Combining Texts

All the ideas for 'Syntagma', 'The Problem of Possibilia' and 'Grundgesetze der Arithmetik 1 (Basic Laws)'

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15 ideas

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]
8. Modes of Existence / B. Properties / 8. Properties as Modes
If matter is entirely atoms, anything else we notice in it can only be modes [Gassendi]
10. Modality / B. Possibility / 1. Possibility
Possible states of affairs are not propositions; a proposition can't be a state of affairs! [Fine,K]
10. Modality / E. Possible worlds / 2. Nature of Possible Worlds / a. Nature of possible worlds
The actual world is a possible world, so we can't define possible worlds as 'what might have been' [Fine,K]
14. Science / D. Explanation / 2. Types of Explanation / j. Explanations by reduction
We observe qualities, and use 'induction' to refer to the substances lying under them [Gassendi]
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]
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / g. Atomism
Atoms are not points, but hard indivisible things, which no force in nature can divide [Gassendi]
How do mere atoms produce qualities like colour, flavour and odour? [Gassendi]