What does a prime (apostrophe) mean before a predicate?

Question

I found this statement in a paper by John McCarthy:

$$ \forall x.ostrich\ x \supset species\ x ={}^\prime{}ostrich $$

I can't figure out what the prime indicates.

Answer 1

It seems to me that it is used as an "operator" for nominalization, in place of the standard $\lambda$ operator.

See :

• Nino Cocchiarella, Conceptual Realism and the Nexus of Predication : Lecture Five (Rome, 2004), page 14 :

Consider, for example, the predicate phrase "is famous", which can be symbolized as a $\lambda$-abstract $[\lambda xFamous(x)]$ as well as simply by $Famous( )$. The $\lambda$-abstract is preferable as a way of representing the infinitive "to be famous", which is one form of nominalization:

to be famous $\to$ to be an $x$ such that $x$ is famous $\to$ $[\lambda xFamous(x)]$.

The $\lambda$-abstract $[\lambda xFamous(x)]$ acts as a term, and thus can fill the argument-place of a predicate (like : $x = t$).

Answer 2

An apostrophe before the name of a predicate has no standard meaning. I believe McCarthy is just using it as a systematic way for assigning symbolic identifiers to classes, so that he can economise on axioms. I.e., if instead of saying $ostrich(x)$ you say $species(x) = 452$ and instead of saying $penguin(x)$ you say $species(x) = 453$, then you avoid the possibility of having an $x$ that satisfies $ostrich(x) \land penguin(x)$. $'ostrich$ and $'penguin$ are McCarthy's convention for naming the symbolic identifiers, rather than using specific identifiers like $452$ and $453$.