On Saturday, December 29, 2018 at 3:58:26 AM UTC-6, Bruno Marchal wrote: > > > On 27 Dec 2018, at 21:57, Philip Thrift <[email protected] <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 [email protected]. To post to this group, send email to [email protected]. Visit this group at https://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
