Notes and comments on Leibniz's Contigency Florian Millo* Abstract Contigency is a definition for which is noted for not having the principle of contradiction in itself, for which gives a different truths from what we are used to derive from geometry as an essential field for knowledge of creating strong logics. Leibniz clearly states one of his ideas for God, and why there must be contigent truths and necessary truths. *florian.millo@u-psud.fr Universite Paris-Saclay, Department of Physics 1 The Argument Contigency was first thought from Aristotle as he states on Physics that there should be a first principe for Universe to exists. This is also noted as Cosmological Argument in nowadays language. Aristotle was not the first to question this, before and after him, this question was always a problem of first reason, or first principle. In natural theology, we have seen the strong logics of Thomas Aquinas, his definitions of omni-things. As he always wanted to explain by his thesis that everything is strongly related from cause, essence, becoming. This argument for which we will explain later in paragraphs comes in a form of proving that contigent truths exists and is related to PSR principle of sufficient reason. In this article Leibniz is trying to defend Parmenides inference that, nothing comes from nothing, ex nihilo nihil fit. 2 Notions and logics First in this article we see a strongly statement of Leibniz that, God is a necessary being, as for which one with a capacity of logics and knowledge of metaphysics, one can say that, for all ends to exists, there must be a metaphysical premise. In one way telling that everything has a beginning must have a metaphysical reason. As for contigency, Creature are contigent, meaning, their existence does not follow from their essence. Necessary truths are those that can be demonstrated through an analysis of terms, so that in the end they become identities. We can understand this logic clearly, that if we take apart all problems of a problem, by deduction, we would go to identities. He clearly states that necessary truths depends upon principle of contradiction, for which, there would be no way we could reach identites. Par contrary, contigent truths cannot be reduced to this principle, because logically, all truths would be necessary. There must be a common language or notion between contigent existence and of essential truths. We must deeply think what is the reason governing all, why we must have a metaphysical principle to explain other physical principles. A meaningful statement of Leibniz, that says, every true affirmative proposition, either necessary or contigent, has some connection between subject and predicate. In identites this connection is obvious and self-evident, in other propositions it must appear through an analysis of terms. This can only be understood clearly for those who studied geometry, as for necessity truths, from axioms we would go to an identity equation that expresses the rigorosity of our train of thought. Otherwise, if we do not go to this equation, we will diverge, and ergo contigency will arise. Leibniz is trying to prove that we have to start from a strong principle, for explaining all, nothing exists without there being a greater reason for it to exist than or it not to exist, meaning, an incontestable, axiomatical truth. In a way he is merging the religionist view of omnisciencia with Aristotle's thesis that there is a first principle or are some 'first' principles for nature to exist. Therefore, we must know truths of contigent things a posteriori, meaning knowledge of thing and their truths from experience. And by dictating the PSR, one now can say that the proposition that has the greater reason for existing is necessary. 1 As for Leibniz, a necessary truth to derive all truths must be that, God always acts with the hightest wisdom. Then, definitions of necessary truths must rise now. What is chosen from God does not mean that is necessary, that he chose the best, or that the best is necessary. Further, Leibniz introduces these definitions, he explains the distinction between necessity of the consequence [necessitas consequentiae] and necessity of consequent [necessitas consequentis]. God now becomes the proposition that is a necessity of consequence not of consequence. Since he is saying this, he deduces that, only God must or have the highest wisdom for which is the primary reason for all to happen. 3 A simple proof Proposition: The part is less than the whole. Leibniz defends this statement with identities. By defining less as not as much as the other thing, and defining much as a observable quantity. Proof: The part is equal to a part of the whole, and what is equal to a part of a whole is less than the whole, therefore the part is less than the whole. In this method, for which Leibniz is not the first deriving, Aristotle based upon this logic made syllogisms, a deduction method base upon principle of identities. Leibniz is trying to say by this simple proof, that analysis of notions made in accordance of PSR is a method to find primary truths, and then after we can see that primary truths may or may not be contigent or neccesary. Acknowledgement I thank Prof. Rofer Ariew and Prof. Daniel Garber for a translation that is very handful and understandable, for which is a good source for me on studying the philosophy of Leibniz and oberving the method . References [1] Philosophical Essays. Translation by Roger Ariew and Daniel Garber [2] Image Other Works: [3] A brief explanation of Kant's Enlightenment article Florian Millo [4] Observation of high-energy astrophysical neutrinos in three years of IceCube Data Florian Millo [5] High Velocity Cloud Analysis in HI4PI Data Florian Millo [6] γ − β Spectrometry of 207 Bi Florian Millo