Quote from dandl on November 17, 2021, 9:33 am

A type is a named set of values, in TTM and in most other languages. You won't easily find a contradiction in that definition. It seems to have stood the test of time.

No, you are conflating essence with representation. It's fine to represent a type as a set of all possible values, but that's not what it "is", any more than an integer "is" a certain number of bits. The type of type is type, but you can produce a set of all types, where type is a member.

Definitions again. What do you mean 'essence', 'is', 'representation', etc?

No, a type is not a representation, it is a named set of values (in a programing language). The type exists because the program defined it, gave it a name and specified the values that belong to it. The set of values might be enumerated or defined by underlying hardware or by a predicate or by the grammar.

You might say that the concept of 'type' is a mental construct devised to satisfy certain desirable purposes, but that still isn't what it is. It is what it is defined to be.

BTW the language that comes to mind in this context is Smalltalk. If memory serves every value is an object, an object belongs to a class, a class is a value, there is a 'class of class' and an ingenious (or desperate) bit of trickery to avoid the regress.

A class in smalltalk is an object.

At least we agree on that, because that's what I said. A class is a value and a value is an object. Was there something else?