Vc:3b:-(SSO·b)=c
-3b:Vc:(SSO·b)=c
3b:-Vc:(SSO·b)=c
3b:Vc:-(SSO·b)=c(Second hint: Either four of them are true and two false, or four false and
two true.)How to Distinguish True from False?
At this juncture, it is worthwhile pausing for breath and contemplating
what it would mean to have a formal system that could sift out the true ones
from the false ones. This system would treat all these strings-which to us
look like statements-as designs having form, but no content. And this
system would be like a sieve through which could pass only designs with a
special style-the "style of truth". If you yourself have gone through the six
formulas above, and have separated the true from the false by thinking
about meaning, you will appreciate the subtlety that any system would have
to have, that could do the same thing-but typographically! The boundary
separating the set of true statements from the set of false statements (as
written in the TNT-notation) is anything but straight; it is a boundary with
many treacherous curves (recall Fig. 18), a boundary of which mathemati-
cians have delineated stretches, here and there, working over hundreds of
years. Just think what a coup it would be to have a typographical method
which was guaranteed to place any formula on the proper side of the
border!The Rules of Well-FormednessIt is useful to have a table of Rules of Formation for well-formed formulas.
This is provided below. There are some preliminary stages, defining nu-
merals, vt'friables, and terms. Those three classes of strings are ingredients of
well-formed formulas, but are not in themselves well-formed. The smallest
well-formed formulas are the atoms; then there are ways of compounding
atoms. Many of these rules are recursive lengthening rules, in that they
take as input an item of a given class and produce a longer item of the same
class. In this table, I use 'x' and 'y' to stand for well-formed formulas, and
'5', 't', and 'u' to stand for other kinds of TNT-strings. Needless to say,
none of these five symbols is itself a symbol of TNT.NUMERALS.
o is a numeral.
A numeral preceded by S is also a numeral.
Examples: 0 SO SSO SSSO SSSSO SSSSSOTypographical Number Theory 213