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Full Idea
In 'Principia' a young science was enriched with a new abstract theory of relations, ..and not only Cantor's set theory but also ordinary arithmetic and the theory of measurement are treated from this abstract relational standpoint.
Gist of Idea
In 'Principia' a new abstract theory of relations appeared, and was applied
Source
report of B Russell/AN Whitehead (Principia Mathematica [1913]) by Kurt Gödel - Russell's Mathematical Logic p.448
Book Ref
'Philosophy of Mathematics: readings (2nd)', ed/tr. Benacerraf/Putnam [CUP 1983], p.448
A Reaction
I presume this is accounting for relations in terms of ordered sets.
| 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] |