On Saturday, December 29, 2018 at 3:58:26 AM UTC-6, Bruno Marchal wrote: > > > On 27 Dec 2018, at 21:57, Philip Thrift <cloud...@gmail.com <javascript:>> > wrote: > > > What if conventional mathematics itself is in error by assuming its > primary elements are numbers? > > > Conventional mathematics is informal. It does not assume primary notion. > Now, numbers are implicitly accepted as elementary notion, but so are > finite sets, combination, strings of symbols, etc. > > With mechanism, all you need to assume explicitly is one universal > machinery. If you use the comboantors S and K, the numbers can be defined, > like with Barendrecht numbers VfI, Vf(VfI), Vf(Vf(VfI))), … as I have > illustrated recently in the Combinator Thread, or like with Church’s > numbers, etc. > We could have used the Game-of-Life Patterns, or the lambda expression, or > a von Neuman (virtual) machine, etc. > > I use number because people are more familiar with them. Most people can > easily conceived that “17 is odd” is true independently of them, but would > have an harder time to conceive that KKK=K independent of them, even if > this does not mean much more than the first (left) projection of (K, K) is > K. > >
> (There is arguably something to category/type theory that maybe gets away > from this.) > > > What if primary elements include/are non-numbers - (qualitative*) > experiences? > > > I do not conceive easily that the qualitative can be primary. It is like > starting from the mystery (qualia, consciousness) to explain the simple > (numbers, addition, multiplication). > With mechanism, the qualitative requires some machinery (neurons, > transistors, or numbers, or finite sets, symbols, etc.). > > Bruno > > > * > > HUMANA.MENTE Journal of Philosophical Studies > Vol 9 No 31 (2016) > <http://secure-web.cisco.com/1if8W1c5rc-A9K41fpkmpzYjvw71w9n3k9Xz0wJ2kQL4kudLalW4KgLlF-zEFiQp42QRd5gQtUY5Q7_09q2vSuMD4PG-qapkWUAikQ9ObQNJHmDnMkOCKbAiRTmdEhZHiRmSTNjWVAyyIKfcVTFpd5IQKyRonR4SImenwN7AngKzy-5KV5fxFmtHEELCXFPVNoXzGPFn9G9KkupZOXB9hcvXhEMZ3-V-zXdIls0YL4WGUzTqQnddLBl0TNswNA4kkWQFGy4koDoYXFr9Qu352Tw/http%3A%2F%2Fwww.humanamente.eu%2Findex.php%2FHM%2Fissue%2Fview%2F23>: > > The Enactive Approach to Qualitative Ontology: In Search of New Categories > > Introduction > <https://secure-web.cisco.com/1J6l3f-Kg39Bb0IFSVaQWiO8rRC7K6do2TJBgaW7bBtp-M_f2pdHIZpPEi0xvRzhaPUb9qImM0gfZ4d7i-zC8aSNHvlE9wnczI-rU5yFmje582HgbqSLt667xQoKwEwcZiU3JfaMI0szw5O2d_B3IlVooCTpX2jen_-J8liu6UlMVT5x9oGJ099IiiGHwqi-ays6Xgz7jWvukRT1KP1OHoTyiFxn1HLVD8BsCvUsdCZE55jqCly1BGFntz1WgDHgJj6XZCy0WdL_kFjiVvqAMHg/https%3A%2F%2Fphilarchive.org%2Farchive%2FPACITT> > : > – the enactive approach opposes the Cartesian bifurcation of reality into > psychological and physical > – complements quantitative categories, offering a mathematical treatment > of qualitative aspects of reality > > In "the qualitative requires some machinery (neurons, transistors, or numbers, or finite sets, symbols, etc.)": Neurons and transistors are typically seen as being made of *matter* - *chemicals, atoms, etc.* - whereas numbers, finite sets, symbols are *something else* (whatever mathematical ontology one has). But matter itself has psychical (in addition to physical/numerical) constituents, according to the "enactive approach" (above). - pt -- 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 everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at https://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
