Combining Texts

All the ideas for 'Essays on Intellectual Powers: Conception', 'De Ente et Essentia (Being and Essence)' and 'Higher-Order Logic'

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30 ideas

2. Reason / D. Definition / 5. Genus and Differentia
13070 If definitions must be general, and general terms can't individuate, then Socrates can't be defined [Aquinas, by Cover/O'Leary-Hawthorne]
11197 The definitions expressing identity are used to sort things [Aquinas]
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]
7. Existence / A. Nature of Existence / 3. Being / e. Being and nothing
11195 If affirmative propositions express being, we affirm about what is absent [Aquinas]
8. Modes of Existence / B. Properties / 8. Properties as Modes
11201 Properties have an incomplete essence, with definitions referring to their subject [Aquinas]
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
11205 If the form of 'human' contains 'many', Socrates isn't human; if it contains 'one', Socrates is Plato [Aquinas]
9. Objects / A. Existence of Objects / 5. Individuation / a. Individuation
13090 The principle of diversity for corporeal substances is their matter [Aquinas, by Cover/O'Leary-Hawthorne]
9. Objects / D. Essence of Objects / 1. Essences of Objects
11202 It is by having essence that things exist [Aquinas]
9. Objects / D. Essence of Objects / 2. Types of Essence
11203 Specific individual essence is defined by material, and generic essence is defined by form [Aquinas]
9. Objects / D. Essence of Objects / 4. Essence as Definition
11200 The definition of a physical object must include the material as well as the form [Aquinas]
23647 Objects have an essential constitution, producing its qualities, which we are too ignorant to define [Reid]
9. Objects / D. Essence of Objects / 5. Essence as Kind
11196 Essence is something in common between the natures which sort things into categories [Aquinas]
9. Objects / D. Essence of Objects / 6. Essence as Unifier
11208 A simple substance is its own essence [Aquinas]
10. Modality / D. Knowledge of Modality / 4. Conceivable as Possible / b. Conceivable but impossible
11958 Impossibilites are easily conceived in mathematics and geometry [Reid, by Molnar]
14. Science / D. Explanation / 2. Types of Explanation / k. Explanations by essence
11198 Definition of essence makes things understandable [Aquinas]
19. Language / B. Reference / 1. Reference theories
23646 Reference is by name, or a term-plus-circumstance, or ostensively, or by description [Reid]
19. Language / B. Reference / 3. Direct Reference / c. Social reference
23645 A word's meaning is the thing conceived, as fixed by linguistic experts [Reid]
19. Language / C. Assigning Meanings / 3. Predicates
11206 The mind constructs complete attributions, based on the unified elements of the real world [Aquinas]
26. Natural Theory / C. Causation / 5. Direction of causation
11207 A cause can exist without its effect, but the effect cannot exist without its cause [Aquinas]