Combining Philosophers

All the ideas for Philodemus, Bernard Bolzano and James Van Cleve

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15 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]
4. Formal Logic / F. Set Theory ST / 1. Set Theory
An aggregate in which order does not matter I call a 'set' [Bolzano]
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 / 5. The Infinite / a. The Infinite
A truly infinite quantity does not need to be a variable [Bolzano]
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]
12. Knowledge Sources / E. Direct Knowledge / 2. Intuition
Bolzano wanted to avoid Kantian intuitions, and prove everything that could be proved [Bolzano, by Dummett]
13. Knowledge Criteria / A. Justification Problems / 2. Justification Challenges / a. Agrippa's trilemma
There are five possible responses to the problem of infinite regress in justification [Cleve]
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / a. Foundationalism
Modern foundationalists say basic beliefs are fallible, and coherence is relevant [Cleve]
14. Science / C. Induction / 3. Limits of Induction
From the fact that some men die, we cannot infer that they all do [Philodemus]
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]
23. Ethics / C. Virtue Theory / 3. Virtues / a. Virtues
Don't fear god or worry about death; the good is easily got and the terrible easily cured [Philodemus]