Leibniz's Law

Intro
Well Leibniz put forward a principal which finds great use in wide swathes of philosophy, especially in metaphysics, but that's not important right now.

Breakdown
It looks a bit like this: ' ∀ F ( Fx  ↔  Fy ) →  x = y . but for those of us who didn't take either symbolic logic or klingon, it would be better summarised as:" 'No two objects can share all their properties; so that if what appear to be two objects turn out to have all the same properties then they must be one object.' "This can still be a little confusing, for example, if you were confronted with two factory-made pens, which both had exactly the same measurements, took up identical amounts of space and had no differences in appearance, you would probably say that they were identical. However, they are composed of different atoms and take up different locations in space; they only way they could be identical is if they took up exactly the same space and used exactly the same atoms, but then they would be the same object.

Masked Man Fallacy
The fallacy surfaces when one makes an incorrect usage of Leibniz's Law. For our purposes, it is used to disprove the indivisibility argument. If two things have different properties, then they can't be the same thing, but if you don't know that they have the same properties, then that leads to an incorrect application of the Law.

For example: Even if you have reached the conclusion logically, the premises may be true and the conclusion false if the person speaking is unaware of Max's murderous moonlighting. Therefore the argument is a fallacious one.
 * I know who Max is.
 * I do not know who the Axe Murderer is.
 * Therefore Max is not the Axe Murderer.

A different example: (I've been binge-watching Daredevil lately, no spoilers please).
 * Foggy Nelson believes that The Devil of Hell's Kitchen can perform intense acrobatics
 * Foggy Nelson does not believe that Matthew Murdock can perform intense acrobatics
 * Therefore, Matthew Murdock cannot be The Devil of Hell's Kitchen

In Symbolic Form Overall, just because you don't think two things are connected, doesn't mean that they are.
 * I know who X is
 * I don't know who Y is
 * Therefore X is not Y

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