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All the ideas for 'Realistic Rationalism', 'Sets, Aggregates and Numbers' and 'Truth by Convention'

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24 ideas

1. Philosophy / D. Nature of Philosophy / 3. Philosophy Defined
Traditionally philosophy is an a priori enquiry into general truths about reality [Katz]
Most of philosophy begins where science leaves off [Katz]
1. Philosophy / F. Analytic Philosophy / 6. Logical Analysis
If if time is money then if time is not money then time is money then if if if time is not money... [Quine]
2. Reason / D. Definition / 7. Contextual Definition
Definition by words is determinate but relative; fixing contexts could make it absolute [Quine]
5. Theory of Logic / C. Ontology of Logic / 3. If-Thenism
Quine quickly dismisses If-thenism [Quine, by Musgrave]
5. Theory of Logic / C. Ontology of Logic / 4. Logic by Convention
Logic needs general conventions, but that needs logic to apply them to individual cases [Quine, by Rey]
Claims that logic and mathematics are conventional are either empty, uninteresting, or false [Quine]
Logic isn't conventional, because logic is needed to infer logic from conventions [Quine]
If a convention cannot be communicated until after its adoption, what is its role? [Quine]
6. Mathematics / A. Nature of Mathematics / 2. Geometry
If analytic geometry identifies figures with arithmetical relations, logicism can include geometry [Quine]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
How many? must first partition an aggregate into sets, and then logic fixes its number [Yourgrau]
Nothing is 'intrinsically' numbered [Yourgrau]
6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry
There are four different possible conventional accounts of geometry [Quine]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers
Defining 'three' as the principle of collection or property of threes explains set theory definitions [Yourgrau]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / b. Mathematics is not set theory
We can't use sets as foundations for mathematics if we must await results from the upper reaches [Yourgrau]
You can ask all sorts of numerical questions about any one given set [Yourgrau]
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / b. Against mathematical platonism
'Real' maths objects have no causal role, no determinate reference, and no abstract/concrete distinction [Katz]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
If mathematics follows from definitions, then it is conventional, and part of logic [Quine]
12. Knowledge Sources / A. A Priori Knowledge / 5. A Priori Synthetic
We don't have a clear enough sense of meaning to pronounce some sentences meaningless or just analytic [Katz]
12. Knowledge Sources / D. Empiricism / 5. Empiricism Critique
Experience cannot teach us why maths and logic are necessary [Katz]
19. Language / A. Nature of Meaning / 1. Meaning
Structuralists see meaning behaviouristically, and Chomsky says nothing about it [Katz]
19. Language / B. Reference / 4. Descriptive Reference / a. Sense and reference
It is generally accepted that sense is defined as the determiner of reference [Katz]
19. Language / C. Assigning Meanings / 5. Fregean Semantics
Sense determines meaning and synonymy, not referential properties like denotation and truth [Katz]
19. Language / D. Propositions / 2. Abstract Propositions / a. Propositions as sense
Sentences are abstract types (like musical scores), not individual tokens [Katz]