[FOM] Mathematics ***is*** formalising of our thought and intuition

[Paddy Hackett]

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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