Combining Texts

All the ideas for 'Higher-Order Logic', 'Summula philosophiae naturalis' and 'Metaphysics: the logical approach'

expand these ideas     |    start again     |     specify just one area for these texts

41 ideas

1. Philosophy / E. Nature of Metaphysics / 1. Nature of Metaphysics
3358 Metaphysics focuses on Platonism, essentialism, materialism and anti-realism [Benardete,JA]
1. Philosophy / F. Analytic Philosophy / 5. Linguistic Analysis
3312 There are the 'is' of predication (a function), the 'is' of identity (equals), and the 'is' of existence (quantifier) [Benardete,JA]
1. Philosophy / F. Analytic Philosophy / 7. Limitations of Analysis
3352 Analytical philosophy analyses separate concepts successfully, but lacks a synoptic vision of the results [Benardete,JA]
1. Philosophy / G. Scientific Philosophy / 1. Aims of Science
3329 Presumably the statements of science are true, but should they be taken literally or not? [Benardete,JA]
4. Formal Logic / F. Set Theory ST / 1. Set Theory
3326 Set theory attempts to reduce the 'is' of predication to mathematics [Benardete,JA]
3327 The set of Greeks is included in the set of men, but isn't a member of it [Benardete,JA]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
3335 The standard Z-F Intuition version of set theory has about ten agreed axioms [Benardete,JA, by PG]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
10301 The axiom of choice is controversial, but it could be replaced [Shapiro]
5. Theory of Logic / A. Overview of Logic / 5. First-Order Logic
10588 First-order logic is Complete, and Compact, with the Löwenheim-Skolem Theorems [Shapiro]
5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
10298 Some say that second-order logic is mathematics, not logic [Shapiro]
10299 If the aim of logic is to codify inferences, second-order logic is useless [Shapiro]
5. Theory of Logic / B. Logical Consequence / 1. Logical Consequence
10300 Logical consequence can be defined in terms of the logical terminology [Shapiro]
5. Theory of Logic / G. Quantification / 5. Second-Order Quantification
10290 Second-order variables also range over properties, sets, relations or functions [Shapiro]
5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
10590 Up Löwenheim-Skolem: if natural numbers satisfy wffs, then an infinite domain satisfies them [Shapiro]
10296 The Löwenheim-Skolem Theorems fail for second-order languages with standard semantics [Shapiro]
10297 The Löwenheim-Skolem theorem seems to be a defect of first-order logic [Shapiro]
10292 Downward Löwenheim-Skolem: if there's an infinite model, there is a countable model [Shapiro]
6. Mathematics / A. Nature of Mathematics / 2. Geometry
3332 Greeks saw the science of proportion as the link between geometry and arithmetic [Benardete,JA]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number
3330 Negatives, rationals, irrationals and imaginaries are all postulated to solve baffling equations [Benardete,JA]
3337 Natural numbers are seen in terms of either their ordinality (Peano), or cardinality (set theory) [Benardete,JA]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / e. Peano arithmetic 2nd-order
10294 Second-order logic has the expressive power for mathematics, but an unworkable model theory [Shapiro]
7. Existence / B. Change in Existence / 4. Events / a. Nature of events
3310 If slowness is a property of walking rather than the walker, we must allow that events exist [Benardete,JA]
7. Existence / C. Structure of Existence / 8. Stuff / a. Pure stuff
12793 Early pre-Socratics had a mass-noun ontology, which was replaced by count-nouns [Benardete,JA]
7. Existence / E. Categories / 5. Category Anti-Realism
16608 Ockham was an anti-realist about the categories [William of Ockham, by Pasnau]
8. Modes of Existence / B. Properties / 11. Properties as Sets
10591 Logicians use 'property' and 'set' interchangeably, with little hanging on it [Shapiro]
8. Modes of Existence / D. Universals / 6. Platonic Forms / d. Forms critiques
3353 If there is no causal interaction with transcendent Platonic objects, how can you learn about them? [Benardete,JA]
9. Objects / C. Structure of Objects / 4. Quantity of an Object
16599 Ockham says matter must be extended, so we don't need Quantity [William of Ockham, by Pasnau]
16681 Matter gets its quantity from condensation and rarefaction, which is just local motion [William of Ockham]
9. Objects / C. Structure of Objects / 5. Composition of an Object
3304 Why should packed-together particles be a thing (Mt Everest), but not scattered ones? [Benardete,JA]
9. Objects / D. Essence of Objects / 6. Essence as Unifier
3350 Could a horse lose the essential property of being a horse, and yet continue to exist? [Benardete,JA]
9. Objects / E. Objects over Time / 2. Objects that Change
3309 If a soldier continues to exist after serving as a soldier, does the wind cease to exist after it ceases to blow? [Benardete,JA]
9. Objects / E. Objects over Time / 8. Continuity of Rivers
3351 One can step into the same river twice, but not into the same water [Benardete,JA]
9. Objects / F. Identity among Objects / 5. Self-Identity
3314 Absolutists might accept that to exist is relative, but relative to what? How about relative to itself? [Benardete,JA]
3323 Maybe self-identity isn't existence, if Pegasus can be self-identical but non-existent [Benardete,JA]
12. Knowledge Sources / A. A Priori Knowledge / 1. Nature of the A Priori
3306 The clearest a priori knowledge is proving non-existence through contradiction [Benardete,JA]
12. Knowledge Sources / A. A Priori Knowledge / 5. A Priori Synthetic
3349 If we know truths about prime numbers, we seem to have synthetic a priori knowledge of Platonic objects [Benardete,JA]
3341 Logical positivism amounts to no more than 'there is no synthetic a priori' [Benardete,JA]
3344 Assertions about existence beyond experience can only be a priori synthetic [Benardete,JA]
3345 Appeals to intuition seem to imply synthetic a priori knowledge [Benardete,JA]
27. Natural Reality / C. Space / 3. Points in Space
3334 Rationalists see points as fundamental, but empiricists prefer regions [Benardete,JA]
28. God / B. Proving God / 2. Proofs of Reason / a. Ontological Proof
3308 In the ontological argument a full understanding of the concept of God implies a contradiction in 'There is no God' [Benardete,JA]