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

[Keith Brian Johnson]

I entirely agree with Paddy Hackett:  It is by observation, including experimentation, that the scientist determines which patterns are concretely instantiated.  He then applies mathematics to those concretely instantiated patterns, using logic to reason validly (and, if his descriptions of his observations are correct, soundly) from premisses at least some of which are about those observations to conclusions.  He trusts those conclusions to the extent that he trusts his descriptions of his observations to be correct and to the extent that he trusts mathematics' analyses of patterns in the abstract to be correct and to the extent that he trusts logic's formalization of legitimate thought processes to be correct.  

Keith Brian Johnson

> 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 <> ymailto="mailto:joyfuloctopus at yahoo.com" 
> href="mailto:joyfuloctopus at yahoo.com">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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