This I take it are the common elements of Analytic Philosophy inherited from the bastardized philosophies of the logical positivists.
While PH throws around the term 'fact' as if it is of something credible within philosophy, actually his term 'fact' has no groundings to reality at all.
I noted PH et. al. and me had been discussing pass each other because they conflated the two perspectives of 'what is fact'. i.e. the typical definition of fact with his bastardized version of fact i.e. as from Analytic Philosophy.
Note this SEP article on 'What is Fact' which focused on the Analytic Philosophy perspective.
https://plato.stanford.edu/entries/facts/
The word “fact” is used in at least two different ways.
First:
In the locution “matters of fact”, facts are taken to be
what is contingently the case, or
that of which we may have empirical or a posteriori knowledge.
Thus Hume famously writes at the beginning of Section IV of An Enquiry concerning Human Understanding:
“All the objects of human reason or inquiry may naturally be divided into two kinds, to wit, Relations of Ideas and Matters of Fact”.
Second;
The word [fact] is also used in locutions such as
In this second use, the functor (operator, connective) “It is a fact that” takes a sentence to make a sentence
- • It is a fact that Sam is sad
• That Sam is sad is a fact
• That 2+2=4 is a fact.
(an alternative view has it that “It is a fact” takes a nominalised sentence, a that-clause, to make a sentence),
and the predicate “is a fact” is either elliptic for the functor, or takes a nominalised sentence to make a sentence.
It is locutions of this second sort that philosophers have often employed in order to claim (or deny) that facts are part of the inventory of what there is, and play an important role in semantics, ontology, metaphysics, epistemology and the philosophy of mind.
Humean Facts versus Functorial Facts
We may, then, distinguish between Humean facts and functorial facts.
With the help of this distinction, two philosophical options can be formulated.
One may think that
there are facts in the functorial sense of the word which are contingent—the fact that Sam is sad—
and facts in the functorial sense which are not contingent—the fact that 2+2=4.
Or one may think that all facts in the functorial sense are contingent, are Humean matters of fact.