more from this thinker | more from this text
Full Idea
Everything one needs to do with relations in mathematics can be done by taking a relation to be a set of ordered pairs. (Ordered triples etc. can be defined as order pairs, so that <x,y,z> is <x,<y,z>>).
Gist of Idea
The mathematics of relations is entirely covered by ordered pairs
Source
Charles Chihara (A Structural Account of Mathematics [2004], 07.2)
Book Ref
Chihara,Charles: 'A Structural Account of Mathematics' [OUP 2004], p.174
A Reaction
How do we distinguish 'I own my cat' from 'I love my cat'? Or 'I quite like my cat' from 'I adore my cat'? Nevertheless, this is an interesting starting point for a discussion of relations.
| 13501 | De Morgan found inferences involving relations, which eluded Aristotle's syllogistic [De Morgan, by Hart,WD] |
| 17744 | De Morgan started the study of relations and their properties [De Morgan, by Walicki] |
| 19238 | The logic of relatives relies on objects built of any relations (rather than on classes) [Peirce] |
| 8492 | Relations are functions with two arguments [Frege] |
| 10036 | In 'Principia' a new abstract theory of relations appeared, and was applied [Russell/Whitehead, by Gödel] |
| 21698 | All relations, apart from ancestrals, can be reduced to simpler logic [Quine] |
| 10816 | We can use mereology to simulate quantification over relations [Lewis] |
| 8525 | Relations need terms, so they must be second-order entities based on first-order tropes [Campbell,K] |
| 9926 | A relation is either a set of sets of sets, or a set of sets [Burgess/Rosen] |
| 9561 | The mathematics of relations is entirely covered by ordered pairs [Chihara] |
| 23627 | 'Before' and 'after' are not two relations, but one relation with two orders [Hossack] |