Combining Texts

All the ideas for 'Thinking About Mathematics', 'Truth-makers and dependence' and 'Naming and Necessity notes and addenda'

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38 ideas

3. Truth / B. Truthmakers / 2. Truthmaker Relation
Truth-maker theory can't cope with non-causal dependence [Liggins]
3. Truth / B. Truthmakers / 12. Rejecting Truthmakers
Truthmakers for existence is fine; otherwise maybe restrict it to synthetic truths? [Liggins]
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 / A. Nature of Existence / 5. Reason for Existence
Either p is true or not-p is true, so something is true, so something exists [Liggins]
7. Existence / C. Structure of Existence / 1. Grounding / b. Relata of grounding
The dependence of {Socrates} on Socrates involves a set and a philosopher, not facts [Liggins]
7. Existence / C. Structure of Existence / 4. Ontological Dependence
Non-causal dependence is at present only dimly understood [Liggins]
7. Existence / C. Structure of Existence / 5. Supervenience / c. Significance of supervenience
Necessities supervene on everything, but don't depend on everything [Liggins]
9. Objects / A. Existence of Objects / 5. Simples
We might fix identities for small particulars, but it is utopian to hope for such things [Kripke]
9. Objects / C. Structure of Objects / 6. Constitution of an Object
A different piece of wood could have been used for that table; constitution isn't identity [Wiggins on Kripke]
9. Objects / F. Identity among Objects / 5. Self-Identity
A relation can clearly be reflexive, and identity is the smallest reflexive relation [Kripke]
9. Objects / F. Identity among Objects / 9. Sameness
A vague identity may seem intransitive, and we might want to talk of 'counterparts' [Kripke]
10. Modality / A. Necessity / 7. Natural Necessity
What many people consider merely physically necessary I consider completely necessary [Kripke]
What is often held to be mere physical necessity is actually metaphysical necessity [Kripke]
10. Modality / B. Possibility / 1. Possibility
Unicorns are vague, so no actual or possible creature could count as a unicorn [Kripke]
10. Modality / E. Possible worlds / 1. Possible Worlds / e. Against possible worlds
Possible worlds are useful in set theory, but can be very misleading elsewhere [Kripke]
10. Modality / E. Possible worlds / 3. Transworld Objects / b. Rigid designation
Kaplan's 'Dthat' is a useful operator for transforming a description into a rigid designation [Kripke]
10. Modality / E. Possible worlds / 3. Transworld Objects / c. Counterparts
The best known objection to counterparts is Kripke's, that Humphrey doesn't care if his counterpart wins [Kripke, by Sider]
12. Knowledge Sources / A. A Priori Knowledge / 8. A Priori as Analytic
The a priori analytic truths involving fixing of reference are contingent [Kripke]
12. Knowledge Sources / C. Rationalism / 1. Rationalism
Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro]
14. Science / D. Explanation / 1. Explanation / a. Explanation
'Because' can signal an inference rather than an explanation [Liggins]
14. Science / D. Explanation / 2. Types of Explanation / a. Types of explanation
Value, constitution and realisation are non-causal dependences that explain [Liggins]
If explanations track dependence, then 'determinative' explanations seem to exist [Liggins]
15. Nature of Minds / A. Nature of Mind / 1. Mind / a. Mind
I regard the mind-body problem as wide open, and extremely confusing [Kripke]
19. Language / B. Reference / 3. Direct Reference / c. Social reference
A description may fix a reference even when it is not true of its object [Kripke]
19. Language / B. Reference / 4. Descriptive Reference / b. Reference by description
Even if Gödel didn't produce his theorems, he's still called 'Gödel' [Kripke]