Combining Texts

All the ideas for 'Theory of Science (4 vols)', 'Mathematical Explanation' and 'The Epistemology of Essence (draft)'

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16 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 / 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 / D. Essence of Objects / 3. Individual Essences
Particular essence is often captured by generality [Steiner,M]
10. Modality / D. Knowledge of Modality / 4. Conceivable as Possible / a. Conceivable as possible
If conceivability is a priori coherence, that implies possibility [Tahko]
12. Knowledge Sources / E. Direct Knowledge / 2. Intuition
Bolzano wanted to avoid Kantian intuitions, and prove everything that could be proved [Bolzano, by Dummett]
14. Science / D. Explanation / 2. Types of Explanation / e. Lawlike explanations
Maybe an instance of a generalisation is more explanatory than the particular case [Steiner,M]
14. Science / D. Explanation / 2. Types of Explanation / k. Explanations by essence
Essences are used to explain natural kinds, modality, and causal powers [Tahko]
14. Science / D. Explanation / 2. Types of Explanation / m. Explanation by proof
Explanatory proofs rest on 'characterizing properties' of entities or structure [Steiner,M]
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]
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / a. Scientific essentialism
Scientific essentialists tend to characterise essence in terms of modality (not vice versa) [Tahko]
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / b. Scientific necessity
If essence is modal and laws are necessary, essentialist knowledge is found by scientists [Tahko]