Combining Philosophers

Ideas for Rescher,N/Oppenheim,P, Benjamin Libet and Gottlob Frege

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41 ideas

6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
13874 Numbers seem to be objects because they exactly fit the inference patterns for identities [Frege]
13875 Frege's platonism proposes that objects are what singular terms refer to [Frege, by Wright,C]
7731 How can numbers be external (one pair of boots is two boots), or subjective (and so relative)? [Frege, by Weiner]
7737 Identities refer to objects, so numbers must be objects [Frege, by Weiner]
8635 Numbers are not physical, and not ideas - they are objective and non-sensible [Frege]
8652 Numbers are objects, because they can take the definite article, and can't be plurals [Frege]
9580 Our concepts recognise existing relations, they don't change them [Frege]
9589 Numbers are not real like the sea, but (crucially) they are still objective [Frege]
6. Mathematics / C. Sources of Mathematics / 2. Intuition of Mathematics
17816 Frege's logicism aimed at removing the reliance of arithmetic on intuition [Frege, by Yourgrau]
9831 Geometry appeals to intuition as the source of its axioms [Frege]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism
8633 There is no physical difference between two boots and one pair of boots [Frege]
9577 The naïve view of number is that it is like a heap of things, or maybe a property of a heap [Frege]
6. Mathematics / C. Sources of Mathematics / 5. Numbers as Adjectival
9951 It appears that numbers are adjectives, but they don't apply to a single object [Frege, by George/Velleman]
9952 Numerical adjectives are of the same second-level type as the existential quantifier [Frege, by George/Velleman]
11031 'Jupiter has many moons' won't read as 'The number of Jupiter's moons equals the number many' [Rumfitt on Frege]
8637 The number 'one' can't be a property, if any object can be viewed as one or not one [Frege]
9999 For science, we can translate adjectival numbers into noun form [Frege]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
18166 The loss of my Rule V seems to make foundations for arithmetic impossible [Frege]
7739 Arithmetic is analytic [Frege, by Weiner]
9945 Logicism shows that no empirical truths are needed to justify arithmetic [Frege, by George/Velleman]
8782 Frege offered a Platonist version of logicism, committed to cardinal and real numbers [Frege, by Hale/Wright]
13608 Mathematics has no special axioms of its own, but follows from principles of logic (with definitions) [Frege, by Bostock]
16905 Arithmetic must be based on logic, because of its total generality [Frege, by Jeshion]
5658 Numbers are definable in terms of mapping items which fall under concepts [Frege, by Scruton]
8655 Arithmetic is analytic and a priori, and thus it is part of logic [Frege]
16880 Frege aimed to discover the logical foundations which justify arithmetical judgements [Frege, by Burge]
8689 Eventually Frege tried to found arithmetic in geometry instead of in logic [Frege, by Friend]
8487 Arithmetic is a development of logic, so arithmetical symbolism must expand into logical symbolism [Frege]
18165 My Basic Law V is a law of pure logic [Frege]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / b. Type theory
10607 Frege's logic has a hierarchy of object, property, property-of-property etc. [Frege, by Smith,P]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
10831 Frege only managed to prove that arithmetic was analytic with a logic that included set-theory [Quine on Frege]
13864 Frege's platonism and logicism are in conflict, if logic must dictates an infinity of objects [Wright,C on Frege]
10033 Why should the existence of pure logic entail the existence of objects? [George/Velleman on Frege]
10010 Frege's belief in logicism and in numerical objects seem uncomfortable together [Hodes on Frege]
9545 Late in life Frege abandoned logicism, and saw the source of arithmetic as geometrical [Frege, by Chihara]
6. Mathematics / C. Sources of Mathematics / 7. Formalism
9631 Formalism fails to recognise types of symbols, and also meta-games [Frege, by Brown,JR]
9887 Formalism misunderstands applications, metatheory, and infinity [Frege, by Dummett]
8751 Only applicability raises arithmetic from a game to a science [Frege]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / b. Intuitionism
9875 Frege was completing Bolzano's work, of expelling intuition from number theory and analysis [Frege, by Dummett]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / c. Conceptualism
8642 Abstraction from things produces concepts, and numbers are in the concepts [Frege]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / e. Psychologism
8621 Mental states are irrelevant to mathematics, because they are vague and fluctuating [Frege]