Combining Texts

All the ideas for 'Knowledge by Agreement', 'Structures and Structuralism in Phil of Maths' and 'Theories of Everything'

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64 ideas

3. Truth / C. Correspondence Truth / 1. Correspondence Truth
Correspondence could be with other beliefs, rather than external facts [Kusch]
3. Truth / F. Semantic Truth / 1. Tarski's Truth / a. Tarski's truth definition
Tarskians distinguish truth from falsehood by relations between members of sets [Kusch]
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 / 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]
8. Modes of Existence / E. Nominalism / 6. Mereological Nominalism
A nominalist might avoid abstract objects by just appealing to mereological sums [Reck/Price]
11. Knowledge Aims / A. Knowledge / 4. Belief / a. Beliefs
We can have knowledge without belief, if others credit us with knowledge [Kusch]
11. Knowledge Aims / C. Knowing Reality / 4. Solipsism
Methodological Solipsism assumes all ideas could be derived from one mind [Kusch]
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / f. Foundationalism critique
Foundations seem utterly private, even from oneself at a later time [Kusch]
13. Knowledge Criteria / B. Internal Justification / 5. Coherentism / a. Coherence as justification
Testimony is reliable if it coheres with evidence for a belief, and with other beliefs [Kusch]
The coherentist restricts the space of reasons to the realm of beliefs [Kusch]
13. Knowledge Criteria / B. Internal Justification / 5. Coherentism / c. Coherentism critique
Individualistic coherentism lacks access to all of my beliefs, or critical judgement of my assessment [Kusch]
Individual coherentism cannot generate the necessary normativity [Kusch]
13. Knowledge Criteria / C. External Justification / 2. Causal Justification
Cultures decide causal routes, and they can be critically assessed [Kusch]
13. Knowledge Criteria / C. External Justification / 3. Reliabilism / a. Reliable knowledge
Process reliabilism has been called 'virtue epistemology', resting on perception, memory, reason [Kusch]
13. Knowledge Criteria / C. External Justification / 6. Contextual Justification / a. Contextualism
Justification depends on the audience and one's social role [Kusch]
13. Knowledge Criteria / C. External Justification / 7. Testimony
Testimony is an area in which epistemology meets ethics [Kusch]
Powerless people are assumed to be unreliable, even about their own lives [Kusch]
Testimony does not just transmit knowledge between individuals - it actually generates knowledge [Kusch]
Some want to reduce testimony to foundations of perceptions, memories and inferences [Kusch]
Testimony won't reduce to perception, if perception depends on social concepts and categories [Kusch]
A foundation is what is intelligible, hence from a rational source, and tending towards truth [Kusch]
Vindicating testimony is an expression of individualism [Kusch]
13. Knowledge Criteria / C. External Justification / 8. Social Justification
Myths about lonely genius are based on epistemological individualism [Kusch]
Communitarian Epistemology says 'knowledge' is a social status granted to groups of people [Kusch]
Private justification is justification to imagined other people [Kusch]
16. Persons / E. Rejecting the Self / 2. Self as Social Construct
To be considered 'an individual' is performed by a society [Kusch]
18. Thought / D. Concepts / 1. Concepts / a. Nature of concepts
Our experience may be conceptual, but surely not the world itself? [Kusch]
19. Language / F. Communication / 1. Rhetoric
Often socialising people is the only way to persuade them [Kusch]
24. Political Theory / D. Ideologies / 7. Communitarianism / a. Communitarianism
Communitarianism in epistemology sees the community as the primary knower [Kusch]
26. Natural Theory / B. Natural Kinds / 7. Critique of Kinds
Natural kinds are social institutions [Kusch]
27. Natural Reality / A. Classical Physics / 2. Thermodynamics / b. Heat
Work degrades into heat, but not vice versa [Close]
27. Natural Reality / A. Classical Physics / 2. Thermodynamics / c. Conservation of energy
First Law: energy can change form, but is conserved overall [Close]
27. Natural Reality / A. Classical Physics / 2. Thermodynamics / d. Entropy
Third Law: total order and minimum entropy only occurs at absolute zero [Close]
27. Natural Reality / B. Modern Physics / 1. Relativity / a. Special relativity
All motions are relative and ambiguous, but acceleration is the same in all inertial frames [Close]
The electric and magnetic are tightly linked, and viewed according to your own motion [Close]
27. Natural Reality / B. Modern Physics / 1. Relativity / b. General relativity
The general relativity equations relate curvature in space-time to density of energy-momentum [Close]
27. Natural Reality / B. Modern Physics / 2. Electrodynamics / a. Electrodynamics
Photon exchange drives the electro-magnetic force [Close]
Electric fields have four basic laws (two by Gauss, one by Ampère, one by Faraday) [Close]
Light isn't just emitted in quanta called photons - light is photons [Close]
In general relativity the energy and momentum of photons subjects them to gravity [Close]
Electro-magnetic waves travel at light speed - so light is electromagnetism! [Close]
In QED, electro-magnetism exists in quantum states, emitting and absorbing electrons [Close]
27. Natural Reality / B. Modern Physics / 2. Electrodynamics / b. Fields
Quantum fields contain continual rapid creation and disappearance [Close]
27. Natural Reality / B. Modern Physics / 2. Electrodynamics / c. Electrons
Electrons get their mass by interaction with the Higgs field [Close]
Dirac showed how electrons conform to special relativity [Close]
27. Natural Reality / B. Modern Physics / 4. Standard Model / a. Concept of matter
Modern theories of matter are grounded in heat, work and energy [Close]
27. Natural Reality / B. Modern Physics / 5. Unified Models / a. Electro-weak unity
The Higgs field is an electroweak plasma - but we don't know what stuff it consists of [Close]
27. Natural Reality / C. Space / 6. Space-Time
Space-time is indeterminate foam over short distances [Close]
28. God / A. Divine Nature / 4. Divine Contradictions
Omniscience is incoherent, since knowledge is a social concept [Kusch]