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

See the summary I provided above for Moliere. — Count Timothy von Icarus

Where?

You appear here to have gone to great lengths to explain what your argument is not, without explaining what it is. Your reply is in such broad terms as to say very little.

Added: links and citations are conducive to clarity. It might be helpful if you did not remove them.

I hope not.

It's like because its trite, immature and ignores the specific criteria that causes prostitution to obtain. — AmadeusD

Love your sense of irony. Is professional sport that bad?

I think professional sports of all sorts are prostitution; why single out sex? — unenlightened

I don't think this reply received the attention it deserves.

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?

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.

At this point I'm wondering if the difference in positions is that I think of "underdetermination" with respect to scientific theories, especially -- rather than applying to the radical skeptical position. — Moliere

Well, that's how it is used, apart from Tim's modification. Any finite set of observations can be satisfied by innumerable general theories.

Tim argues that scepticism follows from his version of "underdetermination", and so is using that term in an unconventional way. He seems to think that since evidence can't determine which of the competing theories is true, we cannot chose one theory to go on with - as if the only basis for choosing were deductive.

But of course we can choose Einsteinian relativistics over Newtonian relativistics, for all sorts of reasons that are not merely deductive.

Added: But of course Wittgenstein and Quine are not sceptics in the way Tim suggests. Each provides a way to move on without the need for deductive certainty.

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.

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...

...or, the flip side of "underdetermination" is confirmation bias. — Moliere

My point, in so few words. Nice.

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.

But that's exactly what I am arguing — litewave

More's the pity. Ok.

...you are conflating arguments from underdetermination and skepticism. — Count Timothy von Icarus

Not so much, although your walking back on scepticism is positive.

Your main argument is that underdetermination only seems feasible because of the rejection of your two metaphysical principles. From this you deduce that "...the skepticism resulting from underdetermination has been seen as a serious threat and challenge". But what you call "underdetermination" here is very different to the use of that term in Duhem and Quine. Where they showed us specific cases in which we could not decide between competing theories, you suppose that we can never decide between any cases, unless we accept your two premises. Doing so lumps together quite disparate approaches, flattening the philosophical landscape, reduces complex positions to caricatures. Your "argument" consists in labelling.

We ought look a those two premises closely.

The first supposes that every event has a cause, inviting your rhetorical ploy 'If you want to argue that things.. are "for no reason at all," without causes, feel free.' The issue here is not that there are uncaused events, so much as that a method that supposes explanation in terms only of ultimate cause is no explanation at all. Consider the extreme case, where god is the cause of all things. That the coin we flip comes up heads is supposedly explained as "the will of God"; but that explanation will work equally well if the coin had come up tails. Regardless of what happens, the explanation is "God caused it to happen that way", and so we never learn why this happened and not that; this is no explanation at all.

If presenting a cause is to function as an explanation, it must say why this even happened and not some other event. Saying that "Things/events have causes" is trivial, indeed frivolous. What makes talk of causes useful is their role in setting out what happens from what might happen.

"God wills it" satisfies your rejection of "underdetermination", but at the cost of providing no explanation at all.

The second supposes that there is always an explanation. Given my argument above, this is again trivially true. "God wills it" will explain everything, and yet is no explanation at all. But more, what you are setting aside here is humility, the capacity of admitting "I don't know". You would prefer an explanation that it complete yet wrong to one that is incomplete yet right; you would prefer a complete lie to a partial truth.

You picture yourself as defending rationality when you are denying it. Underdetermination is a feature rather than a flaw, marking the difference between rationality and dogmatism.

Several quite different points, all of them muddled together.

First point. might be understood as saying that in addition to the set consisting of {book, car, apple} there is a fourth item, grouping these together, the box the set comes in, as it where. That's not right. There is nothing in addition to the elements.

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 .

Third point. {a,c,b} and {a,b,c} are the same set in that they are extensionally identical, but are not identical in that they are written down differently. That the description is different does not make them different sets.

Forth point. Similarly, The set of the first three letters of the alphabet is extensionally identical to {a,b,c}. Again, how the members are specified is not a part of the set. Only the elements are apart of the set.

Fifth point. Those first four points hopefully server to show that the members are what count in determining a set. Now from the other direction, the apple in hand is not the set {apple}. This difference is usually set out by saying the set is an abstract individual apart form the apple. The tricky part is realising that this does not contradict those first four points. We do not write apple={apple}. .

That might clear things up. Maybe. But the thread "An unintuitive logic puzzle" got to fifteen pages.

OK. :grimace:

Keep reading.

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

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

Oops.

The set is this membership criteria, not the actual teachers. — frank

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

All a property, in the broadest sense, is just an attribute or quality possessed by something. — Count Timothy von Icarus

You say that with great certainty, as if it were an explanation of what a property is. But what is an attribute, if not what we attribute to something? Etymology: "assign, bestow," from Latin attributus, past participle of attribuere "assign to, allot, commit, entrust;" figuratively "to attribute, ascribe, impute," from assimilated form of ad "to" (see ad-) + tribuere "assign, give, bestow"

So it's whatever we say it is? Cool. But I doubt that's what you meant.

Otherwise, yep. Except that you shouldn't include the modal operator in Leibniz' Law without some clarification.

Ah - Brassica rapa subsp. rapa. Ok. Neither is worth substituting for potato.

Brassica napobrassica

https://en.wikipedia.org/wiki/Rutabaga

So are swedes and rutabegas and purple top turnips extensionally identical?

If so, we may substitute one for the other and achieve the same distasteful result.

I think it's pretty easy to identify red things — Count Timothy von Icarus

Me too.

I don't think anyone here is suggesting there are no red things or no triangles.

"nothing has the property of being triangular" which would seem to imply that nothing is triangular. — Count Timothy von Icarus

The picture holds you. Can't we just say that there are triangles, and leave "there is a property of triangularity" or whatever as a slip into reification?

The slide from "there are red things" to "therefore redness must be a thing" and then to Platonic forms floating in metaphysical space and all the historic mess that followed. No, but there is that car and that sunset.

Are you saying that we can't tell rutabegas from swedes? I thought they were the same. These things:

Taste like squashed bugs. Or at least, how I supose squashed bugs might taste, not having tasted them... to the best of my knowledge.

I suppose they might be OK with enough maple syrup. But even then, better just to eat the syrup.

But I think it is important to emphase the identity of a set as a single thing, distinct from its elements, — litewave

I don't see what "distinct from" does here. S is different from a, but is it different from a, b and c? Extensionally, no.

Perhaps you are trying to capture the unity of the set. I'd see that as what we do in deciding to talk about a, b, and c together, rather than something in addition to a, b, and c.

What I want to be clear about is that there is no "box" - those curly brackets mark the set but do not add something to it like the box would.

I'll leave you to it.

I don't disagree with that, with some caution. So {a,b,c}= {a,c,b}. The care is that {a,b,c} is not other than [a,c,b}. So some caution with "It means that we identify the thing in relation to other things".

So again, when we say a set is identical to it's elements, we just mean that for example S = {a,b,c} and (extensionally) that where we can speak of S we can also speak of {a,b,c} and substitute one for the other.

I don't think we have a substantive difference in our opinions here.

Different versions of the same property are actually different properties — litewave

Yep. {a, b, c} is different to {a, b, d}. It would only amount to equivocation if we were to say that they were the same. Tim's objection is unclear.

If redness is all things that are red in all possible worlds, then that set is infinite as is the set of of all things we're not sure are red. If there is infinitely uncertainty as to redness, then what value is our redness set in telling us what is red? — Hanover

Why would being infinite make it uncertain? There are infinite odd numbers, but no uncertainty here. Infinity does not lead automatically to vagueness.

I really don't think that a set is identical to its elements. — litewave

Sure. We both need to keep track of what is being said here. We are talking at cross purposes.

"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.

If there are no properties, in virtue of what would some things be members of "the set of red things" but not others? — Count Timothy von Icarus

Yep.

What's your answer? That red things are exactly those that have the property "red"?

And you think this helpful?

If I ask you what it is to have the property of red, will you say that it is to have redness?

Do you like merry-go-rounds?

I'm inclined to agree that defining "properties" in such broad terms is fraught with difficulties. An answer might be to drop "property" rather than extensionality.

Unless, perhaps, you can offer a definition of "property" that we might use? I suspect this will bring us back to your circular definitions of "essence".

I guess something has to be said.

Mashing Hume, Wittgenstein, Kripke, Duhem, Quine, Kuhn, Mill, Feyerabend, and Goodman together and calling them "sceptics" ought ring alarm bells with anyone.

And those two supposed foundations - That things do not happen “for no reason at all" and that everything has an explanation - at least some discussion might be worthwhile, rather than mere assertion.

But the Law of Diminishing Returns applies here. It's harder to critique than to make stuff up.

Yep.

But I still have questions, above, about the identification of property with set, for litewave to consider. — J

Yep. The answer might be to drop the notion of "property", which is somewhat anachronistic anyway. It reifies a semantic difference.

, I supose that answers your question? THere is a difference between why we count an animal as having a heart, and that we cont an animal as having a heart.

Now I do not think that there is general answer to the question of why we group some things together. And I think Thomistic talk of essences tries to paper over that difference, by pretending that it's essence all the way down, while never quite telling us what an essence is.

Added: case in point, as it seems.

That's all very rough, of course. More detail can be found at The IterativeConception

"Classes" is a more specialised term. If we stick to sets, we can start with individuals - a,b,c; and form sets of these - {a,b}, {b,c} - and then sets of these - {{a,b},{b,c}} - but avoid mixing them - {a, {a, b}}. Then we have a hierarchy that avoids Russell's little conundrum.

A set is a single object. Elements are multiple objects. So a set is not identical to its elements. — litewave

A bit of care is needed here. A set is identical to its elements, and nothing more. No box. I hope we agree on that. So we can write that the set S = {a,b,c}; and say that S is identical to {a, b, c}; and by that we would mean that where we write "S" we might instead write {a, b, c}, and vice versa.