Combining Texts
Ideas for
'fragments/reports', 'Grundlagen der Arithmetik (Foundations)' and 'Prescriptivism'
expand these ideas
|
start again
|
choose
another area for these texts
display all the ideas for this combination of texts
28 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]
|
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]
|
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]
|
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
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]
|
5658
|
Numbers are definable in terms of mapping items which fall under concepts [Frege, by Scruton]
|
16905
|
Arithmetic must be based on logic, because of its total generality [Frege, by Jeshion]
|
8655
|
Arithmetic is analytic and a priori, and thus it is part of logic [Frege]
|
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]
|
6. Mathematics / C. Sources of Mathematics / 7. Formalism
9631
|
Formalism fails to recognise types of symbols, and also meta-games [Frege, by Brown,JR]
|
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]
|