Nationalize everything!

A set is an abstract object.

A set is a collection of objects — litewave

Not in set theory. A set is criteria. It's an abstract object.

She has never seen a universal though. But she has seen collections (sets), so she may know more about collections than about universals. — litewave

You think knowledge is limited to what you can see? If so, she's never seen a set. A set is an abstract object.

She also doesn't know about the general property of redness, which probably cannot even be visualized. She only knows particular instances of redness. — litewave

She probably knows about redness as a universal.

set S = set of all elements that have property P

This is an intensional definition of a set, a definition by specifying a common property of the set's elements. — litewave

A set won't give an adequate intensional definition of a property, though.

1. Redness = the set of all red things
2. Karen believes the rose has the property of redness
3. Therefore, Karen believes the rose has the property of the set of all red things.

If Karen doesn't know anything about sets, the substitution fails.

I get it, I'm just saying that elements of a thing's structure and potential can also be counted as properties.

I think the idea of properties is pretty flexible. It's like thinking of an object as a solar system with a core of identity, and transient orbiting properties.

Hume pointed out that an object with no properties is inconceivable, so we might think of properties as a product of analysis. We divide up the inherently united thing into parts: identity and properties. As you say, some properties cash out as events of interaction.

Mode (internal disposition): This is the objectively existing structure of the apple’s embodied being—its surface texture and chemical composition—that predisposes it to reflect light of a certain wavelength. This mode exists independently of both light and observer. It remains even in complete darkness. This aligns fully with realism. — Astorre

Wouldn't surface texture also count as a property? Can we think of surface texture as a realized event?

This leads pretty quickly to Russell's paradox. Consider "the property of being a property that doesn't apply to itself." — Banno

Set theory itself leads straight to Russell's paradox. There's nothing particularly intuitive about axioms that block it. They just wanted to use set theory without paradoxes.

I didn't know there could be the property of having a property, so I learned something.

I think probabilities (epistemic), not just "possibilities" (speculative), are existential modalities which matter more for flourishing — 180 Proof

I think flourishing comes from being your authentic self, as opposed to what das Man tells you to be. If being authentic means admitting that you believe in life after death, that's the direction you should take, damn the torpedoes.

I have wondered why a topic like this would be cause frustration, say for people like Richard Dawkins. It just comes down to what you're inclined to believe, which is probably related to your worldview. That's as far as you can go: you reflect the times you live in and that's it.

For example, let's take property red or redness (X = red): The property of "being in set red" is the same as the property of "having property red", which is the same as the property of "being red", which is the same as property red. So, the property of "being in set red" and property red are one and the same property. — litewave

Having the property red is not the same as the property red. Having a ball is not the same thing as the ball.

These two properties have exactly the same instances and if I got it right, they are one and the same property, just described differently. — litewave

Membership in the red set entails having red as a property. Entailment doesn't get you to identity, though. Or if so, how?

For example, let's take property red or redness (X = red): The property of "being in set red" is the same as the property of "having property red", which is the same as the property of "being red", which is the same as property red. So, the property of "being in set red" and property red are one and the same property. — litewave

So if I say the peony is red, I mean it's in the set of all red things. So did we change from the set is the property to being in the set is the property?

yes :heart:

Okey dokey

And all he had to do was fire the people who report the economic data and install his own people! — Mr Bee

That was the labor secretary.

Clearly, his anger caused your anger. But I don't think that's the same as experiencing his anger. Do you think you could become angry from looking at a photograph of someone who is obviously angry? — Patterner

For me, at base, it's not my anger or your anger. It's just anger. Telling who it belongs to is an intellectual matter.

We can't get rid of properties or talk of properties. Fear not.

Oh yeah I don't think logic is intuitive at all. — Moliere

Oh, sorry. I thought that's what you were looking for in set theory. I think logic is fairly intuitive, though.

GDP is up 3.3% QoQ!!! Trump is a genius! And the economy always gets better after the first quarter.

The point of my OP is that the set actually is the property. That may not be obvious. — litewave

I think I understand what you mean.

By being an element of the set, thus having what all the other elements of the set have. — litewave

So you're saying that having a property is a matter of being a member of the set of all things that have that property. That's trivially true.

So the peony has the set of all red things. How does it have that set?

Because a collection is something different than its elements, yet it is also something that is common to the elements. — litewave

1. The property of redness is the set of all red things.
2. A peony has the property of redness.
3. A peony has the set of all red things.

Help me out here. That doesn't make sense.

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.

I said instances of redness have the property of redness. — litewave

A red ball has the property of redness. A red ball is not the property of redness, though. They're two different things, so it's hard to see how a collection of red things would be equivalent to redness.

My point is more about how it can feel like anything. I do not see how appreciation of time can happen either in a moment or across a period without some atemporal element being involved. What that means in terms of our physical understanding of the universe is rather nonsensical to us though. — I like sushi

I understand what you're saying, but I think it's relative. If you're watching the passage of time, you're stationary. But you're also in the stream of time, moving past various points, the points in time are stationary. The distance between you and the American Revolution grows bigger every day. You're the one that's moving, not the revolution.

Shades and hues of red are instances of redness, so they all have the property of redness. — litewave

Red has the property of redness? That doesn't sound right.

When I say that a property is identical to the set of all objects that have this property, I mean that the property is completely specified and thus the set is completely specified. In practice we usually don't have such complete specifications and we talk about approximately specified properties like "redness", but that doesn't refute my claim that a property (completely specified) is identical to the set of all objects that have this property. — litewave

So if it's the property red, then the set contains things past, present, and future. It contains things like my blood in the light (my blood isn't red inside my body, just when it spurts out of an open wound.)

It's just seems like you're mixing categories if you say redness is the set of red things. It's closer the set of all shades and hues of red.

a single moment
— frank

It is more or less this that flumoxes me.

Is time discrete? If not, or if so, how can we have any appreciation of it? — I like sushi

It appears to be both. If we're listening to music and clapping along, awareness of is in the anticipation, and then the gratification of all clapping at the same time, a single moment. But at other times, it feels like a flow.

This is Aristotle territory.

I agree. All I know of consciousness is that I am conscious. All the words I have to speak about it are community property, gaining meaning in practical situations. I think there is an implied commonality in the fact that we use the same words. And this sense of commonality extends to the whole world, where thunderstorms seem angry, and quiet meadows seem happy.

I think at the point we decide that you have some quality of being that belongs uniquely to you, we're laying a particular worldview over the scene. We could just as easily believe that our common language about experience has an external referent in something like the mind of God that dwells all around, and we participate in it, resonating with it, injecting our own emotions into it like a cloud. We just don't have that worldview, so we imagine distinct pockets, containing unknowable beetles.

As you say, this is metaphysics that goes beyond the character of linguistic expression. So it's not just that I can deem experience in itself as beyond language, the whole scheme that distributes beetles into boxes is also trying to express something beyond language.

I think that means that to the extent that your experience is private, what I'm talking about is your history, your unique POV, all the external trappings of personhood, with the expertise at lawyering and the owning of things.

When you seek to discuss the actual internal state as to what it is, the private sensation, you are outside what Wittgenstein would allow language to do. You're discussing metaphysics. Language isn't for that sort of discussion because meaning is use, not meaning is internal referent. — Hanover

So when someone tells me they're in pain, we aren't investigating an internal state, because language doesn't do that. It's more that they're announcing that they're conscious of something bad? And they're using language to give a warning, ask for help, or just get acknowledgement?

Beyond that, we have to be satisfied that we don't have any linguistic fingers that can't touch consciousness?

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

So litewave wants the property P to be equal to the set of all things that have P, we'll call it set Q. But we can't say that P=Q? Because they're different types of things?

Yes! Exactly. — Patterner

Panpsychism fan?

How can you anticipate though. That is where our reasoning breaks down. — I like sushi

There's anticipation in agriculture, where the farmer waits for the last frost date. There's anticipation in music, as when you clap along to the beat. What you're anticipating there is a single moment in the future. Everyone anticipates the same moment and claps at the same time.

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

I stumbled over this same issue, so you're not alone, but you're wrong. In the club metaphor, the set is the membership list, not the members themselves.

A set is an abstract object. That's the part you have to get in order to understand set theory.

Nuh. The set is the teachers. The criteria are not the set. — Banno

nope. Read Mary Tiles' book on set theory. The club metaphor is from her book.

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 not its elements. Imagine a club that all teachers automatically belong to, by virtue of being teachers. The set is this membership criteria, not the actual teachers. A set is an abstract object.