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Single Idea 13043
[filed under theme 8. Modes of Existence / A. Relations / 4. Formal Relations / a. Types of relation
]
Full Idea
A set is called a 'relation' if every element of it is an ordered pair.
Gist of Idea
A relation is a set consisting entirely of ordered pairs
Source
Michael Potter (Set Theory and Its Philosophy [2004], 04.7)
Book Ref
Potter,Michael: 'Set Theory and Its Philosophy' [OUP 2004], p.65
A Reaction
This is the modern extensional view of relations. For 'to the left of', you just list all the things that are to the left, with the things they are to the left of. But just listing the ordered pairs won't necessarily reveal how they are related.
The
14 ideas
from 'Set Theory and Its Philosophy'
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10702
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Set theory's three roles: taming the infinite, subject-matter of mathematics, and modes of reasoning
[Potter]
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10703
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Supposing axioms (rather than accepting them) give truths, but they are conditional
[Potter]
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10704
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We can formalize second-order formation rules, but not inference rules
[Potter]
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10707
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Mereology elides the distinction between the cards in a pack and the suits
[Potter]
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13041
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Collections have fixed members, but fusions can be carved in innumerable ways
[Potter]
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10708
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Nowadays we derive our conception of collections from the dependence between them
[Potter]
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10709
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Priority is a modality, arising from collections and members
[Potter]
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13042
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If dependence is well-founded, with no infinite backward chains, this implies substances
[Potter]
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10712
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If set theory didn't found mathematics, it is still needed to count infinite sets
[Potter]
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10713
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Usually the only reason given for accepting the empty set is convenience
[Potter]
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13043
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A relation is a set consisting entirely of ordered pairs
[Potter]
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13044
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Infinity: There is at least one limit level
[Potter]
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17882
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It is remarkable that all natural number arithmetic derives from just the Peano Axioms
[Potter]
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13546
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The 'limitation of size' principles say whether properties collectivise depends on the number of objects
[Potter]
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