[FOM] Mathematics ***is*** formalising of our thought and intuition
Paddy Hackett
rasherrs at eircom.net
Sun Jun 6 05:43:16 EDT 2010
Perhaps i misunderstand you. The scientist also draws from experience -
experimention. It is this that distinguishes him from the
mathematician and logician
Paddy
Kind regards
Paddy hackett
On 5 Jun 2010, at 17:16, Keith Brian Johnson <joyfuloctopus at yahoo.com>
wrote:
>
>
> Isn't logic the formalization of what is thought to be correct or
> legitimate thought, with application to any possible objects,
> abstract or concrete?
> Isn't theoretical mathematics the use of logic to describe patterns,
> with those patterns conceived abstractly--and therefore the
> formalization of the application of logic to patterns--and applied
> mathematics the use of logic to describe patterns, with those
> patterns instantiated concretely--i.e., ultimately the application
> of theoretical mathematics's formalized pattern analysis--although,
> of course, we may in fact do applied mathematics first and do
> theoretical mathematics second?
>
> Mathematicians may certainly use their intuitions and unformalized
> thought to arrive at mathematical results, but isn't it precisely
> the role of foundational mathematics to demonstrate how those
> results can be derived from the application of logic to patterns,
> and the role of logic to formalize how we think about anything at
> all--i.e., to formalize the process of legitimately deriving
> conclusions from premisses? Once that process has been formalized,
> then the results can be applied to the study of abstract patterns;
> and the results of the study of abstract patterns can then be
> applied to concretely instantiated patterns. (Admittedly, this may
> be the reverse of how we initially learn about such things; but such
> is the nature of formalization--it follows intuition rather than
> preceding it.)
>
> Thus, I take economists, political scientists, biologists, chemists,
> and physicists to be *using* mathematics and logic, *applying* them
> to concretely instantiated patterns, and thus to be species of
> applied mathematicians (when using mathematical thought processes; I
> do not claim that economists and political scientists always do so).
> I take theoretical/pure mathematicians to be *using* logic in order
> to *formalize* our thought and intuitions about patterns in the
> abstract.
> I take logicians to be *formalizing* our thought and intuitions
> themselves--to be formalizing what we take to be proper reasoning
> processes.
>
> (Of course, someone whose job title is "physicist" might do
> theoretical/pure mathematics; someone whose job title is "economist"
> might do logic. I am only claiming that a physicist qua physicist
> is only applying mathematics and logic, and that an economist qua
> economist is only applying mathematics and logic.)
>
> Keith Brian Johnson
>
>
>
>
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