Combining Texts

All the ideas for 'The Evolution of Logic', 'Repetition' and 'New work for a theory of universals'

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80 ideas

1. Philosophy / C. History of Philosophy / 4. Later European Philosophy / c. Eighteenth century philosophy
We are all post-Kantians, because he set the current agenda for philosophy [Hart,WD]
1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / d. Philosophy as puzzles
The problems are the monuments of philosophy [Hart,WD]
1. Philosophy / F. Analytic Philosophy / 4. Conceptual Analysis
In addition to analysis of a concept, one can deny it, or accept it as primitive [Lewis]
1. Philosophy / F. Analytic Philosophy / 6. Logical Analysis
To study abstract problems, some knowledge of set theory is essential [Hart,WD]
3. Truth / A. Truth Problems / 8. Subjective Truth
Subjective truth can only be sustained by repetition [Kierkegaard, by Carlisle]
3. Truth / C. Correspondence Truth / 2. Correspondence to Facts
Tarski showed how we could have a correspondence theory of truth, without using 'facts' [Hart,WD]
3. Truth / F. Semantic Truth / 1. Tarski's Truth / b. Satisfaction and truth
Truth for sentences is satisfaction of formulae; for sentences, either all sequences satisfy it (true) or none do [Hart,WD]
3. Truth / F. Semantic Truth / 2. Semantic Truth
A first-order language has an infinity of T-sentences, which cannot add up to a definition of truth [Hart,WD]
4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / c. Derivation rules of PL
Conditional Proof: infer a conditional, if the consequent can be deduced from the antecedent [Hart,WD]
4. Formal Logic / C. Predicate Calculus PC / 2. Tools of Predicate Calculus / e. Existential quantifier ∃
∃y... is read as 'There exists an individual, call it y, such that...', and not 'There exists a y such that...' [Hart,WD]
4. Formal Logic / F. Set Theory ST / 1. Set Theory
Set theory articulates the concept of order (through relations) [Hart,WD]
Nowadays ZFC and NBG are the set theories; types are dead, and NF is only useful for the whole universe [Hart,WD]
4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / a. Symbols of ST
∈ relates across layers, while ⊆ relates within layers [Hart,WD]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set
Without the empty set we could not form a∩b without checking that a and b meet [Hart,WD]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / i. Axiom of Foundation VIII
In the modern view, foundation is the heart of the way to do set theory [Hart,WD]
Foundation Axiom: an nonempty set has a member disjoint from it [Hart,WD]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
We can choose from finite and evident sets, but not from infinite opaque ones [Hart,WD]
With the Axiom of Choice every set can be well-ordered [Hart,WD]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / o. Axiom of Constructibility V = L
If we accept that V=L, it seems to settle all the open questions of set theory [Hart,WD]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / d. Naïve logical sets
Naïve set theory has trouble with comprehension, the claim that every predicate has an extension [Hart,WD]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / e. Iterative sets
The iterative conception may not be necessary, and may have fixed points or infinitely descending chains [Hart,WD]
4. Formal Logic / F. Set Theory ST / 6. Ordering in Sets
A 'partial ordering' is irreflexive and transitive; the sets are ordered, but not the subsets [Hart,WD]
A partial ordering becomes 'total' if any two members of its field are comparable [Hart,WD]
'Well-ordering' must have a least member, so it does the natural numbers but not the integers [Hart,WD]
Von Neumann defines α<β as α∈β [Hart,WD]
4. Formal Logic / F. Set Theory ST / 8. Critique of Set Theory
Maybe sets should be rethought in terms of the even more basic categories [Hart,WD]
5. Theory of Logic / G. Quantification / 3. Objectual Quantification
The universal quantifier can't really mean 'all', because there is no universal set [Hart,WD]
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
Modern model theory begins with the proof of Los's Conjecture in 1962 [Hart,WD]
Model theory studies how set theory can model sets of sentences [Hart,WD]
Model theory is mostly confined to first-order theories [Hart,WD]
Models are ways the world might be from a first-order point of view [Hart,WD]
5. Theory of Logic / K. Features of Logics / 6. Compactness
First-order logic is 'compact': consequences of a set are consequences of a finite subset [Hart,WD]
5. Theory of Logic / L. Paradox / 4. Paradoxes in Logic / c. Berry's paradox
Berry's Paradox: we succeed in referring to a number, with a term which says we can't do that [Hart,WD]
5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / c. Burali-Forti's paradox
The Burali-Forti paradox is a crisis for Cantor's ordinals [Hart,WD]
5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / a. The Liar paradox
The machinery used to solve the Liar can be rejigged to produce a new Liar [Hart,WD]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
The less-than relation < well-orders, and partially orders, and totally orders the ordinal numbers [Hart,WD]
The axiom of infinity with separation gives a least limit ordinal ω [Hart,WD]
There are at least as many infinite cardinals as transfinite ordinals (because they will map) [Hart,WD]
Von Neumann's ordinals generalise into the transfinite better, because Zermelo's ω is a singleton [Hart,WD]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
19th century arithmetization of analysis isolated the real numbers from geometry [Hart,WD]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
We can establish truths about infinite numbers by means of induction [Hart,WD]
6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry
Euclid has a unique parallel, spherical geometry has none, and saddle geometry has several [Hart,WD]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
Mathematics makes existence claims, but philosophers usually say those are never analytic [Hart,WD]
7. Existence / C. Structure of Existence / 2. Reduction
Supervenience is reduction without existence denials, ontological priorities, or translatability [Lewis]
7. Existence / C. Structure of Existence / 5. Supervenience / c. Significance of supervenience
A supervenience thesis is a denial of independent variation [Lewis]
7. Existence / C. Structure of Existence / 8. Stuff / a. Pure stuff
Mass words do not have plurals, or numerical adjectives, or use 'fewer' [Hart,WD]
7. Existence / D. Theories of Reality / 6. Physicalism
Materialism is (roughly) that two worlds cannot differ without differing physically [Lewis]
8. Modes of Existence / B. Properties / 1. Nature of Properties
Universals are wholly present in their instances, whereas properties are spread around [Lewis]
8. Modes of Existence / B. Properties / 5. Natural Properties
Natural properties figure in the analysis of similarity in intrinsic respects [Lewis, by Oliver]
Lewisian natural properties fix reference of predicates, through a principle of charity [Lewis, by Hawley]
Objects are demarcated by density and chemistry, and natural properties belong in what is well demarcated [Lewis]
Reference partly concerns thought and language, partly eligibility of referent by natural properties [Lewis]
Natural properties tend to belong to well-demarcated things, typically loci of causal chains [Lewis]
For us, a property being natural is just an aspect of its featuring in the contents of our attitudes [Lewis]
All perfectly natural properties are intrinsic [Lewis, by Lewis]
Natural properties fix resemblance and powers, and are picked out by universals [Lewis]
8. Modes of Existence / B. Properties / 6. Categorical Properties
Lewis says properties are sets of actual and possible objects [Lewis, by Heil]
Any class of things is a property, no matter how whimsical or irrelevant [Lewis]
8. Modes of Existence / B. Properties / 10. Properties as Predicates
There are far more properties than any brain could ever encodify [Lewis]
We need properties as semantic values for linguistic expressions [Lewis]
8. Modes of Existence / B. Properties / 11. Properties as Sets
Properties are classes of possible and actual concrete particulars [Lewis, by Koslicki]
8. Modes of Existence / C. Powers and Dispositions / 3. Powers as Derived
Lewisian properties have powers because of their relationships to other properties [Lewis, by Hawthorne]
8. Modes of Existence / C. Powers and Dispositions / 7. Against Powers
Most properties are causally irrelevant, and we can't spot the relevant ones. [Lewis]
8. Modes of Existence / D. Universals / 1. Universals
I suspend judgements about universals, but their work must be done [Lewis]
8. Modes of Existence / D. Universals / 2. Need for Universals
Physics aims to discover which universals actually exist [Lewis, by Moore,AW]
8. Modes of Existence / E. Nominalism / 1. Nominalism / b. Nominalism about universals
The One over Many problem (in predication terms) deserves to be neglected (by ostriches) [Lewis]
8. Modes of Existence / E. Nominalism / 5. Class Nominalism
To have a property is to be a member of a class, usually a class of things [Lewis]
Class Nominalism and Resemblance Nominalism are pretty much the same [Lewis]
12. Knowledge Sources / A. A Priori Knowledge / 2. Self-Evidence
Fregean self-evidence is an intrinsic property of basic truths, rules and definitions [Hart,WD]
12. Knowledge Sources / A. A Priori Knowledge / 11. Denying the A Priori
The failure of key assumptions in geometry, mereology and set theory throw doubt on the a priori [Hart,WD]
17. Mind and Body / E. Mind as Physical / 1. Physical Mind
Psychophysical identity implies the possibility of idealism or panpsychism [Lewis]
18. Thought / D. Concepts / 3. Ontology of Concepts / c. Fregean concepts
The Fregean concept of GREEN is a function assigning true to green things, and false to the rest [Hart,WD]
19. Language / F. Communication / 6. Interpreting Language / c. Principle of charity
A sophisticated principle of charity sometimes imputes error as well as truth [Lewis]
We need natural properties in order to motivate the principle of charity [Lewis]
23. Ethics / F. Existentialism / 8. Eternal Recurrence
Life is a repetition when what has been now becomes [Kierkegaard]
26. Natural Theory / C. Causation / 9. General Causation / c. Counterfactual causation
Counterfactuals 'backtrack' if a different present implies a different past [Lewis]
Causal counterfactuals must avoid backtracking, to avoid epiphenomena and preemption [Lewis]
26. Natural Theory / D. Laws of Nature / 1. Laws of Nature
Physics discovers laws and causal explanations, and also the natural properties required [Lewis]
Physics aims for a list of natural properties [Lewis]
26. Natural Theory / D. Laws of Nature / 4. Regularities / b. Best system theory
A law of nature is any regularity that earns inclusion in the ideal system [Lewis]