Lewis (1997) proposed that:
Something x is disposed at time t to give response r to stimulus s if and only if, for some intrinsic property B that x has at t, for some time t’ after t, if x were to undergo stimulus s at time t and retain property B until t’, s and x’s having of B would jointly be an x-complete cause of x’s giving response r.
There are lots of things to say about this, but one of them is that we sometimes seem to have dispositions based on extrinsic properties. For instance, I am disposed to get upset when someone is rotten to Muriel, and the underlying basis of this disposition is that I like her. Liking Muriel is, however, surely an extrinsic property of mine rather than an intrinsic one.
The restriction to intrinsic bases is introduced to resolve certain problem cases which occur if we leave it out. A sorcerer watches over a fragile glass, prepared to make it cease to be fragile if it is ever struck. Why doesn't that mean the glass has a disposition to lose its fragility when struck? According to Lewis, it's because the property which served as the basis of the proposed 'disposition' would not be intrinsic to the glass.
But maybe Lewis puts the intrinsicness requirement in the wrong place. Maybe what matters is that s and x's having of B cause changes in the intrinsic properties of x which are sufficient to bring it about that x gives response r to the stimulus s.
If that's right, the real reason the glass does not have the disposition to lose its fragility when struck is that the striking and the property of being watched over by a sorcerer do not cause a change in the glass's intrinsic properties that suffices to bring about the loss of fragility. The way this property and this stimulus bring about that response is through causing changes in the sorcerer and his relation to the glass.
By contrast, the cases where we seem to have dispositions with extrinsic bases are ones where the relevant extrinisic property, together with the stimulus, brings about the response just by causing some change in the intrinsic properties of the bearer of the disposition. For instance, I get upset when someone is rotten to Muriel because of the way that the rottenness and my liking for Muriel cause changes in my intrinsic properties.