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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
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The normative view says laws show the natural behaviour of natural kind members
[Lowe, by Mumford/Anjum]
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4205
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'Is non-self-exemplifying' is a predicate which cannot denote a property (as it would be a contradiction)
[Lowe]
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4195
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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]
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4207
|
We might eliminate 'possible' and 'necessary' in favour of quantification over possible worlds
[Lowe]
|
4196
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The main categories of existence are either universal and particular, or abstract and concrete
[Lowe]
|
4197
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The category of universals can be sub-divided into properties and relations
[Lowe]
|
4208
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'If he wasn't born he wouldn't have died' doesn't mean birth causes death, so causation isn't counterfactual
[Lowe]
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4209
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The theories of fact causation and event causation are both worth serious consideration
[Lowe]
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4210
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If the concept of a cause says it precedes its effect, that rules out backward causation by definition
[Lowe]
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4211
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Causal overdetermination is either actual overdetermination, or pre-emption, or the fail-safe case
[Lowe]
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4212
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Hume showed that causation could at most be natural necessity, never metaphysical necessity
[Lowe]
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4213
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Causation may be instances of laws (seen either as constant conjunctions, or as necessities)
[Lowe]
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4214
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Maybe such concepts as causation, identity and existence are primitive and irreducible
[Lowe]
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4194
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Metaphysics is concerned with the fundamental structure of reality as a whole
[Lowe]
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4193
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The behaviour of persons and social groups seems to need rational rather than causal explanation
[Lowe]
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4215
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It seems proper to say that only substances (rather than events) have causal powers
[Lowe]
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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]
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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
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Unfalsifiability may be a failure in an empirical theory, but it is a virtue in metaphysics
[Lowe]
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4224
|
If motion is change of distance between objects, it involves no intrinsic change in the objects
[Lowe]
|
4225
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Events are changes in the properties of or relations between things
[Lowe]
|
4227
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Surfaces, lines and points are not, strictly speaking, parts of space, but 'limits', which are abstract
[Lowe]
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4198
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If 5% replacement preserves a ship, we can replace 4% and 4% again, and still retain the ship
[Lowe]
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4228
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If space is entirely relational, what makes a boundary, or a place unoccupied by physical objects?
[Lowe]
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4199
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A renovation or a reconstruction of an original ship would be accepted, as long as the other one didn't exist
[Lowe]
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4229
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An infinite series of tasks can't be completed because it has no last member
[Lowe]
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4200
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If old parts are stored and then appropriated, they are no longer part of the original (which is the renovated ship).
[Lowe]
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4232
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Nominalists believe that only particulars exist
[Lowe]
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4233
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If 'blueness' is a set of particulars, there is danger of circularity, or using universals, in identifying the set
[Lowe]
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4234
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Trope theory says blueness is a real feature of objects, but not the same as an identical blue found elsewhere
[Lowe]
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4235
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Maybe a cushion is just a bundle of tropes, such as roundness, blueness and softness
[Lowe]
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4236
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Tropes seem to be abstract entities, because they can't exist alone, but must come in bundles
[Lowe]
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4237
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Concrete and abstract objects are distinct because the former have causal powers and relations
[Lowe]
|
4238
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The centre of mass of the solar system is a non-causal abstract object, despite having a location
[Lowe]
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4239
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Nominalists deny abstract objects, because we can have no reason to believe in their existence
[Lowe]
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4241
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If there are infinite numbers and finite concrete objects, this implies that numbers are abstract objects
[Lowe]
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4240
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It might be argued that mathematics does not, or should not, aim at truth
[Lowe]
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4201
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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]
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4202
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Change can be of composition (the component parts), or quality (properties), or substance
[Lowe]
|
4203
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Identity of Indiscernibles (same properties, same thing) ) is not Leibniz's Law (same thing, same properties)
[Lowe]
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4204
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Statues can't survive much change to their shape, unlike lumps of bronze, which must retain material
[Lowe]
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