70. What happens when a proposition is taken into a language: what is
the criterion for it being a proposition?
In this respect the concept of number is like the concept of
proposition. On the other hand the concept of cardinal number can be called a
rigorously circumscribed concept, that is to say, that is to say it’s a concept
in a different sense of the word.
a proposition is a proposal –
what happens when a new proposition is taken into the language – is that
it is proposed – and each time it is
used – it is proposed
what is the criterion for it being a proposition?
that it is proposed
a concept is if you like a back story for a proposition –
a way of talking about it
it is not that the concept of number is like that of the concept of a
proposition –
numbers are propositions
if it’s proposed – it’s a proposition
the cardinal number – ‘a rigorously circumscribed concept’?
the cardinal number is a proposal – is a proposition
a proposal in number theory –
‘rigorously circumscribed’ –
is to say that in the practice of
number theory – this proposal –
is described as having certain
characteristics and functions
as the history of cardinals shows
–
these characteristics and
functions – the descriptions –
are open to question – to interpretation
–
open to exploration
© greg t. charlton. 2014.