Return-Path: Received: from catseye.idbsu.edu by xiron.pc.helsinki.fi with smtp (Linux Smail3.1.28.1 #1) id m0r2KAV-00005YC; Tue, 1 Nov 94 16:26 EET Message-Id: Received: by catseye.idbsu.edu (1.38.193.4/16.2) id AA10621; Tue, 1 Nov 1994 07:27:22 -0700 Date: Tue, 1 Nov 1994 07:27:22 -0700 From: Randall Holmes To: holmes@catseye.idbsu.edu, veion@xiron.pc.helsinki.fi Subject: Re: The "problem" with external quantifiers Content-Length: 431 Lines: 9 Numerical quantifiers can be expressed using the usual quantifiers and identity. "I ate 3 apples" need not involve any reference to sets. For practical reasons such quantifiers should be primitive items in a language like Lojban! However, one doesn't go far in discourse about numbers before one wants to treat them as objects themselves, and as soon as one does this one needs sets (or higher-order predicates). --Randall