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In David Rynin's 1956 address to the American Philosophical Association, "Vindication of L*G*C*L P*S*T*V*SM", he remarks upon the "tenuous logical relationship" between a general statement, "For any substance there exists some solvent" and a singular statement, "Substance A is a soluble in Substance B".

He comments that tho a name is not important, he is at a loss for a suitable name for this kind of logical relationship. Specifically he is pointing out that while the singular statement describes a sufficient condition for the satisfaction of a necessary condition, it does not describe a necessary condition for the general statements necessary condition, and therefore the general statement is not a strictly falsifiable hypothesis.

How then to describe this tenuous relationship?


EDIT: if you register w/Jstor, their basic & free membership allows access to articles (for a limited time, like two weeks iirc). This article by David Rynin (former Professor Emeritus @ UCBerkeley) is one of the ones freely available. Apologies as I am not trying to spam for Jstor, but he is an excellent author and otherwise difficult to find online without co$t.

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  • It seems to me that we can cosnider it a particular case of instantiation : perhaps a "double instantiation". From : ∀x∃yPxy we derive : ∃yPay. We may translate it as : "substance a is soluble". Then we verify the solubility of a producing a substance b such that Pab holds. Oct 18, 2016 at 9:44
  • Rynin himself says that the name is not important, and later describes it verbosely as "existence of a sufficient condition for the satisfaction of a necessary condition". The issue is that even if S(x,y) is an empirically testable predicate its mixed quantification ∀x∃yS(x,y) has neither necessary nor sufficient truth conditions, i.e. it is neither verifiable nor falsifiable. Both would require testing universal claims (every substance, no solvent). But basing meaningfulness on empirical verifiability popular with logical positivists is now considered unworkable, so the problem is moot.
    – Conifold
    Oct 18, 2016 at 19:53
  • @Conifold, and what little philosophers would speak of without "moot problems"? ;)
    – MmmHmm
    Oct 18, 2016 at 20:15
  • They upload them into richer frameworks. In this case the discussion moved to distinguishing aspects of scientific theories that are holons (empirical in some indirect way) from floaters (empirically idle) , see Bonilla's Meaning and Testability in the Structuralist Theory of Science (2003)
    – Conifold
    Oct 18, 2016 at 20:31
  • @Conifold good stuff there from Jesus. Not so interested in frameworks, myself but I appreciate the richness you speak of with a respect formed by poverty.
    – MmmHmm
    Oct 18, 2016 at 21:49

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