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Single Idea 4240

[filed under theme 6. Mathematics / A. Nature of Mathematics / 1. Mathematics ]

Full Idea

It might be argued that mathematics does not, or should not, aim at truth.

Gist of Idea

It might be argued that mathematics does not, or should not, aim at truth

Source

E.J. Lowe (A Survey of Metaphysics [2002], p.375)

Book Ref

Lowe,E.J.: 'A Survey of Metaphysics' [OUP 2002], p.375

A Reaction

Intriguing. Sounds wrong to me. At least maths seems to need the idea of the 'correct' answer. If, however, maths is a huge pattern, there is no correctness, just the pattern. We can be wrong, but maths can't be wrong. Ah, I see…!

The 45 ideas from 'A Survey of Metaphysics'

14581 The normative view says laws show the natural behaviour of natural kind members [Lowe, by Mumford/Anjum]
4205 'Is non-self-exemplifying' is a predicate which cannot denote a property (as it would be a contradiction) [Lowe]
4195 It is impossible to reach a valid false conclusion from true premises, so reason itself depends on possibility [Lowe]
4206 Conventionalists see the world as an amorphous lump without identities, but are we part of the lump? [Lowe]
4207 We might eliminate 'possible' and 'necessary' in favour of quantification over possible worlds [Lowe]
4197 The category of universals can be sub-divided into properties and relations [Lowe]
4196 The main categories of existence are either universal and particular, or abstract and concrete [Lowe]
4208 'If he wasn't born he wouldn't have died' doesn't mean birth causes death, so causation isn't counterfactual [Lowe]
4209 The theories of fact causation and event causation are both worth serious consideration [Lowe]
4210 If the concept of a cause says it precedes its effect, that rules out backward causation by definition [Lowe]
4211 Causal overdetermination is either actual overdetermination, or pre-emption, or the fail-safe case [Lowe]
4212 Hume showed that causation could at most be natural necessity, never metaphysical necessity [Lowe]
4213 Causation may be instances of laws (seen either as constant conjunctions, or as necessities) [Lowe]
4214 Maybe such concepts as causation, identity and existence are primitive and irreducible [Lowe]
4194 Metaphysics is concerned with the fundamental structure of reality as a whole [Lowe]
4193 The behaviour of persons and social groups seems to need rational rather than causal explanation [Lowe]
4215 It seems proper to say that only substances (rather than events) have causal powers [Lowe]
4217 It is more extravagant, in general, to revise one's logic than to augment one's ontology [Lowe]
4219 Numerically distinct events of the same kind (like two battles) can coincide in space and time [Lowe]
4220 Maybe an event is the exemplification of a property at a time [Lowe]
4221 Maybe modern physics requires an event-ontology, rather than a thing-ontology [Lowe]
4222 If all that exists is what is being measured, what about the people and instruments doing the measuring? [Lowe]
4223 Unfalsifiability may be a failure in an empirical theory, but it is a virtue in metaphysics [Lowe]
4224 If motion is change of distance between objects, it involves no intrinsic change in the objects [Lowe]
4225 Events are changes in the properties of or relations between things [Lowe]
4227 Surfaces, lines and points are not, strictly speaking, parts of space, but 'limits', which are abstract [Lowe]
4198 If 5% replacement preserves a ship, we can replace 4% and 4% again, and still retain the ship [Lowe]
4228 If space is entirely relational, what makes a boundary, or a place unoccupied by physical objects? [Lowe]
4199 A renovation or a reconstruction of an original ship would be accepted, as long as the other one didn't exist [Lowe]
4229 An infinite series of tasks can't be completed because it has no last member [Lowe]
4200 If old parts are stored and then appropriated, they are no longer part of the original (which is the renovated ship). [Lowe]
4232 Nominalists believe that only particulars exist [Lowe]
4233 If 'blueness' is a set of particulars, there is danger of circularity, or using universals, in identifying the set [Lowe]
4234 Trope theory says blueness is a real feature of objects, but not the same as an identical blue found elsewhere [Lowe]
4235 Maybe a cushion is just a bundle of tropes, such as roundness, blueness and softness [Lowe]
4236 Tropes seem to be abstract entities, because they can't exist alone, but must come in bundles [Lowe]
4238 The centre of mass of the solar system is a non-causal abstract object, despite having a location [Lowe]
4237 Concrete and abstract objects are distinct because the former have causal powers and relations [Lowe]
4239 Nominalists deny abstract objects, because we can have no reason to believe in their existence [Lowe]
4241 If there are infinite numbers and finite concrete objects, this implies that numbers are abstract objects [Lowe]
4240 It might be argued that mathematics does not, or should not, aim at truth [Lowe]
4201 Four theories of qualitative change are 'a is F now', or 'a is F-at-t', or 'a-at-t is F', or 'a is-at-t F' [Lowe, by PG]
4202 Change can be of composition (the component parts), or quality (properties), or substance [Lowe]
4203 Identity of Indiscernibles (same properties, same thing) ) is not Leibniz's Law (same thing, same properties) [Lowe]
4204 Statues can't survive much change to their shape, unlike lumps of bronze, which must retain material [Lowe]