Combining Texts

All the ideas for 'Leibniz', 'Higher-Order Logic' and 'Elbow Room: varieties of free will'

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23 ideas

1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / a. Philosophy as worldly
3798 An overexamined life is as bad as an unexamined one [Dennett]
2. Reason / A. Nature of Reason / 9. Limits of Reason
3801 Rationality requires the assumption that things are either for better or worse [Dennett]
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 / 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]
9. Objects / F. Identity among Objects / 7. Indiscernible Objects
7566 The Identity of Indiscernibles is really the same as the verification principle [Jolley]
10. Modality / D. Knowledge of Modality / 4. Conceivable as Possible / c. Possible but inconceivable
3802 Why pronounce impossible what you cannot imagine? [Dennett]
13. Knowledge Criteria / C. External Justification / 2. Causal Justification
3795 Causal theories require the "right" sort of link (usually unspecified) [Dennett]
16. Persons / A. Concept of a Person / 4. Persons as Agents
3797 I am the sum total of what I directly control [Dennett]
16. Persons / F. Free Will / 1. Nature of Free Will
3800 You can be free even though force would have prevented you doing otherwise [Dennett, by PG]
3803 Can we conceive of a being with a will freer than our own? [Dennett]
16. Persons / F. Free Will / 2. Sources of Free Will
3791 Awareness of thought is a step beyond awareness of the world [Dennett]
3794 Foreknowledge permits control [Dennett]
17. Mind and Body / B. Behaviourism / 3. Intentional Stance
3796 The active self is a fiction created because we are ignorant of our motivations [Dennett]