[hist-analytic] A posteriori knowledge of necessary truths
Roger Bishop Jones
rbj at rbjones.com
Sat Dec 18 11:48:13 EST 2010
Here are some observations on your recent message on the
FIrst, I doubt the soundness of your method.
In order to reason soundly you must do so in a context which
is sufficiently well understood for its principles and rules
to be definite and their consistency strength establishable.
I know no way of doing this other than though the
construction of one or more formal models in a well
established logical system.
By this means you would ensure the soundness of your
reasoning, and can then debate how well your models
correspond to ordinary or philosophical usage of natural
languages on the relevant topics.
Second (if I might now disregard my own advice are reason in
an informal context), when making judgements about whether
some knowledge is a priori or a posteriori it is essential
to differentiate between information obtained by experience
according to whether it contributes to establishing the
meaning or the fact.
Our knowledge of the meaning of a natural language is of
course a posteriori, and if the language contains rigid
designators then (in any model I would be likely to work
with) the designatum of a rigid designator will be fixed by
its meaning (if it is not so fixed then it cannot be rigid).
In that case the use of experience in discovering the
designata in an equation of rigid designators will be a case
of knowing the language rather than of knowing the fact.
The fact will be an instance of the reflexivity of identity
and will be knowable a priori.
I would also myself not accept your opinion that the
introduction of an existential quantifier makes a de re
proposition from one which is not de re.
This sounds like the supposition that all existence is
contingent, which for anyone sympathetic to Carnap's stance
on abstract ontology will not be the case.
Sorry not to have undertaken a more thorough critique, but
my dominant sentiment is my first, that formality is
essential in dealing with logical problems of even this
level of complexity.
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