🚀 go-pugleaf

Jonathan Seldin writes:
  > 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.

The indicated argument is invalid:
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	A if and only if B     is paraphrased as     A <-> B   
but	A if             B     is paraphrased as     B  -> A
hence	A        only if B     is paraphrased as     A  -> B
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This is a "subtraction" argument that doesn't look too good.  If 
"A only if B" were correctly paraphrased as the biconditional, then 
"A if and only if B" and "A if B" could still be paraphrased as the 
premises indicate, but the conclusion would then be false.  Of course, 
it would then be redundant to say "if and only if" instead of just 
"only if", but so what?

  > 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.

This argument begs the question.  Anyone who thinks "A only if B" is 
a biconditional will reject your premise that the only excluded case 
is that A is true while B is false.  They will claim that another 
excluded case is that A is false while B is true.

Nonetheless, "A only if B" has to be paraphrased as  A -> B, not the 
biconditional, otherwise (1) would be a downright inconsistency.

(1)	John will dance only if Mary dances, and maybe not even then.

(The "maybe" is just an epistemic modality, not relevant here.)  
The consistency of (1) indicates that "only if" is not a biconditional 
connective, but (1) suggests that perhaps there is a cancelable 
implicature (not entailment) of the converse conditional.  So 
"A only if B" is paraphrased as "A -> B" if you think formal 
paraphrases should capture entailments but not implicatures, i.e., 
if the paraphrase should reveal a "logical form".

B-o} Michael
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Michael Hand                     phone (409)845-5660, fax (409)845-0458
Dept of Philosophy, Texas A&M Univ, College Station TX 77843-4237 U.S.A.