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

Steve Stevenson steve at cs.clemson.edu
Tue Jun 8 10:30:23 EDT 2010

Computation is now recognized as the third leg of the Scientific  
Method and  is virtually impossible today to carry out research  
without computational means (including "experimental mathematics). A  
practical manifestation of the points brought up by Keith and Paddy is  
the "verification" and "validation" (V&V) issue in computational  
science. In FOM context, verification focuses on whether the  
mathematics captures the theory (and therefore a correct specification  
for the computer model) and validation focuses on whether the model  
predictions have anything to do with reality. Based on my experience  
in V&V, I propose a paraphrase of Brouwer's concept: "Mathematics is  
that activity that goes on at the interface of modeling and reasoning".
School of Computing, Clemson University
"As far as the laws of mathematics refer to reality, they are not  
certain; as far as they are certain, they do not refer to  
reality" (Einstein).

On 7Jun 2010, at 2:14, Keith Brian Johnson wrote:

> 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.

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