Conceivability

conceivability.json

https://arbital.com/p/conceivability

by Eliezer Yudkowsky Jul 1 2015 updated Dec 16 2015

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'.

Comments

Alexei Andreev

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\. Whether 91 is prime or compositive is an immediate 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\.

This paragraph is hard to understand. May be rewrite it in a more concrete way, i.e. using "is 91 prime" as an example from the start.