[FOM] A problem with Friedman's Concept Calculus

Frode Bjørdal frode.bjordal at ifikk.uio.no
Mon Aug 12 14:18:31 EDT 2013

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
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