I 4
Conservativity/Field: Conservativity includes some features of necessary truth without actually ever involving truth.
>
Truth transfer.
I 44
Def Conservativity/Mathematics/Field: means that every internally consistent combination of nominalist statements is also consistent with the mathematics. - If we can also show that mathematics is not indispensible, we have no reason to believe in mathematical entities anymore.
>
Mathematical entities.
I 58
Def Conservative/Conservativity/Theory/Mathematics/Field: conservative is a mathematical theory that is consistent with every internally consistent physical theory. - This is equivalent to:
a mathematical theory is conservative iff for each assertion A about the physical world and each corpus N of such assertions, A does not follow from N + M, if it does not follow from N alone.
((s) A mathematical theory adds nothing to a physical theory.)
M: mathematical theory
N: nominalistic physical theory.
>
Nominalism.
Def Anti-Realism/Field: (new): an interesting mathematical theory must be conservative, but it must not be true.
>
Anti-Realism.
Conservative theory:
1) It facilitates inferences
2) It can substantially occur in the premises of the physical theories.
I 59
Conservativity: necessary truth without truth simpliciter. - (i.e. it is has the properties of a necessarily true theory without existing entities.)
>
Truh/Field.
Unlike mathematics: science is not conservative. - It must also have non-trivial nominalist consequences.
>
Science.
I 61
Truth does not imply conservativity, nor vice versa.
I 63
The fact that mathematics never leads to an error shows that it is conservative, not that it is true. - From conservativity follows that statements with physical objects are materially equivalent to statements of standard mathematics. - N.b.: they need not have the same truth value!
>
Truth values.
I 75
Conservativity: can explain what follows, but not what does not follow.
I 59
Mathematics/Truth/Field: Thesis: good mathematics is not only true, but necessarily true. - N.B.: Conservativity: necessary truth without truth simpliciter.
>
Bare truth.
I 159
Conservative expansion does not apply to ontology.
>
Expansion.
- - -
III XI
Def Conservative/Science/Field: every inference from nominalistic premises on a nominalistic conclusion that can be made with by means of mathematics can also be made without it - with theoretical entities, unlike mathematical entities, there is no conservativity principle - i.e. conclusions that are made with the assumption of theoretical entities cannot be made without them.
>
Nominalism, >
Theoretical entities.
