What does it mean for two properties of objects to be of the same class (or even identical)?

For people adhering to a realist ontology, what does it mean for you to say that a property p of an object of species a, and a property q of an object b are of the same class, or even that are objectively identical or the same property?

For some context: I'm currently trying to deepen my knowledge on the concept of natural kinds. According to some realist philosophers I've studied, only particula individuals exist, but a collection of individuals could be of the same natural kind is they have a common law (ontological/natural law) that they follow, i.e. if they follow the same patterns of behavior (under the same or similar initial and boundary conditions).

How can we say (or what is the ontological basis for saying) that those particular objects are following the same pattern? Is it that they share the same (kind of) properties?

I'm starting to suspect that the basis for stating that two properties are the same is whether: a) The behavior of the referred objects seem indistinguishable for us, or b) The objects produce the same effect upon other objects.

And I think that point b) depends on point a), which seems like a circular reasoning.

I hope my question is clear enough. Thanks for your time.

• The question is not really when things share this or that property (hence are of a kind), we typically have definite procedures to determine whether they have it or not. For example, solubles are determined by placing them in water and conductors by running current through them. The question is when those properties are natural, i.e. reflect something in nature rather than something bound to our human interests, like fruits and vegetables. The latter are artificial kinds. And the criterion, roughly, is that the said procedures must capture something our science links to laws of nature. Commented Feb 5, 2023 at 22:37
• @Conifold Thanks for the answer! So, we say that all objects that behave in a way that perceive as the same under the same conditions have the same property (in your example, solubility). And we say that such common behaviour is not arbitrary or by chance, but the result of following the same pattern. Is that it? Am I missing something? Commented Feb 5, 2023 at 23:11
• Yes, but we do not say it because of that. We say it because we have a theory of solubility and that theory that tells us when the conditions and behaviors are relevantly "the same". Commented Feb 6, 2023 at 8:04

2 Answers

The establishment of the identity of particular properties (SEP) is a matter of metaphysical inquiry. For instance, properties themselves have properties, and those properties are used to determine if two properties are the same property, or differ in some way. Terms like co-intensional, co-extensional, intrinsic, extrinsic, and natural properties (SEP) are some terms to describe different types of properties.

But, setting aside, a deep philosophical analysis, how do we generally know if two properties are of the same sort? This can be achieved in several ways.

First, intuitively. It is not unreasonable for a person to say this house looks green, and this tree looks green, so they share the property of green. Children do it everyday. Thus the property of greenness is sufficiently established this way.

At the other end of the spectrum, we have properties that are not immediately empirical and are highly abstract, and exist because of operational definition. Thus, for a psychologist to establish two people are both suffering from vulnerable clinical narcissism means defining it in some specific way, and then administering a psychometric, for instance, to be assured that two people qualify as exhibiting the property of having a specific personality disorder. Those criteria are laid on in the DSM V, and the psychometrics administered help support that conclusion.

Properties may be labels for dispositions or for occurrences. Dispositions are tougher to establish, because they imply a regularity or pattern. For instance, just because someone has killed another human being is not sufficient for entailing the property of being a psychopathic, serial killer. Thus, there may be some degree of justification involved in make a determination of a property, such as meeting a definition set about by criminal law.

Science attempts to use empirical evidence to establish equivalence. For instance, to determine if a house and a tree are both actually, green, optical equipment may be used to measure wavelengths and satisfy an optical, abstract definition of green that goes beyond mere first-person observation. The advantage of this sort of establishment of establishing if two properties are the same is that it avoids difficulties in observer bias. One of two observers, for instance, may have red-green color blindness, in which case, it may be the case that the house is actually red, and despite that it appears to such a person both the house and the tree have the property of greenness, it isn't the case objectively.

Natural kinds (SEP) is a broader discussion than just the ontological, because it not only relies on discussion about properties, but more broadly epistemological, and other metaphysical conceptions (such as metaphysical necessitation) to make a claim about the natural structure of the world, and is therefore a realist claim (as opposed to instrumentalism). Therefore natural kinds revolves not so much around questions of properties and identities (such as Leibniz's Identity of Indiscernibiles), but more about understanding the broader question of how language, knowledge, and things in nature interrelate. From SEP:

This article divides philosophical discussions of natural kinds into four areas: metaphysics, epistemology, philosophy of science, and philosophy of language. The metaphysics of natural kinds asks whether we should think of our supposed natural kinds as genuinely natural. And if they are, what are natural kinds? And, finally, do natural kinds have essences? Philosophy of science is concerned with natural kinds because, as mentioned above, it is the use of natural kinds by the individual (‘special’) sciences that generates our interest in them. So we may ask, whether the kinds appearing in our best scientific theories do indeed satisfy the theories of natural kinds proposed by the metaphysicians.

Thus rejecting natural kinds may focus on showing that the construction of language and the use of linguistic categories is somehow arbitrary, and that a chicken doesn't necessarily have strict boundary conditions, but rather chickens are birds and birds are almost reptiles, and as the genes drift, there may not be strict categories in terms of science, but rather are conveniences of cognition. For instance, Stephen J. Gould once declared there was no such thing as a fish (PDF). Understanding biological categories as Aristotle understood them, and as modern evolutionary biologists who use clades do is an entirely distinct affair.

Ab initio properties were grouped together in particular classes without any metaphysical basis. For example red, blue, etc. were categorized as colors sans the scientific knowledge that they're actually just different wavelengths/frquencies of light.

In short, the OP's question inquires into some kinda rationale for property classification. Why, for example, are circles, rectangles, triangles, etc. classified under geometric shapes? What do we mean by shape? As far as I can tell, to my reckoning, shape possesses an extensional definition (vide supra) but not an intensional definition. To get straight to the point, the class shapes is arbitrary - we simply decided for no reason at all to call the set of triangles, circles, circles, etc. shapes.

• Thanks for the answer! About your first point: now, given that scientific knowledge is an existing element, what should a theory of properties do about what science do with properties? About the second thing: your example makes sense to me, at least in the context of formal knowledge. But what about properties of factual things, where extentional definitions don't seem enough to characterize object because, for instance, to co-extensive properties not necessarily are the same property, i.e. they are not co-intensive. What to do with all of this? Commented Feb 6, 2023 at 5:35
• @BrianDíazFlores, science has become an authority with regard to validation of claims. So, I guess no classification of properties will gain any traction unless underpinned scientifically (colors are a good example). As for the second question, I'm not in a position to answer it. Commented Feb 6, 2023 at 7:05