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All the ideas for 'Structures and Structuralism in Phil of Maths', 'Postscripts on supervenience' and 'Introduction: Truth and Truth-Making'

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35 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 / F. Semantic Truth / 2. Semantic Truth
While true-in-a-model seems relative, true-in-all-models seems not to be [Reck/Price]
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]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
ZFC set theory has only 'pure' sets, without 'urelements' [Reck/Price]
5. Theory of Logic / G. Quantification / 5. Second-Order Quantification
Three types of variable in second-order logic, for objects, functions, and predicates/sets [Reck/Price]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
'Analysis' is the theory of the real numbers [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / a. Axioms for numbers
Mereological arithmetic needs infinite objects, and function definitions [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / e. Peano arithmetic 2nd-order
Peano Arithmetic can have three second-order axioms, plus '1' and 'successor' [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
Set-theory gives a unified and an explicit basis for mathematics [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
Structuralism emerged from abstract algebra, axioms, and set theory and its structures [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / b. Varieties of structuralism
Relativist Structuralism just stipulates one successful model as its arithmetic [Reck/Price]
There are 'particular' structures, and 'universal' structures (what the former have in common) [Reck/Price]
Pattern Structuralism studies what isomorphic arithmetic models have in common [Reck/Price]
There are Formalist, Relativist, Universalist and Pattern structuralism [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / c. Nominalist structuralism
Formalist Structuralism says the ontology is vacuous, or formal, or inference relations [Reck/Price]
Maybe we should talk of an infinity of 'possible' objects, to avoid arithmetic being vacuous [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / d. Platonist structuralism
Universalist Structuralism is based on generalised if-then claims, not one particular model [Reck/Price]
Universalist Structuralism eliminates the base element, as a variable, which is then quantified out [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
The existence of an infinite set is assumed by Relativist Structuralism [Reck/Price]
7. Existence / C. Structure of Existence / 5. Supervenience / c. Significance of supervenience
Supervenience is not a dependence relation, on the lines of causal, mereological or semantic dependence [Kim]
Supervenience is just a 'surface' relation of pattern covariation, which still needs deeper explanation [Kim]
8. Modes of Existence / A. Relations / 2. Internal Relations
Internal relations depend either on the existence of the relata, or on their properties [Rami]
8. Modes of Existence / E. Nominalism / 6. Mereological Nominalism
A nominalist might avoid abstract objects by just appealing to mereological sums [Reck/Price]