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created first law of thought
Makes me think of when is one thing equal to some other thing?.
The formulation of the second law on the Wikipedia page is something I haven’t encountered, $a\neq\neg a$.
Makes me wonder if $a\cong(a\to 0)$, e.g. in particular $*\cong(*\to 0)$, doesn’t make sense somewhere.
In the setting of a category with zero object you have $A\simeq (A\to 0)$. I guess one should point to AT-category.
David, could you explain what you meant in your last comment? What is meant by $A \to 0$?
A side remark is that any cartesian closed category with zero object $0$ is trivial (i.e., equivalent to the terminal category). For any object $A$ we have $A \times 0 \cong 0$ since $0$ is initial and $A \times -$ has a right adjoint; we also have $A \times 0 \cong A$ since $0$ is terminal. Thus $A \cong 0$ for every $A$.
Sorry, I was using Nikolaj’s notation (at least as I guessed what it meant): $A \to 0$ is the function type, ie $Hom(A,0)$…… ./… ….
….
:-(
Blerg, obviously wrong. Never mind, it was just some random emission… :-/ (Edit: Was travelling last night on the train at the end of a long day of travelling, and didn’t think before I posted)
added the following to the list of references:
In Gottfried Leibniz’s unpublished but famous manuscript on logic (from some time in 1683-1716), reproduced In English translation in
it says, after statement of the identity of indiscernibles and then the indiscernibility of identicals, that
$A$ and $A$ are, of course, said to be the same
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