[FOM] Typo in Concept Calculus Paper
hmflogic at gmail.com
Thu Aug 15 16:42:17 EDT 2013
I just saw a typo in the definition of y >ex phi. Change x > z to z > x.
This is an obvious typo because of the informal definition of "exactly
better" in the section Better Than, Much Better Than, which reads:
"We say that x is exactly better than a given range of things if and only
if x is better than every element of that range of things, and everything
that something in that range of things is better than, and nothing else."
On Mon, Aug 12, 2013 at 2:18 PM, Frode Bjørdal
<frode.bjordal at ifikk.uio.no>wrote:
> As I have attempted to come to more clarity on Friedman's Concept Calculus
> it turns out that Lemma 8.2. of
> http://www.math.osu.edu/~friedman.8/pdf/ConcCalcInf103109.pdf is false.
> In defining y>exPhi on page 13 Friedman has Forallz(y>z iff Existsx(Phi
> and (x=z or x>z))).
> However, in proving Lemma 8.2 on page 28 it is presupposed that y>exPhi
> iff Forallz(y>z iff Existsx(Phi and (x=z or y>x>z))).
> But the proof of Lemma 8.2 cannot be rectified even if one changes the
> definition og y>exPhi to the one presupposed in the text. For the step
> indicated by «Suppose Phi. Then x < y.» is a non sequitur, as nothing
> prevents that Phi holds for an x which is incomparable with y.
> It may be that a rectification may be had by presupposing the more
> elaborate definition y>exPhi iff Forallz(y>z iff Existsx(Phi and (x=z or
> y>x>z)) and not Existsx(Phi and x incomparable with y)).
> In my previous post Remarks on the Concept Calculus I make a suggestion
> for domain for MBT which is not quite apt; nevertheless, it may be that a
> rectified Concept Calculus may be modelled by elaborating appropriately
> upon my suggestion.
> Professor Dr. Frode Bjørdal
> Universitetet i Oslo Universidade Federal do Rio Grande do Norte
> quicumque vult hinc potest accedere ad paginam virtualem meam<http://www.hf.uio.no/ifikk/personer/vit/fbjordal/index.html>
> FOM mailing list
> FOM at cs.nyu.edu
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