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Full Idea
The order of the number-series is not governed by an external relation but by an internal relation.
Gist of Idea
The order of numbers is an internal relation, not an external one
Source
Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921], 4.1252)
Book Ref
Macdonald,Cynthia: 'Varieties of Things' [Blackwell 2005], p.27
A Reaction
He seems to mean something like a tautology (see Idea 7968). It is, I take it, part of the concept of any given integer that it has a place in the series. But do the concepts arise self-evidently, or from nature?
Related Idea
Idea 7968 A relation is internal if it is unthinkable that its object should not possess it [Wittgenstein]
| 21347 | If Simmias is taller than Socrates, that isn't a feature that is just in Simmias [Plato] |
| 22080 | The nature of each category relates itself to another [Hegel] |
| 6422 | Internal relations are said to be intrinsic properties of two terms, and of the whole they compose [Bradley, by Russell] |
| 7966 | Relations must be linked to their qualities, but that implies an infinite regress of relations [Bradley] |
| 21342 | A relation is internal if two things possessing the relation could not fail to be related [Moore,GE, by Heil] |
| 7968 | A relation is internal if it is unthinkable that its object should not possess it [Wittgenstein] |
| 7969 | The order of numbers is an internal relation, not an external one [Wittgenstein] |
| 21351 | Truthmaking is a clear example of an internal relation [Heil] |
| 21344 | If R internally relates a and b, and you have a and b, you thereby have R [Heil] |
| 21348 | In the case of 5 and 6, their relational truthmaker is just the numbers [Heil] |
| 18532 | If causal relations are power manifestations, that makes them internal relations [Heil] |
| 21353 | Internal relations are fixed by existences, or characters, or supervenience on characters [MacBride] |
| 7938 | Relational properties are clearly not essential to substances [Macdonald,C] |
| 14925 | The normal assumption is that relations depend on properties of the relata [Ladyman/Ross] |
| 18336 | Internal relations depend either on the existence of the relata, or on their properties [Rami] |