A hy­po­thet­i­cal sce­nario is ‘con­ceiv­able’ or ‘imag­in­able’ when it is not im­me­di­ately in­co­her­ent, al­though it may still con­tain some sub­tle flaw that makes it log­i­cally im­pos­si­ble. If you haven’t yet checked for fac­tors, it’s con­ceiv­able to you that 91 is ei­ther a prime num­ber or a com­pos­ite num­ber, even though only one of these sce­nar­ios is log­i­cally pos­si­ble.

Whether 91 is prime or com­pos­i­tive is a log­i­cal con­se­quence of the defi­ni­tions of ‘prime’ and ‘com­pos­ite’, but it’s not liter­ally and ex­plic­itly writ­ten into our brain’s rep­re­sen­ta­tions of the defi­ni­tions of ‘prime’ and ‘com­pos­ite’ that 91 is a prime/​com­pos­ite num­ber. If you can con­ceive of 91 be­ing prime, this illus­trates that, in your own mind, the prop­erty of 91-ness is not the same writ­ing on your map as the prop­erty of com­pos­ite-ness, but it doesn’t demon­strate that it’s log­i­cally or phys­i­cally pos­si­ble for 91 to be com­pos­ite. If you can con­ceive of a sce­nario in which X is true and Y is false, this demon­strates mainly that X and Y have differ­ent in­ten­sional defi­ni­tions in­side your own mind; you have sep­a­rate con­cepts in your mind for X and Y. It doesn’t demon­strate that a world where ‘X but not Y’ is log­i­cally pos­si­ble, let alone phys­i­cally pos­si­ble, or that X and Y re­fer to two differ­ent things, etcetera.

La­bel­ing a sce­nario ‘con­ceiv­able’ or say­ing ‘we can con­ceive that’ in­tro­duces a sce­nario for dis­cus­sion or re­fu­ta­tion, with­out as­sum­ing in the in­tro­duc­tion that the sce­nario is log­i­cally pos­si­ble (let alone phys­i­cally pos­si­ble, or at all plau­si­ble in our world). Since many true facts are also plau­si­ble, phys­i­cally pos­si­ble, log­i­cally pos­si­ble, and con­ceiv­able, in­tro­duc­ing a sce­nario as ‘con­ceiv­able’ also does not im­ply that it is false. It means that some­one found them­selves able to imag­ine some­thing, per­haps a true thing, per­haps with­out vi­su­al­iz­ing it in the com­plete de­tail that would re­veal its im­pos­si­bil­ity; but if all we know at the start is that some­one felt like they could imag­ine some­thing, we’ll call it ‘con­ceiv­able’ or ‘imag­in­able’.