Combining Philosophers

All the ideas for Roger Penrose, Jean Buridan and Bernard Bolzano

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18 ideas

2. Reason / A. Nature of Reason / 9. Limits of Reason
1403 A rational donkey would starve to death between two totally identical piles of hay [Buridan, by PG]
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]
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]
9. Objects / C. Structure of Objects / 4. Quantity of an Object
16678 Without magnitude a thing would retain its parts, but they would have no location [Buridan]
9. Objects / E. Objects over Time / 8. Continuity of Rivers
16793 A thing is (less properly) the same over time if each part is succeeded by another [Buridan]
12. Knowledge Sources / B. Perception / 2. Qualities in Perception / b. Primary/secondary
16726 Why can't we deduce secondary qualities from primary ones, if they cause them? [Buridan]
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]
14. Science / A. Basis of Science / 2. Demonstration
16577 Induction is not demonstration, because not all of the instances can be observed [Buridan]
14. Science / C. Induction / 2. Aims of Induction
16576 Science is based on induction, for general truths about fire, rhubarb and magnets [Buridan]
15. Nature of Minds / B. Features of Minds / 1. Consciousness / e. Cause of consciousness
4921 Quantum states in microtubules could bind brain activity to produce consciousness [Penrose]
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]