Ideas from 'Theory of Science (4 vols)' by Bernard Bolzano [1837], by Theme Structure

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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]
6. Mathematics / A. Nature of Mathematics / 2. Geometry
Bolzano wanted to reduce all of geometry to arithmetic [Brown,JR]
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