Combining Texts

All the ideas for 'Thinking About Mathematics', 'Moral Relativism' and 'The Case for Contextualism'

expand these ideas     |    start again     |     specify just one area for these texts


24 ideas

5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number
The number 3 is presumably identical as a natural, an integer, a rational, a real, and complex [Shapiro]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / h. Reals from Cauchy
Cauchy gave a formal definition of a converging sequence. [Shapiro]
6. Mathematics / B. Foundations for Mathematics / 1. Foundations for Mathematics
Categories are the best foundation for mathematics [Shapiro]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / f. Zermelo numbers
Two definitions of 3 in terms of sets disagree over whether 1 is a member of 3 [Shapiro]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
Numbers do not exist independently; the essence of a number is its relations to other numbers [Shapiro]
A 'system' is related objects; a 'pattern' or 'structure' abstracts the pure relations from them [Shapiro]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
Logicism seems to be a non-starter if (as is widely held) logic has no ontology of its own [Shapiro]
6. Mathematics / C. Sources of Mathematics / 7. Formalism
Term Formalism says mathematics is just about symbols - but real numbers have no names [Shapiro]
Game Formalism is just a matter of rules, like chess - but then why is it useful in science? [Shapiro]
Deductivism says mathematics is logical consequences of uninterpreted axioms [Shapiro]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / b. Intuitionism
Critics resent the way intuitionism cripples mathematics, but it allows new important distinctions [Shapiro]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / c. Conceptualism
Conceptualist are just realists or idealist or nominalists, depending on their view of concepts [Shapiro]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / d. Predicativism
'Impredicative' definitions refer to the thing being described [Shapiro]
12. Knowledge Sources / B. Perception / 5. Interpretation
When we say 'is red' we don't mean 'seems red to most people' [Foot]
12. Knowledge Sources / C. Rationalism / 1. Rationalism
Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro]
13. Knowledge Criteria / B. Internal Justification / 5. Coherentism / a. Coherence as justification
A contextualist coherentist will say that how strongly a justification must cohere depends on context [DeRose]
13. Knowledge Criteria / C. External Justification / 6. Contextual Justification / a. Contextualism
Classical invariantism combines fixed truth-conditions with variable assertability standards [DeRose]
We can make contextualism more precise, by specifying the discrimination needed each time [DeRose]
In some contexts there is little more to knowledge than true belief. [DeRose]
Contextualists worry about scepticism, but they should focus on the use of 'know' in ordinary speech [DeRose]
13. Knowledge Criteria / C. External Justification / 6. Contextual Justification / b. Invariantism
If contextualism is about knowledge attribution, rather than knowledge, then it is philosophy of language [DeRose]
22. Metaethics / A. Ethics Foundations / 1. Nature of Ethics / e. Ethical cognitivism
All people need affection, cooperation, community and help in trouble [Foot]
22. Metaethics / B. Value / 1. Nature of Value / f. Ultimate value
Do we have a concept of value, other than wanting something, or making an effort to get it? [Foot]