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Single Idea 12688

[filed under theme 6. Mathematics / B. Foundations for Mathematics / 1. Foundations for Mathematics ]

Full Idea

I wish to explore the idea that mathematics is the formal study of the categorical dimensions of things.

Gist of Idea

Mathematics is the formal study of the categorical dimensions of things

Source

Brian Ellis (The Metaphysics of Scientific Realism [2009], 6)

Book Ref

Ellis,Brian: 'The Metaphysics of Scientific Realism' [Acument 2009], p.117

A Reaction

Categorical dimensions are spatiotemporal relations and other non-causal properties. Ellis defends categorical properties as an aspect of science. The obvious connection seems to be with structuralism in mathematics. Shapiro is sympathetic.

The 25 ideas from 'The Metaphysics of Scientific Realism'

23781 Categoricals exist to influence powers. Such as structures, orientations and magnitudes [Ellis, by Williams,NE]
12665 I support categorical properties, although most people only want causal powers [Ellis]
12667 Metaphysics aims at the simplest explanation, without regard to testability [Ellis]
12666 We can base logic on acceptability, and abandon the Fregean account by truth-preservation [Ellis]
12668 Metaphysical necessity holds between things in the world and things they make true [Ellis]
12669 Science aims to explain things, not just describe them [Ellis]
12672 Properties and relations are discovered, so they can't be mere sets of individuals [Ellis]
12670 A physical event is any change of distribution of energy [Ellis]
12673 Physical properties are those relevant to how a physical system might act [Ellis]
12671 I deny forces as entities that intervene in causation, but are not themselves causal [Ellis]
12674 Energy is the key multi-valued property, vital to scientific realism [Ellis]
12681 There are natural kinds of processes [Ellis]
12680 Natural kind structures go right down to the bottom level [Ellis]
12675 Laws of nature are just descriptions of how things are disposed to behave [Ellis]
12682 Essentialism needs categorical properties (spatiotemporal and numerical relations) and dispositions [Ellis]
12684 Spatial, temporal and numerical relations have causal roles, without being causal [Ellis]
12679 A real essence is a kind's distinctive properties [Ellis]
12683 Objects and substances are a subcategory of the natural kinds of processes [Ellis]
12676 Causal powers can't rest on things which lack causal power [Ellis]
12685 Categorical properties depend only on the structures they represent [Ellis]
12686 Causal powers are a proper subset of the dispositional properties [Ellis]
12687 Metaphysical necessities are those depending on the essential nature of things [Ellis]
12688 Mathematics is the formal study of the categorical dimensions of things [Ellis]
12690 The present is the collapse of the light wavefront from the Big Bang [Ellis]
12689 Simultaneity can be temporal equidistance from the Big Bang [Ellis]