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All the ideas for 'Thinking About Mathematics', 'Second Treatise of Government' and 'Potentiality'

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99 ideas

2. Reason / E. Argument / 1. Argument
Slippery slope arguments are challenges to show where a non-arbitrary boundary lies [Vetter]
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / c. System D
Deontic modalities are 'ought-to-be', for sentences, and 'ought-to-do' for predicates [Vetter]
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / h. System S5
S5 is undesirable, as it prevents necessities from having contingent grounds [Vetter]
4. Formal Logic / D. Modal Logic ML / 7. Barcan Formula
The Barcan formula endorses either merely possible things, or makes the unactualised impossible [Vetter]
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 / 1. Nature of Existence
The world is either a whole made of its parts, or a container which contains its parts [Vetter]
7. Existence / C. Structure of Existence / 1. Grounding / b. Relata of grounding
Grounding can be between objects ('relational'), or between sentences ('operational') [Vetter]
7. Existence / C. Structure of Existence / 5. Supervenience / d. Humean supervenience
The Humean supervenience base entirely excludes modality [Vetter]
8. Modes of Existence / B. Properties / 3. Types of Properties
A determinate property must be a unique instance of the determinable class [Vetter]
8. Modes of Existence / C. Powers and Dispositions / 6. Dispositions / a. Dispositions
I have an 'iterated ability' to learn the violin - that is, the ability to acquire that ability [Vetter]
8. Modes of Existence / C. Powers and Dispositions / 6. Dispositions / c. Dispositions as conditional
We should think of dispositions as 'to do' something, not as 'to do something, if ....' [Vetter]
8. Modes of Existence / C. Powers and Dispositions / 6. Dispositions / d. Dispositions as occurrent
Nomological dispositions (unlike ordinary ones) have to be continually realised [Vetter]
8. Modes of Existence / C. Powers and Dispositions / 7. Against Powers
How can spatiotemporal relations be understood in dispositional terms? [Vetter]
9. Objects / E. Objects over Time / 12. Origin as Essential
Why does origin matter more than development; why are some features of origin more important? [Vetter]
We take origin to be necessary because we see possibilities as branches from actuality [Vetter]
10. Modality / A. Necessity / 2. Nature of Necessity
The modern revival of necessity and possibility treated them as special cases of quantification [Vetter]
It is necessary that p means that nothing has the potentiality for not-p [Vetter]
10. Modality / B. Possibility / 1. Possibility
Possibilities are potentialities of actual things, but abstracted from their location [Vetter]
All possibility is anchored in the potentiality of individual objects [Vetter]
Possibility is a generalised abstraction from the potentiality of its bearer [Vetter]
10. Modality / B. Possibility / 4. Potentiality
A potentiality may not be a disposition, but dispositions are strong potentialities [Vetter, by Friend/Kimpton-Nye]
Potentiality does the explaining in metaphysics; we don't explain it away or reduce it [Vetter]
Potentiality logic is modal system T. Stronger systems collapse iterations, and necessitate potentials [Vetter]
Potentiality is the common genus of dispositions, abilities, and similar properties [Vetter]
There are potentialities 'to ...', but possibilities are 'that ....'. [Vetter]
Potentialities may be too weak to count as 'dispositions' [Vetter]
Water has a potentiality to acquire a potentiality to break (by freezing) [Vetter]
10. Modality / E. Possible worlds / 2. Nature of Possible Worlds / c. Worlds as propositions
If worlds are sets of propositions, how do we know which propositions are genuinely possible? [Vetter]
10. Modality / E. Possible worlds / 3. Transworld Objects / e. Possible Objects
Are there possible objects which nothing has ever had the potentiality to produce? [Vetter]
12. Knowledge Sources / C. Rationalism / 1. Rationalism
Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro]
14. Science / D. Explanation / 2. Types of Explanation / a. Types of explanation
Explanations by disposition are more stable and reliable than those be external circumstances [Vetter]
Grounding is a kind of explanation, suited to metaphysics [Vetter]
24. Political Theory / A. Basis of a State / 1. A People / b. The natural life
All countries are in a mutual state of nature [Locke]
We are not created for solitude, but are driven into society by our needs [Locke]
24. Political Theory / A. Basis of a State / 3. Natural Values / a. Natural freedom
In nature men can dispose of possessions and their persons in any way that is possible [Locke]
24. Political Theory / A. Basis of a State / 3. Natural Values / b. Natural equality
There is no subjection in nature, and all creatures of the same species are equal [Locke]
24. Political Theory / A. Basis of a State / 3. Natural Values / c. Natural rights
The rational law of nature says we are all equal and independent, and should show mutual respect [Locke]
The animals and fruits of the earth belong to mankind [Locke]
There is a natural right to inheritance within a family [Locke]
24. Political Theory / B. Nature of a State / 1. Purpose of a State
Politics is the right to make enforceable laws to protect property and the state, for the common good [Locke]
24. Political Theory / B. Nature of a State / 2. State Legitimacy / c. Social contract
The Second Treatise explores the consequences of the contractual view of the state [Locke, by Scruton]
A society only begins if there is consent of all the individuals to join it [Locke]
If anyone enjoys the benefits of government (even using a road) they give tacit assent to its laws [Locke]
A politic society is created from a state of nature by a unanimous agreement [Locke]
24. Political Theory / B. Nature of a State / 2. State Legitimacy / d. General will
A single will creates the legislature, which is duty-bound to preserve that will [Locke]
24. Political Theory / B. Nature of a State / 4. Citizenship
Children are not born into citizenship of a state [Locke]
Anyone who enjoys the benefits of a state has given tacit consent to be part of it [Locke]
You can only become an actual member of a commonwealth by an express promise [Locke]
24. Political Theory / C. Ruling a State / 2. Leaders / b. Monarchy
Absolute monarchy is inconsistent with civil society [Locke]
24. Political Theory / C. Ruling a State / 2. Leaders / c. Despotism
The idea that absolute power improves mankind is confuted by history [Locke]
Despotism is arbitrary power to kill, based neither on natural equality, nor any social contract [Locke]
People stripped of their property are legitimately subject to despotism [Locke]
Legitimate prisoners of war are subject to despotism, because that continues the state of war [Locke]
24. Political Theory / C. Ruling a State / 3. Government / b. Legislature
Even the legislature must be preceded by a law which gives it power to make laws [Locke]
24. Political Theory / C. Ruling a State / 3. Government / c. Executive
The executive must not be the legislature, or they may exempt themselves from laws [Locke]
24. Political Theory / C. Ruling a State / 4. Changing the State / c. Revolution
Any obstruction to the operation of the legislature can be removed forcibly by the people [Locke]
Rebelling against an illegitimate power is no sin [Locke]
If legislators confiscate property, or enslave people, they are no longer owed obedience [Locke]
24. Political Theory / D. Ideologies / 5. Democracy / a. Nature of democracy
Unanimous consent makes a united community, which is then ruled by the majority [Locke]
The people have supreme power, to depose a legislature which has breached their trust [Locke]
25. Social Practice / A. Freedoms / 1. Slavery
A master forfeits ownership of slaves he abandons [Locke]
If you try to enslave me, you have declared war on me [Locke]
Slaves captured in a just war have no right to property, so are not part of civil society [Locke]
25. Social Practice / A. Freedoms / 6. Political freedom
Freedom is not absence of laws, but living under laws arrived at by consent [Locke]
25. Social Practice / B. Equalities / 4. Economic equality
All value depends on the labour involved [Locke]
25. Social Practice / C. Rights / 3. Alienating rights
We all own our bodies, and the work we do is our own [Locke]
There is only a civil society if the members give up all of their natural executive rights [Locke]
25. Social Practice / C. Rights / 4. Property rights
Fountain water is everyone's, but a drawn pitcher of water has an owner [Locke]
Locke (and Marx) held that ownership of objects is a natural relation, based on the labour put into it [Locke, by Fogelin]
Locke says 'mixing of labour' entitles you to land, as well as nuts and berries [Wolff,J on Locke]
A man's labour gives ownership rights - as long as there are fair shares for all [Locke]
If a man mixes his labour with something in Nature, he thereby comes to own it [Locke]
Gathering natural fruits gives ownership; the consent of other people is irrelevant [Locke]
Mixing labour with a thing bestows ownership - as long as the thing is not wasted [Locke]
A man owns land if he cultivates it, to the limits of what he needs [Locke]
Soldiers can be commanded to die, but not to hand over their money [Locke]
25. Social Practice / D. Justice / 2. The Law / a. Legal system
The aim of law is not restraint, but to make freedom possible [Locke]
25. Social Practice / D. Justice / 2. The Law / c. Natural law
It is only by a law of Nature that we can justify punishing foreigners [Locke]
25. Social Practice / D. Justice / 3. Punishment / a. Right to punish
Punishment should make crime a bad bargain, leading to repentance and deterrence [Locke]
Self-defence is natural, but not the punishment of superiors by inferiors [Locke]
Reparation and restraint are the only justifications for punishment [Locke]
25. Social Practice / E. Policies / 4. Taxation
The consent of the people is essential for any tax [Locke]
26. Natural Theory / D. Laws of Nature / 5. Laws from Universals
The view that laws are grounded in substance plus external necessity doesn't suit dispositionalism [Vetter]
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / b. Scientific necessity
Dispositional essentialism allows laws to be different, but only if the supporting properties differ [Vetter]
27. Natural Reality / D. Time / 1. Nature of Time / f. Eternalism
If time is symmetrical between past and future, why do they look so different? [Vetter]
27. Natural Reality / D. Time / 1. Nature of Time / h. Presentism
Presentists explain cross-temporal relations using surrogate descriptions [Vetter]