display all the ideas for this combination of texts
5 ideas
19369 | Lull's combinatorial art would articulate all the basic concepts, then show how they combine [Lull, by Arthur,R] |
Full Idea: Lull proposed a combinatorial art. He wanted to reconcile Islam and Christianity by articulating the basic concepts that their belief systems held in common, and then inventing a device that would allow these concepts to be combined. | |
From: report of Ramon (Ars Magna [1305]) by Richard T.W. Arthur - Leibniz 2 Intro | |
A reaction: Leibniz's Universal Characteristic was an attempt at continuing Lull's project. Lull's plan rested on Aristotle's categories. |
4730 | For Aristotle, the subject-predicate structure of Greek reflected a substance-accident structure of reality [Aristotle, by O'Grady] |
Full Idea: Aristotle apparently believed that the subject-predicate structure of Greek reflected the substance-accident nature of reality. | |
From: report of Aristotle (works [c.330 BCE]) by Paul O'Grady - Relativism Ch.4 | |
A reaction: We need not assume that Aristotle is wrong. It is a chicken-and-egg. There is something obvious about subject-predicate language, if one assumes that unified objects are part of nature, and not just conventional. |
14234 | If you only refer to objects one at a time, you need sets in order to refer to a plurality [Oliver/Smiley] |
Full Idea: A 'singularist', who refers to objects one at a time, must resort to the language of sets in order to replace plural reference to members ('Henry VIII's wives') by singular reference to a set ('the set of Henry VIII's wives'). | |
From: Oliver,A/Smiley,T (What are Sets and What are they For? [2006], Intro) | |
A reaction: A simple and illuminating point about the motivation for plural reference. Null sets and singletons give me the creeps, so I would personally prefer to avoid set theory when dealing with ontology. |
14237 | We can use plural language to refer to the set theory domain, to avoid calling it a 'set' [Oliver/Smiley] |
Full Idea: Plurals earn their keep in set theory, to answer Skolem's remark that 'in order to treat of 'sets', we must begin with 'domains' that are constituted in a certain way'. We can speak in the plural of 'the objects', not a 'domain' of objects. | |
From: Oliver,A/Smiley,T (What are Sets and What are they For? [2006], Intro) | |
A reaction: [Skolem 1922:291 in van Heijenoort] Zermelo has said that the domain cannot be a set, because every set belongs to it. |
14245 | Logical truths are true no matter what exists - but predicate calculus insists that something exists [Oliver/Smiley] |
Full Idea: Logical truths should be true no matter what exists, so true even if nothing exists. The classical predicate calculus, however, makes it logically true that something exists. | |
From: Oliver,A/Smiley,T (What are Sets and What are they For? [2006], 5.1) |