FOM: Non-scientific pseudo-problems

[Soren Riis]

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Non-scientific pseudo-problems
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I will follow Harvey Friedman's advice and make my last
contribution to the "social construction" pseudo-debate.
I hope the following "essay" will clarify my position.
I will assume brief familiarity with Hersh claims.

>>From: Reuben Hersh <rhersh at math.unm.edu>
>>In particular, I have written repeatedly that once a mathematical
>>entity is invented, it has definite properties which we are not
>>free to choose, and which may be difficult or impossible for us
>>to discover.
>
>In that case I see no remaining differences in your position.  
>It seems to me that Hersh, Machover, and I are in essential 
>agreement.
>
> Vaughan Pratt

This view is certainly close to a sensible starting point for a 
meaningful discussion:

I agree with Joe Shipman's reply:

> "Once a mathematical entity is invented, it has definite properties 
> which we are not free to choose, and which may be difficult or 
> impossible for us to discover."
> Did you really mean "impossible"?  That would seem to spell defeat 
> for your position, for how can they be definite and yet impossible 
> for us to discover unless their reality is something other than 
> social?

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Non-questions referring to non-scientific pseudo-problems
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Did 

(a) Daimler invent the four stroke engine 

or did

(b) Daimler discover that we live in a universe where one can 
build a four stroke engine?

Did

(c) the physicists invent a machine which can produce W-particles

or did

(d) the physicists discover the W-particle?

These are non-questions which refer to non-scientific pseudo-problems. 

When this is acknowledged we see that the first part of the sentence: 
"Once a mathematical entity is invented..." is a completely empty
statement which does not add any relevant information to the sentence.

Do we say:
"Once the W-particle was produced it had this or that mass..." ???

No! We prefer to leave out irrelevant and confusing information and 
prefer to say:

"The W-particle has this or that mass..."

If Prof. Hersh would agree to remove the non-scientific loaded 
ideological baggage from his statements he would not be highly 
controversial. It would be a major step forward if we could agree 
and remove all reference to non-scientific pseudo-problems. The 
uncontroversial fact is that:

"Mathematical entities (like N) has definite properties which we
are not free to choose, and which may be difficult or impossible for 
us to discover."

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Attempt to restore consensus and rationality
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I know I have expressed myself rather strongly in my latest 
postings, and I give my full excuse to Prof. Hersh that I 
occasionally have address him without refering to his Professor 
Title. This was unintentionally and English is not my first language.
Still I find that Prof. Hersh's views (I am sure unintentionally) 
is a part of a current social trend which undermines basic Scientific 
ideals. 

I am told that the "professional" philosophers never have been able 
to come up with one single new measurable quantity. Does this not 
indicate that the method of "traditional philosophy" is a failure 
which at best is harmless? 

Is it not correct that the best philosophy tend to produce Theorems or 
other Measurable things? Think of Ernst Mach philosophy (in which he 
denies absolutes!!) + Einsteins own Philosophy based on the 
principle of relativity which lead to the Theory of Relativity? 

Traditional philosophy can however be very dangerous (think of Nietche) 
because usually it is loaded with ideological baggage which people can 
relate to in destructive ways. I would not have taken the time to 
participate in this discussion if I thought that Prof. Hersh ideas were 
"harmless". 

Prof. Hersh book "What is Mathematics, Really" was very well received 
among Social constructivists. This is NOT a coincidence because 95% 
of Prof. Hersh claims are uncontroversial, illuminating, interesting 
and correct and his audience (who mainly are from the humanities 
with no or very little education/talent for critical rational/mathematical 
thinking) are easy targets.

Prof. Hersh manages to distort the overall picture and are in my 
opinion setting a bad example for mathematical/logical/scientific 
thinking. A proof has to be 100% correct. Only 95% will not do, and 
can lead to completely misleading conclusions.

For me this is not the only FOM-discussion we have had which illustrates 
it is virtually impossible to have a serious scientific discussion, 
unless views are been supported by theorems, conjectures, phenomena, 
directions, scientific speculations or other positive "materialistic" 
matters. 

The pointless Cat-fom vs. Set-fom debate would NEVER have gone of the 
track if both sides had shown ease and flair in backing up their views 
with theorems, conjectures or well-defined relevant public accessible 
phenomena. 

I hereby recommend we try to move forward, focus our FOM-activity 
and coach ourselves towards new amazing FOM-related problems/theorems
/conjectures/discussions.

Soren Riis