[FOM] R: 802: Systematic f.o.m./1

[Antonino Drago]

-----Messaggio originale-----
Da: fom-bounces at cs.nyu.edu [mailto:fom-bounces at cs.nyu.edu] Per conto di
Harvey Friedman
Inviato: mercoledì 4 aprile 2018 07:06
A: Foundations of Mathematics
Oggetto: [FOM] 802: Systematic f.o.m./1

In the introduction Friedman recalled Language and Philosophy of Language,
but no Logic. Why? 
Then 
"Now what is the most obvious grammatical phenomena in mathematical
thinking?
Arguably the idea that we can combine two sentences by conjunction to form a
third sentence."
 This idea has two pre-supposition: 
1) the first logical law is that of bivalence (intuitionists and many others
disagree) 
2) one can always select the affirmative sentence representing this idea,
which instead includes always its negated idea.  
I think that textbooks' starting point of educational logic do not
well-address to the search of the foundations of the logical thinking and as
a consequence of the F.o:M.
In addition. The laws of bivalence is a good tool for operating in
mathematics, but it requires a justification. Leibniz. Who tried to suggest
it, paired it with the principle of non-contradiction: "Nothing is without a
reason"; a doubly negated proposition, starting fromn "Nothing", and odd
idea, which surely Friedman did not take as a candidate for his basic idea.

Best greetings
Antonino Drago