Combining Texts

All the ideas for 'The Philosophy of Philosophy', 'Dion and Theon: an essentialist solution' and 'Plurals and Complexes'

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42 ideas

1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / e. Philosophy as reason
Progress in philosophy is incremental, not an immature seeking after drama [Williamson]
3. Truth / C. Correspondence Truth / 3. Correspondence Truth critique
Correspondence to the facts is a bad account of analytic truth [Williamson]
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 / D. Theories of Reality / 4. Anti-realism
The realist/anti-realist debate is notoriously obscure and fruitless [Williamson]
7. Existence / D. Theories of Reality / 10. Vagueness / b. Vagueness of reality
There cannot be vague objects, so there may be no such thing as a mountain [Williamson]
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 / A. Existence of Objects / 5. Individuation / e. Individuation by kind
Persistence conditions cannot contradict, so there must be a 'dominant sortal' [Burke,M, by Hawley]
The 'dominant' of two coinciding sortals is the one that entails the widest range of properties [Burke,M, by Sider]
9. Objects / B. Unity of Objects / 1. Unifying an Object / b. Unifying aggregates
'The rock' either refers to an object, or to a collection of parts, or to some stuff [Burke,M, by Wasserman]
9. Objects / B. Unity of Objects / 3. Unity Problems / b. Cat and its tail
Tib goes out of existence when the tail is lost, because Tib was never the 'cat' [Burke,M, by Sider]
9. Objects / B. Unity of Objects / 3. Unity Problems / c. Statue and clay
Sculpting a lump of clay destroys one object, and replaces it with another one [Burke,M, by Wasserman]
Burke says when two object coincide, one of them is destroyed in the process [Burke,M, by Hawley]
Maybe the clay becomes a different lump when it becomes a statue [Burke,M, by Koslicki]
9. Objects / B. Unity of Objects / 3. Unity Problems / d. Coincident objects
Two entities can coincide as one, but only one of them (the dominant sortal) fixes persistence conditions [Burke,M, by Sider]
9. Objects / B. Unity of Objects / 3. Unity Problems / e. Vague objects
Common sense and classical logic are often simultaneously abandoned in debates on vagueness [Williamson]
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]
10. Modality / D. Knowledge of Modality / 1. A Priori Necessary
Modal thinking isn't a special intuition; it is part of ordinary counterfactual thinking [Williamson]
10. Modality / D. Knowledge of Modality / 4. Conceivable as Possible / a. Conceivable as possible
Williamson can't base metaphysical necessity on the psychology of causal counterfactuals [Lowe on Williamson]
We scorn imagination as a test of possibility, forgetting its role in counterfactuals [Williamson]
12. Knowledge Sources / A. A Priori Knowledge / 2. Self-Evidence
There are 'armchair' truths which are not a priori, because experience was involved [Williamson]
12. Knowledge Sources / E. Direct Knowledge / 2. Intuition
Intuition is neither powerful nor vacuous, but reveals linguistic or conceptual competence [Williamson]
When analytic philosophers run out of arguments, they present intuitions as their evidence [Williamson]
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]
19. Language / A. Nature of Meaning / 6. Meaning as Use
You might know that the word 'gob' meant 'mouth', but not be competent to use it [Williamson]
24. Political Theory / B. Nature of a State / 5. Culture
If languages are intertranslatable, and cognition is innate, then cultures are all similar [Williamson]
27. Natural Reality / C. Space / 2. Space
We could ignore space, and just talk of the shape of matter [Hossack]