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All the ideas for 'Thinking About Mathematics', 'Introduction: Truth and Truth-Making' and 'Method and Results'

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32 ideas

3. Truth / B. Truthmakers / 1. For Truthmakers
There are five problems which the truth-maker theory might solve [Rami]
The truth-maker idea is usually justified by its explanatory power, or intuitive appeal [Rami]
3. Truth / B. Truthmakers / 2. Truthmaker Relation
The truth-making relation can be one-to-one, or many-to-many [Rami]
3. Truth / B. Truthmakers / 3. Truthmaker Maximalism
Central idea: truths need truthmakers; and possibly all truths have them, and makers entail truths [Rami]
3. Truth / B. Truthmakers / 4. Truthmaker Necessitarianism
Most theorists say that truth-makers necessitate their truths [Rami]
3. Truth / B. Truthmakers / 5. What Makes Truths / a. What makes truths
It seems best to assume different kinds of truth-maker, such as objects, facts, tropes, or events [Rami]
3. Truth / B. Truthmakers / 5. What Makes Truths / c. States of affairs make truths
Truth-makers seem to be states of affairs (plus optional individuals), or individuals and properties [Rami]
3. Truth / B. Truthmakers / 5. What Makes Truths / d. Being makes truths
'Truth supervenes on being' only gives necessary (not sufficient) conditions for contingent truths [Rami]
'Truth supervenes on being' avoids entities as truth-makers for negative truths [Rami]
3. Truth / B. Truthmakers / 7. Making Modal Truths
Maybe a truth-maker also works for the entailments of the given truth [Rami]
3. Truth / B. Truthmakers / 11. Truthmaking and Correspondence
Truth-making is usually internalist, but the correspondence theory is externalist [Rami]
3. Truth / C. Correspondence Truth / 1. Correspondence Truth
Correspondence theories assume that truth is a representation relation [Rami]
3. Truth / H. Deflationary Truth / 2. Deflationary Truth
Deflationist truth is an infinitely disjunctive property [Rami]
4. Formal Logic / D. Modal Logic ML / 7. Barcan Formula
Truth-maker theorists should probably reject the converse Barcan formula [Rami]
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]
8. Modes of Existence / A. Relations / 2. Internal Relations
Internal relations depend either on the existence of the relata, or on their properties [Rami]
12. Knowledge Sources / C. Rationalism / 1. Rationalism
Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro]
17. Mind and Body / A. Mind-Body Dualism / 6. Epiphenomenalism
T.H.Huxley gave the earliest clear statement of epiphenomenalism [Huxley, by Rey]
Brain causes mind, but it doesn't seem that mind causes actions [Huxley]