🚀 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.

seldin@alcor.concordia.ca ( JONATHAN SELDIN ) writes:

[stuff deleted]

>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.

I agree totaly in the mathemathical sense. But I think that when
we use the phrase "only if" in language, the "if" part is often
implicite. I would not say "Tom will come only if we invite him",
if I thought that even with an invitation, Tom might not come.
This "if" part might even be considered stronger in the phrase
"Only if we invite him, Tom will come to diner". So, I think
that if you're interpreting a text, the `A <-- B' part should
follow immediatly, while one should somehow look more closely
whether or not `A --> B' is implicitely assumend.

>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

Frank Teusink

In article <7563@charon.cwi.nl>, frankt@cwi.nl (Frank Teusink) writes:
|> I agree totaly in the mathemathical sense. But I think that when
|> we use the phrase "only if" in language, the "if" part is often
|> implicite. I would not say "Tom will come only if we invite him",
|> if I thought that even with an invitation, Tom might not come.

I certainly would say this.  For example, consider the context

	Bob will come if he learns of the party -- whether
	we want him to or not.  But Tom will come only if we
	invite him.

Since we haven't yet invited Tom, we of course have no idea of
whether he will in fact come (once he is invited) since,
for example, he may have a conflict, may want to avoid Bob, etc.

If you don't concede this (rather standard, I think) use of 'only if',
you have a lot of trouble straightforwardly expressing the thought
that Tom is the sort of fellow who won't attend in the absence of
an invitation.
	
I agree that it is sometimes (maybe even often) the case in English
that 'only if' is used in a context where 'if and only if' is implied,
but this does not remove its more fundamental meaning.  And I think
that you have picked a particularly bad example to illustrate the
point.
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