Ideas from 'Theory of Science (4 vols)' by Bernard Bolzano [1837], by Theme Structure
green numbers give full details 
back to texts

expand these ideas
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]

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

Bolzano wanted to reduce all of geometry to arithmetic [Brown,JR]

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 / 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
