Plan Autonómico de Vivienda de la Comunidad Valenciana 2009-2012

icate, which is his successful enterprise, he would bring us to see in fact that the future dictatorship of Caesar had its basis in his concept or nature, so that one would see there a reason why he resolved to cross the Rubicon rather than to stop, and why he gained instead of losing the day at Pharsalus, and that it was reasonable and by consequence assured that this would occur, but one would not prove that it was necessary in itself, nor that the contrary implied a contradiction, almost in the same way in which it is reasonable and assured that God will always do what is best although that which is less perfect is not thereby implied. For it would be found that this demonstration of this predicate as belonging to Caesar is not as absolute as are those of numbers or of geometry, but this predicate presupposes a sequence of things which God has shown by his free will. This sequence is based on the first free decree of God which was to do always that which is the most perfect and upon the decree which God made following the first one, regarding human nature, which is that men should always do, although freely, that which appears to be the best. Now every truth which is founded upon this kind of decree is contingent, although certain, for the decrees of God do not change the possibilities of things and, as I have already said, although God assuredly chooses the best, this does not prevent that which is less perfect from being possible in itself. Although it will never happen, it is not its impossibility but its imperfection which causes him to reject it. But nothing is necessitated whose opposite is possible. One will then be in a po- sition to satisfy these kinds of difficulties, however great they may appear (and in fact they have not been less vexing to all other thinkers who have ever treated this matter), provided that he considers well that all contingent propositions have reasons why they are thus, rather than otherwise, or indeed (what is the same thing) that they have proof a prion of their truth, which render them certain and show that the connection of the subject and the predicate in these propositions has its basis in the nature of the one and of the other, but he must further remember that such contingent propositions have not the demonstra- tions of necessity, since their reasons are founded only on the principle of con- tingency or of the existence of things, that is to say, upon that which is, or which appears to be the best among several things equally possible. Necessary truths, on the other hand, are founded upon the principle of contradiction, and upon the possibility or impossibility of the essences themselves, without regard here to the free will of God or of creatures.

(Foucher de Careil, Nouvelles lettres et opuscules, p. 179; Loemker, pp. 263- 64.; Ariew & Garber, p. 95; "On Freedom" [ca. 1689?].) Having thus recognized the contingency of things, I raised the further questions of a clear concept of truth, for I had a reasonable hope of throwing some light from this upon the problem of distinguishing necessary from contingent truths. For I saw that in every true affirmative proposition, whether universal or singular, necessary or contingent, the predicate inheres in the subject or that the concept of the pred- icate is in some way involved in the concept of the subject. I saw too that this is the principle of infallibility for him who knows everything a priori. But this very fact seemed to increase the difficulty, for, if at any particular time the concept of the predicate inheres in the concept of the subject, how can the predicate ever be denied of the subject without contradiction and impossibility, or without destroying the subject concept? A new and unexpected light arose at last, however, where I least expected it, namely, from mathematical consid- erations of the nature of the infinite.

(Foucher de Careil, Nouvelles lettres et opuscules, p. 180; Loemker, pp. 264- 65; Ariew & Garber, p. 96; "On Freedom" [1689?].) Some immediate truths can be reduced to primary truths <by a finite process of analysis>; the others can be reduced in an infinite progression. The former are necessary; the latter, con- tingent. A necessary proposition is one whose contrary implies a contradiction; such are all identities and all derivative truths reducible to identities. To this genus belong the truths said to be of metaphysical or geometrical necessity. For to demonstrate is merely, by an analysis of the terms of a proposition and the substitution of the definition or a part of it, for the thing defined, to show a kind of equation or coincidence of predicate and subject in a reciprocal prop- osition, or, in other cases, at least an inclusion of the one in the other, so that what was concealed in the proposition or was contained in it only potentially, is rendered evident or explicit by demonstration. . . . In contingent truths, how- ever, though the predicate inheres in the subject, we can never demonstrate this, nor can the proposition ever be reduced to an equation or an identity, but the analysis proceeds to infinity, only God being able to see, not the end of the analysis indeed, since there is no end, but the nexus of terms or the inclusion of the predicate in the subject, since he sees everything which is in the series. Indeed, this truth itself arises in part from his intellect and in part from his will and so expresses his infinite perfection and the harmony of the entire series of things, each in its own particular way.

(Couturat, Opuscules, p. 19; "Necessary and Contingent Truths" [ca. 1686].) Thus, even if one could know the entire series of the universe [tota series univ-

er si) one could not give its sufficient reason unless a comparison has been made

of it with all other possibilities. Whence it becomes clear why no demonstra- tion can be found for a contingent proposition, no matter how far the resolution of concepts is continued.

C O M M E N T A R Y

Contingent truths on the order of "Leibniz wrote section 36 of the Monad- ology with a quill pen" involve an infinitistic resolution into particular causes, regardless of whether we look to causes in the order of physical causation (of efficient causes or motions) or in the order of psychic causation (final causes or reasons).

Contingent truths too—"Caesar crossed the Rubicon," for example—are ac- cordingly also "analytic," albeit in their own (infinitistic) way. For there will always be a line of reasoning to establish how it is better that things are arranged as is rather than otherwise. But any such explanation, which requires discern- ing the whole interrelated complexity of endless detail regarding the arrange- ment of things in this world and comparing this with possible alternatives, is always a reasoning of literally unending (i.e., infinite) ramifications that can be carried through by God alone.

Leibniz connects the infinite analysis of contingent truths with the "endless detail" of the world and the "ad infinitum division" of all bodies in nature. (Note that sec. 65 tells us that "each bit of matter is not merely infinitely di- visible, but is even actually endlessly subdivided.") Explaining why any of the world's facts are as they are involves showing how this is for the best with

everything taken into account—that is, with all its involvement with every-