On the Indemonstrability of the Principle of Contradiction

In this thesis I examine three models of justification for the epistemic authority of the principle of contradiction. Aristotle has deemed the principle that the same attribute cannot at the same time belong and not belong to the same subject and in the same respect the most certain and most prior of all principles, both in the order of nature and in the order of knowledge, and as such it is indemonstrable. The principle of contradiction is involved in any act of rational discourse, and to deny it would be to reduce ourselves to a vegetative state, being incapable of uttering anything with meaning. The way we reach the principle of contradiction is by intuitive grasping (epagoge) from the experience of the particulars, by recognizing the universals in the particulars encountered, and it is different from simple induction, which, in Mill\u27s view, is the process through which we construct a general statement on the basis of a limited sample of observed particulars. Hence, the principle of contradiction, being a mere generalization from experience, through induction, loses its certainty and necessity. Even though it has a high degree of confirmation from experience, it is in principle possible to come across a counter-example which would refute it. Mill\u27s account opens the path to the modern view of the principle of contradiction. In Principia Mathematica, Russell and Whitehead contend that the principle of contradiction is still a tautology, always true, but it is derived from other propositions, set forth as axioms. Its formulation, ~ (p & ~p) is quite different from Aristotle\u27s, and this is why we are faced with the bizarre situation of being able to derive the law of contradiction in a formal system which could not have been built without the very principle of which the law is an expression of. This is perhaps because the principle of contradiction, as a principle, has a much larger range of application and is consequently more fundamental than what we call today the law of contradiction, with its formal function