Combining Texts

All the ideas for '', 'Defending the Axioms' and 'Disputationes metaphysicae'

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27 ideas

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
17610 The Axiom of Choice paradoxically allows decomposing a sphere into two identical spheres [Maddy]
5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
11211 If a sound conclusion comes from two errors that cancel out, the path of the argument must matter [Rumfitt]
5. Theory of Logic / C. Ontology of Logic / 3. If-Thenism
17620 Critics of if-thenism say that not all starting points, even consistent ones, are worth studying [Maddy]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
11212 The sense of a connective comes from primitively obvious rules of inference [Rumfitt]
11210 Standardly 'and' and 'but' are held to have the same sense by having the same truth table [Rumfitt]
5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
17605 Hilbert's geometry and Dedekind's real numbers were role models for axiomatization [Maddy]
17625 If two mathematical themes coincide, that suggest a single deep truth [Maddy]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / g. Continuum Hypothesis
17615 Every infinite set of reals is either countable or of the same size as the full set of reals [Maddy]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
17618 Set-theory tracks the contours of mathematical depth and fruitfulness [Maddy]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism
17614 The connection of arithmetic to perception has been idealised away in modern infinitary mathematics [Maddy]
8. Modes of Existence / B. Properties / 8. Properties as Modes
16665 There are entities, and then positive 'modes', modifying aspects outside the thing's essence [Suárez]
16666 A mode determines the state and character of a quantity, without adding to it [Suárez]
9. Objects / B. Unity of Objects / 2. Substance / a. Substance
16667 Substances are incomplete unless they have modes [Suárez, by Pasnau]
9. Objects / C. Structure of Objects / 2. Hylomorphism / a. Hylomorphism
17007 Forms must rule over faculties and accidents, and are the source of action and unity [Suárez]
9. Objects / C. Structure of Objects / 2. Hylomorphism / d. Form as unifier
16780 Partial forms of leaf and fruit are united in the whole form of the tree [Suárez]
16758 The best support for substantial forms is the co-ordinated unity of a natural being [Suárez]
9. Objects / C. Structure of Objects / 4. Quantity of an Object
16743 We can get at the essential nature of 'quantity' by knowing bulk and extension [Suárez]
9. Objects / D. Essence of Objects / 14. Knowledge of Essences
16742 We only know essences through non-essential features, esp. those closest to the essence [Suárez]
9. Objects / F. Identity among Objects / 1. Concept of Identity
22143 Identity does not exclude possible or imagined difference [Suárez, by Boulter]
22144 Real Essential distinction: A and B are of different natural kinds [Suárez, by Boulter]
22146 Minor Real distinction: B needs A, but A doesn't need B [Suárez, by Boulter]
22145 Major Real distinction: A and B have independent existences [Suárez, by Boulter]
22147 Conceptual/Mental distinction: one thing can be conceived of in two different ways [Suárez, by Boulter]
22148 Modal distinction: A isn't B or its property, but still needs B [Suárez, by Boulter]
10. Modality / D. Knowledge of Modality / 4. Conceivable as Possible / a. Conceivable as possible
22149 Scholastics assess possibility by what has actually happened in reality [Suárez, by Boulter]
19. Language / F. Communication / 3. Denial
11214 We learn 'not' along with affirmation, by learning to either affirm or deny a sentence [Rumfitt]
29. Religion / B. Monotheistic Religion / 4. Christianity / c. Angels
16682 Other things could occupy the same location as an angel [Suárez]