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All the ideas for 'Russell's Mathematical Logic', 'Ideas' and 'Nature's Metaphysics'

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64 ideas

1. Philosophy / A. Wisdom / 3. Wisdom Deflated
Because of Darwin, wisdom as a definite attainable state has faded [Watson]
1. Philosophy / B. History of Ideas / 1. History of Ideas
The three key ideas are the soul, Europe, and the experiment [Watson]
The big idea: imitation, the soul, experiments, God, heliocentric universe, evolution? [Watson]
2. Reason / D. Definition / 8. Impredicative Definition
Impredicative Definitions refer to the totality to which the object itself belongs [Gödel]
2. Reason / E. Argument / 3. Analogy
Babylonian thinking used analogy, rather than deduction or induction [Watson]
4. Formal Logic / D. Modal Logic ML / 7. Barcan Formula
The plausible Barcan formula implies modality in the actual world [Bird]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / p. Axiom of Reducibility
In simple type theory the axiom of Separation is better than Reducibility [Gödel, by Linsky,B]
5. Theory of Logic / A. Overview of Logic / 8. Logic of Mathematics
Mathematical Logic is a non-numerical branch of mathematics, and the supreme science [Gödel]
5. Theory of Logic / G. Quantification / 2. Domain of Quantification
Reference to a totality need not refer to a conjunction of all its elements [Gödel]
5. Theory of Logic / K. Features of Logics / 8. Enumerability
A logical system needs a syntactical survey of all possible expressions [Gödel]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
Mesopotamian numbers applied to specific things, and then became abstract [Watson]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / g. Continuum Hypothesis
The generalized Continuum Hypothesis asserts a discontinuity in cardinal numbers [Gödel]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
Some arithmetical problems require assumptions which transcend arithmetic [Gödel]
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
Mathematical objects are as essential as physical objects are for perception [Gödel]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / d. Predicativism
Impredicative definitions are admitted into ordinary mathematics [Gödel]
7. Existence / A. Nature of Existence / 6. Criterion for Existence
If all existents are causally active, that excludes abstracta and causally isolated objects [Bird]
7. Existence / C. Structure of Existence / 5. Supervenience / c. Significance of supervenience
If naturalism refers to supervenience, that leaves necessary entities untouched [Bird]
8. Modes of Existence / B. Properties / 3. Types of Properties
There might be just one fundamental natural property [Bird]
8. Modes of Existence / B. Properties / 6. Categorical Properties
Categorical properties are not modally fixed, but change across possible worlds [Bird]
The categoricalist idea is that a property is only individuated by being itself [Bird]
If we abstractly define a property, that doesn't mean some object could possess it [Bird]
Categoricalists take properties to be quiddities, with no essential difference between them [Bird]
8. Modes of Existence / B. Properties / 10. Properties as Predicates
To name an abundant property is either a Fregean concept, or a simple predicate [Bird]
8. Modes of Existence / C. Powers and Dispositions / 2. Powers as Basic
Only real powers are fundamental [Bird, by Mumford/Anjum]
8. Modes of Existence / C. Powers and Dispositions / 3. Powers as Derived
If all properties are potencies, and stimuli and manifestation characterise them, there is a regress [Bird]
The essence of a potency involves relations, e.g. mass, to impressed force and acceleration [Bird]
8. Modes of Existence / C. Powers and Dispositions / 6. Dispositions / c. Dispositions as conditional
A disposition is finkish if a time delay might mean the manifestation fizzles out [Bird]
A robust pot attached to a sensitive bomb is not fragile, but if struck it will easily break [Bird]
8. Modes of Existence / C. Powers and Dispositions / 6. Dispositions / d. Dispositions as occurrent
Megarian actualists deny unmanifested dispositions [Bird]
8. Modes of Existence / D. Universals / 3. Instantiated Universals
Why should a universal's existence depend on instantiation in an existing particular? [Bird]
8. Modes of Existence / E. Nominalism / 2. Resemblance Nominalism
Resemblance itself needs explanation, presumably in terms of something held in common [Bird]
10. Modality / A. Necessity / 3. Types of Necessity
If the laws necessarily imply p, that doesn't give a new 'nomological' necessity [Bird]
10. Modality / A. Necessity / 6. Logical Necessity
Logical necessitation is not a kind of necessity; George Orwell not being Eric Blair is not a real possibility [Bird]
10. Modality / D. Knowledge of Modality / 4. Conceivable as Possible / a. Conceivable as possible
Empiricist saw imaginability and possibility as close, but now they seem remote [Bird]
10. Modality / E. Possible worlds / 3. Transworld Objects / d. Haecceitism
Haecceitism says identity is independent of qualities and without essence [Bird]
14. Science / D. Explanation / 1. Explanation / b. Aims of explanation
We can't reject all explanations because of a regress; inexplicable A can still explain B [Bird]
24. Political Theory / D. Ideologies / 5. Democracy / d. Representative democracy
Modern democracy is actually elective oligarchy [Watson]
26. Natural Theory / A. Speculations on Nature / 1. Nature
Greek philosophers invented the concept of 'nature' as their special subject [Watson]
26. Natural Theory / C. Causation / 4. Naturalised causation
We should explain causation by powers, not powers by causation [Bird]
26. Natural Theory / C. Causation / 9. General Causation / b. Nomological causation
Singularism about causes is wrong, as the universals involved imply laws [Bird]
26. Natural Theory / D. Laws of Nature / 1. Laws of Nature
Laws are explanatory relationships of things, which supervene on their essences [Bird]
26. Natural Theory / D. Laws of Nature / 2. Types of Laws
Laws are either disposition regularities, or relations between properties [Bird]
26. Natural Theory / D. Laws of Nature / 4. Regularities / a. Regularity theory
That other diamonds are hard does not explain why this one is [Bird]
Dispositional essentialism says laws (and laws about laws) are guaranteed regularities [Bird]
26. Natural Theory / D. Laws of Nature / 5. Laws from Universals
Laws cannot offer unified explanations if they don't involve universals [Bird]
If the universals for laws must be instantiated, a vanishing particular could destroy a law [Bird]
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / b. Scientific necessity
Salt necessarily dissolves in water, because of the law which makes the existence of salt possible [Bird]
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / c. Essence and laws
Most laws supervene on fundamental laws, which are explained by basic powers [Bird, by Friend/Kimpton-Nye]
26. Natural Theory / D. Laws of Nature / 9. Counterfactual Claims
Essentialism can't use conditionals to explain regularities, because of possible interventions [Bird]
27. Natural Reality / D. Time / 1. Nature of Time / b. Relative time
The relational view of space-time doesn't cover times and places where things could be [Bird]
27. Natural Reality / G. Biology / 3. Evolution
DNA mutation suggests humans and chimpanzees diverged 6.6 million years ago [Watson]
28. God / C. Attitudes to God / 4. God Reflects Humanity
During the rise of civilizations, the main gods changed from female to male [Watson]
29. Religion / A. Polytheistic Religion / 3. Hinduism
Hinduism has no founder, or prophet, or creed, or ecclesiastical structure [Watson]
29. Religion / B. Monotheistic Religion / 2. Judaism
Modern Judaism became stabilised in 200 CE [Watson]
The Israelites may have asserted the uniqueness of Yahweh to justify land claims [Watson]
Monotheism was a uniquely Israelite creation within the Middle East [Watson]
29. Religion / B. Monotheistic Religion / 3. Zoroastrianism
The Gathas (hymns) of Zoroastrianism date from about 1000 BCE [Watson]
Zoroaster conceived the afterlife, judgement, heaven and hell, and the devil [Watson]
29. Religion / B. Monotheistic Religion / 4. Christianity / a. Christianity
Jesus never intended to start a new religion [Watson]
Paul's early writings mention few striking episodes from Jesus' life [Watson]
29. Religion / C. Spiritual Disciplines / 1. Confucianism
Confucius revered the spiritual world, but not the supernatural, or a personal god, or the afterlife [Watson]
29. Religion / C. Spiritual Disciplines / 2. Taoism
Taoism aims at freedom from the world, the body, the mind, and nature [Watson]
29. Religion / D. Religious Issues / 1. Religious Commitment / a. Religious Belief
The three basic ingredients of religion are: the soul, seers or priests, and ritual [Watson]
29. Religion / D. Religious Issues / 2. Immortality / a. Immortality
In ancient Athens the souls of the dead are received by the 'upper air' [Watson]