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Essay / Analysis of Necessary and Infinite Truths - 1803
Leibniz's account of contingency changes the approach we have to the truth of analytical theory. He designs a method for distinguishing the role of necessity and contingency in truth conditions. In Necessary and Contingent Truths, Leibniz draws on mathematics to examine the dichotomy between the finite demonstrability of necessary truths and the infinite demonstrability of contingent truths. Therefore, Leibniz denies the principle of analytical demonstrability according to which a proposition is analytical if it is demonstrable. Indeed, contingent and necessary truths are analytic, but the former cannot be demonstrated while the latter can by virtue of the theory of infinite analysis. The truth of contingent propositions can only be expounded by the vision of the mind of God, while necessary assertions are always proven true regardless of the case. The meaning that Leibniz attributes to contingency is the negation of a contradiction if the contrary case turns out to be true, but this neglects the possibility that it could have been otherwise. This argument therefore seems to limit the meaning of contingency. In addition to this, Leibniz supports the claim that all necessary truths can be demonstrated within a finite series of steps. It does not allow infinite, non-recurring decimal numbers, like cake, to be necessary truths because of the infinite process of steps involved in the proof. The essay will also emphasize the function of Leibniz's account in the possible global context. Finally, it will assess the extent to which contingent truths can be correctly distinguished from necessity. The analysis of infinite series in mathematical propositions is Leibniz's source of inspiration for the acc...... middle of article ......lanation for contingency. Why should we not conclude that some necessary truths are provable and others are not? This new approach to this question would avoid making the distinction between necessity and contingency. Objections raised against Leibniz's argument draw attention to non-recurring infinite decimals and approximations like pi or √2 (square root of 2), in order to show that not all finite propositions are necessary, but that some Necessary truths also rely on infinite proof. . The second objection to this view concerns the notion of possible worlds. A possible world can also exist on its own, and not just in relation to God's decrees. If necessary truths hold in many different contexts, contingency allows different worlds to exist independently of God's will. In conclusion, no satisfactory explanation has been given to the notion of contingency.