Version: v1, Published online: 1998
Retrieved January 23, 2019, from https://www.rep.routledge.com/articles/biographical/leibniz-gottfried-wilhelm-1646-1716/v-1
9. Epistemology: knowledge and probability
In a famous passage of the Monadology (§§31–2) Leibniz writes: ‘Our reasonings are based on two great principles, that of contradiction, in virtue of which we judge that which involves a contradiction to be false, and that which is opposed or contradictory to the false to be true, and that of sufficient reason, by virtue of which we consider that we can find no true or existent fact, no true assertion, without there being a sufficient reason why it is thus and not otherwise’. These two principles correspond to two different kinds of truths, ‘those of reasoning and those of fact’ Monadology §33).
A truth of reason can be known with certainty by a finite demonstration consisting of a finite number of steps containing simple ideas, definitions, axioms and postulates; these truths are necessary and can be known a priori. Sensation can give us particular instances of these truths, but can never attain the kind of universality one finds in necessary truths. As Leibniz wrote in the preface to the New Essays: ‘necessary truths, such as we find in pure mathematics and particularly in arithmetic and geometry, must have principles whose proof does not depend on instances nor, consequently, on the testimony of the senses, even though without the senses it would never occur to us to think of them’.
While Leibniz agreed with Descartes that such truths are innate, he distanced himself from Descartes’ appeal to clear and distinct perception. Against those who appeal to Descartes’ axiom that ‘whatever I clearly and distinctly perceive about a thing is true or is assertable of the thing in question’, Leibniz objected that ‘this axiom is useless unless we use criteria for the clear and distinct, criteria which we have made explicit’ (Meditations [1684a] 1989: 26–7). While Leibniz agreed with Descartes that we have an innate capacity to recognize these innate truths, as a practical matter, he preferred to constrain the mind by formal rules of logic, unlike Descartes, who rejected formal logic (see §10 below).
Since in all predications, the concept of the predicate is contained in the concept of the subject, all knowledge is in principle a priori; if we only had sufficient knowledge of the subject, we could see everything that is true of it, contained in its complete concept. But this is only possible for God. Humans, incapable of performing the analysis that will reveal the truth a priori must make appeal to the senses in order to discover truths of fact. In fact, Leibniz thought, ‘we are all mere Empirics in three fourths of our actions’ (Monadology §28).
Because of the importance of empirical knowledge, Leibniz called for a genuine logic of probability. The modern theory of probability was born in the 1650s with the correspondence between Pascal and Fermat, and then with Christiaan Huygens’ little treatise, Tractus de ratiociniis in aleae ludo (Treatise on reasoning in games of chance) (1657). The theory very quickly developed in the seventeenth century, as new practical applications were quickly found. But Leibniz was not satisfied that it had yet been applied to the most general question of all, the kind of reasoning we do about matters of fact on the basis of sensation when demonstration is impossible. And so, in the New Essays (IV.2.14) he called for a new science: ‘I maintain that the study of the degrees of probability would be very valuable and is still lacking, and that this is a serious shortcoming in our treatises on logic. For when one cannot absolutely settle a question one could still establish the degree of likelihood on the evidence, and so one can judge rationally which side is the most plausible.…I suspect that the establishment of an art of estimating likelihoods would be more useful than a good proportion of our demonstrative sciences, and I have more than once contemplated it’. But even though Leibniz may have contemplated it, he himself never made a serious attempt to develop the logic of probability that he called for here. However, his call was heard by David Hume, who saw his Treatise as, in part, answering Leibniz’s challenge.
Garber, Daniel. Epistemology: knowledge and probability. Leibniz, Gottfried Wilhelm (1646–1716), 1998, doi:10.4324/9780415249126-DA052-1. Routledge Encyclopedia of Philosophy, Taylor and Francis, https://www.rep.routledge.com/articles/biographical/leibniz-gottfried-wilhelm-1646-1716/v-1/sections/epistemology-knowledge-and-probability.
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