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] <javascript:>> > 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) *Material* - things/entities in the material world Semantics and substrates are connected, it not identical. That's my blog. Also There is in my opinion no important theoretical difference between natural languages and the artificial languages of logicians. (Richard Montague) @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/4c4884c5-a658-4112-9602-dc8decf3f5aa%40googlegroups.com.
