Me too.I think it's pretty easy to identify red things — Count Timothy von Icarus
The picture holds you. Can't we just say that there are triangles, and leave "there is a property of triangularity" or whatever as a slip into reification?"nothing has the property of being triangular" which would seem to imply that nothing is triangular. — Count Timothy von Icarus
So are swedes and rutabegas and purple top turnips extensionally identical? — Banno
For example, the property of redness would be identified with the set of all red things, or the property of being a car would be identified with the set of all cars. — litewave
If there are no properties, in virtue of what would some things be members of "the set of red things" but not others?
Or in virtue of what would different individual things he discernible?
Rutabaga has a chromosome number of 2n = 38. It originated from a cross between turnip (Brassica rapa) and Brassica oleracea. The resulting cross doubled its chromosomes, becoming an allopolyploid. This relationship was first published by Woo Jang-choon in 1935 and is known as the Triangle of U.
You say that with great certainty, as if it were an explanation of what a property is. But what is an attribute, if not what we attribute to something? Etymology: "assign, bestow," from Latin attributus, past participle of attribuere "assign to, allot, commit, entrust;" figuratively "to attribute, ascribe, impute," from assimilated form of ad "to" (see ad-) + tribuere "assign, give, bestow"All a property, in the broadest sense, is just an attribute or quality possessed by something. — Count Timothy von Icarus
Identical" is defined extensionally by substitution. I hope we agree that there is nothing more to the set {a, b, c} than a and b and c, no additional "setness" in the way RussellA supposed by adding his box. — Banno
A set is a collection of individuals. They need not have anything related to one another, or share anything at all -- the individuals are the set and there's nothing else to it. The pebble on the ground and the sentence I say 5 miles away can form a set. — Moliere
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
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
Then she is mistaken. Or has been misread.
It does not matter how we specify the set, or how we order its members, or indeed how many times we count its members. All that matters are what its members are.
— Set Theory An Open Introduction — Banno
A set is a different object than any of its elements. But if the box is black then it also contains instances of blackness, not just redness. For example the walls of the box may be black. Your example looks like the property of redness contained in a black box. — litewave
I am proposing that we could plausibly identify a property with the set of all things that have this property. — litewave
Second point. What we mean by identity is when talking about sets is extensionality, that is, that if A and B are sets, then A=B iff every member of A is also a member of B , and vice versa. Read that as a definition of how to use "=". So we should read S={a,b,c} as an identity between S and {a,b,c} and we can say that they are identical. That is reply to ↪litewave. — Banno
First point. ↪RussellA
might be understood as saying that in addition to the set consisting of {book, car, apple} there is a fourth item, grouping these together, the box the set comes in, as it where. That's not right. There is nothing in addition to the elements. — Banno
Properties, qualities, characteristics, and so on, are mental or linguistic abstractions of the things described, or even the descriptions themselves. Your morphological derivations “redness” and “carness” indicate this. They are derivations, not sets or properties. — NOS4A2
Does this not mean that saying the box can only be black if it contains instances of blackness violates the Zermelo-Frankei set theory, in that the singleton set must be distinct from the element it contains? — RussellA
That does not make it invalid to talk about sets of "everything red" for example, but we can know ahead of time that such a concept cannot be developed into something rigorous without axiomatization. — boethius
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