Combining Texts

All the ideas for 'Thinking About Mathematics', 'De Cive' and 'Reason, Truth and History'

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38 ideas

1. Philosophy / A. Wisdom / 1. Nature of Wisdom
For ancient Greeks being wise was an ethical value [Putnam]
3. Truth / A. Truth Problems / 1. Truth
Putnam's epistemic notion of truth replaces the realism of correspondence with ontological relativism [Putnam, by O'Grady]
3. Truth / C. Correspondence Truth / 1. Correspondence Truth
Before Kant, all philosophers had a correspondence theory of truth [Putnam]
3. Truth / C. Correspondence Truth / 3. Correspondence Truth critique
The correspondence theory is wrong, because there is no one correspondence between reality and fact [Putnam, by O'Grady]
3. Truth / E. Pragmatic Truth / 1. Pragmatic Truth
Truth is an idealisation of rational acceptability [Putnam]
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]
5. Theory of Logic / I. Semantics of Logic / 6. Intensionalism
Intension is not meaning, as 'cube' and 'square-faced polyhedron' are intensionally the same [Putnam]
5. Theory of Logic / J. Model Theory in Logic / 2. Isomorphisms
If cats equal cherries, model theory allows reinterpretation of the whole language preserving truth [Putnam]
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
If we try to cure the abundance of theories with causal links, this is 'just more theory' [Putnam, by Lewis]
The sentence 'A cat is on a mat' remains always true when 'cat' means cherry and 'mat' means tree [Putnam]
7. Existence / D. Theories of Reality / 8. Facts / a. Facts
A fact is simply what it is rational to accept [Putnam]
8. Modes of Existence / B. Properties / 12. Denial of Properties
Very nominalistic philosophers deny properties, though scientists accept them [Putnam]
10. Modality / A. Necessity / 11. Denial of Necessity
If necessity is always relative to a description in a language, then there is only 'de dicto' necessity [Putnam, by O'Grady]
12. Knowledge Sources / C. Rationalism / 1. Rationalism
Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro]
13. Knowledge Criteria / E. Relativism / 6. Relativism Critique
Some kind of objective 'rightness' is a presupposition of thought itself [Putnam]
14. Science / B. Scientific Theories / 3. Instrumentalism
Naïve operationalism would have meanings change every time the tests change [Putnam]
18. Thought / A. Modes of Thought / 5. Rationality / b. Human rationality
Rationality is one part of our conception of human flourishing [Putnam]
18. Thought / C. Content / 5. Twin Earth
'Water' on Twin Earth doesn't refer to water, but no mental difference can account for this [Putnam]
18. Thought / C. Content / 6. Broad Content
Reference is social not individual, because we defer to experts when referring to elm trees [Putnam]
18. Thought / D. Concepts / 3. Ontology of Concepts / b. Concepts as abilities
Concepts are (at least in part) abilities and not occurrences [Putnam]
19. Language / B. Reference / 3. Direct Reference / c. Social reference
Neither individual nor community mental states fix reference [Putnam]
Maybe the total mental state of a language community fixes the reference of a term [Putnam]
19. Language / F. Communication / 6. Interpreting Language / b. Indeterminate translation
There are infinitely many interpretations of a sentence which can all seem to be 'correct' [Putnam]
22. Metaethics / B. Value / 1. Nature of Value / b. Fact and value
The word 'inconsiderate' nicely shows the blurring of facts and values [Putnam]
25. Social Practice / E. Policies / 1. War / c. Combatants
I act justly if I follow my Prince in an apparently unjust war, and refusing to fight would be injustice [Hobbes]