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Single Idea 8208

[from 'On Multiplying Entities' by Willard Quine, in 2. Reason / B. Laws of Thought / 6. Ockham's Razor ]

Full Idea

In classical arithmetic, ratios were posited to make division generally applicable, negative numbers to make subtraction generally applicable, and irrationals and finally imaginaries to make exponentiation generally applicable.

Clarification

'Exponentiation' is raising a quantity to a power (e.g. squaring)

Gist of Idea

In arithmetic, ratios, negatives, irrationals and imaginaries were created in order to generalise

Source

Willard Quine (On Multiplying Entities [1974], p.263)

Book Reference

Quine,Willard: 'Ways of Paradox and other essays' [Harvard 1976], p.263


A Reaction

This is part of Quine's proposal (c.f. Idea 8207) that entities have to be multiplied in order to produce simplicity. He is speculating. Maybe they are proposed because they are just obvious, and the generality is a nice side-effect.

Related Idea

Idea 8207 The quest for simplicity drove scientists to posit new entities, such as molecules in gases [Quine]