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Karl Fogel (kfogel@kfogel.org)'s status on Saturday, 25-Jan-2025 05:32:42 JST Karl Fogel

A pattern I've noticed:

For many fields of specialization, the core field-specific concepts that outsiders assume are well-defined and unambiguous to specialists are instead, to those within the field, often fuzzy, ill-defined, highly subject to debate, and in some cases even considered to be of questionable ontological utility.

Examples: "species" for biologists; "languages" and "words" for linguists.

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  soaproot (soaproot@sfba.social)'s status on Wednesday, 29-Jan-2025 01:48:29 JST soaproot
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  @kfogel Would you accept "real number" or "ordinal" in #constructiveMathematics ? Although I suppose that might be too technical of an example; your examples are quite good.
  
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  Karl Fogel (kfogel@kfogel.org)'s status on Wednesday, 29-Jan-2025 01:48:29 JST Karl Fogel
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  @soaproot Heh! I thought about including some things like that from math, but I didn't feel I had enough expertise to be sure about what was and wasn't settled these days. Unlike other fields, math has gone through some cycles of taking care of deferred maintenance -- you know, things like re-establishing calculus on more rigorous basis than its originators had ever bothered with, and the adoption of ZF[C] as a foundational framework. Maybe there are other examples too (https://en.wikipedia.org/wiki/Foundations_of_mathematics#Foundational_crisis for those keeping score at home).
  Math is special, quite unlike other fields in its hypertrophied attention to definitional rigor. To provide an example in mathematics, I would have had to get a Ph.D. first, and, you know, it was just one Fediverse post, so was it really worth half a decade in graduate school? Some might answer "yes" to that question, and, indeed, I'm not sure that the answer is "no", but... it was late and I just wanted to hit Submit.
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    Foundations of mathematics
    
    Foundations of mathematics are the logical and mathematical framework that allows the development of mathematics without generating self-contradictory theories, and, in particular, to have reliable concepts of theorems, proofs, algorithms, etc. This may also include the philosophical study of the relation of this framework with reality. The term "foundations of mathematics" was not coined before the end of the 19th century, although foundations were first established by the ancient Greek philosophers under the name of Aristotle's logic and systematically applied in Euclid's Elements. A mathematical assertion is considered as truth only if it is a theorem that is proved from true premises by means of a sequence of syllogisms (inference rules), the premises being either already proved theorems or self-evident assertions called axioms or postulates. These foundations were tacitly assumed to be definitive until the introduction of infinitesimal calculus by Isaac Newton and Gottfried Wilhelm Leibniz in the 17th century. This new area of mathematics involved new methods of reasoning and new basic concepts (continuous functions, derivatives, limits...

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