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.]

green numbers give full details    |    back to list of philosophers    |     expand these ideas
2. Reason / B. Laws of Thought / 1. Laws of Thought
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
An aggregate in which order does not matter I call a 'set'
6. Mathematics / A. Nature of Mathematics / 2. Geometry
Bolzano wanted to reduce all of geometry to arithmetic [Brown,JR]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
A truly infinite quantity does not need to be a variable
6. Mathematics / C. Sources of Mathematics / 2. Intuition of Mathematics
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
Philosophical proofs in mathematics establish truths, and also show their grounds [Correia/Schnieder]
12. Knowledge Sources / E. Direct Knowledge / 1. Intuition
Bolzano wanted to avoid Kantian intuitions, and prove everything that could be proved [Dummett]
19. Language / D. Propositions / 2. Abstract Propositions / a. Propositions as sense
Propositions are abstract structures of concepts, ready for judgement or assertion [Correia/Schnieder]
A 'proposition' is the sense of a linguistic expression, and can be true or false
19. Language / E. Analyticity / 2. Analytic Truths
The ground of a pure conceptual truth is only in other conceptual truths