infinite = **’unknown, because without context of correspondence we cannot determine limits’**, that’s all it means. Because that’s all it *can* mean and not argumentatively convert from mathematics to theology or fictional justification is perhaps a better term.
The irony is that mathematicians seek precision in their statements and take pride in the precision of their language, but on this subject they do the opposite: obscure.
There is no difference at all between making theological justificationary narratives, and making mathematically platonic justificationary narratives other than in theology and mathematics, theologians and mathematicians both seek to enforce existing dogma, while at the same time obscuring the fact that they have no idea what they’re talking about, and therefore resort to fictional narrative justification.
“God gave us the ten commandments” is a fictional justificationary narrative obscuring the lack of causal understanding, and “evolutionary constraints produced natural laws of cooperation at scale” articulates the causal understanding. I can obey those ten commandments and cooperate at scale whether I use the fictional justificationary narrative, or the causal scientific narrative. So the operations I take are identical. What differs is the consequences of using a fictional justificationary narrative and a causally parsimonious narrative – just as what differs in our ability to make consequential deductions from allegorical justificationary narratives, and axiomatic causal properties differs.
Mathematics is literally full of holdovers from the greek and Christian eras of mysticism as well as the modern era’s rationalism – and mathematicians have not reformed mathematics as science has been reformed. And so mathematics still contain’s is fictional justificationary narratives. This retention of fictional justificationary narratives (the theology of mathematical platonism), does not necessarily inhibit the practice of mathematics any more than obeying the ten commandments inhibits the art of cooperating at scale. What matters is the consequence of teaching mathematics platonically (theologically) and teaching it scientifically (existentially).
Now, in testimonialism we account for the ethics of externality and we require warranty of truthfulness in public speech. Therefore it would be unethical and immoral (and possibly criminal or at least negligent) for mathematicians to continue to teach or publish or speak in public using theological language while at the same time making proof or truth claims – because one cannot warranty due diligence against externality caused by the false statements.
So someday we hope we can reform mathematics so that it is taught scientifically not theologically, and as such by superior methods of teaching, we expand the use of mathematics to increasing numbers of people, and export less theology via fictional justificationary narrative into the public domain.