Identification of properties with sets
I am proposing that we could plausibly identify a property with the set of all things that have this property. This set would be the property, and the elements of this set would be the instances of the property. For example, the property of redness would be identified with the set of all red things, or the property of being a car would be identified with the set of all cars.
At first, one might find such an identification counterintuitive because redness and carness (being a car) seem like something singular that is shared by its instances rather than a multiplicity that encompasses the instances. But a set is a single thing too and its elements can be said to participate in or share the character of this thing.
Another objection might be that visually a set of red things just doesnt look like redness or a set of cars just doesnt look like a car. But what does redness or carness look like? Whenever we try to visualize redness as something that is red or carness as a car we always visualize a particular instance of redness or carness, not the redness itself or the carness itself. Redness and carness seem to elude visualization because they are somehow dispersed across space, time and possible worlds.
Yet another objection might be that a property may be instantiated not only in things existing now but also in things that existed in the past or will exist in the future and that a property would exist even if it is never instantiated. This problem can be fixed by clarifying that a property is 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). There cannot be a property that is never instantiated because it must be at least possible for a property to be instantiated (a property that is impossible to instantiate would contradict the very notion of property as something that can be possessed) and if it is possible for a property to be instantiated then its instance exists in some possible world. Not sure if this requires modal realism (modal fictions might be regarded as elements of a set too).
Finally, there may be a concern that necessarily coextensive properties, for example equilateral triangle and equiangular triangle, collapse into one property because their instances constitute one and the same set. However, I would say that such properties are indeed one and the same property, just described in different words.
At first, one might find such an identification counterintuitive because redness and carness (being a car) seem like something singular that is shared by its instances rather than a multiplicity that encompasses the instances. But a set is a single thing too and its elements can be said to participate in or share the character of this thing.
Another objection might be that visually a set of red things just doesnt look like redness or a set of cars just doesnt look like a car. But what does redness or carness look like? Whenever we try to visualize redness as something that is red or carness as a car we always visualize a particular instance of redness or carness, not the redness itself or the carness itself. Redness and carness seem to elude visualization because they are somehow dispersed across space, time and possible worlds.
Yet another objection might be that a property may be instantiated not only in things existing now but also in things that existed in the past or will exist in the future and that a property would exist even if it is never instantiated. This problem can be fixed by clarifying that a property is 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). There cannot be a property that is never instantiated because it must be at least possible for a property to be instantiated (a property that is impossible to instantiate would contradict the very notion of property as something that can be possessed) and if it is possible for a property to be instantiated then its instance exists in some possible world. Not sure if this requires modal realism (modal fictions might be regarded as elements of a set too).
Finally, there may be a concern that necessarily coextensive properties, for example equilateral triangle and equiangular triangle, collapse into one property because their instances constitute one and the same set. However, I would say that such properties are indeed one and the same property, just described in different words.
Comments (322)
This seems a similar concept to using set theory to define the natural numbers.
Frege and Russell proposed defining a natural number n as the collection of all sets with n elements.
Wikipedia - Set-theoretic definition of natural numbers
Numbers are properties (universals/general entities) too, so defining a number n as a collection of all things that instantiate the number n would be another example of identifying a property with a set (collection). However, a thing need not instantiate a number n only by having n elements. For example, here is a set that has only 1 element but it instantiates number 2 by having 2 embeddings of elements:
{ { { } } }
This is actually how Zermelo defined number 2. Von Neumann defined number 2 as the following set of 2 elements:
{ { }, { { } } }
Both von Neumann's and Zermelo's definitions of number 2 are actually just particular instances of number 2.
Frege and Russell's definition of a natural number n as the collection of all sets with n elements is closer to capturing the general/universal nature of number n, but a complete definition of a natural number n would be a collection of all instances of number n. The property that Frege and Russell defined is not "number n" but "set of n elements" or "set of cardinality n".
I am just wondering:
Suppose only three things in the world have the property of redness.
Consider the set {red car, red apple, red book}
It seems that a set is not the same thing as the elements within the set, as a box is not the same as the things inside the box (an analogy given by Copilot). For example, even though all the things inside the box are red, the box itself could be black.
So to say that we can identify a property with the set of all things that have this property may be like saying we can identify the property of redness with something that is black.
Is this valid?
What exactly do you mean by "identify" here? I suppose one issue might be circularity. How do you know what belongs in a set? Suppose we take "justice" or "just acts." In virtue of what are all "just acts" properly members? If we identify the property of "being just" as simply "being a member of the set of 'just acts'" we don't seem to get anywhere.
Further, even if I had the set of all past just acts to refer to, how exactly does this help me determine which acts would be just in the future, or to identify new just acts? If all I know about justice is that "just acts belong to the set of just acts," then future identification seems impossible. I would have to instead look at the set and reason out a sort of definition, or at least an observable pattern, by which to identify future or potential members. But in this case, it seems to me that it is really the essence of justice, signified by the definition, that is actually what "membership is in virtue of."
I mean that the property is the set. But knowing only that justice is the set of all just acts will not help you know which acts belong to this set or specify what justice means. There may not be a universally agreed specification of justice, so different people may identify justice with different sets of acts. It's easier with redness, which can be specified with reference to a certain range of wavelengths of light, although the exact boundaries of this range may not be universally agreed either.
There are properties that exist that are not of a referent, like the property of being the King of France attaches to no object, yet being the King of France is a property nontheless. There are also no essences of objects that would dictate which set all examples belong, like whether a particular car belongs in the set of cars is contextually dependent.
Searle, Wittgenstein.
Is it possible (logically consistent) for the property of being the king of France to be instantiated? If yes, then it is instantiated in some possible world. If not, then it would be self-contradictory.
Quoting Hanover
It depends on how "car" is specified. Usually it is specified as "self-propelled vehicle on four wheels". In that case, the property of being a car is the set of all self-propelled vehicles on four wheels.
So when you say everything must have a referent, you're speaking modally, meaning it has a hypothetical referent in a possible world? I didn't get that from your OP.
Quoting litewave
Why can't a car have 3 wheels and why wouldn't a broken car still be a car?
Maybe replace "specified" with "used." Otherwise, you just have a purely prescriptive language, and not one that really exists.
Yes, all instances of a property, in all possible worlds, constitute the set that I indentify with the property.
Quoting Hanover
It can. And with such a specification it would be a different property, identical with a different set.
There are problems, though. Perhaps not the ones identified by Hanover and Tim.
Here's perhaps the classic reply. Having a kidney is not the very same as having a heart, and yet all animals with kidney also have hearts. We can say that the extension of "Having kidneys" and the extension of "Having a heart" are the very same.
What we can say is that the extension of a property is just those things to which the property applies,
You are right to puzzle over the notion of a "property".
Identity can be defined extensionally using substitution, and without circularity. That's how it is done in modern logic.
It feels plausible that a set can be identified by a property or even a set of properties.
But, no, they're different -- a set is its' elements, rather than a property which all the elements share.
That might well be what is leaning in to.
Not sure how right I am as I still think on these things.
Quoting Banno
This -- and the earlier queries of @Count Timothy von Icarus and @Hanover -- is where my attention is drawn as well.
The extension, let's say, of all beings with kidneys is the same as that of all beings with hearts. (I don't know if that's true, but no matter). We can also say, The extension of all triangles with equal angles is the same as that of all triangles with equal sides. But if we were to decide, as the OP recommends, that we have identified the properties of having a heart and being equilateral by pointing to their sets, how do we deal with the problem that the reason why the respective sets are co-extensive is different in each case?
In the case of the triangles, it's not implausible, as you point out, to declare that being equilateral and being equiangular are two ways of describing (or should it be "naming"?) the same property. That's because the two descriptors are logical equivalents -- to assert the first is to assert the second, a priori. But hearts and kidneys are different. A posteriori, it turns out that there are biological reasons (again, as we're supposing) for beings with kidneys to have hearts, but that is not a conceptual or logical equivalence.
Does this matter, on the question of whether we're zeroing in on a property, in each case? I'm not sure, because I'm not sure how you understand "property". Are you recommending a new use for the term "property," or a new, improved analysis of what "property" has always meant?
Also, @Count Timothy von Icarus's query is a fair one: Yes, we can define identity in the usual way of modern logic, but the OP is asking us to stretch. Is that kind of identity really intended to be the same? Your answer was: "I mean that the property is the set." That "is" deserves expansion. If all you mean is what @Banno means -- the "is" of logical identity -- fair enough, but we want to be sure.
Thanks. Not on an academic level.
Quoting Banno
As long as it is possible (logically consistent) for an organism to have a heart without a kidney, or vice versa, then the set of all possible instances of having a heart is different than the set of all possible instances of having a kidney, and thus these two properties are differentiated. You don't even need to conceive of some extraterrestrial organism, just take some ordinary animal whose kidneys have been removed while the heart stayed in place. However, as I mentioned in OP, if two properties are necessarily coextensive, for example "equilateral triangle" and "equiangular triangle", then they are one and the same property, just described in different words.
Would that mean that "being in that collection of objects [or individuals, per @Banno]" is a shared property? Can an object "wander in," so to speak, and partake of that property? This may not be a question about your definition so much as an expression of uncertainty about "property".
I think this replies, with a cross-post, to part of my question, thanks.
A set is a collection of individuals. They need not have anything related to one another, or share anything at all -- the individuals are the set and there's nothing else to it. The pebble on the ground and the sentence I say 5 miles away can form a set.
My understanding is that "classes" can include rules, but I don't understand how to do that formally while I do understand naive set theory at least.
Yes, you are basically correct.
Lets take a closer look at what might happen were we to come across an organism with what appeared to be kidneys and yet no heart. We have a choice. We can decide that there are organisms with kidneys and yet no hearts, and say that the extension of "animal with kidneys" is different to the extension of "animal with a heart". Or alternately we could maintain that all animals with hearts also have kidneys, and simply say that although these organs do much the same thing as kidneys do in animals with hearts, they do not count as kidneys.
Now kidneys filter blood, which requires a circulatory system, which typically requires a heart. So the latter is probably the biologist's best option.
The Thomists amongst us see this as somehow nominalist and arbitrary. Btu that's how words work.
A set is a single object. Elements are multiple objects. So a set is not identical to its elements. Even in set theory, a set is an object in its own right: if set A is an element of set B, it doesn't mean that elements of set A are elements of set B.
That single object is the collection, but the thought here is that there's nothing more to that than being the collection of the individuals in the set.
We can name a set, so it can be an element -- and is an element of the set that is itself -- but a set need not be a single object (or name) at all. The empty set comes to mind here.
Best acknowledge early that sets are best formed in stages, so as to avoid Russel's paradox. Start with individuals, then sets of individuals, then sets of sets of individuals, and never the twain.
If so, does it do so by delaying the question? :D
I'm good with forming sets in stages either way. Defining sets in a technical manner is something I still think on and think I don't understand, really.
In a very rough form its how Z works, so yes.
What was the question?
" My understanding is that "classes" can include rules, but I don't understand how to do that formally while I do understand naive set theory at least. "
I suppose I was looking for reassurance of this distinction between sets and classes -- either in the right or wrong way. I've thought of sets as any collection of individuals whatsoever and classes as collections of individuals with inclusion rules. Is that bollox in my head that I'd need to defend or let go of, or something sensible from your perspective?
Why wouldn't a car of any state or component missing be anything but a "piece of metal?" Because a knife is a piece of metal. You can't expect someone to buy or barter for a "piece of metal" without some sot of deeper and thorough designation, could you?
This is interesting, really. Is a pure metal shell of a car with no furnishing, engine, or internal infrastructure a car? Average person would say no (or would they?). Is a car with all those things but that doesn't start or function a car? Average person would say yes and of course call that a "broken car" or a "lemon" or a "clunker," But it's interesting because while one is considered a car that fails to perform the function of a car (yet can be made or altered to do so) the same is true of the shell of the car without any other parts. So explain that, eh?
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.
Yes. So what, if anything, would we want to say about identifying such a set with some property? I take it you don't want "being in set X" to count as a property -- nor could it, on the OP's proposal.
I'm open to 'being in set X' because I think Russell's paradox is legitimate, and generally I like the paradoxes of self-reference as a point of thought -- stuff like the liar's paradox seem to sit here.
But, yes, it could not count on the OP's proposal which is why the paradoxes of self-reference came to mind.
I don't want to say anything about identifying a set with a property for this very reason :D
Gotcha. I was thinking of "identifying" (verb), which made me think of the epistemological questions.
But doesn't this mean that there would be many different versions of the same property? So there would really be "justice(Tom), justice(Greg), justice(Sandra), etc. Given properties' roles in metaphysics, that seems problematic, particularly since the stipulation re modality would seem to indicate that we should be considering "everything that might possibly be considered x." A pretty popular idea in contemporary analytic metaphysics is the "bundle/pin cushion" view where things just are their properties (plus or less a sort of "bare particular substratum" or haecceity). Yet we seem to have opened the door on there potentially being as many properties as there are (potential) opinions. Wouldn't this risk making everything into everything else? This is why I personally prefer an intensional explanation of properties.
Even on deflationary accounts, this still seems like it could present problems because it would mean we are guilty of equivocation any time a different set is specified (and how, in practice, could we even determine that different sets had been specified?).
A similar sort of issue occurs with due to modality. If we're consequentialists, presumably any act might be "just" or "good" as well as "unjust" or "evil" given the right context. Does that mean good and evil represent the same set and thus the same thing? Likewise, wouldn't the set of contingent falsehoods end up being the same as contingent truths? But then are truth and falsehood the same thing unless they are necessary?
Also, what about the property of "being a property?"
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.
Yes, you and @litewave both crossed posts with me. But I still have questions, above, about the identification of property with set, for litewave to consider.
Quoting Banno
Right. The "bleen people" group as they do (choosing bizarre intersections of "green" and "blue"), and while they are doing something we find impractical and hard to parse, they may have their reasons.
Yes. I know you probably don't care for that conclusion, but I think it's exactly what happens. There are indeed different construals and attempts at definition for an abstraction like "justice." 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)." The fact that we cannot define something doesn't mean we can't know anything about it, or can't tell a promising clarification or interpretation from one that isn't. Look at the Republic. Justice never gets a satisfactory definition, but it would be hard to read the book carefully and not believe you've learned something about the subject.
Yep. The answer might be to drop the notion of "property", which is somewhat anachronistic anyway. It reifies a semantic difference.
The more obvious objection, to my mind, ties into the modal caveat in the OP:
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?"
Sure, but lacking a definition seems to me to be much different issue. 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. So, we'd be justifying a positive metaphysical claim using our own profession of ignorance.
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".
If there are no properties, in virtue of what would some things be members of "the set of red things" but not others?
Or in virtue of what would different individual things he discernible?
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 really don't think that a set is identical to its elements. A single object is not identical to many objects. We can write that the set S = {a,b,c} but we cannot write that the set S = a,b,c. Also, in set theory, the set {{a,b,c}} is different than the set {a,b,c}; the first one is a set with one element, while the second one is a set with three elements. I know that in our everyday life this distinction is unimportant because for example a set of three apples weighs the same as the total of the weights of the individual three apples and so the set in itself doesn't add any additional weight to the weights of the apples. Well, that's how our particular world works - forces like gravity act on elementary particles and can be added up. But in a different possible world a force might act only on certain sets and not on their elements; you might then get a set of three apples that weighs a pound while each apple alone is weightless.
Maybe the distinction between a set and its elements is important for the emergence of consciousness from unconscious parts - the whole is conscious while its parts are not, because the whole has an additional property to the total of the properties of its parts.
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.
Mine might just be a vagueness objection that implicates infinite vagueness, but isn't the purpose of the extensionalism exercise to eliminate just that?
Different versions of the same property are actually different properties (although they are similar in some way significantly enough to call them "versions"). Tom may call property X "justice" while Greg may call property Y "justice". Properties X and Y are objective parts of reality and we can all agree what are their instances, but we may not agree which of the properties should be called "justice".
Why would being infinite make it uncertain? There are infinite odd numbers, but no uncertainty here. Infinity does not lead automatically to vagueness.
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.
When we identify some thing extensionally/by substitution, it doesn't mean that we identify the thing with its extension. It means that we identify the thing in relation to other things. For example, we can identify a set extensionally in relation to its elements, which are different things than the set itself. At least that's how I understand extension because I don't think that one thing can be identical to many 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.
Order of elements of a set doesn't matter, I agree. But I think it is important to emphasize the identity of a set as a single thing, distinct from its elements, because I propose to identify a set with a property, which is supposed to be a single thing too rather than multiple things.
That's an interesting point, but doesn't this reference a distinction in categories between analytically defined and empirically defined?
If sorting infinite root vegetables, some will be rutabegas, some we're not sure, and some will be Swedes.
But every other integer after 1 is odd no matter how high we count.
So, the rutebega set is infinite across all possible worlds as is the not-sure-if-rutebega set, but we have zero not-sure-if-odd set.
That is, I feel your odd number counter example was not applicable. It's of a different sort.
I also think my rutebega/Swede distinction raises another sort of problem along the lines of your kidney talk.
I think it's pretty easy to identify red things. Color can be explained in various ways. Likewise, triangular things are those things with three sides, etc.
But even if we were left with properties as some sort of inexplicable metaphysical primitive, that still seems better than "nothing has the property of being triangular" which would seem to imply that nothing is triangular. Or more broadly, "nothing has any properties," which seems absurd. One will just end up reinventing the basic idea of a property under another name in order to say that anything is anything.
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.
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.
Turnips, Purple Tops.
Me too.
I don't think anyone here is suggesting there are no red things or no triangles.
Quoting 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.
If so, we may substitute one for the other and achieve the same distasteful result.
No, rutabaga is a different plant, from the pictured turnips
https://en.wikipedia.org/wiki/Rutabaga
At my grocery store, a rutebega is a large round root with purple on all parts, for some reason with a very waxy exterior. A turnip is smaller, shown in the picture you provided. A Swede is a tall blonde specimen from up north.
Are they extensionally identical? Is water and H2O?
This makes the H2O - water point, right? The scientific term means something different from the common one, but they collapse under the same set, losing that distinction.
The op is messed up. You cannot identify the property of redness with the set of all red thing. The supposed conclusion would actually be inconclusive, requiring a definition. Further, "being a car" cannot be defined as a property.
Ah - Brassica rapa subsp. rapa. Ok. Neither is worth substituting for potato.
All a property, in the broadest sense, is just an attribute or quality possessed by something. So, Socrates is a man, a rose is red, etc. The rose is red, but the rose is not identical with the color red. And there is the idea that multiple things can instantiate the same properties.
For instance, a common simple version of Leibniz' Law is: "Necessarily, no two objects share all their properties." One need not assume redness is a "thing" to make use of this.
There are nominalist accounts of properties. One does not need to be a "Platonist" to make use of properties. It's a quite useful concept because:
Be aware of the mysterious "Triangle of U".
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.
A set is not its elements. Imagine a club that all teachers automatically belong to, by virtue of being teachers. The set is this membership criteria, not the actual teachers. A set is an abstract object.
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.
Nuh. The set is the teachers. The criteria are not the set.
Oops.
nope. Read Mary Tiles' book on set theory. The club metaphor is from her book.
Then she is mistaken. Or has been misread.
Quoting Set Theory An Open Introduction
I stumbled over this same issue, so you're not alone, but you're wrong. In the club metaphor, the set is the membership list, not the members themselves.
A set is an abstract object. That's the part you have to get in order to understand set theory.
Keep reading.
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.
Properties, qualities, characteristics, and so on, are mental or linguistic abstractions of the things described, or even the descriptions themselves. Your morphological derivations redness and carness indicate this. They are derivations, not sets or properties.
Consider the singleton set containing one element, such as Socrates = {Socrates}.
From Zermelo-Fraenkei set theory, no set can be an element of itself, meaning that a singleton set {Socrates} is distinct from the element it contains, Socrates. (Wikipedia - Singleton (mathematics))
Does this not mean that saying the box can only be black if it contains instances of blackness violates the Zermelo-Frankei set theory, in that the singleton set must be distinct from the element it contains?
IE, thinking about set theory, a black box would then not be distinct from the instances of blacknesses within it.
I don't know, but am curious to know.
This is exactly true, contingent on the what we mean by the word "plausible".
We can plausibly do a lot of things that on closer inspection can't be done, but finding that out does not negate that it was plausible to begin with.
In general, these kinds of ideas I would argue are best understood as naive set theory used in ordinary language.
What I mean by that, is that we have a bunch of mathematical concepts about sets that nothing stops us from using in ordinary discourse outside an axiomatic system to discuss various things; both to talk about axiomatic systems from a non-axiomatic point of view (such as to talk about what an axiomatic system "is like" and kinds of things that can be done with it using ordinary language to convey concepts to both experts and non-experts) as well as developing concepts that have nothing to do with axiomatic systems but the words and ideas of set theory are useful for the purpose.
Therefore, such informal use of set-theory language is going to have all the problems of ordinary language. We have zero problem with the fact ordinary language can be used to express all sorts of contradictions, paradox and nonsense, as well as having fundamental unresolvable problems such as delineation, universals, and so on, and throwing in some set theory words isn't going to change the situation.
That does not make it invalid to talk about sets of "everything red" for example, but we can know ahead of time that such a concept cannot be developed into something rigorous without axiomatization.
Once you axiomatize, if all goes well, you can have rigorously defined symbols, rigorously defined acceptable grammar (how you may put those symbols together), and rigorously defined permitted manipulation of those symbols (how you may move those symbols around), but in so doing we know ahead of time that we lose the flexibility of ordinary language; you can no longer just "say things" and hope to express meaning, but rather statements proposed to be true require rigorous proof.
What makes sense depends on what is being talked about.
For example, it makes sense to propose dividing the class into a set of short and a set of tall students. The meaning is clear that the goal is to either by symbolic representation of the students or then physically move them around, to define two groups of students based on height. The meaning can be clear and it can be equally clear that once we have our sets of students we can perform further set operations, such as creating subsets of those sets based on hats or whatever we please, and going on to create unions and bijections and so on.
What is of course not clear is exactly the difference between short and tall, how to handle a new student showing up (do the sets represent the students at the time of creating the sets, or then sets that represent students that may come and go, either by joining the class or then being expelled), and so on. Trying to resolve all these problems will run into all the problems of ordinary language and naive set theory, but the use of such language can be entirely sufficient to accomplish whatever the task was (forming teams by height and hat wearing for some purpose).
So litewave wants the property P to be equal to the set of all things that have P, we'll call it set Q. But we can't say that P=Q? Because they're different types of things?
But that's exactly what I am arguing - there is a fourth object and this fourth object is identical to the set of the three objects. The set as a single object cannot be identical to three objects, so it is identical to a fourth object. The identity of the fourth object is fixed by the three objects because there can only be one set of the three objects, but the set itself is not identical to the three objects.
Collections or sets are not just mental or linguistic abstractions though. As I am typing this I am actually holding a collection called "smartphone".
Aha, I think I see what you mean. The singleton set is distinct from the element it contains and so it is something additional to the element. The element is red and the singleton set is something else (though probably not black, because that would require some more complex structure that can absorb light). 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.
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.
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.
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?
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.
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?
Shades and hues of red are instances of redness, so they all have the property of redness.
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:
Quoting 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."
Quoting 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.
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.
That's what I am saying the property of redness is - the set of all red things (the set of all instances of redness).
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.
Red has the property of redness? That doesn't sound right.
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.
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?
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.
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.
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.
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.
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.
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.
Consider "The set whose elements consist of sets without properties which is a member of itself" -- Quoting 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?
Because a collection is something different than its elements, yet it is also something that is common to the elements.
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.
Well, in predicate logic you have individuals that have/satisfy a property/predicate. I propose that the property is the set of these individuals.
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?
By being an element of the set, thus having what all the other elements of the set have.
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.
The point of my OP is that the set actually is the property. That may not be obvious.
I think I understand what you mean.
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.
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.
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!
Quoting Count Timothy von Icarus
Yes. I don't see this as a defeater to the OP's thesis.
More's the pity. Ok.
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.
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?
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.
Which part exactly?
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).
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 Marybut 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.
OK, fair enough, as long as "knowledge of X" can be acquired without necessarily being able to define X.
Quoting 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?
Quoting 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?
Quoting 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.
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...
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.
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."
Quoting 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.
Quoting Count Timothy von IcarusWell, you will.
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.
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."
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.
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 versanot in any irreversible process mind you, but on average.
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."
If the set really was "only the elements", then the empty set would be impossible. No elements, no set.
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 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.
Quoting J
Yes. Contrast that with the way Tim sticks to stipulated definitions...
Quoting 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?
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.
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?
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).
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, 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.
Sheer stubbornness of the philosopher :D
Quoting 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.
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?
Quoting 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.
Quoting 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.
Quoting 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.
Quoting 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.
Quoting 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 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 . . .
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?
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 [I]said to be[/I] 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.
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 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.
Quoting litewave
Quoting 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?
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.
Right. None of this is cut and dried. What Habermas calls "communicative action" is never a simple process, if engaged in good faith.
Quoting 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.
Quoting 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.
Quoting 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.
Quoting 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.
Quoting 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.
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?
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, sinceunless we are very restrictive about who gets a hearingthey 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.
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.
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 [I]something[/I], but not what they think they are an expert in).
These two properties have exactly the same instances and if I got it right, they are one and the same property, just described differently.
Membership in the red set entails having red as a property. Entailment doesn't get you to identity, though. Or if so, how?
This way:
Quoting litewave
Having the property red is not the same as the property red. Having a ball is not the same thing as the ball.
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 admit, I did some head-scratching! :smile:
Quoting 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.
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.
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.
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.
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.
Not unimportant. And again, speaking in rough outline.
An interesting approachformally 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 abstractsomething 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 objectsor as sets of such objectswe 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 propertieswithout 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 apples embodied beingits surface texture and chemical compositionthat 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 apples 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.
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.
Wouldn't surface texture also count as a property? Can we think of surface texture as a realized event?
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.
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.
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.
Quoting 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?
Quoting 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.
Quoting 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.
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?
Quoting 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.
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?
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.
Quoting 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.
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.
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 probably knows about redness as a universal.
She has never seen a universal though. But she has seen collections (sets), so she may know more about collections than about universals.
You think knowledge is limited to what you can see? If so, she's never seen a set. A set is an abstract object.
A set is a collection of objects. An average person surely knows what a collection is. Not so surely a universal.
Also:
Extensional definition of Ship = {ferry, tankers, icebreakers}
Intensional definition of Ship = {large boat, travels on water}
===============================================================================Quoting litewave
A common example of coextensive properties
The property of "having a heart" = {human, dog, cat}
The property of "having a kidney" = {human, dog, cat}
True, a heart is a distinct thing to a kidney.
However, the above example is invalid, as a human can exist using an external dialysis machines. With medical progress, hearts and kidneys are no longer necessary to what makes a human.
Is "being an instance of redness" referring to one thing
Taken at face value, an instance is one particular thing. This infers that "being an instance of redness" is also one particular thing, meaning that it cannot be a property.
Therefore, the expression "the property of being an instance of redness" is not a valid expression.
Is "being an instance of redness" referring to several things
However, if "being an instance of redness" is referring to several things, as in "being an exemplification of redness", then it means the same as "redness".
"Being an instance of redness" and "redness" are then not distinct as a heart and kidney are distinct, meaning that "the property of redness" and "the property of being an instance of redness" is not an example of coextensive properties.
There may not be examples of genuinely different coextensive properties, meaning that it doesn't prevent us from associating a property with a set.
Not in set theory. A set is criteria. It's an abstract object.
"Being an instance of redness" seems to be a property of all instances of redness, yet it seems to be a different property than redness itself. Both properties have exactly the same instances, which suggests that the properties could be one and the same, but "being an instance of redness" refers to an instance in relation to redness while redness refers only to redness.
Come on, objects that are included in a set satisfy certain criteria (have certain properties) but the set is a collection of those objects.
Though...
I'd put it to you that the collection of individuals is an abstract object. To use your cell phone example -- we can think about the cell phone as a collection of particular objects and then name this in accord with set-theory. I.e. we can make sets which refer to concrete individuals, but to treat something as a set is still an abstraction.
We can also treat the phone as an individual, from the logical point of view. Suppose the set of all of my possessions. Then, even though I can break my phone down into smaller parts in the case of the set of all of my possessions, the phone is merely an individual.
Whether something is within a set or not doesn't reflect upon its ontology -- I'd say that's more of a question for mereology (which the logic we choose to utilize may have implications for, but it's still different from the logic of sets)
The point is a set isn't something you can see, anymore than you can see infinity.
It doesn't matter what's in the set. The validity that's being explored are the inferences one may draw about sets regardless of their contents.
So supposing two sets, supposing B is a subset of A, we can infer that -- no matter what elements are in B, if they are in B then they must be in A.
Right. That's not at odds with the theory that a set is a collection of objects -- as in, any collection of objects, regardless of what those objects are, even if the set does not have any objects in it or some of the objects are infinite.
I don't think sets exist as much as are ways to think about things.
@litewave seemed to be suggesting that people know firsthand about sets because they can see them. That is incorrect. You can't see a set.
I'd call that a hypostization, which is an easy thing to do. Similarly so with treating sets like predicates.
Though, if we're Kantians, it'd seem like you couldn't help but to see the world through categories, so maybe there's a position wherein one could see sets -- but treat them in a logical way.
I prefer to think of sets as abstractions which we stipulate, though.
Quoting litewave
A set is any given collection of objects.
An average person knows what a collection is and so you can start from there.
But the abstraction begins when we stop considering what is in the collections and consider the relationships between collections and the inferences we can draw given any collection whatsoever.
So we name sets things like A and B to signify that we're not talking about particular individuals, or even particular sets -- but rather the valid inferences one can make given any set whatsoever unspecified beyond being a set.
That jump to the "any set whatsoever" is the part the average person has to learn when we're talking about [s]when[/s] learning set theory. Not just a collection, but the very concept of collection and how we can draw inferences from that.
I'm not sure what you're trying to say. The mainstream view among mathematicians is that sets are abstract objects. You can see them with the mind's eye, but not physical eyes.
I'm trying to say that you're correct about sets abstractness (at least, in my view, while acknowledging possibilities), and that @litewave is correct about the definition of a set with a little tweaking.
The words are right, the interpretation isn't quite there.
Quoting J
I'm coming to notice that I'm pretty much avoiding "property" all together and relying upon "predicate" (to circle back to where I left you off and rethink)
And where I've been reflecting from is the logical side, rather than the metaphysical side. I more or less took "property" to be substitutable with predicate, but if the conversation is going towards the perception of wholes then "property" may be the better term over the logical quandaries I've been raising.
In which case I'm on the side that "property" is something we distinguish within a metaphysical context rather than something anything "has" outside of that context. "Property" is an abstraction, too -- a word which can be used in various ways within a particular metaphysical expression. I prefer "affordance" to "property"
I'm not sure what you mean by "abstract" or "abstraction" here. Is the phone a concrete or an abstract object? Is it a collection of other objects or not?
What I mean by "abstraction" is that you can treat the phone in either way without changing anything real.
You can treat the phone as an element -- which is that which is a member of a set -- or you can treat it like a collection -- such that its elements are members of the set "my phone".
It's how you think about it that makes the difference in terms of perceiving the phone as an [s]set[/s] element or a collection of individuals. It is both.
It depends on what we mean by "abstract" and "concrete". It is often said that concrete objects are located in space or in spacetime. Then a collection like a particular phone would be a concrete object. A collection consisting of a phone located in my house and another phone located in my friend's house would be a concrete object too, although some might resist that because the two phones are separated "too much". A collection consisting of my phone and of another phone in a different universe that is in a different spacetime might be regarded as a concrete object because its elements are located in a spacetime but then again, they are in different spacetimes, so this collection transcends a single spacetime. And then there is the general property/universal "phone" (or "phoneness") - that which all particular phones have in common - and I guess this would be regarded as an abstract object by almost anyone because unless we identify it with the set of all phones, it seems to transcend spacetime or be located in spacetime in an especially weird way.
So, to read you here, I'm taking your ideas about each to be:
Concrete:
Quoting litewave
Abstract:
Quoting litewave
And you're noting the weird part where it seems they come together.
yes? No?
So what's your belief with respect to "Identification of properties with sets" now?
I've tried to dissuade you, but are you still committed?
I see what you wrote early on:
Quoting Moliere
But I still don't think that a set is identical to its elements because a single object cannot be identical to multiple objects. So a set is another object, additional to its elements.
Looking at that rendition I agree.
A set is any collection of elements is a better rendition. It's another (logical) object, to the point that its elements aren't a part of how we infer validity between sets.
Right. There is a difference between "element" ("member") and "subset". Outside of set theory they may be both conflated with the concept of "part" but they are parts in different senses.
Supose our domain of discourse - what we are talking about - contains only the letters "a" and "b". How many things are in that domain?
If we listen to Frank, then we have a, and we have b, of course; two things. But we also have the set {a,b}. So there are three things: a, b and {a,b}. But then we also have {a,b,{a,b}} - so there are four things in our domain - a, b, {a,b}, and {a,b,{ab}} - and off we go. I hope folk see the problem inherent in counting a set as a different thing to it's elements.
No, a set is no more than the things it contains.
There's also the problem that if a set consists in a criteria rather than it's members, then we can construct the criteria "the set of sets that do not contain themselves", and upset Bertrand Russell. No, set consists in its elements, not in a description of those elements.
That's part of the axiom of extensionality. We can have innumerably many descriptions of some set - the set of odd number, the set of all numbers one less than an even number, the set of numbers that are two more than the last number in the set, starting at one. These are not three different sets, but three different descriptions of the very same set. It's the elements that count (pun intended), not the description.
What this does is to define what we mean when we say that a set is an abstract object - the set {a ,b} is not something else in addition to it's elements, but a different way of talking about a and b. A bit of extra language, not a bit of extra ontology. We talk as if the set were a new thing, but it isn't one of the things in the domain.
Similarly, when we talk of the red of the sports car and the red of the sunset, we haven't thereby added a new thing to the word - the property of redness. Redness is just a new way of talking about the car and the sunset.
Properties dissolved by analysis. Tim will love it. Not.
I'm thinking "none" at that level of abstraction.
Or perhaps the opposite in reflection.
If our domain of discourse consists of only two letters then, on the first iteration, there is nothing to be said.
However, just that I understood "contains only the letters "a" and "b" " indicates some meta position wherein I can say things like "contains" etc etc.
Quoting Banno
I suspect no one will love what I have to say, but I say it cuz I think it's true.
Not really set theory, otherwise we would need TonesinDeepFreeze.
Glad to see you've since taken the vows of nominalism!
Except me.
Types?
... Nominalism in the sense of, as @Banno says, dissolving properties by analysis.
But not necessarily in any strict sense.
E.g. not in the sense of, as Goodman says, "hyper-extensionalism", i.e. allowing no more than the power set to be defined upon the elements in the domain.
Rather, just in the sense of, as you (and @frank, I think? I need to study the thread) correctly say, extensionalism, i.e. allowing the definition of sets according to their extension to iterate indefinitely. E.g. on the domain {a, b} the sets { }, {a}, {b}, {a, b}, {{a}, a}, {{a}, b}, {{a}, a, b}, {{b}, a}, {{b}, b}, {{b}, a, b}, {{a, b}, a}, {{a, b}, b}, {{a, b}, a, b}, {{{a}}, a}, etc.
Not sure what @Banno is thinking there :chin:
It does indeed continue ad nauseum, but that is indeed set theory.
So much so, that structures in set theory are typically constructed entirely from the empty set.
Yes, where is he!
I missed it.
Yep. Tones can tell me, rightly, how all the stuff I've said here is a gross oversimplification.
@TonesInDeepFreeze?
Hasn't been seen for eight months.
Rereading I want to highlight this bit as a better explanation of what I've been saying.
Naturally I'd accept @TonesInDeepFreeze, though at this point I wonder if that's too much pressure on them.
Tone's last few posts expressed frustration with a particularly recalcitrant contributor. :worry:
Enter the prompt "Is a set identical to its elements?" in ChatGPT, Claude or Gemini. They will all give you the answer No.
"the properties shared by the elements of the first set" might be where @litewave is coming from.
Your expertise is not an intrusion at all.
I think @Banno is there. That's why he posited a difference of hierarchies between elements, sets, sets of sets, etc.
Try "Is a set completely determined by its elements?"
Alas, I have broken the vows in the course of this thread. Although it was not really nominalism about properties; I still regarded them as real separate objects, I just wanted to identify them with sets.
:up:
So the set is another object, in addition to its elements.
You can, easily. Yet choose not to. Like always.
I don't think set theory is easy, intuitive, etc.
Depends on what you mean by individual. There are obviously two elements in this set: a, b. By the way, in pure set theory these two elements are always sets as well.
I'm interested.
Where can I learn more on this?
I'm a naive set theory boi who reads logic texts and that's it.
I don't know what pure set theory is.
A set is pure if all of its members are sets, all members of its members are sets, and so on. For example, the set containing only the empty set is a nonempty pure set. In modern set theory, it is common to restrict attention to the von Neumann universe of pure sets, and many systems of axiomatic set theory are designed to axiomatize the pure sets only. There are many technical advantages to this restriction, and little generality is lost, because essentially all mathematical concepts can be modeled by pure sets.
https://en.m.wikipedia.org/wiki/Set_theory#Ontology
Quoting litewave
Right, but, identify them with sets in the way that model theory maps predicates to sets? (Sets defined on elements in a domain.)
Then you can be at least extensionalist about properties just by replacing them with predicates? Or with the corresponding sets if you prefer, yes!
Hyper-extensionalism is a further economy:
Quoting Goodman, p49
And in this case cancelling out the property is indeed a matter of cancelling out the set. And satisfying @Banno's thirst for a restriction to individuals. See Goodman's "calculus of individuals". (Mereology as @Moliere alluded.)
Why would there be a problem in counting a set as a different thing to its elements?
https://st.openlogicproject.org/settheory-screen.pdf
Heh.
Got it.
That's the next logic textbook cuz of you :D
Sorry.
I wanted to say that the set is the common property of its elements.
Yes, and so does a model theorist? (And earlier theorists of the semantics of first order logic too.) I thought this was what @Banno was pointing out to you 4 years ago? I may have misunderstood.
But in set theory, sets do add to ontology. And in pure set theory all elements of a set are sets too.
That's why nominalists (e.g. Quine) didn't like taking it for granted in logic.
I have not studied model theory.
Thanks for the clarity.
To my eye, this reifies the property, making it a thing alongside the elements of the set.
That is, you now have the set and the property, separately, and are apparently defining the set in terms of the property.
But of course we could then stipulate a set with no common properties.
I had taken you as proposing to eliminate properties in favour of sets. I would agree with that. But it seems you have something else in mind.
And I'm not at all sure what.
Quoting bongo fury
Me, too.
Quoting litewave
What does this mean?
Here's one way to look at it. We have the domain
Are you eliminating properties in favour of sets (which I would support), or making sets into reified metaphysical entities that ground properties?
Well, they are, a bit. :wink:
Mary Tiles (a philosopher of math) says she can imagine mathematicians ditching set theory someday.
Yes, because my attempt to treat the set and the property as one and the same object seems to have failed.
That sets are objects in the ontology of set theory.
:lol:
Which is why these threads are neverending.
And I hope has the sense not to ditch it yet?
That you're willing to say as much is a credit to you.
Why do you say that?
But I hope you see that your intuition - that having the property of being red and being a member of the set of red things say much the same thing - remains valid?
Quoting litewave
And so long as you do not expect to bump in to them as you walk down the street, that's fine, isn't it? What is needed is to keep track of which domain is which.
I think the intuition in the OP is quite right, and in a rough line with Quine and indeed pretty much all of more recent logic.
Cheers. Respect.
I have always treated sets as real metaphysical entities. So if properties were sets, then properties would be real too. If properties are not sets, I am not sure if properties are real, but I tend to think they are.
You think she should throw it out on the basis of of her imaginings?
Yes.
Quoting Banno
I interact with collections of objects all the time.
Do you want me to go on?
What is a real metaphysical entity as contrasted with a real entity? What does the word "metaphysical" do here?
What is a real metaphysical entity as contrasted with a metaphysical entity? What does the word "real" do here?
So what more do we have then "I have always treated sets as entities", which seems quite agreeable.
Just leave aside the baggage of "real" and "Metaphysical".
Quoting litewave
So instead think about these issues in terms of sets, with all the clarity of the formal apparatus that invokes, and just drop the use of "property", or use it as an anachronistic approximation.
Quoting litewave
What does it mean to say they are real? What more can we do with real properties that we can't do just with properties? Or much better, with talk of sets or predicates?
This stuff:
Quoting Banno
Quoting Banno
Sure. Just not in the way you interact with chairs. Different domains.
I was responding to your post in which you used the phrase "reified metaphysical entities". I understood them simply as real entities.
Quoting Banno
It seems that we need real properties to explain in what ways things are similar to each other. The ways are the properties.
Chairs are collections too.
Cool. Too many words, too many crossed discussions. The aim might be to be clear about what the individuals we are talking about are.
So we can talk about a and b. And we can change the game a bit and talk about {a,b}. And in one way we have added a new thing to the conversation, yet in another way we are still just talking about a and b. We may be tempted to ask which way is real, but perhaps that question is irrelevant provided we talk clearly.
Quoting litewave
There's a whole new barrel of fish.
a and b are sets too?
Quoting Banno
I already talked about that here:
Quoting litewave
No, but {a} and {b} are.
Quoting litewave
We'd have to look into Wittgenstien's analysis of simples here, and ask if the chair or the leg or the table set is the individual.
A step too far, I think, for this thread.
Quoting litewave
I spoke a bit about how we might define "abstract" here - that we have a and b and then add the abstract item {a,b} without adding anything to the domain - it still contains just a and b, but we can talk as if there were an abstract thing {a,b}.
Well, in pure set theory a and b are sets too, because it's sets all the way down.
https://en.m.wikipedia.org/wiki/Set_theory#Ontology
Well, trivially, yes, since pure set theory is about nothing but sets of sets and the empty set.
"Being an instance of redness" is not a property.
"Being an instance of redness" is referring to a particular instance, which is a single concrete thing, as in "the first instance of seeing a Northern Cardinal in the wild".
The Northern Cardinal may be red in colour, but "being an instance of redness" is referring to the instance not the colour.
"Being an instance of redness" is an element of the set.
The property redness = {being an instance 1 of redness, being an instance 2 of redness, being an instance 3 of redness}.
Note
Has anyone addressed the core problem of circularity. 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?
Noted. I think you mentioned the choice: extension/intension? I suppose the latter is a proposed solution to
Which isn't a problem (requiring a solution) in natural language. Usage there is guided by exemplification. See Goodman's Languages of Art which cashes in on the theoretical economy of analysing properties (or sets) away as predicates.
In formalised languages, sure. The circularity is famous since Russell B. As plenty here have pointed out.
Yes, this is what I was getting at, or trying to, when I said:
"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?"
And I join @Moliere in appreciating the fact that you can pull back from your original position and freely acknowledge its defects. Not many can do that. Look how much we've all learned as a result!
The hallmark of rationality: speech.
My solution is that it is a feature of the brain that a person can discover family resemblances in different things. For example, a postbox and Northern Cardinal share a family resemblance, and this particular family resemblance has been named "red"
https://thephilosophyforum.com/discussion/comment/1010119
Quoting bongo fury
Suppose a person sees a postbox and a Northern Cardinal. Goodman says "red" doesn't name a universal redness, but just applies to an object. In ordinary language, I can understand a person applying the word "red" to a postbox emitting a wavelength of 650nm, but how do they know to apply the same word to a different object, a Northern Cardinal, emitting a different wavelength of 700nm?
Quoting bongo fury
In formal language, Russell's problem of sets of all sets that do not contain themselves can be formally resolved, such as by using the axiomatic Zermelo-Fraenkel set theory.
But the same problem remains. In the set of red objects R = {postbox, Northern Cardinal}, we understand red by the elements in its set, but we must know that an element is red before putting it in the set.
Yea, but the OP wasn't saying that the set of red things is a definition of red. It was saying the set is redness because it has all the instantiations if it.
Yes, for the OP:
Property redness = {postbox, Northern Cardinal, sunset}
Nelson Goodman proposed that "red" doesn't name a universal redness, but just applies to an object:
Red = {postbox, Northern Cardinal, sunset}
But it seems that the same problem applies to both. We understand the LHS by the elements in the RHS, but the elements in the RHS are determined by the LHS.
Bertrand Russell's Type Theory does not seem to negate this circularity.
One solution is the brain's ability to find family resemblances in different objects. Necessarily a meta-linguistic solution (Wittgenstein, Philosophical Investigations)
Are there other solutions to avoiding this circularity?
I guess he isn't familiar with discussions about color itself, but they're pretty common. I think we just learn to associate a certain word with a certain range of visual experiences?
Let the property of redness = {postbox, Northern Cardinal, sunset}
Suppose we are told to find another object, object X, that has the same property of redness and include it in an enlarged set.
All these objects emit different wavelengths.
How do we learn that object X has the same redness as a postbox, Northern Cardinal and sunset when it will be emitting a different wavelength.
Because we don't learn to associate the word with one wavelength. We associate it with experiences, but those experiences reflect both physiological predisposition and cultural conditioning. Right?
:rofl: :rofl: :rofl:
That's how I see it.
We are physiologically predisposed to see a family resemblance in the wavelengths from 625 to 750nm.
We are then culturally conditioned to call this family resemblance "red".
Quoting Banno
Is the "of" relation an indication that the fish are a subset of the barrel?
:D
Quoting frank
This is basically what I mean by using "affordances" rather than "properties"
"Property" has the meaning that some thing external to myself has this or that regardless.
"Affordance" keeps the "regardless" part, but removes the "external to myself" part -- color blindness is my go-to example here.
That some people see an object differently due to being color-blind does not then mean that the object has multiple properties, but rather an affordance for perception such that people perceive it differently.
Yes, and as @Astorre has proposed, the affordance (or "mode", in their terminology) provides a realist-friendly link with the external world.
That said, we probably need to do some work on "affordance" or "mode" to make sure we're not just employing placeholders.
Definitely.
I tried to do so with the color-blind example, but it's just an example that I'm generalizing from to get at the idea -- maybe an "affordance" allows object-independence but disallows subject-independence to a certain point, while allowing it "somehow".
Just to make things murky, but it's my best first guess.
I tend to say "it's better to drop that notion", mostly indicating that there's nothing separating us from the world we are in. As @Joshs says we enact the world more than the world stands apart from us.
I feel like "affordance" fits better with that model, but I don't have it worked out very well.
Almost like I still comment on these fora because I'm still thinking about this stuff :)
Friday saw you and other participants in this thread ask me some interesting questions, but I wanted to take a short break before I answered. I'll get back to those questions later. But here's what I want to say right now.
My fascination with the processual approach to ontology is a kind of response to speculative ontology (object-oriented ontology and so on). I believe that the "subject" today needs philosophical defense more than ever before. If you're familiar with the works of us contemporaries, I think you'll understand what I'm talking about.
Harman, for instance, argues that the "hammerness" of a hammer is always withdrawn. "Hammerness" is the real being of the hammer as a unified object, which can't be reduced to its relationships with other things (e.g., a hand, a nail, or our thinking). We can't know it completely because:
Objects have "real qualities" that aren't exhausted by their "sensual" manifestations.
Any kind of knowledge is a relation that only reveals aspects of the object, but not its holistic essence.
This withdrawal occurs in three dimensions: the object transcends any attempts to grasp it; it retreats into the background during use; and as a tool, it's always on the verge of breaking, yet remains partially inaccessible.
Harman emphasizes that this isn't skepticism (objects are real) but rather realism: objects exist independently, but their depth is infinite and inaccessible. This distinguishes OOO from relational ontologies, where everything is reduced to connections.
What I Propose:
The modality (or the name can be changed to your liking) of a hammer is its "shadowy depth" (like Harman's), objective and inaccessible in isolation. But when the hammer is used, "hammerness" as a property emerges as an eventdynamic and contextual. This explains why we can't know hammerness statically: it doesn't exist "in the hammer" as a substance, but is born at the boundary of interaction, much like how for Harman, an object is only partially revealed in relationships.
For Harman, the hammer is revealed in its usewe see only one aspect. I propose to refine this: "hammerness" as a property is revealed in an act of participation, an act of encounter, and depends on the participants in the interaction (the hand, the nail, the task, the lighting). For another participant (e.g., a child playing with the hammer) or context (the hammer as a weapon), a different property is revealed, but the hammer's modality remains the same. This helps explain why complete knowledge is impossible: properties infinitely vary in processes, but they never exhaust the modality.
For Harman, the subject is a passive object, equal to others and withdrawn from access. The subject is unremarkable and unnecessary (why do we need it if everything is an object, and the method is objective). In my opinion, on the contrary, the subject (the observer or the "I") is a fully existent being with its own modalities (objective structures, such as the visual system or consciousness). It doesn't disappear or become fully flattened: the subject actively participates in the act of Participation, where properties are revealed. For example, in the case of a red apple, the subject (observer) is one of the participants in the interaction (along with the apple and light), and their modalities (cognitive structures) determine how the event of the property emerges. This overcomes Harman's radicalism, returning a role to the subject in reality, but without idealism: the subject doesn't create properties; it co-participates in their actualization.
I apologize in advance for any discrepancies that may arise due to the translator, as I am not a native English speaker.
Of course, no hurry.
Quoting Astorre
This is a welcome improvement on Harman, as I understand him. (I'm still balking at "hammerness as a property," but that's secondary.). Your version allows the observer to bring whatever concepts and agenda they may have to the encounter. As you say, it's not a one-dimensional "hammer or nothing" situation. Among other virtues, it gives us a way of understanding how an ordinary object like a hammer can become an art object. (See the "What Is a Painting?" thread.)
One question I would raise: This schema is Kantian in structure -- "the subject doesn't create properties; it co-participates in their actualization." How would you differentiate "modality" from "noumenon"? Can Kantian phenomena be understood as a series of co-created properties?
(Whatever translator you're using is doing a great job.)
But now you are back to talking about a somewhat mysterious notion of "hammerness".
Quoting Astorre
As if it were a hammer already, apart from our attribution.
You seem to have rid yourself of properties only to reintroduce them.
The spirit of my idea is close to the Kantian model, but it adds new layers. Kants noumenon can be compared to what I call the modus, and his phenomenon is similar to what I call a property. But note this small, crucial detail: properties are relational.
The property of redness or hammerness can be objective (for a carpenter, a hammer is a useful tool), or it may not be (someone who has been hurt by a hammer may see it as a source of pain). However, in my case, properties are more deeply relational; they are revealed in an act of participation, which can even occur between two objects without an observer present (for example, two rocks striking each other, revealing hardness).
Furthermore, the modus may be change over time. An apple is red, perhaps because this color is evolutionarily more attractive to animals that disperse seeds, who might have been more inclined to eat red apples. My modus is not a static thing-in-itself. So a car can be red because red cars were in demand earlier (and green cars weren't), and this became the result of earlier interactions.
I am defending the subject, but not to the degree of anthropocentrism seen in Kant, whose phenomena are an act of cognition.
Not at all, just try to read it all again. I understand that it's a bit boring
It's not revealed, since that implies that it was a hammer apart from it's use as a hammer. Better to say attributed.
We include that in the set of hammers. It isn't in the set of hammers apart from our so including it.
Hammerness is just an example (and as I mentioned, perhaps with an inaccurate translation). The idea is that a hammer can be used both as a tool for hammering nails and as a stand for a refrigerator. You can also use a microscope to hammer nails... Just consider it an example
Sure.
Does hammerness inhere in the hammer, or is it something we attribute to the hammer?
Is hammerness a permanent, even essential, part of the hammer, or is it something we do with and attribute to the hammer?
The hammer's hammerness is revealed in the act of nailing. I am saying that it was inherent in the hammer before the act (modus), and then became a property in the act of nailing. As a result, we named (or attributed) this hammerness to the hammer for cognitive purposes.
For example, if Mowgli sees a hammer without any explanation of what it is for, then for Mowgli, the hammer will have the properties that Mowgli will use it for (throwing it at Shere Khan). Mowgli will probably not discover the hammer's properties. However, the hammer's properties (such as being used for nailing) will remain intact and will be revealed in the hands of a carpenter.
Ok, so you are saying that the hammerness is already there in the thing, logically prior to the use as a hammer; and that the use brings out the hammerness.
Why not go the whole hog and say that there is no "hammerness", no property of being a hammer already there; but that what happens is that we decide that it counts as a hammer, basically for our own purposes. That there is no "hammerness already there in the thing".
Still, a hammer has a modus (potential, opportunity) to be a hammer, as does a stone, especially when attached to a stick, as does a microscope when used to drive nails. But this property is not in the object or the subject, but in the encounter. In the involvement. After this encounter, as I said, the hammerness remains in our consciousness. Hammerness can be lost in modus (the hammer just rotted and became unusable), hammerness can be lost in act (for example, people started using screwdrivers and stopped hammering nails), and hammerness can be lost in consciousness (we have raised a generation that doesn't know what a hammer is or what to do with it).
I don't know how to make sense of that.
Is your suggestion that hammerness is a potential or opportunity or modus inherent in a microscope?
Much simpler to just say that someone might use a microscope as a hammer. Drop all the hoo-ha.
This way it is easier for me: the hammer appears in the act of meeting; and even more briefly: the thing is revealed in the Participation. You asked questions, so I had to clarify everything, write a lot of words.
That's the analytic approach at work. Thanks for indulging me.
It might well be a language issue, since my reservation rests on that word "revealed". Something is revealed that it is already there but hidden, and comes to be seen. The letter is revealed by opening the envelope, the body revealed by removing the clothing, and so on. But a microscope does not have a hammerness that is revealed by using it as a hammer...
An object in the world such as a rock has an almost infinite number of possible relations. As you say "properties infinitely vary in processes". For example, hitting another rock, hitting a bird, hitting a molecule of air, hitting a different molecule of air, being used by a person as a hammer, being used as a person as a paperweight, being used by a person as an art object, etc.
As you say, "as a property emerges as an event-dynamic and contextual", which cannot be argued against.
But you also say "The modality..............of a hammer is its "shadowy depth"..........objective and inaccessible in isolation"
If the modality of an object can only emerge within dynamic contexts, and there are an almost infinite number of possible dynamic contexts, this makes the modality of an object unknowable.
If the modality of an object is unknowable, then we cannot even talk about an object having a modality.
Then modality is an unknown unknown.
Yes, your judgments look consistent. In all possible acts, the hammer can manifest itself in an unknowable way. Perhaps we will never know it in all its possibilities. What prevents us from acknowledging this and moving forward? This is precisely what science does: it discovers new properties in new combinations, records them, and we use them. Even though we know that the hammer is unknowable, we can still use it to drive nails, right? Further exploration of the properties of a hammer is justified if it has practical benefits.
Your intuition is that anything that exists must have boundaries, must have some limit in order to be an existence. But the modus does not meet this criterion, as it cannot be fully named in all its aspects. Therefore, the modus is again a construct of the mind, rather than something that actually exists. However, consider the universe as an example. It cannot be fully defined yet, but that does not mean that it does not exist. So we come to the fact that when we call something something, we don't necessarily need to know all its boundaries, but they must exist somewhere, and once we know them all, we may call it something else. Therefore, a single definition may not be sufficient to call something something, and as I have mentioned in other topics, it is necessary to introduce multiple characteristics that complement each other and are revealed during the process.
As I have already mentioned, the modus is what is contained in the hammer itself, while the properties are what is created through the interaction of various participants, and our knowledge is our understanding of these properties. In my opinion, this approach does not involve excessive metaphysics and is focused on the process. Without the process, there are no properties. The author's description is a clever way of expressing our understanding (rather than the properties) through sets. Whether this approach is good or bad is a matter of personal opinion.
Maybe this approach will allow us to see more, understand more, or maybe not. We'll see.
That's an interesting point. Yet even in modern "building block ontologies" where things "are what they are composed of," I doubt that you would find many advocates for the idea that properties are "inside" things. They normally say the fundamental building blocks just are their properties, plus some individuating principle.
It's interesting because the original argument for the "primacy" of substance runs something like this:
In the world, we can see red things, red light, but never just "redness." Dogs or trees can be living, tall, fast, but we never have "nothing in particular" that lives or is tall, or a fast motion with nothing moving.
But then substances, originally at least, aren't building blocks. They are the wholes in virtue of which being is many and not only one (although it is also one in another sense). They undergo corruption and generation, and so they are themselves processes in a way. Round substances change. They can cease to be round. What isn't changing would appear to be roundness. But if roundness only exists where there are round things and in the minds that know them, there is a bit of a puzzle here. A process metaphysics still needs unchanging regularities by which to identify processes that are similar, no?
If one considers this from the perspective of a deflationary information theoretic process metaphysics, where all of the universe is something like a changing mathematical "code," it can be helpful. That this is too deflationary is no problem for the example. Within the universal code are subsections of "code" that are more or less intelligible in themselves and self-determining. These are beings/things. There are also accidents, actions preformed by things, properties like color, relations like "being to the left of," etc. The accidents that are not "substance" and so cannot appear except as embedded in or related to some other "thing-unit" of code. They need a substrate to inhere in. The thing-units more fully have essences, in that they do not have a wholly parasitic existence in the way the accidents do. But accidents still have some sort of "essence," in that all instances of roundness, redness, rapidity, etc. will share some sort of morphisms by which they are the same (on pain of equivocation).
I think a key difficulty here that led to a sort of corruption of notions of substance that brings the difficulties you mention, as well as others, is that the term tended to be used in two related but diverse ways. From the perspective of metaphysics, organisms are most properly beings, being organic wholes. Break a dog or tree in half and you get a corpse; break a rock in half and you just get two rocks. Unity and multiplicity are contrary, not contradictory opposites, akin to light and darkness or heat and cold, so we can have greater or lesser unity in metaphysics. But for logic you need univocal terms. With the rise of nominalism and the demand for univocity, you cannot have any play in the terms of substance, leading towards the reductionism that attaches properties to some sort of unchanging building block.
Anyhow, on your point re the relationally of redness; it is worth pointing out that this holds for all properties, not just those involving minds. We can say that 'salt is water soluble," but it only dissolves in water when interacting with water, etc. While modern thought began to center on the epistemic consequences of something akin to the old Scholastic dictum that: "Everything is received in the manner of the receiver," this focus tended to make "the receiver" only a mind, when originally it was anything (likewise the "subject" was originally the "subject of predication" not exclusively the "experiencing subject."
Properties like charge, mass, etc. reveal themselves in interaction. Hence, "properties in themselves" would be epistemically inaccessible but also irrelevant to the world. "Act follows on being."
Of course, terminology evolves, but I call these corruptions because they introduce many of the problems process metaphysicians are often trying to address. But process metaphysicians still need a way, it would seem, to separate substance and accidents, or else there would just be one monoprocess, and a black cat would become a different thing when it fell into brown mud and became brown, etc.
That makes sense. Artifacts seem like a particularly hard place to start. It is debatable if anything used to hammer is a hammer, or if it is just being used for hammering. However, it is simply not the case that everything that is used as a sheep is a sheep. If you try to breed a male pig to your female sheep, you will starve. If you try to get cats to pull your dog sled you will get scratched and go nowhere. But more to the point, not only will the "tool" not work, but the living organism is itself its own goal-directed whole and this is not altered by our use of it.
I suppose though that this could be considered a matter of degree. A volume of water or air never makes for a good hammer. When Rorty debated Eco, he said that what a screwdriver is doesn't necessitate (or even "suggest") how we use it, since we could just as well use it to scratch our ear as turn a screw, and yet in an obvious sense this isn't so. A razor sharp hunting knife is not a good toy to throw into a baby's crib (at the very least, for the baby) because of what both are, and this is true across all cultural boundaries and seems that it must be true. You can use a PC tower as a door stop, but you cannot run Widows or check your email on any other sort of doorstop.
I agree, in that I have the concept of Poland even though I have only visited four of its towns. My concept of Poland is necessarily bounded by my personal experiences, and I infer my concept of Poland is only a pale shadow of its true reality.
However you distinguish between the "modality" of something, objective and inaccessible, and its properties, dynamic and contextual.
I have the concept of a hammer in my mind. My belief is that objects such as hammers don't exist in the world, but what does exist are fundamental particles and forces.
In my terms, the "modus" of the hammer are fundamental particles and forces, which are objective and inaccessible, enable Realism, and do exist in a mind-independent world.
These fundamental particles and forces are the indirect but real cause of my concept of hammerness.
I can explain this property of hammerness as a set of events in which a hammer participates, such as hitting in a nail, hitting a rock, being an art object, being a weapon. A property may be understood by its extension.
The property of hammerness = {hitting in a nail, hitting a rock, being an art object, being a weapon}.
These events are dynamic and exist within a context, in that a hammer in the context of carpentry is a tool for hitting in nails and in the context of war is a weapon. The Context Principle has played an important role since Frege's 1884 Grundlagen der Arithmetik.
As you say "Even though we know that the hammer is unknowable, we can still use it to drive nails, right?".
All we need to know is appearance not the cause of such appearances. All we need to know are the properties of the hammer, not any hypothetical modus of the hammer.
We drive along a road and stop when we see a red light. The fact that colours don't exist in the world but only in our minds as concepts has no bearing on the fact that we stop when we see a red light. In our daily lives we are only interested in the properties of an object, such as the property of redness. We have no practical interest in any hypothetical modus of an object (though we may have a philosophical interest).
By Occam's Razor, there is no reason why we cannot remove the concept of modus altogether, as it serves no purpose. As you say "My fascination with the processual approach to ontology is a kind of response to speculative ontology (object-oriented ontology and so on). "
My modus of the hammer are fundamental particles and forces that I believe do exist in a mind-independent world (accepting that even fundamental particles and forces are concepts).
But is what you mean by modus different to this?
It's unclear to me if Kant thought noumena were static in this sense. I don't see why they would have to be. At any given moment of perception, we have the noumenon and the ensuing phenomenon. "Noumena" is a kind of placeholder, a way of expressing the fact that we don't have access to whatever it is that lies beyond our perceptions. As such, it could be a "different" noumenon five minutes earlier. "Noumenon" is not a name for some essence or quiddity.
Quoting Astorre
Yes, to adequately compare your schema with Kant's, we'd have to go back to my question:
"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?"
I think I've figured out where I was wrong here. Classical philosophy, like our everyday language, is built on the substance paradigm. In it, the world consists of: Things (substances) that exist in themselves. Properties (attributes) that these things "have" or "have".
The question "What is a property?" in this paradigm seeks an answer about a static characteristic attached to an object. For example, "redness" is a quality that an apple has.
The proposed Paradigm: Process. It does not have static "things" with properties. There are only "Beings" - temporary, stable patterns in the flow of becoming and "Interactions" (Meetings) - dynamic events that make up reality.
The mistake was to take the question from the old paradigm ("What does a thing have?") and try to give it a direct answer in the new one, instead of reformulating the question itself.
So what is a property? A property is a name that we give to the event-result of the Meeting.
That's all. It is not a thing, not a characteristic, not a mode. It is an event.
There is an apple-being with its internal structure (we called it Mode). There is a light-being and an observer-being. The Meeting (interaction) occurs between them.
The event of this triple Meeting is "redness". "Redness" is not what the apple has. It is what happens when the apple, the light and the eye meet.
Since the 17th C, with Indirect Realism, I don't think that philosophy has been built on the substance rather than process paradigm. Our language certainly isn't, as Wittgenstein's Language Games illustrates.
Indirect Realism asserts that we don't perceive the world directly but rather though representations in our minds
For example, René Descartes (15961650) argued that we perceive the external world through ideas or representations in the mind, not directly. John Locke (1632-1704) developed this idea. George Berkeley (1685-1753) argued that our perceptions are ideas in the mind and not physical entities. Immanuel Kant (1724-1804) emphasized the role of the mind in shaping our understanding of reality.
We can go back even further to Plato's Theory of Forms, in that we don't directly perceive substances in the world, but are only able to process shadows in our minds.
I don't think it is true to say that Classical philosophy is built on the substance paradigm.
I wonder at what stage in the process of this post's creation you found it appropriate to research the exact years of birth and death for each philosopher?
At the stage of making my point absolutely clear that for at least 400 years Western philosophy has not been built on a substance paradigm to the exclusion of a process paradigm.
So does the redness of the apple disappear when we turn out the lights, or the water solubility of the salt cease when the water it is dissolved in evaporated?
It seems to me that some notion of potential (often invoked in process metaphysics) is needed as well. Consider the apple. When we turn of the light, it ceases to "appear red" to anyone. Yet if we turn on the light, anyone with healthy eyes will be able to see the redness. The apple seems to be potentially red even when this event meeting is not occuring. And this is not the same way in which it is "potentially blue," in that we could cover it in blue paint, but rather that if anyone saw it with healthy eyes under normal conditions, the redness would appear.
If properties are only the actual even meetings, then they would seem to come from nothing. But our experience is that what we call properties are quite stable. Hence, I would say the redness of apples has to do with their potential to appear red in normal lighting to anyone with healthy vision. Even "thing-in-itself" ontologies allow that nothing appears red when no one is looking, but the appearance and the color are distinguished for this reason. But this could be explained as a potentiality grounded in process.
The apple appears red, because when hit by sunlight, the apple absorbs all colours except red, which is then reflected to our eyes.
A mirror reflects red light, but we don't say the mirror has the property of being red.
An apple also reflects red light. It is curious that we say an apple has the property of being red, yet we don't say a mirror has the property of being red.
Indeed. But wouldn't this be because the mirror reflects any light, and not just red? Likewise, we call certain things "magnetic" but it isn't that electromagnetism is wholly absent from other things. All sorts of things emit photons, but we only call those that emit discernible amounts of light "bright." Likewise we call a boulder "heavy" and yet it would be relatively weightless on Pluto. Yet this sort of variance only makes sense if properties are relational and involve interaction (or are revealed in interaction).
I think the property itself is often conceived of as the actuality that is prior to any specific interaction that reveals the property (there must be something that causes things to interact one way and not any other). That's the original idea of a "nature." However, it's questionable if this "actuality" can be thought of without the interaction itself. It is rather a potency/power that is actualized in the interaction (e.g., salt only dissolves in water when in water, lemons only taste sour when in the mouth, etc.). Yet a particular potency/power to act in a given way must itself be actual. That is, it isn't a sheer potency to act in any way at all, but a potential to interact in specific ways. The property is a (sometimes confusion) way of grouping this potency and actuality.
In scientific terms:
Suppose a boulder has a mass of 100kg.
When the boulder interacts with Earth's gravity, there is a force of 981 N pulling it towards the Earth. When the boulder interacts with Pluto's gravity, there is a force of 62 N pulling it towards Pluto. If the boulder was in outer space and not in a gravitational field, there would be no force on it.
The boulder has an "actuality" of 100kg regardless of any interaction.
The property of the heaviness of the boulder can vary between being heavy, being light or being weightless dependent upon location, but where this property is relative to a human on Earth.
The boulder's "potency" of 981 N is a function of its 100kg "actuality" and is "actualised" in an interaction with a gravitational field of 9.81 m/s sq.
The heaviness of the boulder (where heaviness is a property) is a function of its "actuality" (100kg) and the particular gravitational field it is interacting with relative to Earth's gravitational field.