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All the ideas for 'Axiomatic Theories of Truth (2005 ver)', 'Analyticity Reconsidered' and 'Philosophy of Mathematics'

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31 ideas

2. Reason / D. Definition / 4. Real Definition
A sentence may simultaneously define a term, and also assert a fact [Boghossian]
3. Truth / A. Truth Problems / 2. Defining Truth
Truth definitions don't produce a good theory, because they go beyond your current language [Halbach]
3. Truth / F. Semantic Truth / 1. Tarski's Truth / c. Meta-language for truth
In semantic theories of truth, the predicate is in an object-language, and the definition in a metalanguage [Halbach]
3. Truth / G. Axiomatic Truth / 1. Axiomatic Truth
Instead of a truth definition, add a primitive truth predicate, and axioms for how it works [Halbach]
Should axiomatic truth be 'conservative' - not proving anything apart from implications of the axioms? [Halbach]
If truth is defined it can be eliminated, whereas axiomatic truth has various commitments [Halbach]
Axiomatic theories of truth need a weak logical framework, and not a strong metatheory [Halbach]
3. Truth / H. Deflationary Truth / 2. Deflationary Truth
Deflationists say truth merely serves to express infinite conjunctions [Halbach]
4. Formal Logic / F. Set Theory ST / 1. Set Theory
To prove the consistency of set theory, we must go beyond set theory [Halbach]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / d. Naïve logical sets
Naïve set theory says any formula defines a set, and coextensive sets are identical [Linnebo]
5. Theory of Logic / C. Ontology of Logic / 1. Ontology of Logic
We can use truth instead of ontologically loaded second-order comprehension assumptions about properties [Halbach]
5. Theory of Logic / E. Structures of Logic / 7. Predicates in Logic
Instead of saying x has a property, we can say a formula is true of x - as long as we have 'true' [Halbach]
5. Theory of Logic / I. Semantics of Logic / 1. Semantics of Logic
In classical semantics singular terms refer, and quantifiers range over domains [Linnebo]
5. Theory of Logic / I. Semantics of Logic / 2. Formal Truth
Conventionalism agrees with realists that logic has truth values, but not over the source [Boghossian]
5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
The axioms of group theory are not assertions, but a definition of a structure [Linnebo]
To investigate axiomatic theories, mathematics needs its own foundational axioms [Linnebo]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
You can't prove consistency using a weaker theory, but you can use a consistent theory [Linnebo]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
Mathematics is the study of all possible patterns, and is thus bound to describe the world [Linnebo]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
Logical truth is true in all models, so mathematical objects can't be purely logical [Linnebo]
6. Mathematics / C. Sources of Mathematics / 7. Formalism
Game Formalism has no semantics, and Term Formalism reduces the semantics [Linnebo]
12. Knowledge Sources / A. A Priori Knowledge / 4. A Priori as Necessities
'Snow is white or it isn't' is just true, not made true by stipulation [Boghossian]
12. Knowledge Sources / A. A Priori Knowledge / 8. A Priori as Analytic
The a priori is explained as analytic to avoid a dubious faculty of intuition [Boghossian]
That logic is a priori because it is analytic resulted from explaining the meaning of logical constants [Boghossian]
We can't hold a sentence true without evidence if we can't agree which sentence is definitive of it [Boghossian]
12. Knowledge Sources / A. A Priori Knowledge / 11. Denying the A Priori
We may have strong a priori beliefs which we pragmatically drop from our best theory [Boghossian]
12. Knowledge Sources / E. Direct Knowledge / 2. Intuition
If we learn geometry by intuition, how could this faculty have misled us for so long? [Boghossian]
19. Language / A. Nature of Meaning / 7. Meaning Holism / c. Meaning by Role
'Conceptual role semantics' says terms have meaning from sentences and/or inferences [Boghossian]
If meaning depends on conceptual role, what properties are needed to do the job? [Boghossian]
19. Language / A. Nature of Meaning / 8. Synonymy
Could expressions have meaning, without two expressions possibly meaning the same? [Boghossian]
19. Language / E. Analyticity / 2. Analytic Truths
There are no truths in virtue of meaning, but there is knowability in virtue of understanding [Boghossian, by Jenkins]
19. Language / E. Analyticity / 3. Analytic and Synthetic
Epistemological analyticity: grasp of meaning is justification; metaphysical: truth depends on meaning [Boghossian]