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All the ideas for 'Axiomatic Theories of Truth (2005 ver)', 'Abstract Objects:intro to Axiomatic Metaphysics' and 'Principia Mathematica'

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53 ideas

1. Philosophy / D. Nature of Philosophy / 1. Philosophy
Philosophy must abstract from the senses [Newton]
3. Truth / A. Truth Problems / 2. Defining Truth
Truth definitions don't produce a good theory, because they go beyond your current language [Halbach]
3. Truth / F. Semantic Truth / 1. Tarski's Truth / c. Meta-language for truth
In semantic theories of truth, the predicate is in an object-language, and the definition in a metalanguage [Halbach]
3. Truth / G. Axiomatic Truth / 1. Axiomatic Truth
Should axiomatic truth be 'conservative' - not proving anything apart from implications of the axioms? [Halbach]
If truth is defined it can be eliminated, whereas axiomatic truth has various commitments [Halbach]
Axiomatic theories of truth need a weak logical framework, and not a strong metatheory [Halbach]
Instead of a truth definition, add a primitive truth predicate, and axioms for how it works [Halbach]
3. Truth / H. Deflationary Truth / 2. Deflationary Truth
Deflationists say truth merely serves to express infinite conjunctions [Halbach]
4. Formal Logic / F. Set Theory ST / 1. Set Theory
To prove the consistency of set theory, we must go beyond set theory [Halbach]
5. Theory of Logic / C. Ontology of Logic / 1. Ontology of Logic
We can use truth instead of ontologically loaded second-order comprehension assumptions about properties [Halbach]
5. Theory of Logic / E. Structures of Logic / 7. Predicates in Logic
Instead of saying x has a property, we can say a formula is true of x - as long as we have 'true' [Halbach]
6. Mathematics / A. Nature of Mathematics / 2. Geometry
Newton developed a kinematic approach to geometry [Newton, by Kitcher]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / l. Limits
Quantities and ratios which continually converge will eventually become equal [Newton]
8. Modes of Existence / C. Powers and Dispositions / 2. Powers as Basic
I suspect that each particle of bodies has attractive or repelling forces [Newton]
9. Objects / A. Existence of Objects / 2. Abstract Objects / a. Nature of abstracta
Abstract objects are constituted by encoded collections of properties [Zalta, by Swoyer]
9. Objects / A. Existence of Objects / 2. Abstract Objects / c. Modern abstracta
Properties make round squares and round triangles distinct, unlike exemplification [Zalta, by Swoyer]
9. Objects / B. Unity of Objects / 1. Unifying an Object / b. Unifying aggregates
Particles mutually attract, and cohere at short distances [Newton]
9. Objects / C. Structure of Objects / 8. Parts of Objects / b. Sums of parts
The place of a thing is the sum of the places of its parts [Newton]
14. Science / B. Scientific Theories / 6. Theory Holism
If you changed one of Newton's concepts you would destroy his whole system [Heisenberg on Newton]
14. Science / C. Induction / 1. Induction
Science deduces propositions from phenomena, and generalises them by induction [Newton]
14. Science / D. Explanation / 2. Types of Explanation / g. Causal explanations
We should admit only enough causes to explain a phenomenon, and no more [Newton]
Natural effects of the same kind should be assumed to have the same causes [Newton]
14. Science / D. Explanation / 2. Types of Explanation / k. Explanations by essence
From the phenomena, I can't deduce the reason for the properties of gravity [Newton]
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / c. Ultimate substances
Newton's four fundamentals are: space, time, matter and force [Newton, by Russell]
26. Natural Theory / A. Speculations on Nature / 7. Later Matter Theories / a. Early Modern matter
Mass is central to matter [Newton, by Hart,WD]
26. Natural Theory / A. Speculations on Nature / 7. Later Matter Theories / b. Corpuscles
An attraction of a body is the sum of the forces of their particles [Newton]
26. Natural Theory / C. Causation / 1. Causation
Newtonian causation is changes of motion resulting from collisions [Newton, by Baron/Miller]
26. Natural Theory / D. Laws of Nature / 6. Laws as Numerical
You have discovered that elliptical orbits result just from gravitation and planetary movement [Newton, by Leibniz]
We have given up substantial forms, and now aim for mathematical laws [Newton]
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / c. Essence and laws
I am not saying gravity is essential to bodies [Newton]
27. Natural Reality / A. Classical Physics / 1. Mechanics / a. Explaining movement
Newton reclassified vertical motion as violent, and unconstrained horizontal motion as natural [Newton, by Harré]
27. Natural Reality / A. Classical Physics / 1. Mechanics / b. Laws of motion
Inertia rejects the Aristotelian idea of things having natural states, to which they return [Newton, by Alexander,P]
1: Bodies rest, or move in straight lines, unless acted on by forces [Newton]
Newton's Third Law implies the conservation of momentum [Newton, by Papineau]
2: Change of motion is proportional to the force [Newton]
3: All actions of bodies have an equal and opposite reaction [Newton]
27. Natural Reality / A. Classical Physics / 1. Mechanics / c. Forces
Newton's idea of force acting over a long distance was very strange [Heisenberg on Newton]
Newton introduced forces other than by contact [Newton, by Papineau]
Newton's laws cover the effects of forces, but not their causes [Newton, by Papineau]
Newton's forces were accused of being the scholastics' real qualities [Pasnau on Newton]
I am studying the quantities and mathematics of forces, not their species or qualities [Newton]
The aim is to discover forces from motions, and use forces to demonstrate other phenomena [Newton]
27. Natural Reality / A. Classical Physics / 1. Mechanics / d. Gravity
Newton showed that falling to earth and orbiting the sun are essentially the same [Newton, by Ellis]
27. Natural Reality / A. Classical Physics / 2. Thermodynamics / c. Conservation of energy
Early Newtonians could not formulate conservation of energy, having no concept of potential energy [Newton, by Papineau]
27. Natural Reality / C. Space / 4. Substantival Space
Absolute space is independent, homogeneous and immovable [Newton]
27. Natural Reality / D. Time / 1. Nature of Time / a. Absolute time
Newton needs intervals of time, to define velocity and acceleration [Newton, by Le Poidevin]
Newton thought his laws of motion needed absolute time [Newton, by Bardon]
Time exists independently, and flows uniformly [Newton]
Absolute time, from its own nature, flows equably, without relation to anything external [Newton]
27. Natural Reality / D. Time / 2. Passage of Time / g. Time's arrow
Newtonian mechanics does not distinguish negative from positive values of time [Newton, by Coveney/Highfield]
27. Natural Reality / D. Time / 3. Parts of Time / d. Measuring time
If there is no uniform motion, we cannot exactly measure time [Newton]
28. God / A. Divine Nature / 3. Divine Perfections
If a perfect being does not rule the cosmos, it is not God [Newton]
28. God / B. Proving God / 3. Proofs of Evidence / b. Teleological Proof
The elegance of the solar system requires a powerful intellect as designer [Newton]