Leibniz writes in Monadology that his Principles of Contradiction and Sufficient Reason are the basis of the theories found within the work. While the principles alone may be said to be rudimentary, one may find that, together with the Principle of the Best, the Principle of the Predicate in the Notion, the Principle of the Complete Concept and the Principle of the Identity of Indiscernibles, the group of axioms cement a highly convincing argument. The Principle of Contradiction states that a proposition cannot be true and false at the same time. Truths can be understood as propositions in which the predicate is contained in the subject. Primary truths are more easily understood in this regard, since these truths are identities in which the predicate is not simply contained in the subject, but is itself explicitly identical to the subject (and vice versa): A = A. These sentences do not require proof because their negations (A is not A) create contradictions. However, Leibniz introduces the principle of the predicate into the notion to postulate that in every true affirmative propositional sentence the notion of the predicate is somehow contained in that of the subject. The combination of these two principles demonstrates that all affirmative propositional statements can be reduced to primary truths by resolving the notions on both sides into the simplest ideas - in the same way that a mathematician reduces theorems into definitions, axioms, postulates, and finally , simple ideas, of which definitions cannot be given (AW, 278). However, the above example concerns truths of reasoning (which are necessary), but other propositions can be labeled as truths of fact or contingent truths: these are truths whose opposites are plausibly possible. Yet even these truths, which refer to... the center of the paper... to movement, are not things but phenomena of the perceiver. Bodily substances follow efficient causes, that is, the laws of motion, but act in perfect conformity with the monads and the rest of the world. Thus monads are tied to a body in which they reside or to which they perceive themselves to be attached. Each monad is therefore a window created by God through which it can perceive the world from another perspective, and each monad and group of monads acts according to sufficient reason in its continuous change as its complete concept unfolds. Although Leibniz, in his Monadology, does not depend on logical principles that seem quite obvious, the Law of Contradiction and the Principle of Sufficient Reason, in coalition with other logical axioms, ensure that the philosopher's metaphysical, ontological and epistemological theories are cohesive, coherent and explain fully.
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