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I'm majored in mathematics, but not philosophy. I have encountered this question many times for months, but it is seemingly not belongs to mathematics, so I come and ask here.

The question is, it appears to me that while talking on the attributes/properties for an object, the attributes are actually a function that takes the object as an argument, and return the quantity or quality of it. For example, "The color of the apple is red." The apple is the object, color is one of attributes/properties, and be treated as a function(applying at that object), and then red is the function value at that object. In a mathematical way, it can be written as Color[the apple]=red. Other examples are:

Color[the apple]=red

Height[Eric]=180cm

Mood[Janny]=Happy

Radius[that circle]=5

Branch[Brian]=Army

AccountID[Jennifer]=9876-5432

So, do we do we usually treat one object's attributes/properties as function values? I haven't studied any philosophy books, and I'm curious about what did the philosophers discuss and understand on this topic, maybe it is belongs to metaphysics?

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    Welcome to Philosophy.SE. Depending on the perspective you're looking for, this may be relevant on Psychology & Neuroscience or Linguistics as well. – user2953 Oct 15 '16 at 14:17
  • As far as I am aware of it is more common to express these in the form ∃x((Apple)x ∧ (Red)x) or, in an easier form, Ra, which can be read as (Red)Apple (=> see predicate Symbols) - but I am not an expert in logic. – Philip Klöcking Oct 15 '16 at 16:07
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    It really depends on what you mean by "do we usually treat". Do you mean (a) how do we usually model properties in logic; (b) what model of attributes does everyday language convey; (c) how do we think about attributes; (d) something else? Please edit your post to clarify what perspective you're looking for - and in case it is (b) or (c) I think this would suit better on Linguistics or Psychology & Neuroscience, respectively - but I have no experience on either of these sites, so I'm not certain what kind of questions they accept. – user2953 Oct 16 '16 at 12:22
  • Can you see that color is very different than height? If something's height is 1 meter, two individual observers can simultaneously observer the object and a 1-meter stick and agree that the height of the object is 1 meter. But if they both see a color and they agree they call that color "red," we can not know for sure if they both see the same color! Maybe you see what I call blue but you call it red. So color has a subjective, experiential quality that height does not. The experience of color is in the observer, not the observed. – user4894 Oct 16 '16 at 19:55
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It's actually more convenient [at least in extensional first-order logic] to think of properties mathematically as sets and the objects that have that property as elements of the set.

I don't need to know, from the point of the existential quantifier, what the property F is or how to define it. I just need to know whether it has any members. If so, Ex.Fx is true, otherwise it is false.

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The model that you describe is currently known as determinates vs. determinables. As in:

determinable      determinate

Color             red

Height            180cm

Mood              Happy

Radius            5

This model has been used in modern philosophy, although quite rarely. It is similar to Aristotle's distinctions between genus-differentia-species, which are now used mainly in biology.

It is more common in philosophy to regard properties and attributes as already determinate. In logic, this corresponds to predicates, or equivalently to boolean functions:

Color_red (the apple) = true

Color_red (the bird) = false

Height_180cm(Tom) = true

Height_180cm(Jerry) = false
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Quine in discussing vagueness, similarity and natural kinds in a natural context decides ultimately that we do not. Function values are definite, and the values of properties are, in fact not so in general. Referents are vague, principles of similarity are not complete enough to totally separate one answer from another without context, etc.

So, in the simplified world of abstract logic, we can model properties as functions, but that can be no more than a model. It does not have strong enough semantics to cover ordinary usage.

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