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The naive view is that a class of objects can be defined by identifying a property which each of the members have, and which no non-members have.

This is obviously too much to hope for in most circumstances, but nevertheless provides a starting point. I'm aware also of attempts of defining classes of objects by the use of 'familial resemblance' which can be made concrete by the use of probability functions.

I was wondering what accounts are given of how an object might be defined in the absence of fixed properties. For example, one might have an object 'x' and it has properties 'a', 'b', 'c' and time 't_0', but these are not fixed and change to 'd', 'e', 'f' and time 't_1'.

Moreover, can anyone recommend any texts which deal with something like a philosophy of definitions or a theory of definitions?

Edit:

Also, I'm looking for answer which isn't "Object x is the object which has properties 'a', 'b', 'c' and time 't_0' and 'd', 'e', 'f' and time 't_1', etc". Something more elegant than this would nice.

Thank you!

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    Any formula of predicate calculus with a single free variable defines a class of objects that satisfy it, this is too broad for a distinction between "fixed" and time-varying "properties" (1-place predicates) to make sense. You can have no "properties" in that formula at all, only relations (multi-place predicates), and your relations can have a time variable in them, which results in different "properties" at different times. So ∀t P(x,t) defines a class of objects that satisfy a time-varying "property" P(x,t) (it is a 1-place predicate for each fixed t). Commented Nov 23, 2024 at 10:54
  • This question is too vague. What is an example of something that has no fixed properties but you want to define it anyway? Commented Nov 23, 2024 at 12:44
  • @DavidGudeman What about a cloud in sky? Commented Nov 23, 2024 at 12:57
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    @JoWehler, a cloud as a location in space, a visual appearance, and other properties. Commented Nov 23, 2024 at 13:09
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    @MichaelHall To classify an object, and to define it, are not the same. I think your point is valid (i.e. what is your purpose) iff my intention was to classify an object. I don't wish to classify some object/s as belonging to some categories. I wish to formulate a description of an object/s which exactly mark out the object in question and nothing else. To what purpose? Well, for the common purpose of giving nouns meaning in the context of a broader language. But maybe I've missed your point, is what I wrote convincing? Commented Nov 25, 2024 at 0:32

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