[hist-analytic] The "Analytic A Posteriori"
Baynesr at comcast.net
Baynesr at comcast.net
Tue Sep 1 14:35:58 EDT 2009
Sometimes identities, when true, are described as
true ‘analytic a posteriori ’ propositions. This is not,
always an altogether easy determination. The sentence
‘a=b’ may be a posteriori and true, but even if we concede
the force of the Barcan principle and it follows that
‘necessarily (a=b)’ it does not follow from this that
‘necessarily (a=b)’ is a posteriori . That is, empirical
knowledge, knowledge that is possible "only…through
experience." (Kant First Critique B3). It is true that,
traditionally, the sole alternative to a posteriori is a priori ,
and that to be known a priori is to be known "absolutely
independently of all experience." (ibid) This would suggest
to some that ‘necessarily (a=b)’ cannot be a priori because
it is from the identity ‘a=b’ that we come to know ‘necessarily
(a=b)’ and, ‘a=b" can be known only through experience,
rendering ‘necessarily (a=b)’ a posteriori . But the proposition
‘necessarily (a=b)’ does not follow from anything but the
Barcan Principle applied to some proposition asserting identity.
We ought no more consider ‘necessarily (a=b)’ a posteriori than
we would consider ‘The cat has two heads or the cat does not
have two heads’ as a posterior i. Both follow from logic, alone,
applied to propositions, which are not propositions of logic, viz.
‘a=b’ and ‘The cat has two heads or the cat does not have two
heads’, both of which may be a posteriori. Schematically the
similarity can be represented thusly,
(…or ~…) /<p>
(nec …) /<p>
Where an I going with this? Short answer: Hume and Descartes
reason analogously from the independence in thought of certain
concepts; bodies and souls; causes and effects. Pursing that
analogy is productive; disposing of the analytic a posteriori is
essential to one aspect of what I have to say on these, separate,
but related lines of reasoning.
Steve Bayne
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