Combining Texts

All the ideas for 'Realism in Mathematics', 'Grundgesetze der Arithmetik 1 (Basic Laws)' and 'Shame and Necessity'

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23 ideas

4. Formal Logic / F. Set Theory ST / 7. Natural Sets
8755 Maddy replaces pure sets with just objects and perceived sets of objects [Maddy, by Shapiro]
5. Theory of Logic / F. Referring in Logic / 2. Descriptions / b. Definite descriptions
13733 Frege considered definite descriptions to be genuine singular terms [Frege, by Fitting/Mendelsohn]
5. Theory of Logic / G. Quantification / 4. Substitutional Quantification
9874 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
18252 Real numbers are ratios of quantities, such as lengths or masses [Frege]
6. Mathematics / B. Foundations for Mathematics / 1. Foundations for Mathematics
18271 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
10623 Frege defined number in terms of extensions of concepts, but needed Basic Law V to explain extensions [Frege, by Hale/Wright]
9975 Frege ignored Cantor's warning that a cardinal set is not just a concept-extension [Tait on Frege]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
10718 A natural number is a property of sets [Maddy, by Oliver]
6. Mathematics / C. Sources of Mathematics / 2. Intuition of Mathematics
8756 Intuition doesn't support much mathematics, and we should question its reliability [Maddy, by Shapiro]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism
17733 We know mind-independent mathematical truths through sets, which rest on experience [Maddy, by Jenkins]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
18165 My Basic Law V is a law of pure logic [Frege]
16. Persons / F. Free Will / 5. Against Free Will
2181 It is an absurd Kantian idea that at the limit rationality and freedom coincide [Williams,B]
2176 There is only a problem of free will if you think the notion of 'voluntary' can be metaphysically deepened [Williams,B]
18. Thought / D. Concepts / 3. Ontology of Concepts / c. Fregean concepts
9190 A concept is a function mapping objects onto truth-values, if they fall under the concept [Frege, by Dummett]
13665 Frege took the study of concepts to be part of logic [Frege, by Shapiro]
20. Action / B. Preliminaries of Action / 2. Willed Action / d. Weakness of will
4317 We judge weakness of will by an assessment after the event is concluded [Williams,B, by Cottingham]
20. Action / C. Motives for Action / 4. Responsibility for Actions
2174 Responsibility involves cause, intention, state of mind, and response after the event [Williams,B]
22. Metaethics / A. Ethics Foundations / 1. Nature of Ethics / g. Moral responsibility
2178 In bad actions, guilt points towards victims, and shame to the agent [Williams,B]
23. Ethics / C. Virtue Theory / 1. Virtue Theory / a. Nature of virtue
2169 Greek moral progress came when 'virtue' was freed from social status [Williams,B]
23. Ethics / D. Deontological Ethics / 2. Duty
2172 The modern idea of duty is unknown in archaic Greece [Williams,B]
23. Ethics / D. Deontological Ethics / 6. Motivation for Duty
2179 If the moral self is seen as characterless, then other people have a very limited role in our moral lives [Williams,B]
2180 If reason cannot lead people to good, we must hope they have an internal voice [Williams,B]
29. Religion / D. Religious Issues / 3. Problem of Evil / a. Problem of Evil
2175 There is a problem of evil only if you expect the world to be good [Williams,B]