Combining Texts

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

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34 ideas

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
The Axiom of Choice paradoxically allows decomposing a sphere into two identical spheres [Maddy]
5. Theory of Logic / C. Ontology of Logic / 3. If-Thenism
Critics of if-thenism say that not all starting points, even consistent ones, are worth studying [Maddy]
5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
Hilbert's geometry and Dedekind's real numbers were role models for axiomatization [Maddy]
If two mathematical themes coincide, that suggest a single deep truth [Maddy]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / g. Continuum Hypothesis
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
Set-theory tracks the contours of mathematical depth and fruitfulness [Maddy]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism
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
There are entities, and then positive 'modes', modifying aspects outside the thing's essence [Suárez]
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
Substances are incomplete unless they have modes [Suárez, by Pasnau]
9. Objects / C. Structure of Objects / 2. Hylomorphism / a. Hylomorphism
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
Partial forms of leaf and fruit are united in the whole form of the tree [Suárez]
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
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
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
Identity does not exclude possible or imagined difference [Suárez, by Boulter]
Real Essential distinction: A and B are of different natural kinds [Suárez, by Boulter]
Minor Real distinction: B needs A, but A doesn't need B [Suárez, by Boulter]
Major Real distinction: A and B have independent existences [Suárez, by Boulter]
Conceptual/Mental distinction: one thing can be conceived of in two different ways [Suárez, by Boulter]
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
Scholastics assess possibility by what has actually happened in reality [Suárez, by Boulter]
15. Nature of Minds / C. Capacities of Minds / 1. Faculties
There are 23 core brain functions, with known circuit, transmitters, genes and behaviour [Watson]
17. Mind and Body / E. Mind as Physical / 1. Physical Mind
Traditional ideas of the mind were weakened in the 1950s by mind-influencing drugs [Watson]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / e. Human nature
Humans have been hunter-gatherers for 99.5% of their existence [Watson]
26. Natural Theory / C. Causation / 7. Eliminating causation
The Uncertainty Principle implies that cause and effect can't be measured [Watson]
27. Natural Reality / B. Modern Physics / 2. Electrodynamics / a. Electrodynamics
The interference of light through two slits confirmed that it is waves [Watson]
27. Natural Reality / B. Modern Physics / 2. Electrodynamics / c. Electrons
Electrons rotate in hyrogen atoms 10^13 times per second [Watson]
27. Natural Reality / B. Modern Physics / 2. Electrodynamics / d. Quantum mechanics
Quantum theory explains why nature is made up of units, such as elements [Watson]
27. Natural Reality / B. Modern Physics / 4. Standard Model / a. Concept of matter
Only four particles are needed for matter: up and down quark, electron, electron-neutrino [Watson]
27. Natural Reality / F. Chemistry / 1. Chemistry
The shape of molecules is important, as well as the atoms and their bonds [Watson]
27. Natural Reality / G. Biology / 2. Life
In 1828 the animal substance urea was manufactured from inorganic ingredients [Watson]
Information is physical, and living can be seen as replicating and preserving information [Watson]
29. Religion / B. Monotheistic Religion / 4. Christianity / c. Angels
Other things could occupy the same location as an angel [Suárez]