A secondary intension is the component of a term’s meaning that fixes its referent based on how the actual world turns out to be — the metaphysical dimension of intension. David Chalmers introduced the concept alongside primary intension as part of his two-dimensional semantic framework.
The secondary intension of a term is a function from counterfactual worlds to extensions, evaluated with the actual world held fixed as a reference point. For “water,” once we discover that water in the actual world is H2O, the secondary intension maps every counterfactual world to whatever is H2O in that world — even if H2O is not the clear drinkable liquid there, and even if some other substance fills the water-role.
This contrasts with primary intension, which tracks the water-role rather than the substance. If a counterfactual world has XYZ in its lakes instead of H2O, the primary intension of “water” picks out XYZ (the role-filler), while the secondary intension picks out H2O (the actual-world substance), wherever H2O appears in that world.
Secondary intension corresponds closely to what Saul Kripke described with rigid designation. A rigid designator picks out the same thing in every possible world; the secondary intension formalizes this by anchoring reference to the actual world and then projecting across counterfactual scenarios. “Water” rigidly designates H2O because its secondary intension maps every world to H2O.
The two-dimensional framework explains a puzzle about necessity and knowledge. “Water is H2O” is metaphysically necessary (true in every possible world, per the secondary intension) but epistemically contingent (we had to investigate the world to learn it, because the primary intension left it open). The two intensions capture these two dimensions of the same statement.
Related terms
- primary intension — the epistemic dimension that tracks the role a term picks out
- intension — the general concept of a meaning-rule determining reference
- extension — the actual referent in a given world
- rigid designation — terms that refer to the same object across all possible worlds