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.

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    I already read linguistics.stackexchange.com/q/2157/5306.
    – NNOX Apps
    Nov 13 '16 at 8:08
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    "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.
    – lemontree
    Nov 13 '16 at 15:24
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    This question appears to address the interpretation of symbols in formal logic. That's relevant to linguistics, but isn't linguistics itself. Jan 3 '17 at 19:12
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    I'm voting to close this question as off-topic because the question concerns the interpretation of formal logic symbols rather than linguistics. Jan 3 '17 at 19:12
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