# What is an object's properties?

What can we consider an object's properties, for example, when can we consider an object's properties as 'changing'? For example, if I move an object from my desk to my table, has it changed? If I take a number and write it's numeral on my board, or write 2+2 on a piece of paper, does it change the object as it gains the attribute of being the number that I've decided to write the value of the sum with itself on my particular paper in my particular office? If Mike becomes the chef at a restaurant does Mike change? He gains the attribute that he's a 'chef' but has he 'changed'? When I move from position a to position b do I 'change'?

Such a question is valid when considering mathematics and logic as the question 'if a variable takes a value, does it change the value?' can be approached in this way, what about a mathematical object defines 'it'?

• See Properties Sep 18, 2022 at 12:22
• The object's properties will change according to whatever happens to that object or around it. Just as the taste of an apple changes over time, properties can change too. It's extremely dependent on what the situation is. Sep 20, 2022 at 19:04

A simple model of an object's properties can be expressed with first-order predicate logic. This model assumes that we have a set of logical objects, and certain predicates these objects satisfy. If b is an object and P_ is a one-place predicate then if Pb is true, then b has the property expressed by predicate P_.

If we restrict ourselves to one-place predicates, we have what we could call non-relational properties. If we look at predicates with two or more arguments we get relational properties. For example, b is to the left of c, is not a property of either b or c taken in isolation but a property of the two in an ordered relation bLc.

However, this logic-based account of properties may be metaphysically implausible. For example, if Pb is true for any predicate, then Pb ∨ Q is also true for any proposition Q (here "∨" is the symbol for logical "or").

We can define a new predicate P' as: P'_ if and only if P_ ∨ Q

It is easy to prove that P_ implies P'_ since P'_ is always true if P_ is true.

Yet, it might seem implausible metaphysically to say, for example, that an "an apple being red" implies that the apple also has the property of "being red or pigs fly". Thus, some philosophers might require a more substantive (evidence-based) argument for asserting that a given predicate P_ expresses a real property. We can still say that all properties can be expressed as logical predicates, but not all logical predicates express real properties. It is then the job of the metaphysician to determine which predicates correspond to real properties on a case by case basis.

The other part of the question is about changing properties. If we look at an object as existing in 3-spatial dimensions at a moment in time, it appears to have certain properties which we can call synchronic. If we consider something that has a property which holds across across time, we can call this a diachronic property. For example, the property of turbulent flow in water is a diachronic property. Now, if we are looking at a synchronic property changing between two times, in the background there needs to be a diachronic property that describes the object's capacity to change while maintaining its metaphysical identity across time. In general, an object b's capacity to change certain properties while remaining b is a diachronic property of b. Historically, philosophers have called the properties that can change without causing b to cease being b, the accidental properties of b.

Let's consider your example of Mike becoming the chef at a restaurant. We generally assume that the capacity to maintain personal identity across time is a diachronic property of persons (although this could be challenged). For example, when I wake this morning I'm slightly different than I was before I went to sleep, but I'm not a distinct person. Certain kinds of change can cause a loss of personal identity, for example, if a person dies their body ceases to be the person they were although the body continues to share some of the properties that were previously possessed by the person. However, in Mike's case becoming a chef is not a sufficiently radical change for Mike to cease being himself. In this case, Mike simply gains the additional property of being a chef.

• If I take a supposedly 'unchanging' abstract object and decide that it's 'my number' I may make decisions based of this number, it's not just a name, it's an associating of the number that I have made, does the number 'change'? Similarly to Mike becoming a chef? Or does the concept of 'relations' imply that this is a relation? For example '5 is my number' is a relation it has with itself, if 'my number' is a name, or it could be a property. Sep 18, 2022 at 21:33
• In the case of numbers do we just ignore the synchronic properties in favour of diasynchronic algebraic properties which define the numbers? Sep 18, 2022 at 21:33

Would you insist that it must be the case that the object either changes or it doesn't change?

I think both. The object --- let's say that paper you're writing on --- hasn't undergone any substantial change: it's still the same paper it was before. Its properties have nevertheless changed: like you pointed out writing on the paper changes its properties. Even though its properties changed, it's still a piece of paper: its substance, or its being hasn't changed.

It's possible to have so much change that the thing you started with becomes something other than what it was. In that case the object's identity as a piece of paper itself would have been changed. E.g. I write on it so much that it's all covered with black ink, or I tear it to shreds and burn it. The way the identity accumulates and manifests change is equivalent to the heap problem.

• I have to agree, I'm trying to determine something like this: is the idea of many abstracts as 'inert' somewhat fallacious does me associating the number with things change it? In this way the heap idea doesn't apply because anyone can discern the concept of '2' and '3' but are they in constant change? Sep 18, 2022 at 21:16
• @user1007028 even you thinking about things differently changes the object. (But that's a stronger claim than what my answer relies on) Sep 19, 2022 at 0:06

In Aristotle, there is a distinction between intrinsic & extrinsic properties. An objects mass is intrinsic but its location in space is extrinsic.