GAMES ITERATION NUMBERS

Is it possible to conceive two perfectly identical objects Is identity even possible withoutindividuality How would a perfectly symmetrical universe be The current philosophical debate on identity and in particular on the necessity of the Leibniz39s principle of the identity of indiscernibles is complex and multifaceted Recent works have indicated that the problem becomes increasingly complex if we apply it to mathematical objects Is it possible to speak of ‘identity’ for numbers How can we identify numbersDrawing on philosophical accounts on identity and individuality in contemporary metaphysics analytic and continental this book explores a new path The author argues that an identity without individuality is possible By means of a critique of the idea of the identity of indiscernibles the book formulates the concept of 39manifold identity39 through the concept of 39iteration39 Iteration is a specific transgression of the identity of indiscernibles arising from the collision of two forms of identity qualitative identity and numerical identity Nonetheless a pair of perfectly identical objects is still a paradox a contradictionThe first thesis of the book is that iteration is a paraconsistent and dialethetical logical structure which allows for true contradiction The author applies recent works in nonstandard logic and dialetheism Priest Routley Berto to illustrate how we can make sense of the idea that objects can be perfectly identical but discernibleThe second thesis of the book is that iteration is the basis of enumerability and computability A 39computable object39 is an object constructed on the basis of an iterative logic It is possible to reinterpret all the primary concepts of computability theory through the logic of iteration