Combining Texts

All the ideas for 'General Facts,Phys Necessity, and Metaph of Time', 'Higher-Order Logic' and 'The Mysterious Flame'

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21 ideas

1. Philosophy / E. Nature of Metaphysics / 5. Metaphysics beyond Science
2546 Philosophy is a magnificent failure in its attempt to overstep the limits of our knowledge [McGinn]
3. Truth / B. Truthmakers / 3. Truthmaker Maximalism
17962 The truth-maker principle is that every truth has a sufficient truth-maker [Forrest]
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 / E. Structures of Logic / 1. Logical Form
2544 Thoughts have a dual aspect: as they seem to introspection, and their underlying logical reality [McGinn]
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 / 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]
8. Modes of Existence / B. Properties / 11. Properties as Sets
10591 Logicians use 'property' and 'set' interchangeably, with little hanging on it [Shapiro]
15. Nature of Minds / C. Capacities of Minds / 1. Faculties
2539 Mental modules for language, social, action, theory, space, emotion [McGinn]
16. Persons / F. Free Will / 1. Nature of Free Will
2545 Free will is mental causation in action [McGinn]
17. Mind and Body / A. Mind-Body Dualism / 3. Panpsychism
2543 Brains aren't made of anything special, suggesting panpsychism [McGinn]
17. Mind and Body / D. Property Dualism / 6. Mysterianism
2540 Examining mind sees no brain; examining brain sees no mind [McGinn]
19. Language / C. Assigning Meanings / 6. Truth-Conditions Semantics
2547 There is information if there are symbols which refer, and which can combine into a truth or falsehood [McGinn]
26. Natural Theory / C. Causation / 4. Naturalised causation
2542 Causation in the material world is energy-transfer, of motion, electricity or gravity [McGinn]