🚀 go-pugleaf

In article   writes:
...
>In article <rkaivola.718902434@mits> rkaivola@mits.mdata.fi (Risto Kaivola) writes:
>>
>>  The following is no doubt a little trivial for the participants of this
>>group, but I hope someone is willing to help me, nevertheless.
>>  Exactly how should one formalize the English notion of 'only if'
>>in the language of the propositional calculus?
...  (Formalization of A only if B requested.)
>>A  -->  B
... (blank lines omitted)
>>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)?
...
>>(Internet address:   rkaivola@mits.mdata.fi)
>
>I'd go for:
>
>(B --> A) & (-B --> -A)
>
>
>Antoni Diller

No!!!

Think of A if and only if B.  This is A <--> B; A if B is clearly
B --> A, and so A only if B must be A --> B.

Another way to think of this is in terms of truth table values.
In A only if B, the case that is excluded is that A is true and B
is false; A only if B is true (truth functionally) in all other
cases.  This gives us the truth table for A --> B.

So rkaivola@mits.mdata.fi was right the first time.

-- 
Jonathan P. Seldin
Department of Mathematics                 seldin@alcor.concordia.ca
Concordia University			   seldin@vax2.concordia.ca
7141 Sherbrooke Street West, Montreal, Quebec, Canada, H4B 1R6