On Tue, Dec 18, 2018 at 3:38 PM Jason Resch <jasonre...@gmail.com> wrote:
> On Mon, Dec 17, 2018 at 12:26 PM Brent Meeker <meeke...@verizon.net> > wrote: > >> >> But mathematical objects are completely defined by their axioms. >> > > Are they? > > Two is a mathematical object. > One of the properties of two is the number of primes it separates. For > example "3 and 5", "5 and 7", etc. > Definitions do not necessarily specify all the relationships into which things can enter -- if that was necessary for a definition, no definition would be possible. Clearly, common ostensive definitions do not have to specify all the properties of an object, or even what it is made of: "That is a rock" is a useful ostensive definition, but it does not commit one to a full geological understanding of rocks, their formation and properties. If mathematical objects are completely defined by their axioms, then > shouldn't this property be defined and known for two? Yet we don't even > know the answer to this question, we don't know if it is infinite or > finite. It might even be that no proof exists under the axioms we > currently use. > Mathematical objects may be completely defined by their definitions, in that the definition corresponds to that unique object. But that does not commit one to knowledge of all the relationships that might be true about that object. You are requiring too much from a definition. > There is no possibility of ostensive or empirical definition. That's the >> strength of mathematics; it's "truths" are independent of reality, they are >> part of language. >> >> But in any case, the axioms don't define arithmetical truth, which is my >> only point. >> >> >> No, but they define arithmetic, without which "arithmetical truth" would >> be meaningless. >> > > Was the physical universe meaningless before Newton? > The physical universe is defined ostensively -- neither Newton not Einstein brought it into existence. Bruce -- 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.
