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- From: rar@csl.sri.com (Bob Riemenschneider)
- Newsgroups: sci.logic
- Subject: Re: A only if B
- Date: 16 Oct 92 14:02:05
- Organization: Computer Science Lab, SRI International, Menlo Park, CA.
- Lines: 37
- Message-ID: <1bnaggINNn6r@roche.csl.sri.com>
- References: <rkaivola.718902434@mits>
- NNTP-Posting-Host: birch.csl.sri.com
- In-reply-to: rkaivola@mits.mdata.fi's message of Mon, 12 Oct 1992 15:07:14 GMT
-
- 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
-
- Yes.
-
- Think about it this way: When is "Tom will visit us only if we invite
- him" false? It's certainly false if Tom visits without being invited,
- i.e., if A is true and B is false. If the sentence is true, any of the
- other cases -- Tom is invited and visits, Tom is invited but doesn't
- visit, and Tom is not invited and doesn't visit -- is possible. Well,
- those are precisely the truth conditions for A -> B. So if you're going
- to treat "Tom will visit us only if we invite him" as a truth-functional
- compound of "Tom will visit us" and "We invite him", it's simply a
- conditional. (Of course some, including myself, would argue that
- attempting to treat this as a truth-functional compound is not good
- enough for some purposes. For example,
-
- Tom will visit us only if we invite him.
-
- might be thought of as indicating a general disinclination of Tom to
- visit uninvited, making this something like a universal generalization
- of a conditional rather than a conditional. But this is beside the
- point, which is that "only if" corresponds to -> in the same way that
- "if" corresponds to <-.)
-
- -- rar
-