Paul Taylor wrote:
Mathematical terminology should not employ words that are merely value judgements, without relevant content.
Does "equi-unstable" have enough relevant content for you? Or do any of the proposals so far have enough relevant content for you? (I mean the pithy proposals contained in Joyal's list; there is always the longer "non-invariant under equivalence".) The quotation above seems to effectively summarize what the rant is all about; I think I can do without the judgment or projection that I or anyone else is taking "dictation from God".
Let's have a bit of imagination with language, please.
Yes, let's. I look forward to other suggestions as well.
So my suggestion is that you play around with skeletons, bones or even the Grim Reaper for something more suitable.
Thanks for the suggestion, but I don't much care for it if it merely evokes skeletal subcategories -- that is only one application of the concept we're discussing. Do you have a positive contribution you'd like to make, Paul? Todd ----- Original Message ----- From: "Paul Taylor" <pt10@PaulTaylor.EU> To: "Categories list" <categories@mta.ca> Sent: Saturday, October 02, 2010 1:43 PM Subject: categories: potential names
Todd Trimble wrote:
Of the choices offered here, I like "precarious", "unstable", or "fragile". I just thought of "risky" myself. Good, experienced mathematicians will know when it's okay to take "risks" (and will be aware of what the risks are).
"Unstable" seems like a very sober choice, not too likely to ruffle feathers.
Mathematical terminology should not employ words that are merely value judgements, without relevant content. It doesn't make any difference whether they are offensive or inoffensive value-judgement words. This is not how we should choose scientific terminology.
We are already cursed with vast over-use of the words "regular" and "normal" in mathematics. Roughly translated, these mean "the objects that I want to study" - other people may have very good reasons for studying other kinds of objects.
("Stable" and "sober" already have several meanings.)
There is a problem here in that there is nothing in the education of a pure mathematician that teaches how to make a professional judgement. I never thought I would find myself defending software engineering (the religion whose creed it is that programs are better if their authors wear suits, draw diagrams and attend committee meetings) but when computer science students are subjected to this at least they learn that, whatever they do, they are making professional judgements.
Since pure mathematicians do nothing similar in their training they are easily mis-led by the use of terminology that is based on value judgements. They just think that they are taking dictation from God.
Even if there is a very strong argument in favour of a particular value judgement (as there may well be in the case under discussion) we should still not use words that have no other content, simply because we will want to make OTHER value judgements in future.
The English language reportedly now contains over a million words. Can you really not find anything in this vast thesaurus (=treasury) that describes the situation more appropriately and precisely? There is less, not more, of an excuse if you speak French, Spanish or another language: English allows almost completely free immigration of words.
Let's have a bit of imagination with language, please.
Despite the abuse that I received for it here, I am rather pleased with my introduction of the words "prone" and "supine" for the two different orthogonal notions to "vertical" in a fibration.
A word was needed to replace "open" for an object whose terminal projection is an open map, since subobjects with this property have a habit of being closed subspaces. The rich English vocabulary offered "overt", which means "explicit". Since I first used this word, it has emerged that this idea is very closely related to recursive enumerability, ie to having an explicit presentation, so this has turned out to be a very good choice of word.
On the other hand, I regret introducing "bilimit" and "bifinite" in domain theory.
In the case under discussion we need to distinguish between equal and isomorphic objects. In existing terminology, a category in which isomorphic objects are equal is called "skeletal", although I doubt whether this word ever gets another outing after the definition of a category and basic concepts therein has been given for the first time to students.
So my suggestion is that you play around with skeletons, bones or even the Grim Reaper for something more suitable.
Paul Taylor
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