Re: The extent of the mistake

From: |-|erc (h_at_r.c)
Date: 12/13/04 

Date: Tue, 14 Dec 2004 00:49:43 +1000

"Barb Knox" <see@sig.below> wrote in
> poopdeville@gmail.com wrote:
>
> >John Jones wrote:
> >> Here I present a short list of some of the mistakes that riddle logic
> >> and arithmetic.
> >>
> >> 1. A list of numbers is not a list of numbers, but a list of
> >numerals.
> >> Succession, represented by [1,2,3,4..] is not a defining property of
> >> number.
> >> 2. A set of numbers is not a set. This is because a number is a
> >number
> >> in its application and not outside it. It is also the case that
> >> numbers are not transferable between applications.
> >
> >I'm sure you're just trying to be cute here, but the numeral's referent
> >is fixed to the number. So, sequence of numerals 1,2,3... refers to a
> >sequence of numbers -- the obvious ones.
> >
> >> 3. The largest number is the number you count to. The count of three
> >> is the largest number, unless I count to four. It is not sufficient
> >> to say five is the largest number because if five is merely stated
> >> and not counted, then five is a numeral. Again, numbers are not
> >> transferable between applications.
> >
> >Gibberish.
> >
> >> 4. There is no infinite number. Number is defined by a limit of an
> >> operation, so no limit means no number.
> >
> >More gibberish. What the hell is "a limit of an operation" supposed to
> >mean?
> >
> >> 5. A proposition of logic presents no meaning but assumes one. The
> >> meaning of a proposition of logic comes from placing the proposition
> >> in a particular case. The particular case confirms a proposition as
> >> being true or false only on the assumption of a particular case. For
> >> example, 'cats have tails' assumes meaning, yet has none unless we
> >> place it in a particular case. If the particular case is as a
> >> password between spies, then 'cats have tails' can be true or false
> >> on the assumption of the particular case of a password between
> >> spies.
> >
> >Very insightful -- natural languages are context sensitive. So what
> >does that have to do with logic?
> >
> >>
> >> Have I not thrashed the notions of arithmetic and logic? knocked them
> >> to their foundations?
> >> JJ
> >
> >No. Just misunderstood them.
>
> JJ is is an interesting case. From previous interactions with him I'd say
> he has something like a "Representationalist" and "Finitist" view of
> mathematics, but not very well thought through.
>
> Regarding Representationalism, he has often said things to the effect that
> mathematical entities only exist as marks on paper, and that it is
> meaningless to talk about a "number" or "set" in the abstract.
>
> Regarding Finitism, he has been thoroughly opposed to infinite series, and
> has argued strenuously (if incoherently) against 0.333... = 1/3.
>

Useful though, stops you maths types abondoning English meanings and thinking you can "take the set",
"use a proof", "select members". I'd call it objective semantics, he isolates mathematical entities from
meanings in popular use.

Herc