Dear Gabriel  (if I may)

Regarding the implications of Cohen’s work, I found this paper, by the man himself, very useful.  He takes the trouble to spell matters out in a generously accessible way, I quote his own conclusion.

http://rsta.royalsocietypublishing.org/content/363/1835/2407.full

“Therefore, my conclusion is the following. I believe that the vast majority of statements about the integers are totally and permanently beyond proof in any reasonable system. Here I am using proof in the sense that mathematicians use that word. Can statistical evidence be regarded as proof? I would like to have an open mind, and say ‘Why not?’. If the first ten billion zeros of the zeta function lie on the line whose real part is 1/2, what conclusion shall we draw? I feel incompetent even to speculate on how future generations will regard numerical evidence of this kind.”

On my reading Cohen is far distancing himself from the transcendentalist, theistic, Platonistic stance taken by Goedel.

I fear my own stance on this matter is rather contrary to your own?  I judge discussion of the paradoxical findings in foundations of maths and quantum mechanics have become important, but as the casual stock in trade of many post-modern writings.  Such writings in actuality achieve the important anti-scholarly objective of befuddling the lay man.  I believe my conclusion on that is much like that of Sokal.

As it happens I am currently trying to raise discussion elsewhere on a 2nd century AD Roman text – the  “Distributio” of Maecianus.  I am struggling a bit, since my latin is even worse than my maths, and this crucial document on Roman metrology has, as far as I can find, never been translated.

It appears to me that  Maecianus was allied with a version of stoicism that had in a general way something in common with 20th century post modern writings.  Cumo recently fittingly analysed his position according to the philosophy of Latour.  It appears to me  that  Maecianus must have deliberately set out to confuse the reader by conflating metrological usages of terms in three different contexts, weight itself, different usages of the terms in the context of Roman probate law, and different usages again in regard to coin denomination.

I mention this here because along the way he does seem, at one point, to give a nod to Aristotle’s treatment of the paradoxes of the continuum

Personally, Maecianus seems to me to delight in paradox as part of a project aiming to disguise the (relatively modest) rates of inflation being imposed by the Roman state in the 2nd century.  Whether 2nd century propaganda on such matters had a bearing upon the hyperinflation of the Roman 3rd and 4th centuries is a further question which naturally follows.

Rob Tye



https://www.academia.edu/40577417/Puzzles_about_Roman_Weight_Standards

https://www.academia.edu/s/db1878a859/puzzles-about-roman-weight-standards