[FOM] Epistemology for new axioms (Joe Shipman)

[Paul Blain Levy]

Before we start adding axioms to ZFC, I would advocate that we take 
something away!  Namely unrestricted quantification, whose meaning is 
not at all clear.

https://urldefense.proofpoint.com/v2/url?u=https-3A__arxiv.org_abs_1905.02718&d=DwIDaQ&c=slrrB7dE8n7gBJbeO0g-IQ&r=xXZM6ZrkjVxXknjzIxhAvQ&m=SbZg4RtGnHNQOlJ5HkgG-uCl76F_BA79JR9D1j2xNrc&s=lbA8TRSIgL14Ww--eyyULwMZ9eh8A7hp16KrGilA1l0&e= 

Paul

> Date: Tue, 3 Sep 2019 14:53:12 -0700
> From: Joe Shipman <joeshipman at aol.com>
> To: fom at cs.nyu.edu
> Subject: [FOM] Epistemology for new axioms
> Message-ID: <EE8B1CCB-45A1-4BEB-AA51-7E284145D93A at aol.com>
> Content-Type: text/plain; charset="utf-8"
>
> I didn?t get any responses to my queries about absoluteness, so I challenge you to argue against the following:
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> ***There is no proposition of any mathematical interest that is known (by ZFC proof) to be relatively consistent with and independent of ZFC, such that mathematicians will eventually have a consensus view that it should be considered as a fundamental axiom with which ZFC should be augmented.***
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> Here ?a consensus view? means comparable to the view that Zermelo set theory should be augmented with the Replacement Axiom to give ZF.