Our reasonings are grounded upon two great principles, that of contradiction, in virtue of which we judge false that which involves a contradiction, and true that which is opposed or contradictory to the false.
Gottfried LeibnizI also readily admit that there are animals, taken in the ordinary sense, that are incomparably larger than those we know of, and I have sometimes said in jest that there might be a system like ours which is the pocketwatch of some enormous giant.
Gottfried LeibnizGod, possessing supreme and infinite wisdom, acts in the most perfect manner, not only metaphysically, but also morally speaking, and ... with respect to ourselves, we can say that the more enlightened and informed we are about God's works, the more we will be disposed to find them excellent and in complete conformity with what we might have desired.
Gottfried LeibnizThe larger the mass of collected things, the less will be their usefulness. Therefore, one should not only strive to assemble new goods from everywhere, but one must endeavor to put in the right order those that one already possesses.
Gottfried LeibnizThere are also two kinds of truths, those of reasoning and those of fact. Truths of reasoning are necessary and their opposite is impossible, and those of fact are contingent and their opposite is possible. When a truth is necessary its reason can be found by analysis, resolving it into more simple ideas and truths until we reach those which are primitive.
Gottfried LeibnizWhen a truth is necessary, the reason for it can be found by analysis, that is, by resolving it into simpler ideas and truths until the primary ones are reached. It is this way that in mathematics speculative theorems and practical canons are reduced by analysis to definitions, axioms and postulates.
Gottfried Leibniz