Intrinsic and extrinsic properties have been used by philosophers to mean different things, so before I begin allow me to explain how I am using them. By an intrinsic property I mean a property of an object that can be explained by is constituent parts. This is not to say that one of the parts that make up the object must have that property, new properties can emerge from combinations of other properties, for example when two atoms combine to form a molecule that has properties found in neither atom. Intrinsic properties, however, are ultimately explainable by, and reducible to, the constituent parts of the object they are properties of; two objects with the same composition will share the same intrinsic properties. Extrinsic properties, on the other hand, are not determined by the object’s constituent parts. The simplest example I can give of an extrinsic property is that of being authentic (versus counterfeit). A piece of “money” may be counterfeit even if it exactly identical to an authentic piece of money, and thus we can argue that the property of “authenticity” is extrinsic to the piece of money.
The question is: are there any real extrinsic properties or is it the case that all properties are intrinsic, and we simply are not looking at the complete “object” when we judge a property to be extrinsic. Consider again the case of counterfeit money; I would argue that the property of being “authentic” isn’t really an extrinsic property. Sure it is extrinsic to the physical piece of money at a specific instant, but it is intrinsic to that piece of money plus its history. In this case we haven’t been looking at what the property really applies to, a piece of money and its history. And how do we know that the property really applies to the money and its history? Because without the history it would be impossible to tell in some cases if the money was counterfeit instead of authentic (for example, in the case of a perfect copy).
We might attempt to settle this question (whether extrinsic properties really exist) from some other metaphysical first principles, but such an argument is unlikely to make real headway, since such principles are often just as questionable. What I will do instead is present the strongest example of an extrinsic property that I know of, or at least the example that tends to convince the most people that extrinsic properties exist. (It certainly convinced Lynne Rudder Baker.) If I can show that this example of an extrinsic property is simply a case of not considering the complete “object” then I will assume that all other cases of extrinsic properties can be likewise explained away (although I admit that obviously this isn’t a proof, simply suggestive).
The example is the statue known as David. Let us distinguish the physical statue, which we will call the Piece, from the artwork, which we will call David. It is argued that David is extrinsic to the Piece. Why? Well, consider a world without people, or without art. In such a world the Piece remains the same, but there is no David. And since all the components remained the same, but David existed in one situation but not in the other, we can conclude that the property of being David is extrinsic to the Piece.
So, if I am to defend the hypothesis that all properties are intrinsic to something I must show that there is something the property of being David is intrinsic to. I would claim that the property of being David is intrinsic to the combination of Piece and viewer. The viewer, who is able to appreciate art, is what makes the Piece David. This should seem plausible at least, because the worlds where the piece isn’t David are ones without viewers who can recognize it as David. But does this explanation make sense? I think it does, because David, as David the art, is something that exists in our minds, and not really a feature of the stone at all. And so I conclude that the property of being David isn’t extrinsic.
Is this a good way to eliminate extrinsic properties? Certainly we could argue that given some object there are some properties that are extrinsic, relative to it. However the set of properties that would be extrinsic to an object in this sense would be the set of all properties minus the ones that are intrinsic to that object, and clearly this set is too large to be of any use. And so I would conclude that while we might talk about some properties as extrinsic simply for convenience there are no real such things.