On Tuesday, July 9, 2019 at 6:52:06 AM UTC-5, Bruno Marchal wrote: > > > On 8 Jul 2019, at 12:42, Philip Thrift <[email protected] <javascript:>> > wrote: > > > > On Monday, July 8, 2019 at 4:58:32 AM UTC-5, Bruno Marchal wrote: >> >> >> On 6 Jul 2019, at 13:32, Philip Thrift <[email protected]> wrote: >> >> >> >> On Saturday, July 6, 2019 at 1:42:20 AM UTC-5, Bruno Marchal wrote: >>> >>> >>> On 6 Jul 2019, at 05:57, Philip Thrift <[email protected]> wrote: >>> >>> >> Whatever logic it is, its semantics (of a theory in that logic) is the >> elephant in the room. >> >> - https://en.wikipedia.org/wiki/Semantics_of_logic >> - https://en.wikipedia.org/wiki/Model_theory >> e.g. *Whereas universal algebra provides the semantics for a signature, >> logic provides the syntax.* >> - https://plato.stanford.edu/entries/model-theory/ >> >> *Semantics is the wild, wild west of logic.* >> >> >> >> You might try to make a point, perhaps. Semantic is obviously very >> important. >> >> Logic can be divided in three chapters: >> >> - theory of theories and proofs (cf Gödel) >> >> - semantics (Model theory) (cf Lowenheim, Skolem and Tarski, Mostowski, …) >> >> - the relation between, theories and models, that is the study of (all) >> theories and all their semantics, usually through completeness and >> incompleteness theorems. >> >> Semantic is the heart of “modern logic”. I do avoid using it here to >> much, because it is quickly rather technical. I hope people have some idea >> that the structure (N, 0, +, *) (which is the set N with the usual standard >> interpretation of + and *) is a model of both RA and PA. I might say a bit >> more in the glossary I am preparing. All “rich” theories have infinitely >> many non isomorphic models, and by incompleteness no theories at all can >> study its own semantics, but some theories can still say a lot about it, >> like its own incompleteness. >> >> Bruno >> >> >> > Semantics is real thing, so to speak, to me. > > There are two types of semantics: > > *Fictional* - regarding all the mathematical structures of standard > model theory you refer to above (Hartry Field) > > > The non standard model would be less fictional? > > The word “fiction” can be misleading. I prefer to use “immaterial”, or > “spiritual”, or “mental”, perhaps. > > > > *Material* - things/entities in the material world > > > Those are important, but if we assume mechanism, I don’t think we can > assume matter, but we can explain its appearances from the machine’s > consciousness theory (theology) and test it empirically. Up to now, the > evidences favours mechanism. > > > > > > Semantics and substrates are connected, it not identical. That's my blog. > > > I can’t really make sense of this. > > > > > Also > > There is in my opinion no important theoretical difference between natural > languages and the artificial languages of logicians. (Richard Montague) > > > For a monist, the difference between natural and artificial is artificial, > and indeed natural for those entities which develop a big ego and feel > different. > > Of course there is a difference between the formal languages and the > “natural” languages, and Richard Montague attempt to develop a sort of > polymodal rich lambda calculus for the treatment of natural language is > very interesting. > So I appreciate your opinion that there is no fundamental difference > between those type of languages. When I was younger I have made a universal > programming language (ANIMA° which was also a subset of natural language > (English). You could ask the computer things like, “could you please find a > file with some document on number in my computer, and if not, on the net?”. > But it was very slow, and people prefer shortcuts … > > Bruno > > > > Semantics and substrates are connected, *if *not identical. [corrected]
I first learned mathematical logic - ML (up to the incompleteness theorems) - in the summer of 1970 (I was 17) at The Ohio State University Ross Mathematics Program [ https://en.wikipedia.org/wiki/Arnold_Ross#Ross_Mathematics_Program ]. So I've known about the models/interpretations of ML since then. Going from ML to programming, semantics gets more interesting *Modeling Languages:* *Syntax, Semantics and all that Stuff* *(or, What’s the Semantics of “Semantics”?)* http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.58.3075&rep=rep1&type=pdf "Motivated by the confusion surrounding the proper definition of complex modeling languages, especially the UML, we discuss the distinction between syntax and true semantics, and the nature and purpose of each." Now that we are entering the age of the *matter compiler,* once SF, now getting real, Neal Stephenson’s *The Diamond Age *(1995) https://csi.asu.edu/project-archive/optimism/the-diamond-age-technology/ the semantics of programs lie in the materiality (substrate) of their expression. @philipthrift -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/d7e9e7b6-f5ef-4e67-bf59-1fc8643e3a41%40googlegroups.com.
