I'm trying to find whether there is a technical name for something like this:

$(A \iff B)$ given $C$

So $A$ and $B$ imply each other only if $C$ applies. For example, "August" and "hot" (fuzzily?) imply each other given that you are in the northern hemisphere.

Would it be reasonable to call this a second-order conditional? Since it is a conditional relationship that is itself conditional on something else.


  • $\begingroup$ "Second-order conditional" isn't a good descriptor for a conditional (hypothetical?) equivalence, as it suggests second-order logic. $\endgroup$
    – ryang
    Nov 30 '21 at 16:49
  • $\begingroup$ I would like to apply this to a context where the word "equivalence" would seem odd. Like the example I gave: "hot" and "August" imply or strongly indicate each other in the northern hemisphere, but "hot" and "August" are not "equivalent", they are different things. $\endgroup$
    – eparra
    Nov 30 '21 at 17:03
  • $\begingroup$ Then you want the word "suggest" instead, since in logic and mathematics, 'imply' $(\Rightarrow)$ has an even stronger mean than 'strongly indicate' ('suggest' typically also has a slightly stronger connotation than 'propose/hint/evoke'). In any case, consider supplying, in your Question, the full context that you mention; this increases the chance of getting an Answer. $\endgroup$
    – ryang
    Nov 30 '21 at 17:24

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