Combining Texts

All the ideas for 'Equality and Partiality', 'Plurals and Complexes' and 'Event Causation: counterfactual analysis'

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35 ideas

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 / 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 / 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 / B. Change in Existence / 4. Events / a. Nature of events
Maybe each event has only one possible causal history [Bennett]
Maybe an event's time of occurrence is essential to it [Bennett]
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]
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
Leibniz's Law argues against atomism - water is wet, unlike water molecules [Hossack]
The fusion of five rectangles can decompose into more than five parts that are rectangles [Hossack]
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]
20. Action / C. Motives for Action / 5. Action Dilemmas / c. Omissions
Noninterference requires justification as much as interference does [Nagel]
22. Metaethics / A. Ethics Foundations / 1. Nature of Ethics / a. Preconditions for ethics
Morality must be motivating, and not because of pre-moral motives [Nagel]
23. Ethics / B. Contract Ethics / 6. Game Theory
Game theory misses out the motivation arising from the impersonal standpoint [Nagel]
23. Ethics / D. Deontological Ethics / 3. Universalisability
In ethics we abstract from our identity, but not from our humanity [Nagel]
23. Ethics / D. Deontological Ethics / 4. Categorical Imperative
I can only universalise a maxim if everyone else could also universalise it [Nagel]
24. Political Theory / D. Ideologies / 6. Liberalism / c. Liberal equality
A legitimate system is one accepted as both impartial and reasonably partial [Nagel]
25. Social Practice / B. Equalities / 2. Political equality
Democracy is opposed to equality, if the poor are not a majority [Nagel]
26. Natural Theory / C. Causation / 1. Causation
Delaying a fire doesn't cause it, but hastening it might [Bennett]
Either cause and effect are subsumed under a conditional because of properties, or it is counterfactual [Bennett]
26. Natural Theory / C. Causation / 2. Types of cause
Causes are between events ('the explosion') or between facts/states of affairs ('a bomb dropped') [Bennett]
26. Natural Theory / C. Causation / 9. General Causation / c. Counterfactual causation
The full counterfactual story asserts a series of events, because counterfactuals are not transitive [Bennett]
A counterfactual about an event implies something about the event's essence [Bennett]
27. Natural Reality / C. Space / 2. Space
We could ignore space, and just talk of the shape of matter [Hossack]