[FOM] Odd Thought About Identity

Paul Hollander paul at paulhollander.com
Fri May 22 22:17:33 EDT 2009

Correction to my previous submission. Vaught uses the word 'schematic' 
twice in R. Vaught, Axiomatizability by a schema, The Journal of 
Symbolic Logic, vol. 32 (1967), pp. 473– 479.

In both cases he is uses the expression 'schematic axiomatizability'.

The first is in footnote 4 on p. 473, where he writes:

    The question of the schematic axiomatizability of these induced
    theories, brought to the author's attention by Dana Scott, was the
    initial stimulus for the work reported here.

The second is on p. 478 in the body of the text, where he writes:

    Nevertheless, there do not appear to be any very interesting
    theories whose schematic axiomatizability is obtainable from Theorem
    2 but not from Theorem 1.

It seems 'schematic axiomatizability' is a synonym for 'axiomatizability 
by a schema', which as Richard pointed out is not at issue.

So the question remains, what is Vaught's own side condition for 
Leibniz's Law (or his analogue of Leibniz's Law), and does it correspond 
to Richard's or Alex's side condition (or neither)?


More information about the FOM mailing list