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All the ideas for 'Structures and Structuralism in Phil of Maths', 'The Theory of Relativity and A Priori Knowledge' and 'Thinking about Consciousness'

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58 ideas

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]
12. Knowledge Sources / B. Perception / 5. Interpretation
Kant showed that our perceptions are partly constructed from our concepts [Reichenbach]
12. Knowledge Sources / B. Perception / 7. Causal Perception
Perceptual concepts can't just refer to what causes classification [Papineau]
15. Nature of Minds / A. Nature of Mind / 1. Mind / e. Questions about mind
The only serious mind-brain theories now are identity, token identity, realization and supervenience [Papineau]
15. Nature of Minds / A. Nature of Mind / 3. Mental Causation
Maybe mind and body do overdetermine acts, but are linked (for some reason) [Papineau]
15. Nature of Minds / A. Nature of Mind / 4. Other Minds / c. Knowing other minds
Young children can see that other individuals sometimes have false beliefs [Papineau]
Do we understand other minds by simulation-theory, or by theory-theory? [Papineau]
15. Nature of Minds / A. Nature of Mind / 8. Brain
Researching phenomenal consciousness is peculiar, because the concepts involved are peculiar [Papineau]
15. Nature of Minds / B. Features of Minds / 1. Consciousness / a. Consciousness
Whether octopuses feel pain is unclear, because our phenomenal concepts are too vague [Papineau]
Our concept of consciousness is crude, and lacks theoretical articulation [Papineau]
We can’t decide what 'conscious' means, so it is undecidable whether cats are conscious [Papineau]
15. Nature of Minds / B. Features of Minds / 1. Consciousness / e. Cause of consciousness
Maybe a creature is conscious if its mental states represent things in a distinct way [Papineau]
15. Nature of Minds / B. Features of Minds / 1. Consciousness / f. Higher-order thought
The 'actualist' HOT theory says consciousness comes from actual higher judgements of mental states [Papineau]
Actualist HOT theories imply that a non-conscious mental event could become conscious when remembered [Papineau]
States are conscious if they could be the subject of higher-order mental judgements [Papineau]
Higher-order judgements may be possible where the subject denies having been conscious [Papineau]
17. Mind and Body / A. Mind-Body Dualism / 6. Epiphenomenalism
The epiphenomenal relation of mind and brain is a 'causal dangler', unlike anything else [Papineau]
Maybe minds do not cause actions, but do cause us to report our decisions [Papineau]
17. Mind and Body / C. Functionalism / 8. Functionalism critique
Role concepts either name the realising property, or the higher property constituting the role [Papineau]
17. Mind and Body / D. Property Dualism / 2. Anomalous Monism
If causes are basic particulars, this doesn't make conscious and physical properties identical [Papineau]
17. Mind and Body / D. Property Dualism / 5. Supervenience of mind
Supervenience can be replaced by identifying mind with higher-order or disjunctional properties [Papineau]
17. Mind and Body / E. Mind as Physical / 1. Physical Mind
The completeness of physics is needed for mind-brain identity [Papineau]
17. Mind and Body / E. Mind as Physical / 2. Reduction of Mind
Mind-brain reduction is less explanatory, because phenomenal concepts lack causal roles [Papineau]
Weak reduction of mind is to physical causes; strong reduction is also to physical laws [Papineau]
17. Mind and Body / E. Mind as Physical / 5. Causal Argument
It is absurd to think that physical effects are caused twice, so conscious causes must be physical [Papineau]
17. Mind and Body / E. Mind as Physical / 6. Conceptual Dualism
Accept ontological monism, but conceptual dualism; we think in a different way about phenomenal thought [Papineau]
17. Mind and Body / E. Mind as Physical / 7. Anti-Physicalism / c. Knowledge argument
Mary acquires new concepts; she previously thought about the same property using material concepts [Papineau]
18. Thought / A. Modes of Thought / 1. Thought
Thinking about a thing doesn't require activating it [Papineau]
Consciousness affects bodily movement, so thoughts must be material states [Papineau]
18. Thought / C. Content / 6. Broad Content
Most reductive accounts of representation imply broad content [Papineau]
If content hinges on matters outside of you, how can it causally influence your actions? [Papineau]
19. Language / A. Nature of Meaning / 5. Meaning as Verification
Verificationists tend to infer indefinite answers from undecidable questions [Papineau]
19. Language / C. Assigning Meanings / 2. Semantics
Teleosemantics equates meaning with the item the concept is intended to track [Papineau]
19. Language / C. Assigning Meanings / 8. Possible Worlds Semantics
Truth conditions in possible worlds can't handle statements about impossibilities [Papineau]
Thought content is possible worlds that make the thought true; if that includes the actual world, it's true [Papineau]
26. Natural Theory / C. Causation / 8. Particular Causation / b. Causal relata
Causation is based on either events, or facts, or states of affairs [Papineau]
Causes are instantiations of properties by particulars, or they are themselves basic particulars [Papineau]
26. Natural Theory / D. Laws of Nature / 10. Closure of Physics
The completeness of physics cannot be proved [Papineau]
Determinism is possible without a complete physics, if mental forces play a role [Papineau]
Modern biological research, especially into the cell, has revealed no special new natural forces [Papineau]
27. Natural Reality / A. Classical Physics / 2. Thermodynamics / c. Conservation of energy
Quantum 'wave collapses' seem to violate conservation of energy [Papineau]