Combining Texts

All the ideas for 'fragments/reports', 'Substitutional Classes and Relations' and 'Axiomatic Theories of Truth (2013 ver)'

expand these ideas     |    start again     |     specify just one area for these texts


15 ideas

2. Reason / D. Definition / 7. Contextual Definition
Any linguistic expression may lack meaning when taken out of context [Russell]
2. Reason / F. Fallacies / 8. Category Mistake / a. Category mistakes
'The number one is bald' or 'the number one is fond of cream cheese' are meaningless [Russell]
3. Truth / A. Truth Problems / 2. Defining Truth
If we define truth, we can eliminate it [Halbach/Leigh]
3. Truth / F. Semantic Truth / 1. Tarski's Truth / b. Satisfaction and truth
If a language cannot name all objects, then satisfaction must be used, instead of unary truth [Halbach/Leigh]
3. Truth / F. Semantic Truth / 1. Tarski's Truth / c. Meta-language for truth
Semantic theories need a powerful metalanguage, typically including set theory [Halbach/Leigh]
3. Truth / F. Semantic Truth / 2. Semantic Truth
The T-sentences are deductively weak, and also not deductively conservative [Halbach/Leigh]
3. Truth / G. Axiomatic Truth / 1. Axiomatic Truth
A natural theory of truth plays the role of reflection principles, establishing arithmetic's soundness [Halbach/Leigh]
If deflationary truth is not explanatory, truth axioms should be 'conservative', proving nothing new [Halbach/Leigh]
3. Truth / G. Axiomatic Truth / 2. FS Truth Axioms
The FS axioms use classical logical, but are not fully consistent [Halbach/Leigh]
3. Truth / G. Axiomatic Truth / 3. KF Truth Axioms
KF is formulated in classical logic, but describes non-classical truth, which allows truth-value gluts [Halbach/Leigh]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / p. Axiom of Reducibility
Axiom of Reducibility: there is always a function of the lowest possible order in a given level [Russell, by Bostock]
6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry
Archimedes defined a straight line as the shortest distance between two points [Archimedes, by Leibniz]
8. Modes of Existence / A. Relations / 1. Nature of Relations
There is no complexity without relations, so no propositions, and no truth [Russell]
8. Modes of Existence / B. Properties / 12. Denial of Properties
We can reduce properties to true formulas [Halbach/Leigh]
8. Modes of Existence / E. Nominalism / 1. Nominalism / c. Nominalism about abstracta
Nominalists can reduce theories of properties or sets to harmless axiomatic truth theories [Halbach/Leigh]