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All the ideas for 'Thinking About Mathematics', 'Introduction: Truth and Truth-Making' and 'Why the Universe Exists'

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71 ideas

3. Truth / B. Truthmakers / 1. For Truthmakers
There are five problems which the truth-maker theory might solve [Rami]
The truth-maker idea is usually justified by its explanatory power, or intuitive appeal [Rami]
3. Truth / B. Truthmakers / 2. Truthmaker Relation
The truth-making relation can be one-to-one, or many-to-many [Rami]
3. Truth / B. Truthmakers / 3. Truthmaker Maximalism
Central idea: truths need truthmakers; and possibly all truths have them, and makers entail truths [Rami]
3. Truth / B. Truthmakers / 4. Truthmaker Necessitarianism
Most theorists say that truth-makers necessitate their truths [Rami]
3. Truth / B. Truthmakers / 5. What Makes Truths / a. What makes truths
It seems best to assume different kinds of truth-maker, such as objects, facts, tropes, or events [Rami]
3. Truth / B. Truthmakers / 5. What Makes Truths / c. States of affairs make truths
Truth-makers seem to be states of affairs (plus optional individuals), or individuals and properties [Rami]
3. Truth / B. Truthmakers / 5. What Makes Truths / d. Being makes truths
'Truth supervenes on being' only gives necessary (not sufficient) conditions for contingent truths [Rami]
'Truth supervenes on being' avoids entities as truth-makers for negative truths [Rami]
3. Truth / B. Truthmakers / 7. Making Modal Truths
Maybe a truth-maker also works for the entailments of the given truth [Rami]
3. Truth / B. Truthmakers / 11. Truthmaking and Correspondence
Truth-making is usually internalist, but the correspondence theory is externalist [Rami]
3. Truth / C. Correspondence Truth / 1. Correspondence Truth
Correspondence theories assume that truth is a representation relation [Rami]
3. Truth / H. Deflationary Truth / 2. Deflationary Truth
Deflationist truth is an infinitely disjunctive property [Rami]
4. Formal Logic / D. Modal Logic ML / 7. Barcan Formula
Truth-maker theorists should probably reject the converse Barcan formula [Rami]
5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number
The number 3 is presumably identical as a natural, an integer, a rational, a real, and complex [Shapiro]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / h. Reals from Cauchy
Cauchy gave a formal definition of a converging sequence. [Shapiro]
6. Mathematics / B. Foundations for Mathematics / 1. Foundations for Mathematics
Categories are the best foundation for mathematics [Shapiro]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / f. Zermelo numbers
Two definitions of 3 in terms of sets disagree over whether 1 is a member of 3 [Shapiro]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
Numbers do not exist independently; the essence of a number is its relations to other numbers [Shapiro]
A 'system' is related objects; a 'pattern' or 'structure' abstracts the pure relations from them [Shapiro]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
Logicism seems to be a non-starter if (as is widely held) logic has no ontology of its own [Shapiro]
6. Mathematics / C. Sources of Mathematics / 7. Formalism
Term Formalism says mathematics is just about symbols - but real numbers have no names [Shapiro]
Game Formalism is just a matter of rules, like chess - but then why is it useful in science? [Shapiro]
Deductivism says mathematics is logical consequences of uninterpreted axioms [Shapiro]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / b. Intuitionism
Critics resent the way intuitionism cripples mathematics, but it allows new important distinctions [Shapiro]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / c. Conceptualism
Conceptualist are just realists or idealist or nominalists, depending on their view of concepts [Shapiro]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / d. Predicativism
'Impredicative' definitions refer to the thing being described [Shapiro]
8. Modes of Existence / A. Relations / 2. Internal Relations
Internal relations depend either on the existence of the relata, or on their properties [Rami]
12. Knowledge Sources / C. Rationalism / 1. Rationalism
Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro]
27. Natural Reality / A. Classical Physics / 1. Mechanics / d. Gravity
Gravity is unusual, in that it always attracts and never repels [New Sci.]
27. Natural Reality / B. Modern Physics / 1. Relativity / b. General relativity
In the Big Bang general relativity fails, because gravity is too powerful [New Sci.]
27. Natural Reality / B. Modern Physics / 2. Electrodynamics / a. Electrodynamics
Quantum electrodynamics incorporates special relativity and quantum mechanics [New Sci.]
Photons have zero rest mass, so virtual photons have infinite range [New Sci.]
27. Natural Reality / B. Modern Physics / 2. Electrodynamics / b. Fields
In the standard model all the fundamental force fields merge at extremely high energies [New Sci.]
27. Natural Reality / B. Modern Physics / 2. Electrodynamics / c. Electrons
Electrons move fast, so are subject to special relativity [New Sci.]
27. Natural Reality / B. Modern Physics / 3. Chromodynamics / a. Chromodynamics
The strong force is repulsive at short distances, strong at medium, and fades at long [New Sci.]
Gluons, the particles carrying the strong force, interact because of their colour charge [New Sci.]
The strong force binds quarks tight, and the nucleus more weakly [New Sci.]
27. Natural Reality / B. Modern Physics / 3. Chromodynamics / b. Quarks
Quarks in threes can build hadrons with spin ½ or with spin 3/2 [New Sci.]
Classifying hadrons revealed two symmetry patterns, produced by three basic elements [New Sci.]
Three different colours of quark (as in the proton) can cancel out to give no colour [New Sci.]
27. Natural Reality / B. Modern Physics / 4. Standard Model / b. Standard model
The four fundamental forces (gravity, electromagnetism, weak and strong) are the effects of particles [New Sci.]
The weak force explains beta decay, and the change of type by quarks and leptons [New Sci.]
Three particles enable the weak force: W+ and W- are charged, and Z° is not [New Sci.]
The weak force particles are heavy, so the force has a short range [New Sci.]
Why do the charges of the very different proton and electron perfectly match up? [New Sci.]
The Standard Model cannot explain dark energy, survival of matter, gravity, or force strength [New Sci.]
27. Natural Reality / B. Modern Physics / 4. Standard Model / c. Particle properties
Spin is a built-in ration of angular momentum [New Sci.]
Quarks have red, green or blue colour charge (akin to electric charge) [New Sci.]
Fermions, with spin ½, are antisocial, and cannot share quantum states [New Sci.]
Spin is akin to rotation, and is easily measured in a magnetic field [New Sci.]
Particles are spread out, with wave-like properties, and higher energy shortens the wavelength [New Sci.]
27. Natural Reality / B. Modern Physics / 4. Standard Model / d. Mass
The mass of protons and neutrinos is mostly binding energy, not the quarks [New Sci.]
Gravitional mass turns out to be the same as inertial mass [New Sci.]
27. Natural Reality / B. Modern Physics / 4. Standard Model / e. Protons
Neutrons are slightly heavier than protons, and decay into them by emitting an electron [New Sci.]
Top, bottom, charm and strange quarks quickly decay into up and down [New Sci.]
27. Natural Reality / B. Modern Physics / 4. Standard Model / f. Neutrinos
Neutrinos were proposed as the missing energy in neutron beta decay [New Sci.]
Only neutrinos spin anticlockwise [New Sci.]
27. Natural Reality / B. Modern Physics / 4. Standard Model / g. Anti-matter
Standard antineutrinos have opposite spin and opposite lepton number [New Sci.]
27. Natural Reality / B. Modern Physics / 5. Unified Models / a. Electro-weak unity
The symmetry of unified electromagnetic and weak forces was broken by the Higgs field [New Sci.]
27. Natural Reality / B. Modern Physics / 5. Unified Models / b. String theory
String theory is now part of 11-dimensional M-Theory, involving p-branes [New Sci.]
String theory might be tested by colliding strings to make bigger 'stringballs' [New Sci.]
String theory offers a quantum theory of gravity, by describing the graviton [New Sci.]
Supersymmetric string theory can be expressed using loop quantum gravity [New Sci.]
27. Natural Reality / B. Modern Physics / 5. Unified Models / c. Supersymmetry
Only supersymmetry offers to incorporate gravity into the scheme [New Sci.]
Supersymmetry says particles and superpartners were unities, but then split [New Sci.]
Supersymmetry has extra heavy bosons and heavy fermions [New Sci.]
The evidence for supersymmetry keeps failing to appear [New Sci.]
27. Natural Reality / C. Space / 4. Substantival Space
The Higgs field means even low energy space is not empty [New Sci.]
27. Natural Reality / E. Cosmology / 8. Dark Matter
Dark matter must have mass, to produce gravity, and no electric charge, to not reflect light [New Sci.]