display all the ideas for this combination of texts
6 ideas
10888 | Sets can be defined by 'enumeration', or by 'abstraction' (based on a property) [Zalabardo] |
Full Idea: We can define a set by 'enumeration' (by listing the items, within curly brackets), or by 'abstraction' (by specifying the elements as instances of a property), pretending that they form a determinate totality. The latter is written {x | x is P}. | |
From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §1.3) |
10889 | The 'Cartesian Product' of two sets relates them by pairing every element with every element [Zalabardo] |
Full Idea:
The 'Cartesian Product' of two sets, written A x B, is the relation which pairs every element of A with every element of B. So A x B = { |
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From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §1.6) |
10890 | A 'partial ordering' is reflexive, antisymmetric and transitive [Zalabardo] |
Full Idea: A binary relation in a set is a 'partial ordering' just in case it is reflexive, antisymmetric and transitive. | |
From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §1.6) |
10886 | Determinacy: an object is either in a set, or it isn't [Zalabardo] |
Full Idea: Principle of Determinacy: For every object a and every set S, either a is an element of S or a is not an element of S. | |
From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §1.2) |
10887 | Specification: Determinate totals of objects always make a set [Zalabardo] |
Full Idea: Principle of Specification: Whenever we can specify a determinate totality of objects, we shall say that there is a set whose elements are precisely the objects that we have specified. | |
From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §1.3) | |
A reaction: Compare the Axiom of Specification. Zalabardo says we may wish to consider sets of which we cannot specify the members. |
13282 | Aristotle relativises the notion of wholeness to different measures [Aristotle, by Koslicki] |
Full Idea: Aristotle proposes to relativise unity and plurality, so that a single object can be both one (indivisible) and many (divisible) simultaneously, without contradiction, relative to different measures. Wholeness has degrees, with the strength of the unity. | |
From: report of Aristotle (works [c.330 BCE]) by Kathrin Koslicki - The Structure of Objects 7.2.12 | |
A reaction: [see Koslicki's account of Aristotle for details] As always, the Aristotelian approach looks by far the most promising. Simplistic mechanical accounts of how parts make wholes aren't going to work. We must include the conventional and conceptual bit. |