Combining Texts

All the ideas for 'Mathematical Methods in Philosophy', 'A Structural Account of Mathematics' and 'Potentiality'

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60 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 / 3. Types of Set / b. Empty (Null) Set
Realists about sets say there exists a null set in the real world, with no members [Chihara]
We only know relational facts about the empty set, but nothing intrinsic [Chihara]
In simple type theory there is a hierarchy of null sets [Chihara]
The null set is a structural position which has no other position in membership relation [Chihara]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / c. Unit (Singleton) Sets
What is special about Bill Clinton's unit set, in comparison with all the others? [Chihara]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / a. Sets as existing
The set theorist cannot tell us what 'membership' is [Chihara]
4. Formal Logic / F. Set Theory ST / 7. Natural Sets
ZFU refers to the physical world, when it talks of 'urelements' [Chihara]
4. Formal Logic / F. Set Theory ST / 8. Critique of Set Theory
A pack of wolves doesn't cease when one member dies [Chihara]
5. Theory of Logic / A. Overview of Logic / 9. Philosophical Logic
Three stages of philosophical logic: syntactic (1905-55), possible worlds (1963-85), widening (1990-) [Horsten/Pettigrew]
5. Theory of Logic / E. Structures of Logic / 1. Logical Form
Logical formalization makes concepts precise, and also shows their interrelation [Horsten/Pettigrew]
5. Theory of Logic / E. Structures of Logic / 6. Relations in Logic
The mathematics of relations is entirely covered by ordered pairs [Chihara]
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
Models are sets with functions and relations, and truth built up from the components [Horsten/Pettigrew]
5. Theory of Logic / K. Features of Logics / 2. Consistency
Sentences are consistent if they can all be true; for Frege it is that no contradiction can be deduced [Chihara]
6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry
Analytic geometry gave space a mathematical structure, which could then have axioms [Chihara]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / c. Nominalist structuralism
We can replace existence of sets with possibility of constructing token sentences [Chihara, by MacBride]
7. Existence / A. Nature of Existence / 1. Nature of Existence
If 'exist' doesn't express a property, we can hardly ask for its essence [Horsten/Pettigrew]
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
If a successful theory confirms mathematics, presumably a failed theory disconfirms it? [Chihara]
No scientific explanation would collapse if mathematical objects were shown not to exist [Chihara]
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 / 1. Possible Worlds / a. Possible worlds
A Tarskian model can be seen as a possible state of affairs [Horsten/Pettigrew]
The 'spheres model' was added to possible worlds, to cope with counterfactuals [Horsten/Pettigrew]
10. Modality / E. Possible worlds / 1. Possible Worlds / b. Impossible worlds
Epistemic logic introduced impossible worlds [Horsten/Pettigrew]
10. Modality / E. Possible worlds / 1. Possible Worlds / e. Against possible worlds
Possible worlds models contain sets of possible worlds; this is a large metaphysical commitment [Horsten/Pettigrew]
Using possible worlds for knowledge and morality may be a step too far [Horsten/Pettigrew]
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]
18. Thought / E. Abstraction / 7. Abstracta by Equivalence
I prefer the open sentences of a Constructibility Theory, to Platonist ideas of 'equivalence classes' [Chihara]
19. Language / B. Reference / 3. Direct Reference / b. Causal reference
Mathematical entities are causally inert, so the causal theory of reference won't work for them [Chihara]
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 / B. Modern Physics / 4. Standard Model / a. Concept of matter
'Gunk' is an individual possessing no parts that are atoms [Chihara]
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]