The Probability Of Freedom: A Critique Of Spinoza’s Demonstration Of Necessity -- By: E. D. Roe
BSac 51:204 (Oct 1894) p. 641
The Probability Of Freedom: A Critique Of Spinoza’s Demonstration Of Necessity
I.— Fundamental And Requisite Positions Of Spinoza
FIRSTLY in this article will be examined some of the chief positions of Spinoza, which are fundamental, and requisite to the maintenance of his doctrine of necessity, or at least induced him thereto. The classification of these positions is not supposed to be logically mutually exclusive, as then, e. g., the first would include the second, the second the third, and similarly with others; but it has been adopted for the practical purpose of more clearly extending the refutation of demonstrated necessity, to divers aspects of its assumption by Spinoza, before giving the refutation of all such demonstrations in general.
§ 1. Mathematical form.—If necessity prevail, and be capable of proof, i.e., of being known by reason, it must be known either immediately, as being self-evident, as an axiom, or by being capable of being expressed in propositions whose validity is certified by this, that they are referred to, as, upon analysis, exemplifying instances of self-evident axioms. In other words, if there be a knowledge of necessity, the form of such knowledge must be that of self-evident cognition, or of logical deduction based upon self-evident cognition, or deductive knowledge. If it is desired to make practical employment of this conclusion of reason, so as to evolve a system of necessity for knowledge, it is necessary only to seek such a form, and inform it with a proper content. That is,
BSac 51:204 (Oct 1894) p. 642
we need seek none other than the form of mathematics, especially of pure, or ancient geometry, as contradistinguished from analytic, or modern geometry. Ancient geometry furnishes exactly such a form in its native and ideal purity. It comprises only definitions, and axioms, constructed by the subject, and these not arbitrarily, but according to reason, and propositions, and conclusions, which issue therefrom by deduction. All these cannot contain more than has been previously introduced into the definitions, and axioms. But they must contain as much, and, since the latter have been constructed by reason, and are in the subject, as general, the propositions must also be universal, and necessary to the same. Conversely, with a mathematical form, and proper content, we obtain necessity. In other words: Given, necessity; it must have been obtained by a mathematical form; or, given, a mathematical form, and necessity must be obtained. But this necessity of knowing, always depends upon the very definitions, and axioms, which have been constructed by the subject; they have been constructed by, and are in, the subject, else no universality could result for such a sub...
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