[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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