Combining Texts

All the ideas for 'Fragments of Pherecydes', 'A Priori' and 'Grundgesetze der Arithmetik 2 (Basic Laws)'

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27 ideas

1. Philosophy / E. Nature of Metaphysics / 7. Against Metaphysics
After 1903, Husserl avoids metaphysical commitments [Mares]
2. Reason / D. Definition / 2. Aims of Definition
Later Frege held that definitions must fix a function's value for every possible argument [Frege, by Wright,C]
2. Reason / D. Definition / 7. Contextual Definition
We can't define a word by defining an expression containing it, as the remaining parts are a problem [Frege]
2. Reason / D. Definition / 11. Ostensive Definition
Only what is logically complex can be defined; what is simple must be pointed to [Frege]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number
Cardinals say how many, and reals give measurements compared to a unit quantity [Frege]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
Real numbers are ratios of quantities [Frege, by Dummett]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / a. Axioms for numbers
The truth of the axioms doesn't matter for pure mathematics, but it does for applied [Mares]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers
Frege's biggest error is in not accounting for the senses of number terms [Hodes on Frege]
A number is a class of classes of the same cardinality [Frege, by Dummett]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism
Mathematics is relations between properties we abstract from experience [Mares]
6. Mathematics / C. Sources of Mathematics / 7. Formalism
Formalism misunderstands applications, metatheory, and infinity [Frege, by Dummett]
Only applicability raises arithmetic from a game to a science [Frege]
9. Objects / B. Unity of Objects / 3. Unity Problems / e. Vague objects
The first demand of logic is of a sharp boundary [Frege]
10. Modality / D. Knowledge of Modality / 2. A Priori Contingent
Light in straight lines is contingent a priori; stipulated as straight, because they happen to be so [Mares]
12. Knowledge Sources / A. A Priori Knowledge / 6. A Priori from Reason
Aristotelians dislike the idea of a priori judgements from pure reason [Mares]
12. Knowledge Sources / C. Rationalism / 1. Rationalism
Empiricists say rationalists mistake imaginative powers for modal insights [Mares]
13. Knowledge Criteria / B. Internal Justification / 5. Coherentism / a. Coherence as justification
The most popular view is that coherent beliefs explain one another [Mares]
14. Science / B. Scientific Theories / 3. Instrumentalism
Operationalism defines concepts by our ways of measuring them [Mares]
18. Thought / D. Concepts / 2. Origin of Concepts / b. Empirical concepts
Aristotelian justification uses concepts abstracted from experience [Mares]
18. Thought / D. Concepts / 4. Structure of Concepts / c. Classical concepts
The essence of a concept is either its definition or its conceptual relations? [Mares]
18. Thought / E. Abstraction / 3. Abstracta by Ignoring
The modern account of real numbers detaches a ratio from its geometrical origins [Frege]
18. Thought / E. Abstraction / 8. Abstractionism Critique
If we abstract the difference between two houses, they don't become the same house [Frege]
19. Language / C. Assigning Meanings / 8. Possible Worlds Semantics
Possible worlds semantics has a nice compositional account of modal statements [Mares]
19. Language / D. Propositions / 3. Concrete Propositions
Unstructured propositions are sets of possible worlds; structured ones have components [Mares]
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]
27. Natural Reality / C. Space / 3. Points in Space
Maybe space has points, but processes always need regions with a size [Mares]
29. Religion / D. Religious Issues / 2. Immortality / a. Immortality
Pherecydes was the first to say that the soul is eternal [Pherecydes, by Cicero]