Keep in mind that what an "abstraction" is means different things to mathematical nominalists, constructivists, platonists.
- pt On Sunday, December 16, 2018 at 3:37:44 PM UTC-6, Brent wrote: > > Numbers are an abstraction and generalization from counting. But > counting takes seeing some things a similar enough to be counted, yet not > identical. I can count the dogs in my yard because what's a dog and what's > not seems clear. But it's hard to count trees in my yard: Is that a bush > or a tree? Is that sprout a tree, or does it have to grow up first? > > Brent > > On 12/16/2018 1:29 AM, 'scerir' via Everything List wrote: > > A *numerus* (literally: "number"*i*) was the term used for a unit of the > Roman > army <https://en.wikipedia.org/wiki/Roman_army>.. In the Imperial Roman > army <https://en.wikipedia.org/wiki/Imperial_Roman_army> (30 BC – 284 > AD), it referred to units of barbarian > <https://en.wikipedia.org/wiki/Barbarian> allies who were not integrated > into the regular army structure of legions > <https://en.wikipedia.org/wiki/Roman_legion> and auxilia > <https://en.wikipedia.org/wiki/Auxiliaries_(Roman_military)>. > > I'm inclined to think that numbers - for there obiectivity - need a good > "counter" (somebody or somethink). > > 'I raised just this objection with the (extreme) ultrafinitist Yessenin > Volpin during a lecture of his. He asked me to be more specific. I then > proceeded to start with 2^1 and asked him whether this is "real" or > something to that effect. He virtually immediately said yes. Then I asked > about 2^2, and he again said yes, but with a perceptible delay. Then 2^3, > and yes, but with more delay. This continued for a couple of more times, > till it was obvious how he was handling this objection. Sure, he was > prepared to always answer yes, but he was going to take 2^100 times as long > to answer yes to 2^100 then he would to answering 2^1. There is no way that > I could get very far with this.' -Harvey M. Friedman > > Dunno if in each every part of this universe there is a good "counter". > Maybe universe itself, as a whole, is a "counter"?. > > 'Paper in white the floor of the room, and rule it off in one-foot > squares. Down on one's hands and knees, write in the first square a set of > equations conceived as able to govern the physics of the universe. Think > more overnight. Next day put a better set of equations into square two. > Invite one's most respected colleagues to contribute to other squares. At > the end of these labors, one has worked oneself out into the doorway. Stand > up, look back on all those equations, some perhaps more hopeful than > others, raise one's finger commandingly, and give the order "*Fly*!" Not > one of those equations will put on wings, take off, or fly. *Yet the > universe "flies"*.(Wheeler on page 1208 of *Gravitation*) > > > > > -- 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.
