🚀 go-pugleaf

In article <rkaivola.718902434@mits> rkaivola@mits.mdata.fi (Risto Kaivola) writes:
>  Exactly how should one formalize the English notion of 'only if'
>in the language of the propositional calculus?
>  That is, given the sentence
>"Tom will visit us only if we invite him.",
>is the correct formalization
>
>A = "Tom will visit us."
>B = "We invite him."
>
>A  -->  B
>
>Or, should this perhaps be B --> A (not in my opinion), or A <--> B
>(this last alternative is more likely to be correct than B --> A, in my
>opinion)?

Right the first time.

B --> A would be "Tom will visit us if we invite him"; the "only" makes the
implication go the other way.

Note that mathematicians say "if and only if" (usually written "iff") for
A <--> B.  It can be argued that some actual instances of "A only if B" in
speech mean A <--> B, but I think a better interpretation in such cases is
A --> B, with the B --> A part being taken for granted.

The problem with A --> B is that we think of --> as representing *causal*
implication, which would mean "Because Tom will visit us, we will invite
him."  But the propositional implication does not have this meaning.