Combining Texts

All the ideas for 'fragments/reports', 'Plurals and Complexes' and 'Properties'

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43 ideas

2. Reason / C. Styles of Reason / 1. Dialectic
Like spiderswebs, dialectical arguments are clever but useless [Ariston, by Diog. Laertius]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
The Axiom of Choice is a non-logical principle of set-theory [Hossack]
The Axiom of Choice guarantees a one-one correspondence from sets to ordinals [Hossack]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / e. Iterative sets
In the iterative conception of sets, they form a natural hierarchy [Swoyer]
4. Formal Logic / F. Set Theory ST / 8. Critique of Set Theory
Maybe we reduce sets to ordinals, rather than the other way round [Hossack]
4. Formal Logic / G. Formal Mereology / 3. Axioms of Mereology
Extensional mereology needs two definitions and two axioms [Hossack]
5. Theory of Logic / E. Structures of Logic / 1. Logical Form
Logical Form explains differing logical behaviour of similar sentences [Swoyer]
5. Theory of Logic / F. Referring in Logic / 2. Descriptions / b. Definite descriptions
Plural definite descriptions pick out the largest class of things that fit the description [Hossack]
5. Theory of Logic / G. Quantification / 6. Plural Quantification
Plural reference will refer to complex facts without postulating complex things [Hossack]
Plural reference is just an abbreviation when properties are distributive, but not otherwise [Hossack]
A plural comprehension principle says there are some things one of which meets some condition [Hossack]
5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / d. Russell's paradox
Plural language can discuss without inconsistency things that are not members of themselves [Hossack]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
The theory of the transfinite needs the ordinal numbers [Hossack]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
I take the real numbers to be just lengths [Hossack]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / e. Peano arithmetic 2nd-order
A plural language gives a single comprehensive induction axiom for arithmetic [Hossack]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
In arithmetic singularists need sets as the instantiator of numeric properties [Hossack]
Set theory is the science of infinity [Hossack]
7. Existence / C. Structure of Existence / 5. Supervenience / a. Nature of supervenience
Supervenience is nowadays seen as between properties, rather than linguistic [Swoyer]
7. Existence / D. Theories of Reality / 4. Anti-realism
Anti-realists can't explain different methods to measure distance [Swoyer]
7. Existence / D. Theories of Reality / 11. Ontological Commitment / a. Ontological commitment
We are committed to a 'group' of children, if they are sitting in a circle [Hossack]
8. Modes of Existence / B. Properties / 1. Nature of Properties
Can properties have parts? [Swoyer]
If a property such as self-identity can only be in one thing, it can't be a universal [Swoyer]
8. Modes of Existence / B. Properties / 5. Natural Properties
There are only first-order properties ('red'), and none of higher-order ('coloured') [Swoyer]
8. Modes of Existence / B. Properties / 11. Properties as Sets
The best-known candidate for an identity condition for properties is necessary coextensiveness [Swoyer]
8. Modes of Existence / D. Universals / 1. Universals
Various attempts are made to evade universals being wholly present in different places [Swoyer]
8. Modes of Existence / E. Nominalism / 4. Concept Nominalism
Conceptualism says words like 'honesty' refer to concepts, not to properties [Swoyer]
9. Objects / A. Existence of Objects / 2. Abstract Objects / a. Nature of abstracta
If properties are abstract objects, then their being abstract exemplifies being abstract [Swoyer]
9. Objects / C. Structure of Objects / 5. Composition of an Object
Complex particulars are either masses, or composites, or sets [Hossack]
The relation of composition is indispensable to the part-whole relation for individuals [Hossack]
9. Objects / C. Structure of Objects / 8. Parts of Objects / c. Wholes from parts
The fusion of five rectangles can decompose into more than five parts that are rectangles [Hossack]
Leibniz's Law argues against atomism - water is wet, unlike water molecules [Hossack]
10. Modality / E. Possible worlds / 1. Possible Worlds / e. Against possible worlds
One might hope to reduce possible worlds to properties [Swoyer]
12. Knowledge Sources / D. Empiricism / 5. Empiricism Critique
Extreme empiricists can hardly explain anything [Swoyer]
18. Thought / A. Modes of Thought / 1. Thought
A thought can refer to many things, but only predicate a universal and affirm a state of affairs [Hossack]
18. Thought / C. Content / 8. Intension
Intensions are functions which map possible worlds to sets of things denoted by an expression [Swoyer]
18. Thought / D. Concepts / 4. Structure of Concepts / e. Concepts from exemplars
Research suggests that concepts rely on typical examples [Swoyer]
19. Language / C. Assigning Meanings / 3. Predicates
The F and G of logic cover a huge range of natural language combinations [Swoyer]
19. Language / D. Propositions / 2. Abstract Propositions / a. Propositions as sense
Maybe a proposition is just a property with all its places filled [Swoyer]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / f. The Mean
The chief good is indifference to what lies midway between virtue and vice [Ariston, by Diog. Laertius]
23. Ethics / D. Deontological Ethics / 1. Deontology
Ariston says rules are useless for the virtuous and the non-virtuous [Ariston, by Annas]
26. Natural Theory / D. Laws of Nature / 4. Regularities / a. Regularity theory
If laws are mere regularities, they give no grounds for future prediction [Swoyer]
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / a. Scientific essentialism
Two properties can have one power, and one property can have two powers [Swoyer]
27. Natural Reality / C. Space / 2. Space
We could ignore space, and just talk of the shape of matter [Hossack]