more on this theme
|
more from this thinker
Single Idea 10170
[filed under theme 3. Truth / F. Semantic Truth / 2. Semantic Truth
]
Full Idea
While truth can be defined in a relative way, as truth in one particular model, a non-relative notion of truth is implied, as truth in all models.
Gist of Idea
While true-in-a-model seems relative, true-in-all-models seems not to be
Source
E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §4)
A Reaction
[The article is actually discussing arithmetic] This idea strikes me as extremely important. True-in-all-models is usually taken to be tautological, but it does seem to give a more universal notion of truth. See semantic truth, Tarski, Davidson etc etc.
Related Ideas
Idea 10017
Truth in a model is more tractable than the general notion of truth [Hodes]
Idea 13634
Satisfaction is 'truth in a model', which is a model of 'truth' [Shapiro]
The
18 ideas
from 'Structures and Structuralism in Phil of Maths'
10166
|
ZFC set theory has only 'pure' sets, without 'urelements'
[Reck/Price]
|
10165
|
'Analysis' is the theory of the real numbers
[Reck/Price]
|
10164
|
Peano Arithmetic can have three second-order axioms, plus '1' and 'successor'
[Reck/Price]
|
10167
|
Structuralism emerged from abstract algebra, axioms, and set theory and its structures
[Reck/Price]
|
10168
|
Formalist Structuralism says the ontology is vacuous, or formal, or inference relations
[Reck/Price]
|
10172
|
Set-theory gives a unified and an explicit basis for mathematics
[Reck/Price]
|
10174
|
Mereological arithmetic needs infinite objects, and function definitions
[Reck/Price]
|
10169
|
Relativist Structuralism just stipulates one successful model as its arithmetic
[Reck/Price]
|
10171
|
The existence of an infinite set is assumed by Relativist Structuralism
[Reck/Price]
|
10173
|
A nominalist might avoid abstract objects by just appealing to mereological sums
[Reck/Price]
|
10170
|
While true-in-a-model seems relative, true-in-all-models seems not to be
[Reck/Price]
|
10176
|
Universalist Structuralism is based on generalised if-then claims, not one particular model
[Reck/Price]
|
10177
|
Universalist Structuralism eliminates the base element, as a variable, which is then quantified out
[Reck/Price]
|
10175
|
Three types of variable in second-order logic, for objects, functions, and predicates/sets
[Reck/Price]
|
10178
|
Maybe we should talk of an infinity of 'possible' objects, to avoid arithmetic being vacuous
[Reck/Price]
|
10179
|
There are 'particular' structures, and 'universal' structures (what the former have in common)
[Reck/Price]
|
10181
|
Pattern Structuralism studies what isomorphic arithmetic models have in common
[Reck/Price]
|
10182
|
There are Formalist, Relativist, Universalist and Pattern structuralism
[Reck/Price]
|