0

I'm asking for multiple languages, and use grey colour to refer to the concepts denoted by the English words.

Abbreviate Necessary Condition to NC, Sufficient Condition to SC. I already know that:

  1. If P, then Q. (In French: 'Si P, alors Q.' In German: 'Wenn P dann Q.')
    =  P only if Q. ('P seulement si Q.'  In German: 'P nur wenn Q.')
    = P is a SC for Q.    = Q is a NC for P.

In the first two implications, if precedes a SC, and only if a NC.

  1. Does the adverb only cause the logical difference between if and only if?

  2. If so, then how does only cause this? Does only cause only if to incorporate more conditions than 'if'? I've tried to illustrate below that SC ⊆ NCC, where 'only' ∈ SC\NC.

enter image description here

imz -- Ivan Zakharyaschev
  • 392
  • 3
  • 21
  • 1
    I already read http://linguistics.stackexchange.com/q/2157/5306. –  Nov 13 '16 at 08:08
  • 1
    "If P then Q = P only if Q" This is wrong. "If P then Q" = "Q if P." "Only if P then Q" = "Q only if P". But both logicicians and native speakers pretty sure would disagree that "If P then Q" (= "Q if P") is equivalent to "Q only if P". The order in which natural language realizes this relation is irrelevant, so whether you say "If P then Q" or "Q if P" amounts to the same (roughly, of course fucus structure etc. plays a role). The rest ist trivial, namely that "only" makes the implication a biimplication. – Natalie Clarius Nov 13 '16 at 15:24
  • BTW, this is not saying that the general natural language use of "if then" is equivalent to material implication in logic, because most speaker's intuitions say that it is not; what I'm saying is only that you can't just set "If p then q" equivalent with "Only if p then q" (which is what you were doing), neither in the way it is used naturally nor in mathematics. – Natalie Clarius Nov 13 '16 at 15:30
  • 1
    This question appears to address the interpretation of symbols in formal logic. That's relevant to linguistics, but isn't linguistics itself. – James Grossmann Jan 03 '17 at 19:12
  • 2
    I'm voting to close this question as off-topic because the question concerns the interpretation of formal logic symbols rather than linguistics. – James Grossmann Jan 03 '17 at 19:12
  • 1
    http://philosophy.stackexchange.com/q/40060/8572 –  Jan 03 '17 at 19:48
  • Indeed, it's interesting to cp Ger je, En only, ever and everything else under OE aen- incl. variants, and Gothic jabaida "if", Ger ob, the question markers Goth nu, Lat ne-, privative in-, i-, Ger nur wenn "only if"; further topical would be anyhow, although, also, but, Ger wobei, aber, jedoch, etc. insofar, Ger immerhin ... Only, this is not to be confused with other uses of only (as in this sentence). – vectory Dec 27 '19 at 17:24
  • I'd speculatively try to assume in- as contrast to ex-* in exclude, except, include, given that but only if is most often used to denote necessary exception, though in- "not; in-", un- "not, one" can't be easily confused. Also cp but once this became clear, since, likewise while vs Ger weil "because". At any rate "only if" might be calqued from late latin, given how similar the translations are. The question then is which form was original to the Latin form (if late latin may well have calqued it itself). – vectory Dec 27 '19 at 17:32
  • Also cp uncertainty about si, sibi etc as per your own question https://latin.stackexchange.com/questions/381/what-underlying-semantic-notions-connect-s%c4%ab-to-the-pie-root-se-to-own-posse/383?r=SearchResults#383 Also cp Ger solange, En so long as, as long as vs solo (assuming corruption solo > solang; consider that to long for inherently denotes subjunctive mood, ie. "pray the weather remain stable, we won't have problems", vs "so long the weather remain stable"), also Ger langen "suffice". – vectory Dec 27 '19 at 17:46
  • 1
    Latin.SE on "if and only if" pointing out that the formalized notion settled rather recently, but had been used variously much earlier at least in Latin – vectory Dec 29 '19 at 06:38
  • 1
    @JamesGrossmann I don't agree. The Q is about the meaning of if, only if,onlyin natural language; it's not about the interpretation of formal mathematical notation, which is assumed to be well understood by the reader and would help to understand the essence of the Q. The use ofifandonly ifin natural language and their use by mathematicians are consistent. Suggesting a theory whereifandonly` would have a meaning and where their composition would give the observed phenomena in the meaning of complete sentences is a topic for formal semantics, part of theoretical linguistics – imz -- Ivan Zakharyaschev Jan 06 '20 at 03:07

0 Answers0