IDENTITY OF INDISCERNIBLES.pptx, a phlosphical outlook

Philosophy presentation

1. IDENTITY OF INDISCERNIBLES

2. Gottfried Leibniz The identity is a part of a collective of principles under Leibniz’s laws He was a polymath active as a mathematician, philosopher and diplomat Primarily known for co inventing calculus, he is one of the most prominent figures in the history of mathematics

3. Definition If two objects have the same properties, then they are identical x=y→∀F( Fx ↔ Fy ) [x and y are identical if and only if both x and y have the same property F] In another way, any two objects with different properties are non identical

4. Note that the object, in all possible worlds, is identical with itself i.e. x=x. Whatever is true of x will be true of x, whatever is possibly true of x will always be possibly true of x and in all possible worlds, x will always be x. If x = y, whatever is true for x will always be true of y.

5. Argument Take for example: I could survive the destruction of my body. My body could not survive the destruction of my body. In conclusion, I am not identical to my body. This is a valid argument, because the premise is logically conceivable. LOGIC Let X be could survive the destruction of the body y be a name for myself z be a name for my body Xy ~ Xz ⊢ ~ (y = z) Xy is not identical to Xz proves that y is not equal to z

6. Second argument Consider a statue made of a lump of clay. We say that, since the stature of the statue is identical to the lump of clay, there is only one object. >But consider the following argument: The lump of clay could survive being squashed. The statue could not survive being squashed. Therefore the lump of clay is not identical to the statue. LOGIC Let X be surviving the squashing y be the lump of clay z be the statue Xy ~ Xz ⊢ ~ (y = z) Xy is not identical to Xz proves that y is not equal to z