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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeDec 23rd 2015
   • PermaLink
   Author: Urs
   Format: MarkdownItexcreated _[[first law of thought]]_

   created first law of thought

2. • CommentRowNumber2.
   • CommentAuthorNikolajK
   • CommentTimeDec 23rd 2015
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   Author: NikolajK
   Format: MarkdownItexMakes me think of [when is one thing equal to some other thing?](http://www.math.harvard.edu/~mazur/preprints/when_is_one.pdf). The formulation of the [second law](https://en.wikipedia.org/wiki/Law_of_thought#Four_laws) 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.

   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.

3. • CommentRowNumber3.
   • CommentAuthorDavidRoberts
   • CommentTimeDec 24th 2015
   • (edited Dec 25th 2015)
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   Author: DavidRoberts
   Format: MarkdownItex<del>In the setting of a category with zero object you have $A\simeq (A\to 0)$. I guess one should point to [[AT-category]].</del>

   In the setting of a category with zero object you have $A\simeq (A\to 0)$. I guess one should point to AT-category.

4. • CommentRowNumber4.
   • CommentAuthorTodd_Trimble
   • CommentTimeDec 25th 2015
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   Author: Todd_Trimble
   Format: MarkdownItexDavid, 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 $A$.

   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 $A$.

5. • CommentRowNumber5.
   • CommentAuthorDavidRoberts
   • CommentTimeDec 25th 2015
   • (edited Dec 25th 2015)
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   Author: DavidRoberts
   Format: MarkdownItexSorry, 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)

   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)

6. • CommentRowNumber6.
   • CommentAuthorUrs
   • CommentTimeSep 23rd 2022
   • (edited Sep 23rd 2022)
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   Author: Urs
   Format: MarkdownItexadded 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 * [[Clarence I. Lewis]], Appendix (p. 373) of: *A Survey of Symbolic Logic*, University of California (1918) &lbrack;[pdf](https://ncatlab.org/nlab/files/LewisAppendix-LeibnizIndiscernibles.pdf)&rbrack; 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 *** <a href="https://ncatlab.org/nlab/revision/diff/first+law+of+thought/3">diff</a>, <a href="https://ncatlab.org/nlab/revision/first+law+of+thought/3">v3</a>, <a href="https://ncatlab.org/nlab/show/first+law+of+thought">current</a>

   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

   • Clarence I. Lewis, Appendix (p. 373) of: A Survey of Symbolic Logic, University of California (1918) [pdf]

   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

   ---

   diff, v3, current