitions of notions indispensable to the description of reality, Spinoza attempted to prove not only propositions of a metaphysical system as ambitious as any since Plato, but also the precepts of rational conduct and the description of our moral and emotional nature. His system moves with equal geometrical rigour towards the proposition that ‘a substance is prior in nature to its modifications’ and towards the proposition that ‘there cannot be too much merriment, but it is always good; but on the other hand melancholy is always bad.’ (The proof of this second proposition involves, when traced back to original axioms, something like a hundred separate steps; it looks less inaccessible to rational thought when placed beside Spinoza’s view that merriment can be ‘more easily conceived than observed’.)
    Substance
    The Cartesian notion of substance, appealing though it was on logical, scientific and metaphysical grounds, gave rise to problems that steadily increased in significance as their depth was perceived. What is the relation between substance construed as individual and substance construed as matter or stuff? How many substances are there? How, if at all, can we explain their interaction? If they can sustain themselves in existence, why do we need an explanation of their origin? Descartes and the Cartesians gave various answers to those questions, none of them felt to be satisfactory. Spinoza was quick to observe that the concept of substance is, nevertheless, the cornerstone of Cartesian metaphysics. Hence each of those questions must be answered unequivocally and consistently if the metaphysical structure is to stand up to philosophical examination. If metaphysics collapses, then, Spinoza believed (and in this he was at one with all rationalist thinkers), so does the possibility of science.
    In the Principles Descartes had touched on the problems posed by the concept of substance and made a distinction between the ‘principal attribute’ of a substance (the attribute which constitutes its nature, as extension is the nature of physical things and thought the nature of mind) and its ‘modifications’ or ‘modes’—the properties in respect of which it can change without ceasing