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All the ideas for 'Structures and Structuralism in Phil of Maths', 'Intro to Positive Philosophy' and 'Nature's Metaphysics'

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65 ideas

1. Philosophy / B. History of Ideas / 1. History of Ideas
All ideas must be understood historically [Comte]
Our knowledge starts in theology, passes through metaphysics, and ends in positivism [Comte]
1. Philosophy / E. Nature of Metaphysics / 6. Metaphysics as Conceptual
Metaphysics is just the oversubtle qualification of abstract names for phenomena [Comte]
1. Philosophy / G. Scientific Philosophy / 2. Positivism
Positivism is the final state of human intelligence [Comte]
Positivism gives up absolute truth, and seeks phenomenal laws, by reason and observation [Comte]
1. Philosophy / G. Scientific Philosophy / 3. Scientism
Science can drown in detail, so we need broad scientists (to keep out the metaphysicians) [Comte]
Only positivist philosophy can terminate modern social crises [Comte]
3. Truth / F. Semantic Truth / 2. Semantic Truth
While true-in-a-model seems relative, true-in-all-models seems not to be [Reck/Price]
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 / a. Axioms for sets
ZFC set theory has only 'pure' sets, without 'urelements' [Reck/Price]
5. Theory of Logic / G. Quantification / 5. Second-Order Quantification
Three types of variable in second-order logic, for objects, functions, and predicates/sets [Reck/Price]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
'Analysis' is the theory of the real numbers [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / a. Axioms for numbers
Mereological arithmetic needs infinite objects, and function definitions [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / e. Peano arithmetic 2nd-order
Peano Arithmetic can have three second-order axioms, plus '1' and 'successor' [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
Set-theory gives a unified and an explicit basis for mathematics [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
Structuralism emerged from abstract algebra, axioms, and set theory and its structures [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / b. Varieties of structuralism
Relativist Structuralism just stipulates one successful model as its arithmetic [Reck/Price]
There are 'particular' structures, and 'universal' structures (what the former have in common) [Reck/Price]
Pattern Structuralism studies what isomorphic arithmetic models have in common [Reck/Price]
There are Formalist, Relativist, Universalist and Pattern structuralism [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / c. Nominalist structuralism
Formalist Structuralism says the ontology is vacuous, or formal, or inference relations [Reck/Price]
Maybe we should talk of an infinity of 'possible' objects, to avoid arithmetic being vacuous [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / d. Platonist structuralism
Universalist Structuralism is based on generalised if-then claims, not one particular model [Reck/Price]
Universalist Structuralism eliminates the base element, as a variable, which is then quantified out [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
The existence of an infinite set is assumed by Relativist Structuralism [Reck/Price]
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]
8. Modes of Existence / E. Nominalism / 6. Mereological Nominalism
A nominalist might avoid abstract objects by just appealing to mereological sums [Reck/Price]
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]
12. Knowledge Sources / D. Empiricism / 4. Pro-Empiricism
All real knowledge rests on observed facts [Comte]
14. Science / A. Basis of Science / 1. Observation
We must observe in order to form theories, but connected observations need prior theories [Comte]
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]
14. Science / D. Explanation / 2. Types of Explanation / e. Lawlike explanations
Positivism explains facts by connecting particular phenomena with general facts [Comte]
16. Persons / C. Self-Awareness / 3. Limits of Introspection
Introspection is pure illusion; we can obviously observe everything except ourselves [Comte]
26. Natural Theory / C. Causation / 4. Naturalised causation
We should explain causation by powers, not powers by causation [Bird]
26. Natural Theory / C. Causation / 7. Eliminating causation
The search for first or final causes is futile [Comte]
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 / 8. Scientific Essentialism / e. Anti scientific essentialism
We can never know origins, purposes or inner natures [Comte]
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]