Combining Texts

All the ideas for 'fragments/reports', 'Human Knowledge: its scope and limits' and 'Grundgesetze der Arithmetik 1 (Basic Laws)'

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16 ideas

5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / c. not
Is it possible to state every possible truth about the whole course of nature without using 'not'? [Russell]
5. Theory of Logic / F. Referring in Logic / 2. Descriptions / b. Definite descriptions
Frege considered definite descriptions to be genuine singular terms [Frege, by Fitting/Mendelsohn]
5. Theory of Logic / G. Quantification / 4. Substitutional Quantification
Contradiction arises from Frege's substitutional account of second-order quantification [Dummett on Frege]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
Real numbers are ratios of quantities, such as lengths or masses [Frege]
6. Mathematics / B. Foundations for Mathematics / 1. Foundations for Mathematics
We can't prove everything, but we can spell out the unproved, so that foundations are clear [Frege]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers
Frege defined number in terms of extensions of concepts, but needed Basic Law V to explain extensions [Frege, by Hale/Wright]
Frege ignored Cantor's warning that a cardinal set is not just a concept-extension [Tait on Frege]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
My Basic Law V is a law of pure logic [Frege]
10. Modality / A. Necessity / 6. Logical Necessity
Some facts about experience feel like logical necessities [Russell]
12. Knowledge Sources / D. Empiricism / 5. Empiricism Critique
It is hard to explain how a sentence like 'it is not raining' can be found true by observation [Russell]
18. Thought / D. Concepts / 3. Ontology of Concepts / c. Fregean concepts
A concept is a function mapping objects onto truth-values, if they fall under the concept [Frege, by Dummett]
Frege took the study of concepts to be part of logic [Frege, by Shapiro]
19. Language / F. Communication / 3. Denial
If we define 'this is not blue' as disbelief in 'this is blue', we eliminate 'not' as an ingredient of facts [Russell]
26. Natural Theory / A. Speculations on Nature / 5. Infinite in Nature
Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius]
27. Natural Reality / A. Classical Physics / 1. Mechanics / a. Explaining movement
Russell's 'at-at' theory says motion is to be at the intervening points at the intervening instants [Russell, by Psillos]
27. Natural Reality / G. Biology / 3. Evolution
Archelaus said life began in a primeval slime [Archelaus, by Schofield]