Combining Texts

All the ideas for 'The Evolution of Logic', 'A Future for Presentism' and 'Epistemology Naturalized'

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67 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 / 6. Logical Analysis
To study abstract problems, some knowledge of set theory is essential [Hart,WD]
2. Reason / B. Laws of Thought / 2. Sufficient Reason
Is Sufficient Reason self-refuting (no reason to accept it!), or is it a legitimate explanatory tool? [Bourne]
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]
3. Truth / H. Deflationary Truth / 1. Redundant Truth
The redundancy theory conflates metalinguistic bivalence with object-language excluded middle [Bourne]
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
With the Axiom of Choice every set can be well-ordered [Hart,WD]
We can choose from finite and evident sets, but not from infinite opaque ones [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
'Well-ordering' must have a least member, so it does the natural numbers but not the integers [Hart,WD]
A partial ordering becomes 'total' if any two members of its field are comparable [Hart,WD]
A 'partial ordering' is irreflexive and transitive; the sets are ordered, but not the subsets [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
Models are ways the world might be from a first-order point of view [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]
Modern model theory begins with the proof of Los's Conjecture in 1962 [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]
There are at least as many infinite cardinals as transfinite ordinals (because they will map) [Hart,WD]
The axiom of infinity with separation gives a least limit ordinal ω [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 reduces to set theory (which is a bit vague and unobvious), but not to logic proper [Quine]
Mathematics makes existence claims, but philosophers usually say those are never analytic [Hart,WD]
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]
8. Modes of Existence / A. Relations / 1. Nature of Relations
It is a necessary condition for the existence of relations that both of the relata exist [Bourne]
All relations between spatio-temporal objects are either spatio-temporal, or causal [Bourne]
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]
13. Knowledge Criteria / C. External Justification / 9. Naturalised Epistemology
You can't reduce epistemology to psychology, because that presupposes epistemology [Maund on Quine]
We should abandon a search for justification or foundations, and focus on how knowledge is acquired [Quine, by Davidson]
If we abandon justification and normativity in epistemology, we must also abandon knowledge [Kim on Quine]
Without normativity, naturalized epistemology isn't even about beliefs [Kim on Quine]
Epistemology is a part of psychology, studying how our theories relate to our evidence [Quine]
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 / A. Nature of Meaning / 1. Meaning
Inculcations of meanings of words rests ultimately on sensory evidence [Quine]
19. Language / E. Analyticity / 4. Analytic/Synthetic Critique
In observation sentences, we could substitute community acceptance for analyticity [Quine]
27. Natural Reality / B. Modern Physics / 1. Relativity / a. Special relativity
The idea of simultaneity in Special Relativity is full of verificationist assumptions [Bourne]
Relativity denies simultaneity, so it needs past, present and future (unlike Presentism) [Bourne]
27. Natural Reality / D. Time / 1. Nature of Time / a. Absolute time
Special Relativity allows an absolute past, future, elsewhere and simultaneity [Bourne]
27. Natural Reality / D. Time / 1. Nature of Time / g. Growing block
No-Futurists believe in past and present, but not future, and say the world grows as facts increase [Bourne]
27. Natural Reality / D. Time / 1. Nature of Time / h. Presentism
How can presentists talk of 'earlier than', and distinguish past from future? [Bourne]
Presentism seems to deny causation, because the cause and the effect can never coexist [Bourne]
Since presentists treat the presentness of events as basic, simultaneity should be define by that means [Bourne]
27. Natural Reality / D. Time / 2. Passage of Time / d. Time series
Time is tensed or tenseless; the latter says all times and objects are real, and there is no passage of time [Bourne]
B-series objects relate to each other; A-series objects relate to the present [Bourne]
27. Natural Reality / D. Time / 2. Passage of Time / e. Tensed (A) series
Time flows, past is fixed, future is open, future is feared but not past, we remember past, we plan future [Bourne]