Ideas of Bernard Bolzano, by Theme
[Czechoslovakian, 1781  1848, Born in Prague. Germanspeaking. 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
7807

The laws of thought are true, but they are not the axioms of logic [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'

6. Mathematics / A. Nature of Mathematics / 2. Geometry
9618

Bolzano wanted to reduce all of geometry to arithmetic [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

6. Mathematics / C. Sources of Mathematics / 2. Intuition of Mathematics
9830

Bolzano began the elimination of intuition, by proving something which seemed obvious [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 [Correia/Schnieder]

12. Knowledge Sources / E. Direct Knowledge / 2. Intuition
9185

Bolzano wanted to avoid Kantian intuitions, and prove everything that could be proved [Dummett]

19. Language / D. Propositions / 1. Propositions
22276

Bolzano saw propositions as objective entities, existing independently of us [Potter]

19. Language / D. Propositions / 2. Abstract Propositions / a. Propositions as sense
17264

Propositions are abstract structures of concepts, ready for judgement or assertion [Correia/Schnieder]

12232

A 'proposition' is the sense of a linguistic expression, and can be true or false

19. Language / E. Analyticity / 2. Analytic Truths
12233

The ground of a pure conceptual truth is only in other conceptual truths
