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All the ideas for 'fragments/reports', 'Naturalism in Mathematics' and 'Potentiality'

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62 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]
4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / b. Terminology of ST
'Forcing' can produce new models of ZFC from old models [Maddy]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
A Large Cardinal Axiom would assert ever-increasing stages in the hierarchy [Maddy]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / f. Axiom of Infinity V
Axiom of Infinity: completed infinite collections can be treated mathematically [Maddy]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / i. Axiom of Foundation VIII
The Axiom of Foundation says every set exists at a level in the set hierarchy [Maddy]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / p. Axiom of Reducibility
Axiom of Reducibility: propositional functions are extensionally predicative [Maddy]
5. Theory of Logic / E. Structures of Logic / 1. Logical Form
'Propositional functions' are propositions with a variable as subject or predicate [Maddy]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / d. Actual infinite
Completed infinities resulted from giving foundations to calculus [Maddy]
Cantor and Dedekind brought completed infinities into mathematics [Maddy]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / i. Cardinal infinity
Infinity has degrees, and large cardinals are the heart of set theory [Maddy]
For any cardinal there is always a larger one (so there is no set of all sets) [Maddy]
An 'inaccessible' cardinal cannot be reached by union sets or power sets [Maddy]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / l. Limits
Theorems about limits could only be proved once the real numbers were understood [Maddy]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers
The extension of concepts is not important to me [Maddy]
In the ZFC hierarchy it is impossible to form Frege's set of all three-element sets [Maddy]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / e. Caesar problem
Frege solves the Caesar problem by explicitly defining each number [Maddy]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
Making set theory foundational to mathematics leads to very fruitful axioms [Maddy]
Unified set theory gives a final court of appeal for mathematics [Maddy]
Set theory brings mathematics into one arena, where interrelations become clearer [Maddy]
Mathematics rests on the logic of proofs, and on the set theoretic axioms [Maddy]
Identifying geometric points with real numbers revealed the power of set theory [Maddy]
The line of rationals has gaps, but set theory provided an ordered continuum [Maddy]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / b. Indispensability of mathematics
Maybe applications of continuum mathematics are all idealisations [Maddy]
Scientists posit as few entities as possible, but set theorist posit as many as possible [Maddy]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / c. Neo-logicism
We can get arithmetic directly from HP; Law V was used to get HP from the definition of number [Maddy]
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]
7. Existence / D. Theories of Reality / 11. Ontological Commitment / e. Ontological commitment problems
The theoretical indispensability of atoms did not at first convince scientists that they were real [Maddy]
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
Potentiality is the common genus of dispositions, abilities, and similar properties [Vetter]
Water has a potentiality to acquire a potentiality to break (by freezing) [Vetter]
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]
Potentialities may be too weak to count as 'dispositions' [Vetter]
There are potentialities 'to ...', but possibilities are 'that ....'. [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]
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]
15. Nature of Minds / C. Capacities of Minds / 6. Idealisation
Science idealises the earth's surface, the oceans, continuities, and liquids [Maddy]
26. Natural Theory / A. Speculations on Nature / 5. Infinite in Nature
Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius]
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]
27. Natural Reality / G. Biology / 3. Evolution
Archelaus said life began in a primeval slime [Archelaus, by Schofield]