Sorry, corrections in bold:

Jon,The way I learned it, (formal) implication is not the /assertion/ butthe /validity/ of the (material) conditional, so it's a differencebetween 1st-order and 2nd-order logic, a difference that Peircerecognized in some form. If the schemata involving "p" and "q" areconsidered to expose all relevant logical structure (as usually inpropositional logic), then a claim like "p formally implies q" isfalse. On the other hand, a proposition /à la/ "if p then q" (or "pmaterially implies q") is contingent, neither automatically true norautomatically false. I agree that you can see it as the samerelationship on two different levels. That seems the natural way tolook at it.Another kind of implication is expressed by rewriting a propositionlike "Ax(Gx-->Hx)" as "G=>H". In other words "All G is H" getsexpressed "G implies H". In first-order logic, at least, it actuallycomes down to a material conditional compound of two terms in auniversal proposition.If in addition to logical rules one has postulated or generallygranted other rules, say scientific or mathematical rules, then theselead to scientific or mathematical implications, the associatedconditionals being true by the scientific or mathematical rules, notjust contingently on a case-by-case basis. Anyway, all these kinds ofimplication do seem like the same thing in various forms.It's not clear to me how any of this figures into theconcept-vs.-judgment question. The only connection that I've been ableto make out in my haze is that when we say something like "p formallyimplies p", we're thinking of the proposition p as if it were aconcept rather than a judgment; our concern is limited to validity *asof an argument* "p ergo p". If we *_/say/_* 'p, ergo p' or, in akindred sense, "p proves p," we're thinking of p as a judgment, andour concern includes the soundness as well as validity *of theargument "p ergo p"*.Best, Ben On 5/11/2012 2:25 PM, Jon Awbrey wrote:Ben,Just to give a prototypical example, one of the ways that thedistinctionbetween concepts and judgments worked its way through analyticphilosophyand into the logic textbooks that I knew in the 60s was in thedistinctionbetween a "conditional" ( → or -> ) and an "implication" ( ⇒ or =>). Thefirst was conceived as a function (from a pair of truth values to asingletruth value) and the second was conceived as a relation (between twotruthvalues). The relationship between them was Just So Storied by sayingthatasserting the conditional or judging it to be true gave you theimplication.I think it took me a decade or more to clear my head of the dogmaticslumbersthat this sort of doctrine laid on my mind, mostly because theinvestiture oftwo distinct symbols for what is really one and the same notionviewed in twodifferent ways so obscured the natural unity of the function and therelation.Cf. http://mywikibiz.com/Logical_implication Regards, Jon

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