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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