Combining Philosophers

All the ideas for Archimedes, Chris Swoyer and Bernard Bolzano

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35 ideas

2. Reason / B. Laws of Thought / 1. Laws of Thought
7807 The laws of thought are true, but they are not the axioms of logic [Bolzano, by George/Van Evra]
4. Formal Logic / F. Set Theory ST / 1. Set Theory
9987 An aggregate in which order does not matter I call a 'set' [Bolzano]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / e. Iterative sets
10405 In the iterative conception of sets, they form a natural hierarchy [Swoyer]
5. Theory of Logic / E. Structures of Logic / 1. Logical Form
10407 Logical Form explains differing logical behaviour of similar sentences [Swoyer]
6. Mathematics / A. Nature of Mathematics / 2. Geometry
9618 Bolzano wanted to reduce all of geometry to arithmetic [Bolzano, by Brown,JR]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
10856 A truly infinite quantity does not need to be a variable [Bolzano]
6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry
13007 Archimedes defined a straight line as the shortest distance between two points [Archimedes, by Leibniz]
6. Mathematics / C. Sources of Mathematics / 2. Intuition of Mathematics
9830 Bolzano began the elimination of intuition, by proving something which seemed obvious [Bolzano, by Dummett]
7. Existence / A. Nature of Existence / 4. Abstract Existence
14592 Some abstract things have a beginning and end, so may exist in time (though not space) [Swoyer]
7. Existence / C. Structure of Existence / 1. Grounding / c. Grounding and explanation
17265 Philosophical proofs in mathematics establish truths, and also show their grounds [Bolzano, by Correia/Schnieder]
7. Existence / C. Structure of Existence / 5. Supervenience / a. Nature of supervenience
10421 Supervenience is nowadays seen as between properties, rather than linguistic [Swoyer]
7. Existence / D. Theories of Reality / 1. Ontologies
14594 Ontologists seek existence and identity conditions, and modal and epistemic status for a thing [Swoyer]
7. Existence / D. Theories of Reality / 4. Anti-realism
10410 Anti-realists can't explain different methods to measure distance [Swoyer]
8. Modes of Existence / B. Properties / 1. Nature of Properties
10416 Can properties have parts? [Swoyer]
10399 If a property such as self-identity can only be in one thing, it can't be a universal [Swoyer]
14595 Can properties exemplify other properties? [Swoyer]
8. Modes of Existence / B. Properties / 5. Natural Properties
10417 There are only first-order properties ('red'), and none of higher-order ('coloured') [Swoyer]
8. Modes of Existence / B. Properties / 11. Properties as Sets
10413 The best-known candidate for an identity condition for properties is necessary coextensiveness [Swoyer]
8. Modes of Existence / D. Universals / 1. Universals
10402 Various attempts are made to evade universals being wholly present in different places [Swoyer]
8. Modes of Existence / E. Nominalism / 4. Concept Nominalism
10400 Conceptualism says words like 'honesty' refer to concepts, not to properties [Swoyer]
9. Objects / A. Existence of Objects / 2. Abstract Objects / a. Nature of abstracta
10403 If properties are abstract objects, then their being abstract exemplifies being abstract [Swoyer]
9. Objects / A. Existence of Objects / 5. Simples
14593 Quantum field theory suggests that there are, fundamentally, no individual things [Swoyer]
10. Modality / E. Possible worlds / 1. Possible Worlds / e. Against possible worlds
10406 One might hope to reduce possible worlds to properties [Swoyer]
12. Knowledge Sources / D. Empiricism / 5. Empiricism Critique
10404 Extreme empiricists can hardly explain anything [Swoyer]
12. Knowledge Sources / E. Direct Knowledge / 2. Intuition
9185 Bolzano wanted to avoid Kantian intuitions, and prove everything that could be proved [Bolzano, by Dummett]
18. Thought / C. Content / 8. Intension
10408 Intensions are functions which map possible worlds to sets of things denoted by an expression [Swoyer]
18. Thought / D. Concepts / 4. Structure of Concepts / e. Concepts from exemplars
10409 Research suggests that concepts rely on typical examples [Swoyer]
19. Language / C. Assigning Meanings / 3. Predicates
10401 The F and G of logic cover a huge range of natural language combinations [Swoyer]
19. Language / D. Propositions / 1. Propositions
22276 Bolzano saw propositions as objective entities, existing independently of us [Bolzano, by Potter]
19. Language / D. Propositions / 2. Abstract Propositions / a. Propositions as sense
17264 Propositions are abstract structures of concepts, ready for judgement or assertion [Bolzano, by Correia/Schnieder]
12232 A 'proposition' is the sense of a linguistic expression, and can be true or false [Bolzano]
10420 Maybe a proposition is just a property with all its places filled [Swoyer]
19. Language / E. Analyticity / 2. Analytic Truths
12233 The ground of a pure conceptual truth is only in other conceptual truths [Bolzano]
26. Natural Theory / D. Laws of Nature / 4. Regularities / a. Regularity theory
10412 If laws are mere regularities, they give no grounds for future prediction [Swoyer]
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / a. Scientific essentialism
10411 Two properties can have one power, and one property can have two powers [Swoyer]