Final answer:
The possibility of a speaker holding different truth-values for 'S believes that N1 = N1' and 'S believes that N1 = N2' on an externalist theory is due to the justification depending on external contexts and sources which can lead a speaker to recognize or not recognize N1 and N2 as the same.
Step-by-step explanation:
On an externalist theory of concepts, the difference in truth-values for 'S believes that N1 = N1' and 'S believes that N1 = N2' is possible because the justification for a belief may depend on external factors beyond the individual's immediate cognitive grasp. This includes the specific contexts in which a person is introduced to the names 'N1' and 'N2', which may carry separate connotations even if they refer to the same entity. The belief that 'N1 = N1' is reflexively true; whereas, the belief 'N1 = N2' could be false if the speaker, S, does not recognize that N1 and N2 are in fact the same due to the differing circumstances of learning each name.
Externalist theories of justification focus on sources of justification, such as perception or testimony, and the reliability of those sources. So, if the circumstances in which N1 and N2 were introduced to the speaker S differ, it is possible for S to believe that N1 is equal to itself, but also to believe that N1 is equal to N2 based on the different circumstances in which the names were introduced.Reliable sources and past experiences play a significant role in the externalist view. If S came to know 'N1' in a trustworthy context but 'N2' in a suspicious one, S might not have reason to believe 'N1 = N2' even though it is true. Hence, external factors affect the truth-value of S's belief about the equality of N1 and N2, despite the fact that whether N1 actually equals N2 is independent of those beliefs.