CÆTERIS PARIBVS

--- by JLS
------ for the GC

Dale has recently (in "Dale's Law," etc., THIS CLUB) brought up the important idea of this Ciceronian notion,

CÆTERIS PARIBVS.

It works as an operator, for Grice, e.g. -- and symbolised by 'cp':

cp p

It is raining.

Implicature: "Ceteris paribus, it is raining".

It can combine, crucially, in what Grice calls "molecular utterances":

"If it rains I'll stay in"

In symbols

p cp ⊃ q

Since Whitehead-Russell, when introducing the 'horseshoe' were reluctant to admit 'ceteris paribus', it is notationally complex to involve the thing (the horseshoe) with the Ciceronian modifier. It should be read as

p ⊃_cp p

i.e. the 'cp' attaches to the horseshoe directly. The thing is whether horses wear those types of shoes, but I could disgress.