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.

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

If there are abstract properties which define sets without a known common property -- such as the set I proposed grouping an abstract and a concrete individual -- just how does this unknown property come to define the set? What is it that this property does that makes sense of saying sets are defined by properties if there are an infinite amount of abstract properties (considering there's at least an infinite amount of abstract objects this shouldn't be a stretch)?

Is it to say anything more than this set is a collection of these two members? What is this extra "unspoken property" doing for us in understanding what a set is?

You say that with great certainty, as if it were an explanation of what a property is.

I am just explaining how the term is used in metaphysics. Properties are not unique to realism or theories of "abstract objects." Depending on how one views sets, I would think that the original suggestion could also be construed in constructivist or fictionalist terms, or whatever one likes.

"Predicatables" are an older term for instance. But, presumably "getting rid of properties" isn't getting rid of predication or common terms. Which means that what are normally referred to as "properties" will remain.

The closest parallel I can think of would be individuals/particulars. No doubt, it has been difficult to define these and exactly how they are individuated. However, there would be a similar difficulty in eliminating individuals.

A deflationary account of individuals and properties is still a particular account. I am not sure if the presence of disagreement of difficulty suggests any particular account though. It would be a bit like suggesting that, because "life" is difficult to define, and because there is great disagreement surrounding it, we should default to not explaining life, but rather simply looking at what we call "living." This methodological move might be supported in some contexts, but I don't see how any further positive metaphysical claim like "there is no life, or living versus dead versus non-living, but only ways of speaking" could be supported over any others using an appeal to ignorance or difficulty.

I propose that the set of all red objects is the property "redness" but this property probably does not look red, in fact it probably does not look like anything that could be visualized because it is not an object that is contiguous in space or time — litewave

A football team is a set of football players. An example of a set that does not contain itself.

Football team = {player 1, player 2, player 3,............................player 11)

A football team is a distinct thing to 11 football players. 11 random football players does not make a football team. These 11 football players have to work together in order for there to be a football team.

In naive set theory, sets can contain themselves. However the Axiom of Foundation in Zermelo-Fraenkei set theory states that sets cannot contain themselves, in order to avoid Russell's paradox. An example of a set that would contain itself would be a set of sets.

ZF ensures that things like football teams are more than a random collection of football players.

I will stick to Copilot's analogies.

The football team is like a container within which are football players. Such containers are distinct to what is being contained.

In addition, the football team may be thought of as Frege's sense and the football players as Frege's reference. Sense is also distinct from reference.

In addition, within Wittgenstein's language game, the football team may be thought of as a concept and the football players as the context of the concept. Concepts are also distinct to their contexts.

A football team is an abstract entity, whilst the football players are concrete entities.

Generalising, an abstract thing, such as a football team, is a set of concrete things, such as football players.

Equivalent examples would be:

A University (an abstract thing) is a set of buildings and teachers (concrete things)
University = {university building 1, university building 2, teacher 1, teacher 2}

The property redness (an abstract thing) is a set of red things (concrete things)
Redness = {red car, red book, red apple}

Am I right in agreeing with you that the property of redness is the set of all red things?

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. — frank

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

Isn't it possible that people might consider properties all sorts of ridiculous ways? I don't see a mechanism here for dismissing Tom's opinion on the grounds that it is "nonsense" when we have already opened things up to every possible set configuration. Yet this would seem to make "everything to be everything else."

I don't think the "opinion based flexibility" works with the modal expansion. And something like "all possible opinions that aren't 'nonsense,'" seems to ignore that there are many possible opinions about what constitutes "nonsense." This is made more acute by the modal expansion, but I would say it applies just as well for what you've said, since there is the question: "who decides what is nonsense?" — Count Timothy von Icarus

These are two somewhat different objections, I think. To the first, we can't call the ascription of a property "ridiculous" but also accept the OP's thesis. So if I understand you, you want to stick with the ridiculousness and abandon the thesis. I would lean that way too (though there are difficult logical issues involved in @litewave's idea that I'm still pondering). But the other option is to stick with the thesis and deny that any set is ridiculous. This is in the spirit of litewave's reply to me, above:

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

I have problems with this, but I'll save them for a direct reply to litewave. In any case, that's a comment on your first, "ridiculous property via modal expansion" objection. The second objection concerns the familiar question about what entitles us to call one opinion nonsense and another insightful, if we lack a definition of the terms involved. I would appeal to our practice. Reading Locke or Hobbes or Rawls, we don't compare what they're saying to a previous definition of justice upon which we agree. Rather, we decide they deserve a hearing based on their familiarity with, and competence with, the questions about justice, including the previous conversations that have occurred in the various traditions. They "know the subject," we say -- and this is what Nonsensical Tom probably lacks.

So the answer to the question, "Who decides what is nonsense?" is not "The person who looks up the definition of justice in the Great Dictionary of Philosophical Terms," but instead, "The group of people who are competent, by virtue of study and practice, to interpret the question of what justice is, and understand how it connects with other key philosophical issues."

On this account, we don't have many different claims about what justice is, but many different justices. It's a positive metaphysical claim to say that justice just is the set of things each individual considers to be just. — Count Timothy von Icarus

If Tom, Rawls, et al. each make a claim about what justice is, and we don't think any of them can be supported, what is the situation? Do we say, "Each of these people has a different justice. So for them, justice just is what they consider just." No, we say, "None of these people has been able to tell us what justice is. I don't know either, but I don't have to know in order to understand why the proposed definitions are unsatisfactory." This is Socrates' position, more or less. This, I think, rules out the "positive metaphysical claim"; the question is whether @litewave's thesis can also rule it out.

What is this extra "unspoken property" doing for us in understanding what a set is? — Moliere

The extra property (the set) is a thing that is the result of the unification of the elements into one thing (while keeping the elements distinct from each other), which is thereby shared by the elements.

Am I right in agreeing with you that the property of redness is the set of all red things? — RussellA

That's what I am saying the property of redness is - the set of all red things (the set of all instances of redness).

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

It's certainly understandable what is meant, but in so doing in ordinary language you will still have the problem of delineation and universals and so on.

For example, a ball of red atoms.

Is the ball an element in the set? Is each atom an element in the set? Is subset of atoms of the ball in the set? What about the quantum level? Mostly these atoms are red but there will be random fluctuations that cause other colours; if photons are fired at an atom and bounce back another colour, is the atom still an element of the set? If the criteria is the potential to be red, pretty much all atoms can be red through relativistic effects of red-shifting; there are red galaxies in the sky due to red shifting, are they elements of the set of redness, each star, each dust particle, each atom and so on? There will be all these kinds of questions that need to be resolved to rigorously define what redness is and how to separate elements into the set of redness and not-redness; and the basic nature of this problem is that it goes on forever.

When formal structures help us describe things in the real world it is because those real things are in some sort of temporary stability that conforms to the formal structure and then it remains a judgement call when that is no longer the case. For example, computer "should" conform to rigorous formal rules, but it remains a judgement call if that is actually happening as memory and logical operations can be corrupted, so we remain "certain" about the formal structures in our mind but never actually certain an object we think corresponds to a structure actually does.

Of course, doesn't stop us talking about a set of red things, and that can be useful to do, but if you want a rigorous definition you'd need to solve all these problems; otherwise, the definition becomes the set of red things which I will decide on a case by case basis as I get to them to resolve all edge cases in a way I'm confident won't result in any contradictions whatsoever; which is not how a set is usually defined in formal logic.

There is a branch of mathematics that deals with these kinds of issues, called fuzzy logic, as there's certainly nothing stopping us trying to make rigorous treatments of our pretty vague concepts about the real world, which I haven't looked into all that closely but maybe of interest to you.

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.

"unification" -- I'd say this is an extra-logical notion. We may posit the set consisting of ununified elements, for instance -- is this then not a set because the elements are ununified? Is it possible to posit such a set?

Of course, doesn't stop us talking about a set of red things, and that can be useful to do, but if you want a rigorous definition you'd need to solve all these problems; otherwise, the definition becomes the set of red things which I will decide on a case by case basis as I get to them to resolve all edge cases in a way I'm confident won't result in any contradictions whatsoever; which is not how a set is usually defined in formal logic. — boethius

We can agree on many things that should be included as elements in the set of red things (instances of redness), for example ripe tomatoes and their various parts, pools of blood and their various parts etc. If you also include individual atoms, so be it - that will be how you specify the property of redness and thus the set of its instances. If you don't include individual atoms, so be it - you will specify a somewhat different property and set and you will call it redness. Properties and sets objectively exist as completely specified but what you call them is your choice.

So the answer to the question, "Who decides what is nonsense?" is not "The person who looks up the definition of justice in the Great Dictionary of Philosophical Terms," but instead, "The group of people who are competent, by virtue of study and practice, to interpret the question of what justice is, and understand how it connects with other key philosophical issues."

Wouldn't it be "by virtue of what is known through study and practice?" If study and practice are justificatory of themselves, I'd observe that the leaders of ISIS were educated and part of a particular study and practice of justice and ethics (IIRC, al Baghdadi held a doctorate). But then the leaders of ISIS have a very different view of justice from that of Anglo liberals. So either study and practice alone are not enough, or else there is a different justice for each practice (which is closer to @litewave's solution to differing sets of just acts).

Think about it this way: if someone studies snake oil medicine for a long time, and are part of a well-established, does that make them as much of an authority of health as a medical doctor? What if their methods do not promote health, but actually tend to produce disease? The difference between the two would seem to lie in what they know about health and disease, and this affects what they are able to achieve in terms of treatment. Now, in the former case, what is it the legitimate authorities know?

If Tom, Rawls, et al. each make a claim about what justice is, and we don't think any of them can be supported, what is the situation? Do we say, "Each of these people has a different justice. So for them, justice just is what they consider just." No, we say, "None of these people has been able to tell us what justice is. I don't know either, but I don't have to know in order to understand why the proposed definitions are unsatisfactory." This is Socrates' position, more or less. This, I think, rules out the "positive metaphysical claim"; the question is whether @litewave's thesis can also rule it out.

That makes more sense to me. @litewave's response was that, when we have different sets, we have different properties (i.e., different justices, plural); however I think one could retain the notion of a property as a set without necessarily having to be committed to this clarification.

There is a branch of mathematics that deals with these kinds of issues, called fuzzy logic, as there's certainly nothing stopping us trying to make rigorous treatments of our pretty vague concepts about the real world, which I haven't looked into all that closely but maybe of interest to you. — boethius

Ok, I haven't studied fuzzy logic, it may be a useful way of dealing with uncertainties, but ontologically I regard every set as completely specified, just like in set theory.

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

I said instances of redness have the property of redness. The property of redness itself doesn't seem to be red, hence it doesn't instantiate itself.

ontologically I regard every set as completely specified, just like in set theory — litewave

But this is true only in a formal system where everything really is completely specified.

However, outside formal systems, there is no completely specifying anything. For example, try specifying a tree; it's a pretty hard task even for just trees on earth right now (without even addressing questions like when exactly does a seed become a tree and when does a tree become log), but a complete specification would be able to tell us also exact moment the next individual in a species of bushes attains treeness, likewise what organisms on other planets and even other universes entirely would be a tree.

To have a "good idea" of what a tree is, to be certain we'd agree that the trees outside my window right now are indeed trees, is very far from a complete specification of treenness.

To say we know what the specification of set of even numbers in a formal system, does not imply we know exactly what the set of all trees is.

To make sets of objects in the real world you need to define apparatuses and procedures (and procedures to make your apparatuses) and then contend with all the edge cases; i.e. you have to do science in which mathematics is a useful tool but doesn't solve all your problems.

For example, a post-grad laser physics researcher I once knew, worked in a lab that dealt with edge cases by running an algorithm to simply remove outliers from the datasets entirely.

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.

"unification" -- I'd say this is an extra-logical notion. We may posit the set consisting of ununified elements, for instance -- is this then not a set because the elements are ununified? Is it possible to posit such a set? — Moliere

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.

This might make the point better --

Consider "The set whose elements consist of sets without properties which is a member of itself" --

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

The concept of a set could be extra-logical, yes. If I'm talking about a chess set, for instance, I'm not using "set" to talk about logical sets. So in a way what I'm asking here is to say "How does this notion of unification fit within a strict logical definition?"

Intuitively I understand what you mean -- I just think that we can drop this business about sets having properties at all if we can always substitute the members of a set for whatever the property picks out. The abstract property which picks out the nearest pebble and the first sentence I say five miles from now just is that these are in a set, and there is no more to it than that.

It's a set because we decided to treat these elements within a logical structure, not because there's some property which the set has that we pick the elements out with.

It's very unintuitive, I'll grant. But the intuitive statements can easily run into paradoxes which is kind of where I've been coming at the question from: with Russell's Paradox in mind which I tried, in my lasts reply, to reframe in terms of your use of "unificiation" -- it doesn't quite work because to be more precise the set would have to both contain itself and not contain itself, hence the paradox -- I was going for something like "Here's a set which has a property which is unification, and that property for this set is that they are all not unified, in which case the set is both unified and not unified".

Does that make any kind of sense, or is it just boring and not worth investigating?

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. — frank

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

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.

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.

So in a way what I'm asking here is to say "How does this notion of unification fit within a strict logical definition?" — Moliere

Well, in predicate logic you have individuals that have/satisfy a property/predicate. I propose that the property is the set of these individuals.

. 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. — frank

It sounds weird if when you think of the set you think of all the red things. It makes you think that the peony somehow has all the red things, which is absurd. But the set is not all the red things. It is something else, which all the red things have in common.

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

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

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

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 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. — frank

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

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.