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Full Idea
Much of the theory of relations can be developed as a virtual theory, in which we seem to talk of relations, but can explain our notation in terms {finally] of just the logic of truth-functions, quantification and identity. The exception is ancestrals.
Gist of Idea
All relations, apart from ancestrals, can be reduced to simpler logic
Source
Willard Quine (Lecture on Nominalism [1946], §8)
Book Ref
'Oxford Studies in Metaphysics vol.4', ed/tr. Zimmerman,Dean W. [OUP 2008], p.14
A Reaction
The irreducibility of ancestrals is offered as a reason for treating sets as universals.
17744 | De Morgan started the study of relations and their properties [De Morgan, by Walicki] |
13501 | De Morgan found inferences involving relations, which eluded Aristotle's syllogistic [De Morgan, by Hart,WD] |
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] |