Combining Philosophers

All the ideas for Pherecydes, Speussipus and Bernard Bolzano

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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]
9. Objects / B. Unity of Objects / 2. Substance / c. Types of substance
Speusippus suggested underlying principles for every substance, and ended with a huge list [Speussipus, by Aristotle]
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]
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / c. Ultimate substances
Pherecydes said the first principle and element is earth [Pherecydes, by Sext.Empiricus]
28. God / C. Attitudes to God / 5. Atheism
Speusippus said things were governed by some animal force rather than the gods [Speussipus, by Cicero]
29. Religion / D. Religious Issues / 2. Immortality / a. Immortality
Pherecydes was the first to say that the soul is eternal [Pherecydes, by Cicero]