more from this thinker | more from this text
Full Idea
The reason the two predicates 'before' and 'after' are needed is not to express different relations, but to indicate its order. Since there can be difference of order without difference of relation, the nature of relations is not the source of order.
Gist of Idea
'Before' and 'after' are not two relations, but one relation with two orders
Source
Keith Hossack (Knowledge and the Philosophy of Number [2020], 10.3)
Book Ref
Hossack, Keith: 'Knowledge and the Philosophy of Number' [Routledge 2021], p.157
A Reaction
This point is to refute Russell's 1903 claim that order arises from the nature of relations. Hossack claims that it is ordered series which are basic. I'm inclined to agree with him.
| 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] |