Combining Philosophers

All the ideas for George Boole, Earl Conee and Bernard Bolzano

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24 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 / B. Propositional Logic PL / 1. Propositional Logic
8083 Boole applied normal algebra to logic, aiming at an algebra of thought [Boole, by Devlin]
7727 Boole's notation can represent syllogisms and propositional arguments, but not both at once [Boole, by Weiner]
4. Formal Logic / F. Set Theory ST / 1. Set Theory
9987 An aggregate in which order does not matter I call a 'set' [Bolzano]
5. Theory of Logic / A. Overview of Logic / 2. History of Logic
8686 Boole made logic more mathematical, with algebra, quantifiers and probability [Boole, by Friend]
5. Theory of Logic / H. Proof Systems / 2. Axiomatic Proof
22277 Boole's method was axiomatic, achieving economy, plus multiple interpretations [Boole, by Potter]
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 / 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 / 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]
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]
13. Knowledge Criteria / B. Internal Justification / 3. Evidentialism / b. Evidentialism
19520 Evidentialism is not axiomatic; the evidence itself inclines us towards evidentialism [Conee]
13. Knowledge Criteria / C. External Justification / 3. Reliabilism / b. Anti-reliabilism
19521 If pure guesses were reliable, reliabilists would have to endorse them [Conee]
19522 More than actual reliability is needed, since I may mistakenly doubt what is reliable [Conee]
19523 Reliabilism is poor on reflective judgements about hypothetical cases [Conee]
13. Knowledge Criteria / C. External Justification / 6. Contextual Justification / a. Contextualism
19555 People begin to doubt whether they 'know' when the answer becomes more significant [Conee]
13. Knowledge Criteria / C. External Justification / 6. Contextual Justification / b. Invariantism
19557 Maybe low knowledge standards are loose talk; people will deny that it is 'really and truly' knowledge [Conee]
19556 Maybe knowledge has fixed standards (high, but attainable), although people apply contextual standards [Conee]
12890 That standards vary with context doesn't imply different truth-conditions for judgements [Conee]
12892 Maybe there is only one context (the 'really and truly' one) for serious discussions of knowledge [Conee]
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]
19. Language / E. Analyticity / 2. Analytic Truths
12233 The ground of a pure conceptual truth is only in other conceptual truths [Bolzano]