I think that both interpretations have some truth to them, but both leave something to be desired. Locke's ideas seem support the possibility that if the sun were replaced with a similar but different object, and that the viewer was in no obvious way affected by the replacement, it would be prudent to refer to this new object by the same name even though astronomers might call it something new, because as a viewer with no specific knowledge of the sun, it could be that both objects, being similar enough for a layman to not notice a difference, could be referred to with the same name because the idea of what the sun does would be no different to them because of their lack of understanding of the object. Mill in this sense may be closer to the truth, because he talks about the sun being specifically the thing that causes the specific day we have, which would be the same in the minds of everyone who experiences the day and views the sun. This doesn't allow for differences of misunderstanding of the object, like the Locke does, because it refers to the physical properties of the Sun.
The problem I see with Mill's interpretation is it doesn't seem to allow for people to have different 'interpretations' of the Sun - it seems to discount the possibility of an opinion of the sun, because the name 'the sun' only represents the physical, actual properties of the object. This seems objectionable because the sun has connotative meaning to each person based on their experiences with it.
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