Stony Brook University

The explanation for why these truths are not necessary truths is given somewhat later, in
response to Locke’s claim that real existence cannot provide us with any axioms:
One can always say that the proposition I exist is evident in the highest
degree, [being a proposition that is not known to be proven by any other] -
- indeed, that it is an immediate truth. . . . Still, there is some reason for
your not including this proposition among the axioms: it is a proposition
of fact, founded on immediate experience, and is not a necessary
proposition whose necessity is seen in the immediate agreement of ideas.
On the contrary, only God can see how these two terms, I and existence,
are connected—that is, why I exist. (NE 411) 21
This is why, then, that a demonstration beginning with truths of fact cannot be an a priori
necessary demonstration. This is because actual existence is contingent, analysis of facts
is interminable and their reason depends ultimately on God’s choice. Only truths of
reason can be demonstrated with a priori necessity, and they do not depend on God’s
choice. These two types of truth are indemonstrable, but in different ways. Primary truths
of reason are indemonstrable, because they depend on the intuitive immediacy of an
identity, while primary truths of fact are indemonstrable because they depend on the
intuitive immediacy of feeling. 22
To summarize the above formulations, we can say that necessary and contingent
propositions are distinguished by termination and possibility. Thus formally stated: a
proposition is necessarily true, if and only if the analysis of its terms results in an
identical proposition, that is, in a proposition whose contrary is impossible. A proposition
is contingently true, if and only if the analysis of its terms does not result in an identical
proposition, that is, a proposition whose contrary is possible. This may also be explained
in terms of possible worlds: ‘necessary’ means there is no possible world in which
propositions of the form ‘A is not A’ are true. Equally, ‘A is A’ is true in every possible
world. ‘Contingent’ means there is some possible world in which a proposition of the
form ‘A is B’ is true. For most purposes the distinction can be stated simply like this:
A truth is necessary if and only if its denial results in a contradiction.
A truth is contingent if and only if its denial does not result in a contradiction.
The main task for a demonstration, then, is to discover whether the terms of the
proposition can be reduced to an identity or contradiction.
d’un immediation de sentiment. Et c’est icy où a lieu la premiere verité des Cartesiens ou de St. Augustin:
Je pens donc je suis. C’est à dire, je suis une chose qui pense.”
21 "On peut toujours dire que cette Proposition, J'existe, est de la derniere evidence, êtant une proposition,
qui ne sauroit être prouvée par aucune autre, ou bien une verité immediate. . . . Cependent vous pouvés
exclure cette proposition du nombre des Axiomes avec quelque raison, car c'est une proposition de fait,
fondée sur une experience immediate, et ce n'est pas une proposition necessaire, dont on voye la necessité
dans la convenance immediate des idées. Au contraire, il n'y a que Dieu qui voye, comment ces deux
termes, Moi et l'existence, sont liez, c'est à dire pourquoi j'existe."
22 This last point will be especially important to keep in mind for next chapter’s discussion on the
demonstrability of moral principles.
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