that something is an externality is partly a statement about physical reality and partly a statement about the legal system.
What does this mean? I assume the aspect of externality being a physical reality problem is just people only care about self interest so externalities can occur. However I don't understand how something is An externality could be a statement about legal rule.
You don't give the source of the quote, but presumably what is meant is this. Whether X's production or consumption of a good affects Y (in a physical way such as smoke from X's factory or noise from X's playing loud music, not merely through the workings of the price system) is a matter of fact. On the other hand, whether X is required (assuming a negative effect) to bear the costs of the harm to Y, is a matter of law. The implication seems to be that an externality is present only if the law does not so require.
However, some writers would exclude the legal aspect from the definition of an externality. Baumol & Oates, for example, state (quote found here, top of page 5):
"An externality is present whenever some individual's (say A's) utility or production relationships include real (that is, nonmonetary) variables, whose values are chosen by others (persons, corporations, governments) without particular attention to the effect's on A's welfare."
An advantage of this type of definition is that it avoids the implication that an externality is no longer present when it has been addressed by law as above. Instead, we can say that the externality is still present but has been internalized.
