Ideas of Bernard Bolzano, by Theme
[Czechoslovakian, 1781 - 1848, Born in Prague. German-speaking. Catholic priest. Professor at University of Prague. Sacked for liberal views in 1819.]
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2. Reason / B. Laws of Thought / 1. Laws of Thought
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7807
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The laws of thought are true, but they are not the axioms of logic [George/Van Evra]
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4. Formal Logic / F. Set Theory ST / 1. Set Theory
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9987
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An aggregate in which order does not matter I call a 'set'
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6. Mathematics / A. Nature of Mathematics / 2. Geometry
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9618
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Bolzano wanted to reduce all of geometry to arithmetic [Brown,JR]
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6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
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10856
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A truly infinite quantity does not need to be a variable
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6. Mathematics / C. Sources of Mathematics / 2. Intuition of Mathematics
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9830
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Bolzano began the elimination of intuition, by proving something which seemed obvious [Dummett]
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7. Existence / C. Structure of Existence / 1. Grounding / c. Grounding and explanation
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17265
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Philosophical proofs in mathematics establish truths, and also show their grounds [Correia/Schnieder]
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12. Knowledge Sources / E. Direct Knowledge / 2. Intuition
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9185
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Bolzano wanted to avoid Kantian intuitions, and prove everything that could be proved [Dummett]
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19. Language / D. Propositions / 1. Propositions
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22276
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Bolzano saw propositions as objective entities, existing independently of us [Potter]
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19. Language / D. Propositions / 2. Abstract Propositions / a. Propositions as sense
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17264
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Propositions are abstract structures of concepts, ready for judgement or assertion [Correia/Schnieder]
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12232
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A 'proposition' is the sense of a linguistic expression, and can be true or false
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19. Language / E. Analyticity / 2. Analytic Truths
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12233
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The ground of a pure conceptual truth is only in other conceptual truths
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