Combining Texts

All the ideas for 'Higher-Order Logic', 'Intro to 'Modality and Tense'' and '18: Book of Job'

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

22 ideas

1. Philosophy / D. Nature of Philosophy / 7. Despair over Philosophy
9208 Philosophers with a new concept are like children with a new toy [Fine,K]
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
10297 The Löwenheim-Skolem theorem seems to be a defect of first-order logic [Shapiro]
10590 Up Löwenheim-Skolem: if natural numbers satisfy wffs, then an infinite domain satisfies them [Shapiro]
10292 Downward Löwenheim-Skolem: if there's an infinite model, there is a countable model [Shapiro]
10296 The Löwenheim-Skolem Theorems fail for second-order languages with standard semantics [Shapiro]
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 / C. Structure of Existence / 7. Abstract/Concrete / a. Abstract/concrete
9210 Possible objects are abstract; actual concrete objects are possible; so abstract/concrete are compatible [Fine,K]
7. Existence / D. Theories of Reality / 3. Reality
9211 A non-standard realism, with no privileged standpoint, might challenge its absoluteness or coherence [Fine,K]
8. Modes of Existence / B. Properties / 11. Properties as Sets
10591 Logicians use 'property' and 'set' interchangeably, with little hanging on it [Shapiro]
9. Objects / A. Existence of Objects / 3. Objects in Thought
9202 Objects, as well as sentences, can have logical form [Fine,K]
9. Objects / D. Essence of Objects / 7. Essence and Necessity / b. Essence not necessities
9206 We must distinguish between the identity or essence of an object, and its necessary features [Fine,K]
10. Modality / A. Necessity / 3. Types of Necessity
9205 The three basic types of necessity are metaphysical, natural and normative [Fine,K]
10. Modality / A. Necessity / 5. Metaphysical Necessity
9209 Metaphysical necessity may be 'whatever the circumstance', or 'regardless of circumstances' [Fine,K]
10. Modality / A. Necessity / 11. Denial of Necessity
9200 Empiricists suspect modal notions: either it happens or it doesn't; it is just regularities. [Fine,K]
19. Language / C. Assigning Meanings / 8. Possible Worlds Semantics
9207 If sentence content is all worlds where it is true, all necessary truths have the same content! [Fine,K]
29. Religion / D. Religious Issues / 2. Immortality / a. Immortality
7469 There is no hereafter in the Book of Job [Anon (Job), by Watson]