Return-Path: Message-Id: From: cowan (John Cowan) Subject: Re: identity (was: names as predicates) (fwd) To: lojban-list Date: Fri, 14 Jun 91 13:28:04 EDT X-Mailer: ELM [version 2.2 PL13] Status: RO X-From-Space-Date: Fri Jun 14 13:29:03 1991 X-From-Space-Address: cowan Forwarded message: From eric Fri Jun 14 13:22:08 1991 Message-Id: From: eric (Eric S. Raymond) Subject: Re: identity (was: names as predicates) To: cowan (John Cowan) Date: Fri, 14 Jun 91 13:22:02 EDT Cc: In-Reply-To: ; from "John Cowan" at Jun 14, 91 10:25 am X-Mailer: ELM [version 2.2 PL13] > I suppose it depends what you call an "abstraction". To me, numbers and > sets are as "concrete" as rocks and trees. This isn't quite the issue I'm trying to address here, but it is a significant one. Historically, there was at one time a controversy among metamathematicians (people who study the philosophy of mathematics; I used to be one) between `Platonists' like you (who believe that mathematical entities have some sort of `real' existence) and `Formalists' like me (people who regard mathematics as a zero-content formal system, a game played with marks on paper). Platonism seems `natural' to most people, but mathematicians have abandoned it. It starts to look naive when you realize that multiple, mutually inconsistent axiom systems can all be modelled by entities as basic as what we think of as "physical" numbers. A related problem is that you can't really reconcile Platonism with the existence of mathematical paradoxes. And there are some nasty ones out there. Look up Bolzano's sometime. In fact, when you identify a formal mathematical entity (a mark on the paper) like `2' with a model such as a pair of apples, you are making a sophisticated inductive leap. You are generalizing from previous experiences in which the behavior of marks on paper shadows the behavior of physical systems; that it will continue to do so is a hypothesis subject to confirmation and disconfirmation in the same way as any other. There is no mystical connection between the '2' and your pair that makes the `2' real; only the apples are real. Among mathematicians, Platonism has been dead for two generations -- though there is a certain delicate irony all mathematicians are aware of here; though we *reason* like Formalists, we *create* like Platonists; the process of mathematical discovery feels like *discovery*, not invention. What consequences does this have for lojban? Well...we should be careful not to build in Platonist prejudices. The confusion of `formal' equality with has-same-physical-referent would be one of these. It's intuitively appealing, it has a long history...and it's wrong. -- >>eric>>