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An intrinsic rational judgment is one about a proposition, irrespective of anything other than the essence of the subject and the essence of the predicate.

For example: it is intrinsically impossible for a seven-faced cube to exist. This is because a cube is a six-faced shape by virtue of what it is, and so a seven-faced cube would be a seven-faced six-faced shape, which is a contradiction. It’s existence therefore, is said to be impossible in of itself.

On the other hand, an extrinsic rational judgment is one about a proposition, while also taking into consideration other factors that may affect its truth^[1].

For example: it is intrinsically possible for Zayd to occupy a chair. For Zayd’s occupation of a chair, in of itself, is not absurd. However, this can become impossible when we take into consideration the occurrence of something other than Zayd’s occupation of the chair, like ‘Amr’s occupation of the same chair^[2]. In this case, it is said that Zayd’s occupation of the chair is impossible, but for other than itself.

Transformation of Realities 

Extrinsic truths obviously change, since the world is constantly changing. But do intrinsic truths change? Changes in intrinsic truths are called transformations of realities (Inqilab Al-Haqa’iq).

For example: an essence whose existence is an intrinsic possibility, to become intrinsically necessary or impossible.

We claim that the transformation of realties is impossible. This is because what is intrinsic to an essence is that which makes it itself, without which it is not itself. And so claiming that a reality changed, is tantamount to claiming that an essence is no longer itself, and that would be a violation of identity.

For example: if existence were intrinsically possible for a particular essence, then this essence accepts both existence and non-existence by virtue of what it is. So to claim that this essence no longer accepts existence (i.e. that its existence is now an intrinsic impossibility), or non-existence (or an intrinsic necessity), is to claim that this essence is no longer this essence. And that is absurd.

[1] Other factors that are external to the essence of the subject and the essence of the predicate.

[2] Since it is impossible for both Zayd and ‘Amr to occupy the same chair, at the same time.