What does a prime (apostrophe) mean before a predicate? 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.
 A: 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 : $x = t$).
A: 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 $453$.
