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Intension/Chalmers: intension is a function that defines how a concept is used in different situations. It is not the same as "meaning" and also not a definition.
Intension/Chalmers: depending on whether a concept picks out an object in the actual world, or in a counterfactual world, I will speak of primary and secondary intension.
Secondary Intension/Chalmers: secondary intension is therefore, independent of empirical factors. It describes how reference depends on how the outer world turns out. (> twin earth,> rigidity).
When counterfactual worlds are involved, it is not a priori determined what the reference is, since the actual world can be determined by different speakers as their own (mirror-inverted). (> Centered Worlds, Quine) The determination as a primary or secondary intension will then also vary inversely.
Meaning/Chalmers: Both primary as well as secondary intensions are candidates for the "meaning" of a concept. "Water" could mean H2O, or twin earth water, depending on what is meant by the concept in the respective world.
Necessary Truth/Chalmers: both can even be constructed as a necessary truth when possible worlds are conceived as uttering contexts.
Primary Intension/Chalmers: For example, the largest star in the universe: picks out a star in every given centered world. Even non-existent objects have a primary intension, e.g. the Nicholas, (Santa Claus). This primary intension could have picked out an object if the world had turned out accordingly.
For my concept of consciousness, the primary intension is more important than a causal relation to an object.
Also, a zombie can have primary intensions that are overlapping with mine.
Quality/Qualia: primary intensions do not specify Qualia.
The Conscious Mind Oxford New York 1996
Constructing the World Oxford 2014