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, et al, on this matter. Yours, Jeff Jeffrey Downard Associate Professor Department of Philosophy Northern Arizona University (o) 928 523-8354 ________________________________ From: Dan Everett <danleveret...@gmail.com> Sent: Sunday, April 21, 2019 11:47 AM To: Jon Alan Schmidt Cc: peirce-l@list.iupui.edu Subject: Re: [PEIRCE-L] Symbols and Syntax (was Genuinely triadic relations, laws and symbols) Yes, Jon, but Peirce was wrong. These lexical decompositions are done by logicians. Peirce unfortunately missed the boat on this and there is no solution from logic, because it is logic that points out the errors of Peirce's view of giving. I will discuss this at length in my in-progress biography of Peirce, but also point to the overarching utility of his view in the notion of the interpretant. He doesn't have to get everything right. The architectonic matters more than a few errors in specific solutions. Dan On Apr 21, 2019, at 2:44 PM, Jon Alan Schmidt <jonalanschm...@gmail.com<mailto:jonalanschm...@gmail.com>> wrote: Dan, List: Peirce was first and foremost a logician, not a linguist; and from a strictly logical/semeiotic standpoint, the relation that we call "giving" in English is irreducibly triadic. In fact, Peirce repeatedly held it up as a paradigmatic example of just such a relation. Moreover, according to his classification of the sciences, the principles of the Normative Sciences--including Logic as Semeiotic--are more fundamental than those of any Special Science, including linguistics. Hence the triadicity of the relation that we call "giving" is independent of its expression in English, or in any other particular language or Sign System. Regards, Jon Alan Schmidt - Olathe, Kansas, USA Professional Engineer, Amateur Philosopher, Lutheran Layman www.LinkedIn.com/in/JonAlanSchmidt<http://www.linkedin.com/in/JonAlanSchmidt> - twitter.com/JonAlanSchmidt<http://twitter.com/JonAlanSchmidt> On Sun, Apr 21, 2019 at 1:31 AM Dan Everett <danleveret...@gmail.com<mailto:danleveret...@gmail.com>> wrote: Folks, Lexical semantics is a large field and there are various positions specialists take on exactly how word-meanings are best to be characterized. For example, most scholars (not all), argue that there is no simple verb 'to give' but that this English verb is characterized by a representation along the lines of: Anna gave Max a book. give: lambda z lambda y lambda x lamba e act(x) & become poss(y,z)(e) ('lambda' is of course the lambda operator) In other words, any verb, in this case 'give' is broken down into more basic components. No language is required to have a verb that is exactly like the English verb 'to give' but if it does, it must be composed of these finer predicates, so that the triadic semantics of 'to give' (English) is derivative, not basic (though the combinations of these basic predicates in this form will in fact produce a di-transitive or "triadic" syntax). Some linguists would refer to the number of lexical arguments as the valency of the verb and the number of syntactic arguments as the transitivity of the verb (noun, etc). And this can vary radically across languages. For example, in the Piraha language that I have worked on for decades, there are only about 90 or so distinct verb roots (which are not to be confused with verb stems, in turn not to be confused with verbs, and not to be confused with lexical representations). So to produce a verb like 'bring back' (corresponding roughly to a single verb such as 'return', as in 'return the screwdriver when you're finished') in Piraha the actual verb might be: 'go-turn-carry-aspectual distinction affixes...' (i.e. a verb stem composed of several verb roots plus a number of affixes playing derivative semantic roles). In a language like English with an extremely simple verbal morphology (maximum of five forms - sing, sang, sung, sings, singing) this is deceptively easy. In Spanish a verb would have 30-50 forms. But in Piraha (not uncommon for polysynthetic languages of the Americas) each verb can have as many as 65,000 forms (sixty-five thousand). And there simply is no way to compare predicates ilke "give" one-to-one with any Piraha verb. If we consider a basic English-conceived/interpreted predicate like 'give' then of course it is difficult to imagine that it wouldn't have three arguments, e.g. a giver, a thing given, and a recipient. But this simple conception does not manifest itself in all languages. So for example, abstracting away from the much greater complexity of Piraha verbal morphology, there simply is no simple verb 'to give' in the language. There is a combination of verb roots that means, roughly, 'x transfers y to z with the expectation that z will transfer b to x' That is, the concept of giving requires reciprocity in Piraha (a hunter-gatherer culture). In the case of Amele that I mentioned earlier, there is NO verb 'to give.' One can find, for example, 'John apple Bill' with no verb and in the right context imply that 'John gave an apple to Bill.' But there is no actual verb translated 'give' in the language. All languages are severely *underdetermined* meaning that the predicates of the language do not fully specify meanings or even literally specify meanings. Full meanings are supplied by the cultural act of interpretation. These are reasons that I favor the triadic system of semiotics of CSP to the dyadic system of Saussure. But the argumentation is subtle and detailed. And the semiotics has to fit the linguistics - it does not substitute for the linguistics. As far as syntax goes, syntax never, ever fully specifies all the imaginable connections between predicates and arguments. Syntax acts as a filter on potential meanings, guiding the interpretation process to avoid certain interpretations. This active, dynamic role of interpretation is why the Saussurian system cannot work and why I favor Peirce's work. Now to the syntax. If we were to assume that there are three symbols (without worrying about lexical decomposition), e.g. "John," "give," "apple", "Mary," we can think of various ways of combining them. The simplest way would be simple linear concatenation: "John give Mary apple." Another would be hierarchy + concatenation, e.g. "[John [[give Mary] apple]]" and the final would be hierarchy + recursion. Peirce's semiotics is semantically recursive, though the syntax is of almost no concern to that work. Chomsky's grammatical proposals require both syntactic and semantic recursion. My own work requires Peircean recursion, while allowing syntactic recursion to be optional across languages. This would all take a lot more space for me to unpack for non-specialists (i.e. non-linguists). Peirce's discussions of predicates is little more than a first pass. This doesn't mean he was wrong, but that verbal semantics is far more complex than he understood, because it is based on a science that did not exist, except perhaps in an extremely inchoate form that he helped to birth, at the time he was writing. Guessing at whether predicates are triadic or not by non-linguists is akin to me, a non-engineer, telling my grandson, a bio-medical engineer, how I think the best way to design an artificial heart would be. I have referred many times to work of mine and others on these and related subjects. I suggest reading a few of those (or just an introductory linguistics text). Here are a couple of more references: http://www.zas.gwz-berlin.de/fileadmin/mitarbeiter/wunderlich/Wunderlich_14_Lexical_Decomposition.pdf https://dash.harvard.edu/bitstream/handle/1/3353824/Huang_Lexical.pdf http://www.oxfordhandbooks.com/view/10.1093/oxfordhb/9780199541072.001.0001/oxfordhb-9780199541072-e-15 https://www.amazon.com/How-Language-Began-Humanitys-Invention/dp/0871407957 And then for the connoisseur, there are grammars of individual languages. So there is no utility in statements like "I certainly do assume that ... the relation of giving is irreducbly triadic." First, even in English it IS reduceable. Second, there is considerable cross-linguistic variation in the mapping between lexical semantics (i.e. with lexical decomposition) and syntax, or, as I stated earlier, between valency and transitivity. Thus the English verb "to give" is ditransitive, but not necessarily divalent. Dan ----------------------------- PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON PEIRCE-L to this message. PEIRCE-L posts should go to peirce-L@list.iupui.edu<mailto:peirce-L@list.iupui.edu> . To UNSUBSCRIBE, send a message not to PEIRCE-L but to l...@list.iupui.edu<mailto:l...@list.iupui.edu> with the line "UNSubscribe PEIRCE-L" in the BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm .
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