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An intrinsic property is one a thing has purely in virtue of how it itself is, independent of its surroundings — mass, shape, and chemical composition are standard examples. An extrinsic property depends on the thing's relations to other things — being two miles from a barn, being someone's sister, or being famous. The distinction matters because metaphysical principles often turn on it: duplicates share all intrinsic properties; causation is often thought to supervene on intrinsic states; and essentialist claims typically concern intrinsic features. Defining the distinction precisely is harder than it appears — Lewis proposed that intrinsic properties are those shared by all possible duplicates, but this appeals to the notion of duplication, which itself seems to presuppose intrinsicality.
Read Lewis's 'Extrinsic Properties' and Langton and Lewis's 'Defining "Intrinsic".' Test the proposed definitions against edge cases: is being lonely (being the only object in the world) intrinsic or extrinsic? Is shape intrinsic if space is relational?
From your study of substance and property, you know that objects are distinguished from one another partly by the properties they instantiate. But not all properties do the same metaphysical work. Some properties characterize an object purely in virtue of what it is in itself — independent of anything else in the world. Others are relational, holding only because the object stands in certain relations to other things. This is the distinction between intrinsic and extrinsic properties, and it turns up repeatedly in metaphysics wherever we ask what determines an object's nature.
The intuitive cases are clear. A ball's mass is intrinsic: it has that mass regardless of what surrounds it. Its shape is intrinsic: a spherical ball is spherical whether alone in the universe or surrounded by other objects. By contrast, being "two miles from the Eiffel Tower" is extrinsic: this property depends entirely on the ball's spatial relation to a specific external object. Being "the most expensive ball in the room" is extrinsic: it depends on what other balls exist in the room. Being "someone's favorite" is extrinsic: it depends on the psychological states of other people.
The philosophically standard criterion for intrinsicality comes from David Lewis: an intrinsic property is one that is shared by all duplicates. Two objects are duplicates if they are alike in all intrinsic properties — perfect copies down to their internal structure. On this account, duplicates must share their shape, mass, and chemical composition, but need not share their location, their relational history, or their social roles. The criterion is powerful but faces a circularity worry: defining intrinsicality via duplication, when duplication itself seems to presuppose intrinsicality. Langton and Lewis attempted a more refined definition using natural properties and lonely/accompanied scenarios to escape the circle.
The distinction carries genuine metaphysical weight. Many philosophical principles are formulated specifically in terms of intrinsic properties. Supervenience claims — that mental properties supervene on physical properties — are typically meant as claims about intrinsic physical states. Causal powers are usually held to be intrinsic: what an object can do depends on its own nature, not on its environment. Essentialism claims that an object's essential properties are (typically) intrinsic — the properties it has in every possible world where it exists. And Lewis's famous theory of modality relies on the idea that possible worlds are like this world, containing concrete objects with intrinsic properties.
One genuinely tricky edge case: is loneliness (being the only object in the universe) intrinsic or extrinsic? It seems to depend on what else exists, suggesting extrinsicality. But an object's internal nature doesn't change when you add or remove other objects, suggesting something odd is happening. This case (discussed by Langton and Lewis) reveals that the intrinsic/extrinsic line is not always sharp, and that making it precise requires careful choices about what "internal to the object" really means — a question your work on universals and particulars has equipped you to pursue.
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