[FOM] Typo in Concept Calculus Paper
Harvey Friedman
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."
Harvey Friedman
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>
>
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