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Single Idea 9645
[filed under theme 6. Mathematics / C. Sources of Mathematics / 10. Constructivism / a. Constructivism
]
Full Idea
If we define p as '3 if Goldbach's Conjecture is true' and '5 if Goldbach's Conjecture is false', it seems that p must be a prime number, but, amazingly, constructivists would not accept this without a proof of Goldbach's Conjecture.
Clarification
'Goldbach's Conjecture' is probably true, but has not been proved
Gist of Idea
Constructivists say p has no value, if the value depends on Goldbach's Conjecture
Source
James Robert Brown (Philosophy of Mathematics [1999], Ch. 8)
Book Ref
Brown,James Robert: 'Philosophy of Mathematics' [Routledge 2002], p.113
A Reaction
A very similar argument structure to Schrödinger's Cat. This seems (as Brown implies) to be a devastating knock-down argument, but I'll keep an open mind for now.
The
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9645
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Constructivists say p has no value, if the value depends on Goldbach's Conjecture
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8706
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