I lean towards more to Mill's understanding that names in language are not as much significations of abstract ideas but rather refer to the actual thing being named. Locke seems to have this understanding of 'naming' where abstraction is ultimately what is going on and we thus deriving from these abstractions are categorizations or significations. It seems more that in the actual usage of certain names that they are referring to something that is more than just the idea itself and if we want to refer to the idea itself we in fact have different naming schemes to convey this (see: Mill section 4 on 'white' vs. 'whiteness').
Locke's view that signification derives from abstraction seems problematic as abstraction occurs with the use of language, or in other words, abstraction does not seem possible without some use of a language type system.
The question for Mill is considering how far we should take this consideration that names in fact refer to the thing they are describing. Are names just merely referents for things in the world, useful for communication purposes, or is naming in fact the only way for our minds to access the things in the world?
Naming is not the only way for our minds to access things in the world, because even before you know the name for something in language you can still access the image in your mind. It would be interesting to see Mill's interpretation of how humans access the world in case studies when language has not developed (such as severe neglect cases), because those people are still able to access the world - just not communicate the access to others.
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