The point of this post is not so much to answer the titular question (though hopefully commentators take a stab at it) as to sketch some remarks about how to avoid giving question-begging arguments for externalism.
Before diving into the remarks, first some term-defining preliminaries.
Let internalism be the view that whatever makes a personâ€™s mental state the type of mental state that it is, it involves no relations other than relations to other mental states of that person. Let externalism be the view that whatever makes a personâ€™s mental state the type of mental state that it is, it involves at least one relation to things other than mental states of that person. Various externalisms, then, include social externalisms (via essential relations to states of other persons), evolutionary externalisms (via essential relations to states of evolutionary ancestors), embodied cognition views (via essential relations to extra-mental bodily states), and what I shall call referential externalisms (via essential relations to extra-mental entities that constitute the referents of mental states). Iâ€™m particularly interested in referential externalism here, so let me say a bit more about it.
Referential externalism is primarily a theory of mental states that have content and explicates content in terms of a semantic relationâ€”the reference relationâ€”between a mental state and a (typically) extra-mental entity that the mental state designates. On such a view, for example, my belief that Socrates philosophized is the type of mental state that it is in virtue of there being, among other things, a semantic relation between my mental state and Socrates. For examples of referential externalists I offer philosophers that hold the wide-spread view that Twin-Earthlings have different beliefs from Earthlings in virtue of environmental chemical differences between XYZ and H2O.
For the rest of this post I shall refer exclusively to referential externalism by my use of â€œexternalismâ€.
How to avoid giving a question-begging argument for externalism
One good thing to avoid if you want to avoid being a question-begging externalist is characterizing the explanandumâ€”contentâ€”in terms of a reference relation. So, for example, if you characterize what needs to be explained as how your beliefs about Socrates are able to bear the reference relation to Socrates, then your very characterization of the explanandum is going to make everything but externalistic explanations seem totally hopeless. In short, you would be begging the question against the internalist from the outset. Similarly, if your characterization of the explanandum is done in terms of representation instead of reference, you may still be in danger of question-begging if your model of representation is a relation between representer and represented.
Consider that the internalist is very likely going to advocate a conceptual role semantics for mental content. On such a view, what makes beliefs about Socrates the beliefs that they are are relations only to other beliefs (beliefs about Athens, beliefs about Platonic dialogues, etc.). Characterizing the explanandum in terms of a reference relation to extra-mental entities begs the question against this kind of internalist.
What needs to be done, then, is to characterize content in a way that is neutral between internalism and externalism. For propositional attitudes, at least, the topic of content can be introduced as (1) that toward which attitudes are taken and (2) in virtue of which distinct attitudes (e.g. the belief that grass is green, the fear that grass is green) may nonetheless psychologically resemble each other. This characterization leaves it open for externalists to argue that the belief that grass is green involves relations between beliefs and grass and it leaves it open for internalists to argue that the belief that grass is green involves only relations to other beliefs. What this characterization does not do is make essential reference to extra-mental entities (e.g. grass). The use of â€œgrassâ€ in characterizing the belief as a belief about grass does not necessarily involve bearing a reference relation to grass, or so it is open for the internalist to deny.