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57 ~ JOURNAL OF THE HISTORY OF PHILOSOPHY 2~:4 OCT ~983 Michael E. Hobart. Science and Religion in the Thought of Nicolas Malebranche. Chapel Hill: The University of North Carolina Press, 1982. Pp. x + 195. $19.95. Hobart's excellent book is more than a study of Malebranche. It must be read by everyone interested in the development of modern philosophy and science. For what Hobart shows isjust how the model of mathematics or number replaced the model of substance in our understanding of infinity, necessity, and being, in effect, how reason and science replaced faith and religion in the modern world. It is not that our mathematical view of the universe does not rest on assumptions; it is that we need no longer include among these the assumption that there is a God. Descartes and Malebranche (and Pascal, whose peevish ghost hovers throughout the study but who appears in person only in the last line) used the principle of cardinal correlation to isolate discrete elements for clear and distinct perception, and the principle of ordinal recurrence to stress unity and continuity. Their explicit shift was from the ontological essence of substances to the epistemological relations among them. Rather than investigating sensible modifications to classify different material substances, they set forth the quantitative relations among differently figured and moving parts of material substance as such. In their metaphysics they used not the Scholastic logic of terms describing the qualitative powers of substantial entities, but the emerging mathematical logic of propositions stating recurrent relations among anonymous variables. The most important notion in this move from substance to relations is that of mathematical induction. This is the major assumption of recurrence: "Whenever a relation is true for any number of a series n, and is shown to be true as well for its successor, n + l, it may be said to hold true for any number in the series whatsoever because of the mind's ability to conceive the indefinite repetition of the mental act once the act has been proven possible. Once the relation is demonstrated for n and n + l, n + I simply becomes the new n and the proof can be restated ad infinitum" (p. 21). Thus "natural, mathematical order of increasing magnitude.., is everywhere dense. Between terms an infinite number of other terms can be interpolated and any series of terms may be extrapolated infinitely." In this way the human mind can conceive of infinity. This is not yet comprehending infinity, but it is vastly more satisfactory to reason than the notion of an infinite substantial immensity that defies understanding. Necessity is also intelligible in mathematical terms as following from relations of equality and inequality among propositions. Then one can see how the internal relations among propositions can be necessary whether or not they are exemplified by anything in the phenomenal world. The notion of a correspondence theory of truth, with experiments to check to see if the world fits one's hypothetical descriptions, thus is an obvious development of applying the mathematical method in science. Finally, there is a transformation in the concept of being itself. On the model of substance, being is all that there is, and ultimately this is God. The trouble with this is that it leads to Spinozistic pantheism. What Descartes and Malebranche never quite completely substitute for substance is a new notion of being based on the model of number. What Hobart is recognizing by talking of the "model of number" rather BOOK REVIEWS 57 ~ than the "model of mathematics" is that what is being hypostatized is a "pure" set of relations with no content. Both abstract mathematical entities and concrete phenomenal entities provide different possible exemplifications or contents for these relations. Thus it is wrong to say that for Descartes and Malebranche intelligible extension just is the set of axioms and rules of solid Euclidean geometry. Instead, there is "in being" a set of pure and necessary relations that can be expressed in discursive terms, algebraic terms, geometric terms, and by material objects, all of which can be exemplifications of or the content of these relations. The being of the model of number, then, is a set of pure (empty) relations...


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