I can imagine some contexts in which it wouldn't. But my version of "repute" doesn't have to mean "acclaimed by colleagues." I'm struggling to find a term that describes people who "know the subject," as I said earlier. Perhaps there isn't a single term for that. Or is it "expert"? But then I know quite a few subjects while not considering myself an expert. Maybe it's more like, "If you can read an article in a contemporary phil journal, understand the discussion, have read many or most of the references, and are familiar with the issues that have arisen about the position being espoused, then you deserve a respectful hearing in reply." But even that admits of exceptions, of course.

That makes sense to me, but it seems like a criteria for "who gets a hearing" not which positions are accepted. So, in the confines of the original example: determining which acts belong to the set of just ones, we cannot simply rely on who deserves a hearing, since—unless we are very restrictive about who gets a hearing—they will likely present us with mutually exclusive positions. Likewise, if we find none of the options sufficient, and we wish to develop our own, there must be some sort of way for us to determine which new paths are worth pursuing.

Basically: "who deserves a hearing?" and "who is closer to the truth?" are two different questions.

A radical critique need not be accepted in order to gain a hearing. The acceptance involved is "a seat at the table," as described above, not agreement with the critique.

Sure, that seems fair. But as noted above, this moves away from a standard for assent, to merely a standard of what is worth considering.

How do we learn to discriminate? By engaging in the practice with others and watching how they do it, and why.

Well, I don't want to repeat myself, but I suppose my objection here is a variation on what I said earlier. I do agree. I think it is true, in that intellectual virtue is learned/trained in a way analogous to a skill. If one practices, has good teachers, etc., progress can be made. However, I don't think all practice and observation will lead in this direction. It seems equally possible to learn, or be habituated in intellectual vices. I think some theological/philosophical schools have exemplified this problem throughout history. They become dogmatic and parochial, or overly hierarchical, etc., and so they end up tending to habituate their membership with these same vices.

To pick an easy target that a lot of academics (philosophers included) have criticized: elements of "publish or perish" promote bad research habits and have a negative impact on discourse, but moreover they teach certain sorts of intellectual vice. But obviously far more severe examples abound.

So, then to my mind what is important isn't necessarily the persistence in practice, but rather persistence in practices that foster certain skills and, for lack of a better term, virtues (habits). Expertise alone isn't enough either. Astrologers have expertise in astrology, but we might think they are more deluded about how the stars affect our lives than the average person (alternatively, we might say that "expertise" is only truly expertise if it actually involves knowledge of what it claims expertise in. The astrologer is an expert in something, but not what they think they are an expert in).

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? — frank

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

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?

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

This way:

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

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.

Having the property red is not the same as the property red. — frank

Hm yes, the problem will be in the property of being red, which I equated with these two properties. It seems ok to equate being red with having the property red. But being red should not be equated with redness when redness is meant as general redness while being red is meant as particular redness.

Anyway, if there are genuinely different properties that have the same set of instances (for example, properties like general redness and particular redness), then my OP proposal of identifying a property with the set of its instances fails.

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

My reply above was a groaner, wasn't it. — litewave

I admit, I did some head-scratching! :smile:

However, I think that these two properties are not really different; they are one and the same property, just described differently. — litewave

This is similar to your response about being equilateral and being equiangular. In the case of triangles, I was ready to allow the possibility, due to the logical equivalence. I'm less sanguine about saying that the difference between "being X" and "being a member of set X" is one of terminology. (What is the equivalence between a color and an individual in a set?). Your subsequent exchange with @frank brings out some of the problems. (I realize it's ongoing, too, and likely to cross posts with this, so sorry for any confusion.)

I can't help but feel that the term "property" is responsible for some of this. @Banno has raised some important issues here. There's an intuitive rightness to what you're proposing -- that our language for talking about something like "red" can be simplified through analysis and discovered to be largely redundant -- but is "property" the right flag under which to fly this idea? I don't know, and can only say that I'm uneasy about properties in general, and wish I had something clearer to suggest. I also wonder -- and again, there are folks on TPF who know much more about this than I do -- if the issue can be described more fully in Logicalese, which might give us a more precise handle. Volunteers, anyone?

I'll point out again the discourtesy of removing the automatic links when quoting.

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

My advice would be to drop "...the property of..." from all of this. Then "being a member of the set of red things" is the same as "being red".

This kinda cuts to the heart of the issue.

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

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

Hence logicians and mathematicians introduced hierarchies. Individuals, then sets of individuals, then sets of sets of individuals, and so on, without intermingling.

What's curious here is how "the property of..." serves to confuse things. The very grammar of "the property of..." encourages us to think we're talking about entities when we're really just manipulating linguistic constructions.

This is the legacy of syllogistic logic. Since it can only deal in terms of "All S are P", "Some S are P", and so on, it obliges the user to think in terms of substances having properties. It squeezes the world in to an ontology of things and properties. Scholastic metaphysics elaborated on this logical limitation by inventing essences, accidents, substance and so on.

We now have better logical tools for dealing with all of this stuff. The answer on offer to is not to identify properties with sets but to drop talk of properties for talk of sets and predication and extension. Indeed, that is probably the intuition behind the OP.

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.

Those hierarchies are how we keep set theory consistent, underpinning Zermelo set theory, and hence ZFC, the accepted foundation of mathematics.

Not unimportant. And again, speaking in rough outline.

An interesting approach—formally elegant and convenient, especially from the standpoint of set-theoretic formalization. It allows properties to be neatly defined through their instances and resolves the problem of uninstantiated properties via possible worlds.

However:

The set of all red things does not quite align with our intuitive grasp of “redness” as something unified and shared. A set is merely a collection of objects, whereas a property seems to be something more abstract—something that binds those objects together.

Identifying properties such as “equilateral triangle” and “equiangular triangle” as one and the same disregards their contextual distinctions. In geometric analysis, for example, whether emphasis is placed on sides or angles can carry significant implications, even if the extension is the same.

In the end, your approach requires a metaphysical commitment to the reality of possible worlds, which is itself a contested position.

I propose we step away from a substantialist approach to ontology and turn instead toward a processual one, which I am actively developing.

Rather than conceiving of properties as static characteristics inherent in objects—or as sets of such objects—we can understand them as dynamic events that emerge through acts of interaction (or, if you will, participation) between beings. A property is not something a thing has, but something that happens at the threshold where it encounters other beings.

Take “redness” as an example. Under the substantialist view, redness is either an inherent trait of the object or the set of all red things. In processual ontology, redness is an event that unfolds through the interaction of:

The thing (e.g., the apple, whose structure determines how it reflects light);

The light (photons of a particular wavelength);

The observer (a human or other creature interpreting that reflected light through their perceptual apparatus).

Redness, then, is not inside the apple. It is born from the interplay of all three participants. This makes the property contingent: for a different observer (say, someone with color blindness), or under different lighting conditions, redness may not manifest at all.

Another example: “a pleasant scent.” Scent is not a static attribute of a substance. It is an event arising from the interaction of molecular structures, olfactory receptors, and a brain interpreting those signals within the context of memory and experience. What smells pleasant to a human may signal danger to an insect.

But how should we treat uninstantiated properties—without lapsing into subjective idealism?

To relieve this tension, we can distinguish between modes and properties:

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.

Property (realized event): This is the event of redness, which only occurs when the apple’s mode enters into participation with light and an observer. This property does not exist in darkness.

The unactualized mode remains. The potential for redness (the mode) is always there, as long as the apple itself exists. But the redness (the property) is an event that may or may not come into being.

That doesn't seem too far from the treatment of properties as things we actively atribute to individuals, as I suggested teasingly to Tim.

It also serves to bring out something of the intensional character of properties that might be considered to be missing from the extensional account of properties in terms of sets.

I don't know what a "potential for redness" might be, though, and might resist the idea that such an entity somehow inheres in the apple...

A curious approach.

"potential for redness" is of course not an academic term, but simply my way of expressing the idea. In this case, it is the potential inherent in an apple to be perceived as red by a non-colorblind subject in sunlight. That is, the very texture (embodiment, flesh) of the thing. As opposed to a property that manifests itself exclusively in dynamics and 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?

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

Every being has embodiment - its flesh, structure, potential.
But embodiment itself does not yet generate a property.
A property arises when a being enters into active Participation - into interaction with another being.
A property is not something that a being "has", but something that "happens" when they meet.

That was the idea

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.

Redness, then, is not inside the apple. It is born from the interplay of all three participants. — Astorre

Thing A is predisposed to emit a wavelength of 550nm, and an observer perceives colour X. Thing B is predisposed to emit a wavelength of 630nm, and the same observer perceives colour Y. Thing C is predisposed to emit a wavelength of 700nm, and the same observer perceives colour Z.

Although the observer perceives the colours X, Y and Z as different (there can be different shades of the same colour), the observer also perceives a family resemblance between colours Y and Z (such as the concept of redness).

If a person's intuitive grasp of a family resemblance between colours Y and Z is processual, a dynamic interaction between thing, light and observer, what is there in this dynamic interaction that causes the observer to treat colours Y and Z as being different in some kind to colour X (red rather than green)?

As an analogy, my feeling of pain when touching a hot radiator is not caused by the interaction, but is caused by my internal disposition to feeling pain when touching a hot object. An objective, existing mode of my being.

The set of all red things does not quite align with our intuitive grasp of “redness” as something unified and shared. A set is merely a collection of objects, whereas a property seems to be something more abstract—something that binds those objects together. — Astorre

Still, a set (collection) is also treated as a single object in set theory that exists as a single element in other sets. And I don't regard sets as "abstract" objects but rather as objects I can see all around me - there are sets of sets of sets etc. everywhere around. If a set is not an object in its own right then what objects are there? Just non-composite objects (like empty sets) at the bottom? And what if there is no bottom? One may object that there is no order of elements in a set while the sets we see around us are often ordered in intricate ways, but there are various ways of constructing ordered pairs out of unordered sets, for example the Kuratowski definition of an ordered pair.

So a set seems to be a single object that is something additional to its elements, not identical to any one of its elements, and not identical to multiple elements either, since it is a single object. A set somehow unifies/connects/binds its elements. In a sense, one could say that the elements "have" the set "in common", "share" it, or "participate" in it. So in this intuitive sense, a set seems evocative of a property and so I hoped to identify it with the common property of its elements, and thereby also get rid of property as a different kind of object and simplify the metaphysics of reality. But now it seems that there are genuinely different coextensive properties, which would dash the hope of identifying properties with sets.

Admittedly there is also something about the concept of a set that seems a bit jarring with the concept of a common property of the set's elements: a set encompasses or aggregates the elements with both their common and different properties, while a common property of the elements seems to be some commonality that is as if distilled/extracted from the elements rather than the result of encompassing or aggregating the elements. This may be what felt misaligned to you too.

Identifying properties such as “equilateral triangle” and “equiangular triangle” as one and the same disregards their contextual distinctions. In geometric analysis, for example, whether emphasis is placed on sides or angles can carry significant implications, even if the extension is the same. — Astorre

The properties “equilateral triangle” and “equiangular triangle” don't seem meaningfully different to me in any way. One description mentions the equality of sides and the other the equality of angles but the concept of triangle includes both sides and angles and is such that the equality of sides logically necessitates the equality of angles, and vice versa. What implications would the different emphasis in description have for geometrical analysis?

In the end, your approach requires a metaphysical commitment to the reality of possible worlds, which is itself a contested position. — Astorre

I lean to modal realism because I don't see a difference between the existence of a possible (logically consistent) object as "real" and as "merely possible". Logical consistency seems to be just existence in the broadest sense. The challenge is to find which objects are logically consistent, because they must be consistent with everything else in reality (like in mathematics - everything either fits together or falls apart). This might involve looking for the necessary properties or relations of any possible object or analysis of the concept of "object" or "something" itself and build from that. But if reality is complex enough to include the set of natural numbers (arithmetic) then it is impossible to prove that our description of it is consistent, as per Godel's second incompleteness theorem. Sensory detection of objects helps us find consistent objects but the senses have their limitations too.

I propose we step away from a substantialist approach to ontology and turn instead toward a processual one, which I am actively developing. — Astorre

I imagine sets as the fundamental objects in reality, from which everything else might be explained (properties as general objects could be fundamental too, if they are consistent objects other than sets). I am no set theorist or mathematician but my methaphysics is strongly influenced by the wide acceptance of pure set theory as a foundation of mathematics, in which all mathematical concepts can in principle be expressed as pure sets. It would explain the mathematical aspect of reality, if reality consists of sets. A space can be defined as a set with a continuity between the sets inside this set (as defined in general topology). Time can be defined as a special kind of space, as defined in theory of relativity. So it seems that a spacetime, with its spatiotemporal, including causal, relations, could be a certain kind of set. But then spacetimes would be just certain parts of a much greater reality where all possible (logically consistent) sets exist.

Redness, then, is not inside the apple. It is born from the interplay of all three participants. This makes the property contingent: for a different observer (say, someone with color blindness), or under different lighting conditions, redness may not manifest at all. — Astorre

I like your approach, which has the virtue of preserving realism (the mode is an actual internal structure of the apple) while recognizing that the property is contingent on the other factors you name.

On this view, does the property happen in a specifiable location? We require apple, light, and observer in order for the redness to manifest itself; do you want to say that this happens in or to the observer?

That makes sense to me, but it seems like a criteria for "who gets a hearing" not which positions are accepted. — Count Timothy von Icarus

I agree. I took it as read that weren't trying to answer the question of what is just, but set up the parameters for how to discuss it. My own view is that the question doesn't admit of a definitive answer; you perhaps see it differently; but on either view, "Who is closer to the truth?" can only come into play once we have "entered the room" of this particular practice, or communicative action. (I use Habermas' term not to be pedantic, but because I like the way it emphasizes how thinking about something is a process that happens among people, it is a doing. When we think, we are always part of a community, otherwise our concepts would be meaningless.)

I'm still trying to fit all this into @litewave's very interesting conception. If the "set of all just things" is indeterminate, and even contains contradictory elements, it needs another name. "Set of all things called just" won't do; this set is more discriminating than that. What we can say is that the uncertainty about the property of being just is reflected in the uncertainty about what to call the set, so that may be a point in litewave's favor.

In the end, I think we're likely going to abandon the whole "property" notion for justice, and conclude that, even if some things are properties, "being just" isn't one of them.

But now it seems that there are genuinely different coextensive properties, which would dash the hope of identifying properties with sets. — litewave

We learn the concept of an abstract property, such as redness, by discovering a family resemblance between a set of concrete objects in the world, such as a car, flower, cherry, sunset.

This set of concrete objects, being an abstract concept, is distinct from its concrete objects. In other words, the set is not contained within itself.

So it makes sense to identify properties with sets.

Are there really genuinely different coextensive properties?

So it makes sense to identify properties with sets. — RussellA

Or if not identify, then at least associate a set and a property like this:

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. An extensional definition of a set would be a definition by listing all the particular elements.

Are there really genuinely different coextensive properties? — RussellA

What about these two: the property of redness, and the property of being an instance of redness (or the property of having the property of redness). Both properties seem to be instantiated in all instances of redness, so the instances form one and the same set.

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.

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

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

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.

She probably knows about redness as a universal. — frank

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