Combining Texts

All the ideas for 'Isolation and Non-arbitrary Division', 'The Sense of Reality' and 'Theory of Science (Wissenschaftslehre, 4 vols)'

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15 ideas

1. Philosophy / B. History of Ideas / 1. History of Ideas
The great moments are the death of Aristotle, Machiavelli, and Romanticism [Berlin, by Watson]
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 / 4. Using Numbers / a. Units
Objects do not naturally form countable units [Koslicki]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
We can still count squares, even if they overlap [Koslicki]
There is no deep reason why we count carrots but not asparagus [Koslicki]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / d. Counting via concepts
We struggle to count branches and waves because our concepts lack clear boundaries [Koslicki]
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]
7. Existence / C. Structure of Existence / 8. Stuff / a. Pure stuff
We talk of snow as what stays the same, when it is a heap or drift or expanse [Koslicki]
12. Knowledge Sources / E. Direct Knowledge / 2. Intuition
Bolzano wanted to avoid Kantian intuitions, and prove everything that could be proved [Bolzano, by Dummett]
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]