# What is the distinction between A-intension and C-intension?

I'm having a really hard time understanding a concept discussed in “Qualia and Analytic Conditionals” by Braddon-Mitchell and "Why We Need A-Intensions" by Jackson. Here's my extraction of these concepts:

• "I call the set of worlds w such that S is true at w under the supposition that w is actual, the A-intension of S." These deliver representational content.
• I use C-intension for the set of worlds w such that S is true at w – 'C' because all but one of these worlds will be counterfactual." The only difference is that C-intensions include counterfactual worlds or possible worlds, yes?
• "For some sentences, their A-intension is one and the same as their C-intension. Examples are: “There are electrons” and “Some things are square." For them, truth at a world and truth at a world under the supposition it is the actual world are one and the same. "The only difference is that the value at every world but one depends in part or in whole on how things are at another world."

I'm not sure what this means, and the language in these papers is really difficult to understand. Does anyone have a good grasp of the concepts? Could you explain the distinction in relatively simple terms?

• They are treating Kripke's necessary a posteriori in a two-dimensional modal analysis. Kripke's claim that water=H2O necessarily depends on how things are in our actual world, and "necessarily" applies only as long as all other worlds are thought as counterfactual. This is C-intension. Should we shift the actual world, what water is, as discovered in it, would be just as necessary for all of its counterfactual worlds, but it may no longer be H2O. So water=H2O is no longer necessary over such worlds. This is A-intension. The definition of water, but not triangles, depends on actual water. Apr 23, 2020 at 10:34
• @Conifold thank you that's really helpful Apr 23, 2020 at 17:52