Dan, List: To clarify my earlier remarks, it is important to recognize that whenever Peirce discussed *giving* as an irreducibly triadic relation, he was always presenting it as a paradigmatic example to illustrate a *logical* principle--not attempting any kind of *linguistic* analysis of the verb itself.
CSP: So in a triadic fact, say, for example *A* gives *B* to *C*, we make no distinction in the ordinary logic of relations between the *subject nominative*, the *direct object*, and the *indirect object*. We say that the proposition has three *logical subjects*. We regard it as a mere affair of English grammar that there are six ways of expressing this: *A* gives *B* to *C*, *B* enriches *C* at expense of *A*, *C* thanks *A* for *B*, *A* benefits *C* with *B*, *C* receives *B* from *A*, *B* leaves *A* for *C*. These six sentences express one and the same indivisible phenomenon … But a triadic fact is in all cases an intellectual fact. Take *giving* for example. The mere transfer of an object which *A* sets down and *C* takes up does not constitute giving. There must be a transfer of *ownership* and ownership is a matter of Law, an intellectual fact. (EP 2:170-171; 1903) No one, including Peirce, would argue that those six sentences are *synonymous*; i.e., *linguistically* equivalent. Rather, his point was clearly that they are *logically* equivalent, in the sense that they express *one* relation that has *exactly three* correlates and *cannot* be reduced to the *dyadic* relations between them. Regards, Jon S. On Mon, Apr 22, 2019 at 1:43 PM Jon Alan Schmidt <[email protected]> wrote: > Dan, List: > > No, we are *not* talking about the same thing. It was *impossible* for > Peirce to be incorrect or even incomplete in this context; he was referring > to a *logical relation* that is *irreducibly triadic*--one that *always* > has *exactly three* correlates. > > If it helps, we can call it "P-giving" to distinguish it from the English > word "giving." A P-giver stands in the relation of P-giving, of a P-gift, > to a P-recipient. Whether or how well this maps to the *actual* usage of > the verb "giving" by competent English-speakers, let alone the closest > equivalents in other languages, is completely irrelevant. > > That said, since you claim that Peirce got the logic of giving wrong, do > you likewise hold that he got the logic of representing/mediating > wrong--i.e., the irreducibly triadic relation between a Sign, its Object, > and its Interpretant? > > Regards, > > Jon S. > > On Mon, Apr 22, 2019, 12:36 PM Daniel L Everett <[email protected]> > wrote: > >> Actually “incomplete” is a better description than incorrect. >> >> Sent from my iPhone >> >> On Apr 22, 2019, at 13:15, Dan Everett <[email protected]> wrote: >> >> Jon, >> >> No, we are talking about the same thing: a relationship that he >> considered logical, but in fact not. This has nothing to do with the >> English verb per se, but with the logical structure of any act of giving >> that includes three surface arguments. The point is that Peirce got the >> *logic* of giving wrong - for any language. >> >> Dan >> >> Sent from my iPad >> >> On Apr 22, 2019, at 12:59 PM, Jon Alan Schmidt <[email protected]> >> wrote: >> >> Dan, Jeff, List: >> >> DE: I am saying simply that in some cases of lexical analysis modern >> mathematical logic has tools at its disposal that enable analyses >> empirically superior to the the common picture of the valency of some verbs. >> >> >> Again, we are talking about two different things. When Peirce repeatedly >> characterized *giving *as irreducibly triadic, he was not referring to >> the *English verb*, but rather a specific *logical relation*--which is >> more fundamental than, and thus independent of, its *expression *in any >> particular language or other Sign System. In an Existential Graph, no >> matter what symbol we use to label the Spot for that relation, it will >> always have *exactly three* Pegs. >> >> Regards, >> >> Jon Alan Schmidt - Olathe, Kansas, USA >> Professional Engineer, Amateur Philosopher, Lutheran Layman >> www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt >> >> On Mon, Apr 22, 2019 at 3:11 AM Dan Everett <[email protected]> >> wrote: >> >>> Jeff, >>> >>> Let's not read too much into what I said. I am not claiming that triadic >>> relations are reduceable (at least not in all cases) to dyadic relations. >>> Not at all in fact. Nor am I urging the thesis that Quine, Church, Turing, >>> etc. are superior in any way to Peirce. >>> >>> I am saying simply that in some cases of lexical analysis modern >>> mathematical logic has tools at its disposal that enable analyses >>> empirically superior to the the common picture of the valency of some >>> verbs,. Having said that, it may simply be that Peirce's comments on 'give' >>> hold at the level of transitivity, though perhaps not at the level of >>> valency. I am still thinking about that possibilty. >>> >>> Peirce may have made mistakes in many places. This should not bother >>> anyone, though, so long as the mistakes are not at a level that threaten >>> his overall program. I certainly do not believe that any improvements in >>> modern logic and math threaten Peirce's program. >>> >>> Church invented the lambda calculus, identical in power to a universal >>> Turing machine.(https://en.wikipedia.org/wiki/Lambda_calculus) That is >>> a significant discovery/invention/advance. But this in no way means that >>> Church or Turing or Quine were superior to Peirce or that their systems >>> should be taken over his. It means nothing more than that these tools of >>> modern logic, in conjunction with modern linguistics research, offer >>> insights into *some* areas of language that Peirce could not have achieved >>> (and did not). But nothing that they did invalidates his triadic system, >>> his theory of semiotics, etc. >>> >>> Some verbs operate differently than Peirce thought, at least at the >>> level of semantic decomposition, even though their syntactic behavior may >>> conform well to his predictions. Not a threat to him. But perhaps a tool >>> for better understanding him in modern terms. >>> >>> The issues are nuanced. But I believe that sorting through them >>> ultimately makes Peirce more relevant than ever to our understanding of >>> language, logic, etc. >>> >>> Dan >>> >>> On Apr 21, 2019, at 9:28 PM, Jeffrey Brian Downard < >>> [email protected]> wrote: >>> >>> Dan, List, >>> >>> I, for one, don't share your view that Peirce missed the boat on this >>> one. In making the assertion, are you claiming that modern mathematical >>> logic demonstrates that relations that might appear to be genuinely >>> triadic--- such as giving, or mediating or thinking--can be >>> entirely reduced to dyadic relations using logical resources that do not, >>> themselves, employ those very relations? Or, are you saying that this has >>> been shown in modern philosophical logic? >>> >>> In both areas of inquiry, I do not think the matter is--by any >>> means--somehow now settled. Here, at the beginning of the 21st century, >>> there are plenty of reasons to doubt the assertions of Quine, Church, >>> Turing, e*t al*, on this matter. >>> >>> Yours, >>> >>> Jeff >>> >>> Jeffrey Downard >>> Associate Professor >>> Department of Philosophy >>> Northern Arizona University >>> (o) 928 523-8354 >>> >>>
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