[FOM] reply to Gabriel's reply

Martin Davis martin at eipye.com
Thu Apr 20 14:39:40 EDT 2006

First I want to apologize for the tone of my message. It's the sort of 
thing the moderator is supposed to stop. In this case the moderator needed 
moderating. As mitigation for my cranky state, I plead my having just 
emerged from the hospital where good folks were manipulating my coronary 
artery system,  and then found myself with a nasty case of bronchitis, 
Finally, the moderator doesn't have the subscriber's privilege of picking 
and choosing which posts to read, and patience sometimes wears thinner than 
it should. Again, apologies.

Not to get into an infinite dialog, just a few explanatory comments.

Referring to Gabriel's two "mindsets" I wrote:

 > We can't know until we experience it ourselves. This
 > does remind one of things one is more likely to hear in a Church
 > sermon than in a Mathematics colloquium talk - but no matter.

Gabriel replied:

 >I don't think churches get into Gestalt switches of the kind I'm
 >talking about.

Sorry for being unclear. The analogy I had in mind is with the state of 
"faith" which is not to be understood until it is personally experienced.

Gabriel wrote:

 >Also, notice what happens if we say about classical mathematics
 >what you say above about constructive mathematics.
 >"We can't know classical mathematics until we experience
 >it ourselves."
 >Do you have a problem with this?

Yes I do  I have learned mathematics, a body of knowledge and a 
methodology. Moreover as a worker in foundations I have learned how to 
notice carefully which proof methods I actually use in a given context. I 
have no more acquired a "mindset" than I do when I learn chemistry.

Gabriel wrote:

 >If you don't, why do you have one with constructive mathematics?

I don't have any problem at all with constructive mathematics. I'm a great 
admirer of Bishop. I once supervised a master's thesis based on his 
"Constructive Analysis". My only problem is with what I see as your 
mystification of something very straightforward: doing mathematics while 
employing only constructive methods.


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