Pardon the intrusion. I haven't read all the posts. You have a set {1,3,5} , and then you have another set that has as elements the properties shared by the elements of the first set. If this derived set is a singleton, then one could identify the elements of the first set. — jgill
What this does is to define what we mean when we say that a set is an abstract object - the set {a ,b} is not something else in addition to it's elements, but a different way of talking about a and b. A bit of extra language, not a bit of extra ontology. We talk as if the set were a new thing, but it isn't one of the things in the domain. — Banno
Supose our domain of discourse - what we are talking about - contains only the letters "a" and "b". How many things are in that domain? — Banno
Properties dissolved by analysis. Tim will love it. Not. — Banno
But I still don't think that a set is identical to its elements because a single object cannot be identical to multiple of object. So a set is another object, additional to its elements. — litewave
A collection consisting of a phone located in my house and another phone located in my friend's house would be a concrete object too, although some might resist that because the two phones are separated "too much". A collection consisting of my phone and of another phone in a different universe that is in a different spacetime might be regarded as a concrete object because its elements are located in a spacetime but then again, they are in different spacetimes, so this collection transcends a single spacetime. — litewave
And then there is the general property/universal "phone" (or "phoneness") - that which all particular phones have in common - and I guess this would be regarded as an abstract object by almost anyone because unless we identify it with the set of all phones, it seems to transcend spacetime or be located in spacetime in an especially weird way. — litewave
I'm not sure what you mean by "abstract" or "abstraction" here. Is the phone a concrete or an abstract object? Is it a collection of other objects or not? — litewave
Would that mean that "being in that collection of objects [or individuals, per Banno]" is a shared property? Can an object "wander in," so to speak, and partake of that property? This may not be a question about your definition so much as an expression of uncertainty about "property". — J
Yes. So what, if anything, would we want to say about identifying such a set with some property? I take it you don't want "being in set X" to count as a property -- nor could it, on the OP's proposal. — J
The mainstream view among mathematicians is that sets are abstract objects. You can see them with the mind's eye, but not physical eyes. — frank
A set is a collection of objects. An average person surely knows what a collection is. Not so surely a universal. — litewave
Why doesn't aporia lead to intellectual anarchy? — J
Oh, sorry. I thought that's what you were looking for in set theory. — frank
For thousands of years mathematicians would have said that set theory is illogical. It flies directly in the face of Aristotle's finitism, but it solves problems that are otherwise unsolvable. Don't look for an intuitive basis for set theory down in your noggin. It's not there. — frank
Well, in predicate logic you have individuals that have/satisfy a property/predicate. I propose that the property is the set of these individuals. — litewave
Well, I'm trying to describe the concept of set in some intuitive terms. You may say that the concept of set is extra-logical but I wouldn't be able to make sense of logic without it. Like, why are the conclusions in syllogisms necessarily true if the premises are true?
The set is an object that somehow unifies different objects without negating their different identities. One over many. — litewave
Even the extravagant set that Moliere has mentioned above is something in addition to the pebble and the sentence, and this something is a property that the pebble and the sentence share. It is an unimportant property for which we have no word, and being in that set means having that property. — litewave
Good. I like Sartre as an "in" to this approach to consciousness and I'm not particularly bothered by the critique in this context (also, my relative lack of knowledge of Husserl means I can't effectively argue the point anyway). — Baden
I'm trying to fill out above a context (more to come) that I'll try to loop back into a fuller application to body image disorders (including body dysmorphic disorder and eating disorders). — Baden
Yes. So what, if anything, would we want to say about identifying such a set with some property? I take it you don't want "being in set X" to count as a property -- nor could it, on the OP's proposal. — J
What was the question? — Banno
A set is a single object. — litewave