Combining Texts

All the ideas for 'How the Laws of Physics Lie', 'Introduction to Russell's Theory of Types' and 'Plurals and Complexes'

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39 ideas

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
The Axiom of Choice is a non-logical principle of set-theory [Hossack]
The Axiom of Choice guarantees a one-one correspondence from sets to ordinals [Hossack]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / p. Axiom of Reducibility
The Axiom of Reducibility is self-effacing: if true, it isn't needed [Quine]
4. Formal Logic / F. Set Theory ST / 8. Critique of Set Theory
Maybe we reduce sets to ordinals, rather than the other way round [Hossack]
4. Formal Logic / G. Formal Mereology / 3. Axioms of Mereology
Extensional mereology needs two definitions and two axioms [Hossack]
5. Theory of Logic / F. Referring in Logic / 2. Descriptions / b. Definite descriptions
Plural definite descriptions pick out the largest class of things that fit the description [Hossack]
5. Theory of Logic / G. Quantification / 6. Plural Quantification
Plural reference will refer to complex facts without postulating complex things [Hossack]
Plural reference is just an abbreviation when properties are distributive, but not otherwise [Hossack]
A plural comprehension principle says there are some things one of which meets some condition [Hossack]
5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / d. Russell's paradox
Plural language can discuss without inconsistency things that are not members of themselves [Hossack]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
The theory of the transfinite needs the ordinal numbers [Hossack]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
I take the real numbers to be just lengths [Hossack]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / e. Peano arithmetic 2nd-order
A plural language gives a single comprehensive induction axiom for arithmetic [Hossack]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
In arithmetic singularists need sets as the instantiator of numeric properties [Hossack]
Set theory is the science of infinity [Hossack]
7. Existence / D. Theories of Reality / 11. Ontological Commitment / a. Ontological commitment
We are committed to a 'group' of children, if they are sitting in a circle [Hossack]
7. Existence / E. Categories / 4. Category Realism
Causality indicates which properties are real [Cartwright,N]
9. Objects / C. Structure of Objects / 5. Composition of an Object
Complex particulars are either masses, or composites, or sets [Hossack]
The relation of composition is indispensable to the part-whole relation for individuals [Hossack]
9. Objects / C. Structure of Objects / 8. Parts of Objects / c. Wholes from parts
Leibniz's Law argues against atomism - water is wet, unlike water molecules [Hossack]
The fusion of five rectangles can decompose into more than five parts that are rectangles [Hossack]
14. Science / D. Explanation / 2. Types of Explanation / a. Types of explanation
Two main types of explanation are by causes, or by citing a theoretical framework [Cartwright,N]
14. Science / D. Explanation / 2. Types of Explanation / c. Explanations by coherence
An explanation is a model that fits a theory and predicts the phenomenological laws [Cartwright,N]
14. Science / D. Explanation / 2. Types of Explanation / e. Lawlike explanations
Laws get the facts wrong, and explanation rests on improvements and qualifications of laws [Cartwright,N]
Laws apply to separate domains, but real explanations apply to intersecting domains [Cartwright,N]
Covering-law explanation lets us explain storms by falling barometers [Cartwright,N]
I disagree with the covering-law view that there is a law to cover every single case [Cartwright,N]
You can't explain one quail's behaviour by just saying that all quails do it [Cartwright,N]
The covering law view assumes that each phenomenon has a 'right' explanation [Cartwright,N]
14. Science / D. Explanation / 3. Best Explanation / c. Against best explanation
In science, best explanations have regularly turned out to be false [Cartwright,N]
18. Thought / A. Modes of Thought / 1. Thought
A thought can refer to many things, but only predicate a universal and affirm a state of affairs [Hossack]
26. Natural Theory / C. Causation / 8. Particular Causation / e. Probabilistic causation
A cause won't increase the effect frequency if other causes keep interfering [Cartwright,N]
26. Natural Theory / D. Laws of Nature / 2. Types of Laws
There are fundamental explanatory laws (false!), and phenomenological laws (regularities) [Cartwright,N, by Bird]
Laws of appearances are 'phenomenological'; laws of reality are 'theoretical' [Cartwright,N]
26. Natural Theory / D. Laws of Nature / 4. Regularities / b. Best system theory
Good organisation may not be true, and the truth may not organise very much [Cartwright,N]
26. Natural Theory / D. Laws of Nature / 11. Against Laws of Nature
To get from facts to equations, we need a prepared descriptions suited to mathematics [Cartwright,N]
Simple laws have quite different outcomes when they act in combinations [Cartwright,N]
There are few laws for when one theory meets another [Cartwright,N]
27. Natural Reality / C. Space / 2. Space
We could ignore space, and just talk of the shape of matter [Hossack]