I'm trying to gain a non-trivial understanding of the Law of Identity, in Logic -- what it MEANS.
Is the emphasis in "Daniel equals Daniel" on the "equals", or on the two "Daniels" on separate sides of the equation. Does this law entail, for example, that if I cloned myself, I would be equal to my clone? Certainly at least in one way we are not equal - in that we take up a different area of space.
If, on the other hand, it just means I am equal to myself, then why place two "Daniels" on separate sides of an equation - like the clones, they take up different space (on the page). What then is the usefulness of this law? When is it used and what does it accomplish? What does it mean for something to equal something else? And why are dialectical, continental philosophers - those heretics with the platitudinous, lazy thoughts - always trying to chip away at the iron armor of this law that seems so obvious as to need no defense?
Finally, what would fall if this law fell?
The Law of Identity states that each object is identical to itself -- hard to deny. "Daniel is identical to Daniel" is a particular instance of that Law. Your clone is not identical to you: if you and your clone we're alone in a room and we counted the number of objects in the room, we'd get two , not one. "Daniel is identical to Daniel" does not express that the word to the left of "is identical to" is the same word as the word to the right of it: it expresses that the object the first word refers to is the same as the object the second one refers to. This can be made plainer by considering, for instance, this claim: "Daniel Defoe is identical to the author of Robinson Crusoe ." This is a true identity claim, even though the words "Daniel Defoe" and "the author of Robinson Crusoe " are not themselves identical. It would be difficult to say why the Law of Identity is true. Any defense of it would either involve using words like "equals," "same as," etc. all over again, or would...