Motorola M500 Manuel d'utilisateur Page 29

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M500 180 Page 27
1 + 1 = 2
Dear Tony,
Maybe I can clarify Malcolm Fowler’s question [M500 178 36] concern-
ing the relationship between Russell and Whitehead’s proof that 1 + 1 = 2
and G¨odel’s Incompleteness Theorem. It is indeed the case that Russell and
Whitehead’s aim in Principia Mathematica was to show that mathematics
can be rigorously constructed from logic, namely their Theory of Types.
Their proof that 1 + 1 = 2 is part of that grand design.
odel’s rightly celebrated Incompleteness Theorem states that any con-
sistent axiomatic system rich enough to encompass the arithmetic of the
positive integers is incomplete. This means that there are true statements
about the positive integers that cannot be proved within the given axiomatic
system. However, odel’s result does not say that we are unable to prove
anything within such an axiomatic system. Clearly, 1 + 1 = 2 is one of the
‘facts’ that the Russell–Whitehead system can prove but G¨odel tells us that
there will be others that it cannot prove.
With best wishes,
John Taylor
Calendar
Dear Eddie,
Thanks a lot for M500 178. I read Singmaster’s enormous article with
great interest. His entry for c.1555 is interesting. Long ago I saw a rhyme
in Latin hexa-meters:
Julius, Aprilis Septemque Novemque tricenos:
Unum plus reliqui; Februs tenet octo vicenos,
At si bissextilis fuerit, superadditur unus.
(July, April, September and November thirty: One more for the rest; Febru-
ary has twenty-eight, But should it be a bissextile year, one more is added.)
This is pretty degenerate Latin and looks medieval, though the hexam-
eters seem fairly metrically kosher (which medieval attempts at hexameters
are usually not). By the way, the Roman month is called Quintilis, not
Quintilius. Singmaster mentions that Quintilis was renamed Julius by a
sycophantic Senate, but not that when Augustus reorganized the Julian
calendar he renamed Sextilis after himself, and furthermore stole a day
from February (which had previously had 29/30 days) so that his month
would have 31 days like Julius.
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