The affirmation, then, of a predicate expresses the relation of identity, and this is why, when this identity does not exist with respect to the predicate in the abstract, it is expressed in the concrete, in order that something involving identity may enter into it. The wall is whiteness: this proposition is false, because it affirms an identity which does not exist; the wall is white: this proposition is true, because white means something which has whiteness, and the wall is really something which has whiteness; here, then, is the identity which the proposition affirms.[18]
17. The predicate is, then, in every affirmative proposition, identified with the subject. When we perceive, therefore, we affirm the identity. Judgment, then, is the perception of the identity. We do not, however, deny that in what we call assent there is often something more than the simple perception of identity; but we do not understand how we need any thing more than to see it evidently in order to assent to it. What we call assent, adhesion of the understanding, seems to be a kind of metaphor, as if the understanding would adhere, would yield itself to the truth, if it were presented; but in reality we very much doubt if, with respect to what is evident, there be any thing but perception of the identity.
18. Hence it follows, that if the same ideas were to correspond in the very same manner to the same words, the opposition and diversity of judgments in different understandings would be impossible. When, then, this diversity or opposition does exist, there is always a discrepancy in the ideas.
19. We conceive of things, and reason upon them abstracted from their existence or non-existence; or we even suppose them not to exist, that is, conceive of relations between predicates and subjects without the existence of either predicates or subjects. And as all contingent beings may either be or cease to be, and even the first moment of their being be designated, it follows that science, or the knowledge of the nature and relations of beings, founded upon certain and evident principles, has nothing contingent for its object inasmuch as it exists. There is, then, an infinite world of truths beyond contingent reality.
We conclude, from our reflections upon this, that there must be beyond the contingent world a necessary being in which may be founded that necessary truth which is the object of science. Science cannot have nothing for its object; but contingent beings, if we abstract their existence, are pure nothing. There can be no essence, no properties, no relations in what is pure nothing; something therefore is necessary whereon to base the necessary truth of those natures, properties, and relations which the understanding conceives of in contingent beings themselves. There is, then, a God; and to deny him, is to make science a pure illusion. The unity of human reason furnishes us one proof of this truth; the necessity of human science furnishes a second, and confirms the first.[19]
20. We find a conditional proposition involved in every necessary proposition, wherein substantive being is not affirmed nor denied, but the relative, as in this; all the diameters of a circle are equal. Thus, the one we have just cited is equivalent to this one; if there exists a circle all its diameters are equal. For in reality did no circle exist, there would be no diameters, no equality, or any thing else; nothing can have no properties; wherefore in all that is thus affirmed we must understand the condition of its existence.
21. In general propositions the union conceived of two objects is affirmed; but we must take good care to notice that although we are wont to say that what is affirmed is the union of two ideas; this is not, therefore, perfectly exact. When we assert that all the diameters of a circle are equal, we do not mean that this is so only in ideas, that we conceive it so to be, but that it really is so, beyond our own understanding and in reality, and this abstracting our ideas and even our own existence. Our understanding sees then a relation, a union of the objects; and it affirms that whenever these exist, there will also really exist the union, provided the conditions under which the object is conceived be fulfilled.