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

[Steve Stevenson]

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".
--
Steve
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.