Helmut, List,
Another way to read the form (a(b))
[in the existential interpretation]
is “not a without b”.
Peirce's approach in these lectures appeals to the line of thinking
that takes implications and the corresponding subject-predicate form
as basic, but that is not the only possible basis for a logical system
of syntax and not the only basis that Peirce himself took up in his many
syntactic experiments. In relating logical signs to logical objects it
normally proves best to remain flexible and to consider the object of
logic that is common to all its avatars.
Regards,
Jon
On 10/31/2017 3:34 AM, Helmut Raulien wrote:
List,
I have thought about how "if-then" translates from the cuts: If a cut would mean
"it is not so, that", it would be: "It is not so, that it rains and it is not
so, that a pear is ripe". This is not sufficient for translation, because an
"and it" may be understood symmetrically, therefore it must be "and then" for
a cut in a cut: "It is not so, that it rains, and then is not so, that a pear
is ripe". Still insufficient, because it must be estimated, that the negation
by the outer cut is valid for all outside, the whole universe (that it is not
so not only in London, but everywhere): "It cannot be, that it rains and then
is not so, that a pear is ripe". Now, by annihilating double negation, "It
cannot be that then not" becomes "if, then".
Best,
Helmut
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