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

Cool. Let's look at this.

If the property is "is the set of these individuals", effectively F in F(x), what is the individual which satisfies this predicate?

It's interesting to try and think of sets in terms of predicate logic -- and I can see the analogy between a predicate and a set since we can quantify over both and make valid deductions between those quantifications. So the temptation is strong to equate a set with a predicate.

The way I was taught*, at least, sets are different from propositions are different from predicates, but they can have relations to one another. If I were to render set theory in terms of predicates I would say "Set theory is the study of validity of the "is a member of" relation", whereas predicate logic is the study** of validity between predicates. So they're kind of just asking after different things -- one is "how do we draw valid inferences between two propositions?" and the other is "how do we draw valid inferences between collections of individuals?"

Now, interestingly, I think we can mix these logics sometimes -- but usually we want to keep them distinct because they're hard enough to understand as it is that it's better to not overgeneralize :D

I'd argue what this shows is that logic is something we choose to utilize. I'm not sure there really is some universally true thing we can say about sets and predicates sans the rest of the logical system. We could choose, for whatever reason (perhaps because this question is interesting and we're interested in how logic works), to start with the equation "Properties are equivalent to sets" and then work out the validity of that identification.

But, at least if we're learning, these are generally treated somewhat separately (even though, yes, there's a lot of overlap between these ways of talking at the intuitive level)

**EDIT: OK, is the result of the study.... a theory is not an -ology

*EDIT: Also, "taught" was by a math instructor and the rest is self-study, so I could be missing something. I don't want to lead people astray but I do like thinking about this stuff.

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

Oh yeah I don't think logic is intuitive at all. It's part of why it's interesting.


Just thinking out loud here about the stuff I like to think about here, I doubt I'm introducing you to anything:


One thing w/ Ari's deductive logic is that it can be reconstructed with the latter inventions of logic. Ari pretty much sets his definitions such that quantification, predication, and sets are all rolled into kinds of propositions and explores the validity between these kinds of propositions.

I find that interesting on many levels -- one, Ari's deductive logic is supportive of his inductive logic due to there being properties which things have that can be discovered. So it's not "innocent" in the sense that it fits into what we tend to interpret as his Philosophical Project: but it is "naive" in the sense that today we'd distinguish these things.

For me, "snake oil" is another way of talking about "nonsense" or "anything goes," so my response is the same. There are reasons why snake oil isn't taken seriously as a nostrum -- reasons that have little to do with knowing how to define health -- and likewise, whatever the equivalent of "justice snake oil" would be, doesn't get a hearing in serious conversations about justice. Why not? Why doesn't "anything go"? Why doesn't aporia lead to intellectual anarchy? See the Republic.

All I can do is appeal again to our actual practice. The fact that we may be puzzled about key aspects of a subject doesn't open the door to any discourse whatsoever. Can you think of a discipline in which that actually occurs? Rather, certain perennial, plausible positions are questioned and refined. By what standards? That's what we talk about, along with the positions!

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. — Count Timothy von Icarus

Yes. I don't see this as a defeater to the OP's thesis.

But that's exactly what I am arguing — litewave

More's the pity. Ok.

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

This is interesting but confusing. Is "Being in that set means having that property" different from "'Being in that set' is a property of the pebble"? I thought we didn't want set membership to count as a property.

There are reasons why snake oil isn't taken seriously as a nostrum -- reasons that have little to do with knowing how todefine health

This is red herring, like the "definition of justice in the Great Dictionary of Philosophical Terms." I said "knowledge of health" (or "knowledge of justice") not "the definition." Do advances in medicine and the development of medical skill not involve knowledge of health and disease?

For me, "snake oil" is another way of talking about "nonsense" or "anything goes," so my response is the same.

Sure, I perhaps made the example too obvious. There are, however, professional philosophers or scientists who publish in philosophy who make claims and counter claims about how each other's traditions are nonsense and sophistry (e.g., the targets of the New Atheists and those who have responded to them). They're both part of broader established traditions.

More to the point, what could have gone wrong in the Salafi tradition? They had discourse and practices. So did German academia in the 1930s, yet many of their ethicist, jurists, and theologians, etc. were enthusiastic or at least stayed about the countries new course. So, it does not seem that "practices" in general lead to what we would probably agree is justice, but only certain sorts of practices.

Why not? Why doesn't "anything go"? Why doesn't aporia lead to intellectual anarchy? See the Republic.

Which part exactly?

Can you think of a discipline in which that actually occurs?

Sure, philosophy. Although its becoming academicized has tempered it (although this is partly from exclusion, and arguably flows more from power dynamics than anything else). From the birth of the printing press to the early 20th century it was full of quite radical positions. Positions like "might makes right" were popular enough to warrant in depth responses from figures like Hegel (when he was already famous).

I am just explaining how the term is used in metaphysics. — Count Timothy von Icarus

Well, no, you're not, since as explained, the use you make of "property" is circular, except for the bit where having a property is attributed - something people do.

Part of the problem here is that properties are taken as fundamental, when they are better understood as one-place predications, set amongst a hierarchy starting with zero placed predicates and working on up - or a hierarchy of individuals, groups of individuals, groups of groups of individuals, and so on.

And this in part comes back, it seems to me, to the inability of syllogistic logic to deal with relations. I don't think it's able to see the difference between the above and ordered n-tuples. "John loves Mary" is different from "Mary loves John" - How does the machinery of syllogistic logic capture this asymmetry? At best, it fakes it by treating “loves-Mary” as a property of John and “loves-John” as a property of Mary—but this obscures the relational structure. Modern predicate logic was invented precisely to fix this gap.

Syllogistic logic is forced to treat the world as consisting of properties. It's the classic example of how our language traps us in an ontology. But perhaps those inside Thomism can't see the bars.

This is red herring, like the "definition of justice in the Great Dictionary of Philosophical Terms." I said "knowledge of health" (or "knowledge of justice") not "the definition." Do advances in medicine and the development of medical skill not involve knowledge of health and disease? — Count Timothy von Icarus

OK, fair enough, as long as "knowledge of X" can be acquired without necessarily being able to define X.

There are, however, professional philosophers or scientists who publish in philosophy who make claims and counter claims about how each other's traditions are nonsense and sophistry — Count Timothy von Icarus

Really? In those words? I'd say that was comparatively rare. Good philosophers tend to be much more interested in understanding and, sometimes, refutation, than in name-calling. Is there some publication or passage you have in mind?

Why not? Why doesn't "anything go"? Why doesn't aporia lead to intellectual anarchy? See the Republic.

Which part exactly? — Count Timothy von Icarus

No one in the Republic suggests that "Justice is really a fish." Why not, if they don't know what justice is? Why doesn't their ignorance open the door to nonsense?

Positions like "might makes right" were popular enough to warrant in depth responses from figures like Hegel (when he was already famous). — Count Timothy von Icarus

Yes, and look what happened: We no longer consider such a position viable. That's how intellectual investigations operate, over time. Less plausible, less defensible positions are weeded out, and newer, stronger possibilities are broached. And the discussion goes on.

No one in the Republic suggests that "Justice is really a fish." Why not, if they don't know what justice is? Why doesn't their ignorance open the door to nonsense? — J

Indeed, agreeing that the proffered definitions of justice are inadequate presupposes agreement concerning what is just and what isn't.

We already had what Socrates was looking for...

I thought we didn't want set membership to count as a property. — J

Indeed, and this is part of what is fraught in thinking of a fourth item it {a,b,c} that makes it a set; if we allow for that, then we need a fifth item that makes the four items a set; and a sixth that makes the five a set; and so on. Bradley's regress attacks!

In the end, isn't it just what we do? That we attribute? That's where 's definition of "property" leads him, against his will.

Part of the problem here is that properties are taken as fundamental, when they are better understood as one-place predications, set amongst a hierarchy starting with zero placed predicates and working on up - or a hierarchy of individuals, groups of individuals, groups of groups of individuals, and so on

In older writings properties are often called "predicables." How are there "predictions" without anything to predicate? This is what I mean by: "we will invariably just end up reinventing properties."

How are there "predictions" without anything to predicate? — Count Timothy von Icarus

The love of reification. We have a predicate - red - so there must be a thing - redness. Why?

As Austin pointed out, there need be nothing in common between the sunset and the sports car, apart from our using the same word for both; apart from our attribution.

"we will invariably just end up reinventing properties." — Count Timothy von Icarus

Well, you will.

Indeed, agreeing that the proffered definitions of justice are inadequate presupposes agreement concerning what is just and what isn't. — Banno

I would put it differently. We (and the Greeks) already know quite a bit about justice, and quite a bit about why drawing a line under the subject is difficult, and quite a bit about the history (and conundrums) of the question. We don't have agreement on what is just; what we do have is agreement on what will count as sensible contributions to the question, "What is justice?" That is ample for keeping the conversation nonsense-free, and for refuting inadequate definitions.

It's all very "building your boat on the ocean," isn't it? And yet we manage not to drown.

Really? In those words? I'd say that was comparatively rare. Good philosophers tend to be much more interested in understanding and, sometimes, refutation, than in name-calling. Is there some publication or passage you have in mind?

Have you read the New Athiests? This isn't anything new. Consider Nietzsche's invective or that Russell writes that the reason Nietzsche made his more misogynistic claims about whipping women is because "he knew that in reality the woman would get the whip away from him and end up beating him."

No one in the Republic suggests that "Justice is really a fish." Why not, if they don't know what justice is? Why doesn't their ignorance open the door to nonsense?

You think "might makes right" is nonsense but not Thrasymachus' claim that justice is "whatever is to the advantage of the stronger?" What about Cleitophon's claim that "justice is just whatever the stronger thinks (appears) is to their advantage?" Or, in other dialogues, Protagoras' claim that whatever one thinks is true is true for that person (a position I am pretty sure you have called nonsense before) and Gorgias' claim that rhetoric is the master art because it can convince powerful people and assemblies to agree with you over experts?

Thrasymachus' silence is generally taken as being a shamed silence after being called out on his nonsense, and he cannot accept Cleitophon's suggestion to save his argument because it would imply that sophists are useless because one is always already right about what one thinks.

Yes, and look what happened: We no longer consider such a position viable.

Who is "we?" That particular take has had a great resurgence on far-right circles that have a good deal of sway these days. I imagine that Bronze Age Pervert has sold a good deal more copies than any academic philosopher in the past decade.

That's how intellectual investigations operate, over time. Less plausible, less defensible positions are weeded out, and newer, stronger possibilities are broached. And the discussion goes on.

Is this something like a "law of history," inexorable in the long term? Something like natural selection, but for truth? Would this imply that more recent philosophy will tend to always be better in the long run?

I would think that history shows that only certain sorts of processes produce such progress, and that it is sometimes reversible, and also uneven. The good is often sewn alongside the bad when it comes to ideas. It does not seem to me that truth is equivalent with something like "fitness" vis-á-vis the reproduction and dispersion of memes, information, theories, or opinions. This is why salacious gossip and implausible urban myths often "replicate" better than true statements.

In technology, where there are a strong, widely applicable incentives in play, there might tend to be a stronger pull towards progress, but this relationship seems more fraught when it comes to ethics and politics. It seems more likely that, in general, vice will tend to beget vice and error to beget error, and vice versa—not in any irreversible process mind you, but on average.

Indeed, agreeing that the proffered definitions of justice are inadequate presupposes agreement concerning what is just and what isn't.

We already had what Socrates was looking for...

To an extent, yes. The reader is supposed to recognize absurdities, although they have to be fully untangled first.

In the dialogues themselves, agreement is rarely reached however. Socrates often switches interlocutors because the original one is intransigent. I think there is a salient dramatic point in that. Normally the sophists just lapse into sullen silence. With Protagoras' this move is quite straightforward. If no one is ever wrong, then no one needs Protagoras as a teacher (his profession). But this often isn't so much agreement about the topic at hand (initially) as it is exposing how these positions refute themselves.

A main theme in the Republic is that reason is itself defenseless. Socrates is forced to go down in Book I because "we are many and you are one."

Only the elements are apart of the set. — Banno

If the set really was "only the elements", then the empty set would be impossible. No elements, no set.

This is interesting but confusing. Is "Being in that set means having that property" different from "'Being in that set' is a property of the pebble"? I thought we didn't want set membership to count as a property. — J

On further thought, I find this confusing too. The property of "being in set X" may seem to be the property of members of set X, but perhaps it is actually the property of the set membership relation instead. (A member is in set X but "being in set X" is not the property of the member but of the set membership relation between the member and set X.) Similarly, the property of "having property X" may seem to be the property of instances of property X, but perhaps it is actually the property of the instantiation relation instead. (An instance has property X but "having property X" is not the property of the instance but of the instantiation relation between the instance and property X.)

Since I equate set with property, members of set are equated with instances of property, and set membership relation is equated with instantiation relation.

I would put it differently. — J

I don't think the difference substantial. Again, after Davidson, I'd suggest that we have overwhelmingly agreement as to what things are just and what are not, developed over time and use, but that we focus on our differences because they are more interesting.

It's all very "building your boat on the ocean," isn't it? — J

Yes. Contrast that with the way Tim sticks to stipulated definitions...

You think "might makes right" is nonsense but not Thrasymachus' claim that justice is "whatever is to the advantage of the stronger?" What about Cleitophon's claim that "justice is just whatever the stronger thinks (appears) is to their advantage?" Or, in other dialogues, Protagoras' claim that whatever one thinks is true is true for that person (a position I am pretty sure you have called nonsense before) and Gorgias' claim that rhetoric is the master art because it can convince powerful people and assemblies to agree with you over experts? — Count Timothy von Icarus

PI §201 yet again: there's a way of understanding justice that is not found in stipulating a definition but is exhibited in what we call "being just" and "being unjust" in actual cases.

You don't seem to be addressing the critique. IS there a way for syllogistic logic to recover here?

I suppose one issue might be circularity. How do you know what belongs in a set? — Count Timothy von Icarus

One possible solution to the problem of circularity.

Suppose the property of redness = {red car, red building, red book}. We understand the property of redness by the elements in its set, but we must know the property of redness before we can include an element in the set.

Suppose there are many different objects of many different colours.

It is a feature of the human brain that a person can discover family resemblances in different things. We cannot explain how the brain does this, but we know that it does.

The family resemblance may be the colour red, being large in size, being angular in shape, being distant from the observer, etc.

Family resemblance is a term used by Wittgenstein on his book Philosophical Investigations 1953.

If a person does discover a family resemblance, this becomes a concept, such as the concept of redness, largeness, angularity, etc.

This concept of redness is abstract and singular, and is different in kind to the concrete instantiations in which the brain discovers family resemblances, such as red car, red building, red book, etc. The property of redness is distinct from its set of concrete instantiations.

Calling these objects a set is an acknowledgement that they are parts of a whole, they are parts of the concept of redness.

This can be formalised as redness = {red car, red building, red book}.

In other words, a red car has the property of redness.

The circularity is broken by the ability of the brain to discover family resemblances in different things.

Yes. Contrast that with the way Tim sticks to stipulated definitions

Where have I done that? The only mention of definitions was @J's usual straw man to the effect that if one mentions knowledge of the relevant subject (i.e., justice, health) as the measure of expertise or wisdom, one must necessarily be appealing to a "Great Philosophical Definition in the Sky."

I don't think anything about my past thoughts would suggest that I think things are "whatever we stipulate them to be."

I asked @J in virtue of what are some opinions nonsense" and he brought up a (IMO false) dichotomy between (great sky) definitions and "practice." One might suppose though that, from an epistemic standpoint, one needs something like a "definition" to determine the members of these sets, so I suppose something like a definition might enter into things there.

But either all practices a justificatory or they aren't. We agree that some aren't. So this isn't an answer. In virtue of what are some practices to be discounted? I'm not sure. Practice seems to have been an incomplete intermediary; the search goes. Athough now it seems to be suggested that some sort of innate knowledge allows us to recognize "nonsense?" But then why do traditions that put forth nonsense not recognize this then? How did Protagoras miss this for instance?

PI §201 yet again: there's a way of understanding justice that is not found in stipulating a definition but is exhibited in what we call "being just" and "being unjust" in actual cases.

Right, hence, the Good is not on the Divided Line. It must be outside of it because it relates to the whole, the apparent and the real, and so it cannot be merely one point upon the line. To be properly absolute, the absolute must include reality and appearances. Likewise, in the cave image, Socrates must break into his own story from without as the sign of the Good. And then the text itself refers outside itself to the historical Socrates at this point, to a life lived.

Plato is (reasonably IMO) quite skeptical of the power of language in this area (e.g., the Seventh Letter).

You don't seem to be addressing the critique. IS there a way for syllogistic logic to recover here?

I pointed out that the rejection of properties (or individuals) is absurd and your response was "yep." What more is there to say? It is possible to explain what a circle is without recourse so "it is the property of being a circle." Even if the case is different for red (as G.E. Moore argued) I don't see the issue. One can know what red is without having a bunch of words formed into an explanation of it, and that red is a predicable. You're the one asking for a definition of red for it to be considered a property, which seems absurd to me.

But red is not a primitive that stands on its own. As Hegel would point out, its intelligibility relies on the broader notion of color, etc. So I would tend to disagree with Moore here; yet even if he is right, I don't really see the issue.

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.

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

Why doesn't aporia lead to intellectual anarchy? — J

Sheer stubbornness of the philosopher :D

Oh, sorry. I thought that's what you were looking for in set theory. — frank

Nope.

The intuitive bit I can see is wanting to equate predicates with sets since we can quantify over both. The unintuitive bit is where I'm arguing there's a difference that maybe doesn't look like there is a difference between these logical objects.

Really? In those words?

Have you read the New Athiests? . . .et al — Count Timothy von Icarus

I haven't read the New Atheists because I wasn't aware they were taken seriously as philosophers. Nietzsche and Russell, sure, but my question stands: Terms like "nonsense" and "sophistry" evidence more than disagreement; they in effect repudiate the user's qualifications to speak at all. Do you find this in the writers you mention? Do you think it characterizes what good philosophers do?

You think "might makes right" is nonsense but not Thrasymachus' claim that justice is "whatever is to the advantage of the stronger?" — Count Timothy von Icarus

But that's just it -- I don't think it's nonsense. It's a position that needs refutation, unlike the position that justice is a fish. My question was, Why is Plato willing to give us the conversation between Thras. and Socrates, but not to bring in some rando who thinks justice is a fish? And my answer would be, Because although we (and Socrates) are ignorant of the ultimate nature of justice, we nonetheless know quite a bit about it, enough to know what counts as a good question.

But then why do traditions that put forth nonsense not recognize this then [an innate knowledge of what is nonsense]? — Count Timothy von Icarus

Are there really philosophical traditions of nonsense? Which ones do you have in mind? And no, there's nothing innate about being able to tell nonsense from insightful discourse. We learn it by joining the conversation. It's the "building the boat on the ocean" idea. We aren't handed a set of rules. We learn what the conversation is about, and what questions respected predecessors and colleagues are pursuing and think worthwhile. I suppose one could step back and ask, "But how do I know all of this isn't nonsense?" It depends how literally one means "nonsense," I think -- whether it's shorthand for "views I don't find defensible." But I don't want to overcomplicate this.

Who is "we?" That particular take has had a great resurgence on far-right circles that have a good deal of sway these days. I imagine that Bronze Age Pervert has sold a good deal more copies than any academic philosopher in the past decade. — Count Timothy von Icarus

(I like that epithet!)

I have no idea what sort of philosophy the far-right circles may be espousing. By "we," I meant philosophers of repute, those who know the history, the questions, and the difficulties.

That's how intellectual investigations operate, over time. Less plausible, less defensible positions are weeded out, and newer, stronger possibilities are broached. And the discussion goes on.

Is this something like a "law of history," inexorable in the long term? — Count Timothy von Icarus

That's a good question, and perhaps highlights something unique about philosophy. Yes, I believe there is philosophical progress, but it has to do with clarifying questions, not producing definitive answers. I wouldn't say there's anything lawlike about it; it just seems to describe (one version of) the history of philosophy. I think we're better able to discuss ontology than Aristotle's contemporaries were, but that doesn't take away anything from his brilliance at showing how the questions might be laid out.

J's usual straw man to the effect that if one mentions knowledge of the relevant subject (i.e., justice, health) as the measure of expertise or wisdom, one must necessarily be appealing to a "Great Philosophical Definition in the Sky." — Count Timothy von Icarus

I feel bad that this could be seen as a straw man, as it suggests I didn't give you a generous enough reading. I truly believed you were focused on definitions rather than knowledge, and claiming that without a definition of, say, the good, we wouldn't know how to recognize good things. My apologies if that led me to construct arguments that weren't to the point. Perhaps you could say more about how the quest for a definition of a concept relates to what we can know about it?

I don't think the difference substantial. Again, after Davidson, I'd suggest that we have overwhelmingly agreement as to what things are just and what are not, developed over time and use, but that we focus on our differences because they are more interesting — Banno

I wish that were true! For me, the question of what sort of economic system can be considered just is the great ethical question of our time. I don't find any agreement about this within philosophy or outside it. Is it just that some people are born in poverty, others in wealth? Is property ownership just? Even such simple questions have no agreed-upon answers, because we haven't decided whether economic justice is a real concept, and if so, where it belongs in liberal democracies. But I go astray . . .

But that's just it -- I don't think it's nonsense. It's a position that needs refutation, unlike the position that justice is a fish.

If nonsense is limited to statements on a level of "justice is a fish," then it seems to keep out very little though, right? But "nonsense" was originally the criteria for what deserves to be taken seriously, no?

But, to anticipate your objection, that doesn't mean that anything goes, that some nonsense from Tom deserves to be taken as seriously as "justice(Rawls)."

By "we," I meant philosophers of repute, those who know the history, the questions, and the difficulties.

So then the standard would really be "what philosophers of repute" take seriously. But I wonder if this really works well for all contexts. In the context of Stalinism or Hitlerism, was it the "philosophers of repute" who had a monopoly on serious claims about justice? Salafi scholars have repute amongst Salafis and are often denigrated in the West. Dugin has great standing in Russia. Nick Land was a professor at one of the most prestigious English language programs in Continental philosophy. He only fell out of repute when he began to espouse far-right views. But then, this seems to leave open the possibility that "what deserves to be taken seriously " is just whatever those who exert control over reputations (i.e., academia) allow. This seems particularly problematic for a field that is routinely criticized by its own membership for being parochial and operating in a siloed echo chamber.

I am certainly not against the idea that wisdom might best be measured by the wise. My point is rather that there seems to me be some significant daylight (sometimes a great deal) between "who is currently said to be wise (in our preferred context presumably)" and who might actually be wise. It does not seem to me that the two must coincide, or even that they must inexorably progress towards coinciding.

Plus, a standard based on the opinions of those with current repute seems to rule out, by definition, any radical critique until that radical critique has already been accepted by those of repute. But if those of repute hold to this standard of only taking the views of those who already have repute seriously, they will never countenance a radical critique.

It depends how literally one means "nonsense," I think -- whether it's shorthand for "views I don't find defensible."

Well, if it was the latter, that seems preferable. "Views that are defensible" are kept out, not merely "views that are wholly ridiculous," or "views espoused by people lacking proper repute within our preferred context." And what "makes a view defensible," is presumably not just that it fails to be absurd, or is put forth by someone of repute. That then, is what I would suggest for a standard.

I truly believed you were focused on definitions rather than knowledge, and claiming that without a definition of, say, the good, we wouldn't know how to recognize good things.

I can see the confusion in context. If we are beholden to the idea that properties are sets of whatever exemplifies a property, then yes, it does seem that something like a definition is required to know what the members of that set ought to be.

Initially though, I was just responding to the possibility that there might be sui generis properties for each person's opinion about each property. Aside from a lack of parsimony, it's hard to see how knowledge would be constituted in this case. I cannot really ever be wrong about what belongs to justice(Tim) or living(Tim). By definition these properties just would be what I think belongs to them. For us to ever be wrong, it must be at least possible for us to be wrong about which common terms apply to which particulars.

the set of all things that have this property. — litewave

a set is a single thing too and its elements can be said to participate in or share the character of this thing. — litewave

the set of not only its presently existing instances but also of its past and future instances and of all its possible instances (existing in possible worlds) — litewave

Can we agree that only one possible world actually exists (the actual world)?

In that case, your set includes "things" that do not exist, never have existed, and never will exist (they are non-actual possibilities). Let's focus on this subset of your big set. Does it have any members? Are the members things? If so, what is a thing?

Can we agree that only one possible world actually exists (the actual world)?

In that case, your set includes "things" that do not exist, never have existed, and never will exist (they are non-actual possibilities). Let's focus on this subset of your big set. Does it have any members? Are the members things? If so, what is a thing? — Relativist

If only the actual world exists, then a property has instances only in the actual world, and the property is still a set of its instances (but the instances exist only in the actual world). The instances of a property are whatever has the property.

My point is rather that there seems to me be some significant daylight (sometimes a great deal) between "who is currently said to be wise (in our preferred context presumably)" and who might actually be wise. It does not seem to me that the two must coincide, or even that they must inexorably progress towards coinciding. — Count Timothy von Icarus

Right. None of this is cut and dried. What Habermas calls "communicative action" is never a simple process, if engaged in good faith.

So then the standard would really be "what philosophers of repute" take seriously. But I wonder if this really works well for all contexts. — Count Timothy von Icarus

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.

a standard based on the opinions of those with current repute seems to rule out, by definition, any radical critique until that radical critique has already been accepted by those of repute. — Count Timothy von Icarus

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.

If nonsense is limited to statements on a level of "justice is a fish," then it seems to keep out very little though, right? But "nonsense" was originally the criteria for what deserves to be taken seriously, no? — Count Timothy von Icarus

I think we both fell into using "nonsense" without being clear what we meant. I agree that a position can be safely ignored even if it isn't literally nonsense. How do we learn to discriminate? By engaging in the practice with others and watching how they do it, and why.

I can see the confusion in context. — Count Timothy von Icarus

Good, I wouldn't want you to think I was deliberately blowing smoke. My position is that "knowledge of" doesn't have to start with a lexical identification, so we should resist that. I thought you were placing untoward emphasis on a "definition first" approach, but as you say, the issue raised in the OP is difficult.

This is interesting but confusing. Is "Being in that set means having that property" different from "'Being in that set' is a property of the pebble"? I thought we didn't want set membership to count as a property. — J

On further thought, I find this confusing too. The property of "being in set X" may seem to be the property of members of set X, but perhaps it is actually the property of the set membership relation instead. (A member is in set X but "being in set X" is not the property of the member but of the set membership relation between the member and set X.) Similarly, the property of "having property X" may seem to be the property of instances of property X, but perhaps it is actually the property of the instantiation relation instead. (An instance has property X but "having property X" is not the property of the instance but of the instantiation relation between the instance and property X.)

Since I equate set with property, members of set are equated with instances of property, and set membership relation is equated with instantiation relation. — litewave

My reply above was a groaner, wasn't it. Perhaps the property of "being in set X" could be interpreted as a property of the set membership relation but it is clearly a property of elements of set X, first and foremost.

So, given that I propose identifying property X with the set of instances of property X, it seems that the elements of set X share two properties: property X and the property of "being in set X". And these two properties have the same extension - all elements of set X, so they are coextensive properties. However, I think that these two properties are not really different; they are one and the same property, just described differently. The property of "being in set X" is the same as the property of "having property X", which is the same as the property of "being X", which is the same as property X. So, the property of "being in set X" and property X are one and the same property.

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.

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?