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    • CommentRowNumber1.
    • CommentAuthorzskoda
    • CommentTimeMay 28th 2012

    New (tagged philosophy) entry structuralism, very stubby so far.

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeApr 15th 2015
    • (edited Apr 15th 2015)

    I have expanded at structuralism

    • added a handful of paragraphs on how category theory may be thought of as formalizing the idea of structuralism;

    • added references (including David Corfield’s recent note), beautified existing references, and added pointers to all these from the text;

    • added, inevitably, a relevant quote from the Science of Logic.

    • CommentRowNumber3.
    • CommentAuthorzskoda
    • CommentTimeApr 17th 2015

    added a handful of paragraphs on how category theory may be thought of as formalizing the idea of structuralism

    This is quite reductionistic. The fact is that the natural systems are much of a result of negotiations and not static and perfect systems. There are tensions which put things into a system, and usually never succeed. For example, a particular language in a particular point in time has its phonems more or less as embodiements of several distinguished features. If there is a phonem which is missing in a table it is likely to appear, and if it is somewhat standing out it is likely to disappear. It is easier for the new speakers, say children to acquire the language which has such a system, rather than 30 arbitrary sounds in spirit of different languages. The fact that this come this way is fact of nature and categorizting a particular snapshot is denying the law of nature, so it is forgetting the most important lecture of structuralism, and that is that the structure counts. When I first heard those things I considered them artificial, but after going for many exercises in comparative linguistics I got convinced that it is quite real.

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeApr 17th 2015

    I have edited it to read: “provides a formalization of philosophical structuralism” (here)

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeOct 10th 2018

    In the first sentence in “Formalization in category theory” I added the words “(by the Yoneda lemma)”. Also added some more hyperlinks.

    The entry keeps asking for a citation for that quote from Manin that “category theory regards objects as part of a society”.

    diff, v9, current

    • CommentRowNumber6.
    • CommentAuthorDavid_Corfield
    • CommentTimeOct 10th 2018

    Might people read the “other” of “system of morphisms which relate this object to the other objects of the category” as not including itself? If so, I guess we could drop the word “other”.

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeOct 10th 2018

    How about “…which relate this object to itself and to the other objects…”

    diff, v10, current

    • CommentRowNumber8.
    • CommentAuthorDavid_Corfield
    • CommentTimeOct 10th 2018

    Sounds good.

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