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All the ideas for 'Structures and Structuralism in Phil of Maths', 'Phil of Mathematics: why nothing works' and 'This is Political Philosophy'

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50 ideas

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]
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]
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / b. Against mathematical platonism
How can you contemplate Platonic entities without causal transactions with them? [Putnam]
8. Modes of Existence / E. Nominalism / 6. Mereological Nominalism
A nominalist might avoid abstract objects by just appealing to mereological sums [Reck/Price]
16. Persons / B. Nature of the Self / 6. Self as Higher Awareness
Maybe a person's true self is their second-order desires [Tuckness/Wolf]
23. Ethics / E. Utilitarianism / 1. Utilitarianism
If maximising pleasure needs measurement, so does fulfilling desires [Tuckness/Wolf]
Desire satisfaction as the ideal is confused, because we desire what we judge to be good [Tuckness/Wolf]
24. Political Theory / A. Basis of a State / 1. A People / c. A unified people
In a democracy, which 'people' are included in the decision process? [Tuckness/Wolf]
People often have greater attachment to ethnic or tribal groups than to the state [Tuckness/Wolf]
24. Political Theory / A. Basis of a State / 4. Original Position / a. Original position
For global justice, adopt rules without knowing which country you will inhabit [Tuckness/Wolf]
24. Political Theory / A. Basis of a State / 4. Original Position / b. Veil of ignorance
The veil of ignorance ensures both fairness and unanimity [Tuckness/Wolf]
24. Political Theory / B. Nature of a State / 2. State Legitimacy / a. Sovereignty
Unjust institutions may be seen as just; are they legitimate if just but seen as unjust? [Tuckness/Wolf]
24. Political Theory / C. Ruling a State / 2. Leaders / d. Elites
If winning elections depends on wealth, we have plutocracy instead of democracy [Tuckness/Wolf]
24. Political Theory / D. Ideologies / 5. Democracy / a. Nature of democracy
Epistemic theories defend democracy as more likely to produce the right answer [Tuckness/Wolf]
Which areas of public concern should be decided democratically, and which not? [Tuckness/Wolf]
24. Political Theory / D. Ideologies / 5. Democracy / b. Consultation
If several losing groups would win if they combine, a runoff seems called for [Tuckness/Wolf]
Rights as interests (unlike rights as autonomy) supports mandatory voting [Tuckness/Wolf]
How should democratic votes be aggregated? Can some person's votes count for more? [Tuckness/Wolf]
Discussion before voting should be an essential part of democracy [Tuckness/Wolf]
24. Political Theory / D. Ideologies / 7. Communitarianism / a. Communitarianism
We have obligations to our family, even though we didn't choose its members [Tuckness/Wolf]
25. Social Practice / A. Freedoms / 3. Free speech
Free speech does not include the right to shout 'Fire!' in a crowded theatre [Tuckness/Wolf]
25. Social Practice / B. Equalities / 1. Grounds of equality
Most people want equality because they want a flourishing life [Tuckness/Wolf]
25. Social Practice / B. Equalities / 4. Economic equality
If there is no suffering, wealth inequalities don't matter much [Tuckness/Wolf]
25. Social Practice / C. Rights / 1. Basis of Rights
Some rights are 'claims' that other people should act in a certain way [Tuckness/Wolf]
Choice theory says protecting individual autonomy is basic (but needs to cover infants and animals) [Tuckness/Wolf]
One theory (fairly utilitarian) says rights protect interests (but it needs to cover trivial interests) [Tuckness/Wolf]
Having a right does not entail further rights needed to implement it [Tuckness/Wolf]
25. Social Practice / D. Justice / 2. The Law / a. Legal system
If being subject to the law resembles a promise, we are morally obliged to obey it [Tuckness/Wolf]
If others must obey laws that we like, we must obey laws that they like? [Tuckness/Wolf]
25. Social Practice / D. Justice / 2. The Law / c. Natural law
Instead of against natural law, we might assess unjust laws against the values of the culture [Tuckness/Wolf]
25. Social Practice / D. Justice / 3. Punishment / b. Retribution for crime
How should the punishment fit the crime (for stealing chickens?) [Tuckness/Wolf]
25. Social Practice / E. Policies / 1. War / a. Just wars
Just wars: resist aggression, done on just cause, proportionate, last resort, not futile, legal [Tuckness/Wolf]
25. Social Practice / E. Policies / 1. War / b. Justice in war
During wars: proportional force, fair targets, fair weapons, safe prisoners, no reprisals [Tuckness/Wolf]
25. Social Practice / E. Policies / 2. Religion in Society
If minority views are accepted in debate, then religious views must be accepted [Tuckness/Wolf]
25. Social Practice / F. Life Issues / 3. Abortion
Is abortion the ending of a life, or a decision not to start one? [Tuckness/Wolf]