Combining Texts

All the ideas for 'Thinking About Mathematics', 'Humean metaphysics vs metaphysics of Powers' and 'Grounding: an opinionated introduction'

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

21 ideas

1. Philosophy / E. Nature of Metaphysics / 1. Nature of Metaphysics
17266 Using modal logic, philosophers tried to handle all metaphysics in modal terms [Correia/Schnieder]
2. Reason / B. Laws of Thought / 2. Sufficient Reason
17263 Why do rationalists accept Sufficient Reason, when it denies the existence of fundamental facts? [Correia/Schnieder]
5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
8729 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
8763 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
18249 Cauchy gave a formal definition of a converging sequence. [Shapiro]
6. Mathematics / B. Foundations for Mathematics / 1. Foundations for Mathematics
8764 Categories are the best foundation for mathematics [Shapiro]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / f. Zermelo numbers
8762 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
8760 Numbers do not exist independently; the essence of a number is its relations to other numbers [Shapiro]
8761 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
8744 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
8749 Term Formalism says mathematics is just about symbols - but real numbers have no names [Shapiro]
8750 Game Formalism is just a matter of rules, like chess - but then why is it useful in science? [Shapiro]
8752 Deductivism says mathematics is logical consequences of uninterpreted axioms [Shapiro]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / b. Intuitionism
8753 Critics resent the way intuitionism cripples mathematics, but it allows new important distinctions [Shapiro]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / c. Conceptualism
8731 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
8730 'Impredicative' definitions refer to the thing being described [Shapiro]
7. Existence / C. Structure of Existence / 1. Grounding / a. Nature of grounding
17270 Is existential dependence by grounding, or do grounding claims arise from existential dependence? [Correia/Schnieder]
7. Existence / C. Structure of Existence / 1. Grounding / c. Grounding and explanation
17268 Grounding is metaphysical and explanation epistemic, so keep them apart [Correia/Schnieder]
7. Existence / D. Theories of Reality / 8. Facts / a. Facts
17267 The identity of two facts may depend on how 'fine-grained' we think facts are [Correia/Schnieder]
12. Knowledge Sources / C. Rationalism / 1. Rationalism
8725 Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro]
27. Natural Reality / D. Time / 2. Passage of Time / g. Time's arrow
13440 Causation is the power of one property to produce another, and this gives time its direction [Esfeld]