Re: Name the thesis: "Formal sentences capture informal ones"
Helene.Boucher_at_wanadoo.fr
Date: 02/01/05
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Date: 1 Feb 2005 10:45:04 -0800
tchow@lsa.umich.edu wrote:
> In article <1107276841.434068.138780@c13g2000cwb.googlegroups.com>,
> <Helene.Boucher@wanadoo.fr> wrote:
> <Because you put ZFC in (*), I just presumed that you would have said
> <that (s union s) = d - where s is your favorite way of representing
1
> <in ZFC and d is your favorite way of representing 2 - adequately
> <expresses its informal counterpart, which is 1 + 1 = 2. Am I wrong
in
> <that?
> <
> <Otherwise how can the formal expression of "ZFC is consistent"
> <adequately express the informal assertion that ZFC is consistent??
> <
> <In short, it seems to me - or at least this is where my confusion
lies
> <- that (*) does not itself make the distinction between the two
steps
> <(mathematical informalism to mathematical formalism, mathematical
> <formalism to logical formalism) but conflates them.
>
> First of all, although I did mention ZFC in one attempted
formulation,
> I rejected that later because it put undue emphasis on one particular
> axiomatic system. But never mind that, it's not so important for the
> question at hand.
Sorry I didn't read all the thread. In the post to which I was
replying, your quote of Jamie quoting you (!) had ZFC in it. I didn't
realize this was stale (even though, now that I reread your post, it
even says that!).
>
> I don't completely understand your question. Are you perhaps
identifying
> logic with set theory?
Never not me!!
We were talking about logicism. Frege and the early Russell are the
paradigm logicists - if they aren't logicists, then no one is. As I
understand the historical record - but I could well be in error - both
Frege and the early Russell would claim that their formal systems,
which were akin to set theory, were logics.
Anyway, look at it this way. Define logic* to be logic union set
theory, and consider the thesis that mathematics can be reduced to
logic*. Call this the logicism* thesis.
There is now the following two-step division: expressing informal
mathematics by formal mathematics; expressing formal mathematics by
formal logic*. Do *you* agree that it is useful to distinguish these
two steps (given that logic* is not "just" logic.)
The (*) that I understood does not do make this distinction - informal
into formal mathematics, formal mathematics into formal logic*. But
again, apparently I was arguing from a stale quote, for which I
apologize.
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