Combining Texts

All the ideas for 'fragments/reports', 'Philosophy of Arithmetic' and 'Theory of Science (Wissenschaftslehre, 4 vols)'

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17 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 [Bolzano, by George/Van Evra]
6. Mathematics / A. Nature of Mathematics / 2. Geometry
Bolzano wanted to reduce all of geometry to arithmetic [Bolzano, by Brown,JR]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / l. Zero
0 is not a number, as it answers 'how many?' negatively [Husserl, by Dummett]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / a. Units
Multiplicity in general is just one and one and one, etc. [Husserl]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / e. Counting by correlation
Husserl said counting is more basic than Frege's one-one correspondence [Husserl, by Heck]
6. Mathematics / C. Sources of Mathematics / 2. Intuition of Mathematics
Bolzano began the elimination of intuition, by proving something which seemed obvious [Bolzano, by Dummett]
7. Existence / C. Structure of Existence / 1. Grounding / c. Grounding and explanation
Philosophical proofs in mathematics establish truths, and also show their grounds [Bolzano, by Correia/Schnieder]
9. Objects / C. Structure of Objects / 6. Constitution of an Object
If someone squashed a horse to make a dog, something new would now exist [Mnesarchus]
12. Knowledge Sources / E. Direct Knowledge / 2. Intuition
Bolzano wanted to avoid Kantian intuitions, and prove everything that could be proved [Bolzano, by Dummett]
15. Nature of Minds / C. Capacities of Minds / 3. Abstraction by mind
Husserl identifies a positive mental act of unification, and a negative mental act for differences [Husserl, by Frege]
18. Thought / D. Concepts / 4. Structure of Concepts / b. Analysis of concepts
We clarify concepts (e.g. numbers) by determining their psychological origin [Husserl, by Velarde-Mayol]
18. Thought / E. Abstraction / 8. Abstractionism Critique
Psychologism blunders in focusing on concept-formation instead of delineating the concepts [Dummett on Husserl]
Husserl wanted to keep a shadowy remnant of abstracted objects, to correlate them [Dummett on Husserl]
19. Language / D. Propositions / 1. Propositions
Bolzano saw propositions as objective entities, existing independently of us [Bolzano, by Potter]
19. Language / D. Propositions / 2. Abstract Propositions / a. Propositions as sense
Propositions are abstract structures of concepts, ready for judgement or assertion [Bolzano, by Correia/Schnieder]
A 'proposition' is the sense of a linguistic expression, and can be true or false [Bolzano]
19. Language / E. Analyticity / 2. Analytic Truths
The ground of a pure conceptual truth is only in other conceptual truths [Bolzano]