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Single Idea 18219
[filed under theme 27. Natural Reality / C. Space / 5. Relational Space
]
Full Idea
The problem of the relational view of space is especially acute in the context of physical theories that take the notion of a field seriously, e.g. classical electromagnetic theory.
Gist of Idea
Relational space is problematic if you take the idea of a field seriously
Source
Hartry Field (Science without Numbers [1980], 4)
Book Ref
Field,Hartry: 'Science without Number' [Blackwell 1980], p.35
A Reaction
In the Leibniz-Clarke debate I sided with the Newtonian Clarke (defending absolute space), and it looks like modern science agrees with me. Nothing exists purely as relations.
The
21 ideas
from 'Science without Numbers'
9570
|
In Field's Platonist view, set theory is false because it asserts existence for non-existent things
[Field,H, by Chihara]
|
10260
|
Logical consequence is defined by the impossibility of P and ¬q
[Field,H, by Shapiro]
|
8958
|
In Field's version of science, space-time points replace real numbers
[Field,H, by Szabó]
|
10261
|
The application of mathematics only needs its possibility, not its truth
[Field,H, by Shapiro]
|
8959
|
Field presumes properties can be eliminated from science
[Field,H, by Szabó]
|
18212
|
Nominalists try to only refer to physical objects, or language, or mental constructions
[Field,H]
|
18213
|
Abstract objects are only applicable to the world if they are impure, and connect to the physical
[Field,H]
|
18215
|
It seems impossible to explain the idea that the conclusion is contained in the premises
[Field,H]
|
18214
|
Mathematics is only empirical as regards which theory is useful
[Field,H]
|
18216
|
Abstractions can form useful counterparts to concrete statements
[Field,H]
|
18218
|
Hilbert explains geometry, by non-numerical facts about space
[Field,H]
|
18219
|
Relational space is problematic if you take the idea of a field seriously
[Field,H]
|
18220
|
Both philosophy and physics now make substantivalism more attractive
[Field,H]
|
18221
|
'Metric' axioms uses functions, points and numbers; 'synthetic' axioms give facts about space
[Field,H]
|
18222
|
Beneath every extrinsic explanation there is an intrinsic explanation
[Field,H]
|
9623
|
Field needs a semantical notion of second-order consequence, and that needs sets
[Brown,JR on Field,H]
|
18223
|
In theories of fields, space-time points or regions are causal agents
[Field,H]
|
9917
|
'Abstract' is unclear, but numbers, functions and sets are clearly abstract
[Field,H]
|
8757
|
The Indispensability Argument is the only serious ground for the existence of mathematical entities
[Field,H]
|
18211
|
You can reduce ontological commitment by expanding the logic
[Field,H]
|
18210
|
Why regard standard mathematics as truths, rather than as interesting fictions?
[Field,H]
|