2

I need help formally translating the following definition into FOL: "a property F is essential to an object x if and only if x could not have been the object it is without possessing the property F."

So far I have "F is an essential property of x iffdef ∃x(¬F(x) → x ≠ x)"

Would that be correct?

Improve this question
  • This is a strange sentence to formalise in FOL. It talks about ‘essential’ and ‘could’, both concepts which are more naturally captured in modal logic. It also quantifies over properties – ‘a property’ really means ‘for all properties’ here – and that’s something you can only do in Second-Order Logic. (You can’t formalise ‘F is an essential property’ since you don’t have predicates to apply to F.) You’ll probably need to say something like: For all x, if x is a property, then… - so, have a FO predicate saying ‘…is a property’. – MarkOxford Jul 4 '18 at 10:41
  • @MarkOxford - correct; we need properties of properties. – Mauro ALLEGRANZA Jul 4 '18 at 10:54
1

We need two ingredients : high-order logic, because we have a property of properties.

And, IMO, we need modalities, in order to express the necessary "connection" involved in the concept of essence.

Compare with Gödel's ontological proof.

I would suggest :

Ess(F,x) ↔ ( F(x) & □∀y (~Fy → y ≠ x)).

Improve this answer

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.