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Full Idea
We can simulate quantification over relations using megethology. Roughly, a quantifier over relations is a plural quantifier over things that encode ordered pairs by mereological means.
Clarification
For 'megethology' see Idea 10806
Gist of Idea
We can use mereology to simulate quantification over relations
Source
David Lewis (Mathematics is Megethology [1993], p.18)
Book Ref
-: 'Philosophia Mathematica' [-], p.18
A Reaction
[He credits this idea to Burgess and Haven] The point is to avoid second-order logic, which quantifies over relations as ordered n-tuple 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] |