Combining Texts

All the ideas for 'Thinking About Mathematics', 'Contrib to Critique of Hegel's Phil of Right' and 'Pragmatism and Deflationism'

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30 ideas

3. Truth / E. Pragmatic Truth / 1. Pragmatic Truth
Truth is proper assertion, but that has varying standards [Misak]
For pragmatists the loftiest idea of truth is just a feature of what remains forever assertible [Misak]
Truth isn't a grand elusive property, if it is just the aim of our assertions and inquiries [Misak]
Truth makes disagreements matter, or worth settling [Misak]
'True' is used for emphasis, clarity, assertion, comparison, objectivity, meaning, negation, consequence... [Misak]
'That's true' doesn't just refer back to a sentence, but implies sustained evidence for it [Misak]
3. Truth / F. Semantic Truth / 1. Tarski's Truth / a. Tarski's truth definition
Disquotation is bivalent [Misak]
Disquotationalism resembles a telephone directory [Misak]
Disquotations says truth is assertion, and assertion proclaims truth - but what is 'assertion'? [Misak]
3. Truth / H. Deflationary Truth / 2. Deflationary Truth
Deflating the correspondence theory doesn't entail deflating all the other theories [Misak]
Deflationism isn't a theory of truth, but an account of its role in natural language [Misak]
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]
7. Existence / D. Theories of Reality / 4. Anti-realism
The anti-realism debate concerns whether indefeasibility is a plausible aim of inquiry [Misak]
12. Knowledge Sources / C. Rationalism / 1. Rationalism
Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro]
24. Political Theory / C. Ruling a State / 4. Changing the State / c. Revolution
The middle class gain freedom through property, but workers can only free all of humanity [Marx, by Singer]
Theory is as much a part of a revolution as material force is [Marx]
29. Religion / D. Religious Issues / 1. Religious Commitment / a. Religious Belief
Religion is the opium of the people, and real happiness requires its abolition [Marx]