Combining Texts

All the ideas for 'fragments/reports', 'Set Theory' and 'Mapping the Mind'

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31 ideas

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / b. Axiom of Extensionality I
13030 Extensionality: ∀x ∀y (∀z (z ∈ x ↔ z ∈ y) → x = y) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / c. Axiom of Pairing II
13032 Pairing: ∀x ∀y ∃z (x ∈ z ∧ y ∈ z) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / d. Axiom of Unions III
13033 Union: ∀F ∃A ∀Y ∀x (x ∈ Y ∧ Y ∈ F → x ∈ A) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / f. Axiom of Infinity V
13037 Infinity: ∃x (0 ∈ x ∧ ∀y ∈ x (S(y) ∈ x) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / g. Axiom of Powers VI
13038 Power Set: ∀x ∃y ∀z(z ⊂ x → z ∈ y) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / h. Axiom of Replacement VII
13034 Replacement: ∀x∈A ∃!y φ(x,y) → ∃Y ∀X∈A ∃y∈Y φ(x,y) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / i. Axiom of Foundation VIII
13039 Foundation:∀x(∃y(y∈x) → ∃y(y∈x ∧ ¬∃z(z∈x ∧ z∈y))) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
13036 Choice: ∀A ∃R (R well-orders A) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / k. Axiom of Existence
13029 Set Existence: ∃x (x = x) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / n. Axiom of Comprehension
13031 Comprehension: ∃y ∀x (x ∈ y ↔ x ∈ z ∧ φ) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / o. Axiom of Constructibility V = L
13040 Constructibility: V = L (all sets are constructible) [Kunen]
7. Existence / E. Categories / 2. Categorisation
4913 Brain lesions can erase whole categories of perception, suggesting they are hard-wired [Carter,R]
9. Objects / C. Structure of Objects / 6. Constitution of an Object
6019 If someone squashed a horse to make a dog, something new would now exist [Mnesarchus]
12. Knowledge Sources / B. Perception / 5. Interpretation
4910 Sense organs don't discriminate; they reduce various inputs to the same electrical pulses [Carter,R]
4911 The recognition sequence is: classify, name, locate, associate, feel [Carter,R, by PG]
12. Knowledge Sources / E. Direct Knowledge / 4. Memory
4919 There seems to be no dividing line between a memory and a thought [Carter,R]
15. Nature of Minds / A. Nature of Mind / 7. Animal Minds
4908 No one knows if animals are conscious [Carter,R]
15. Nature of Minds / A. Nature of Mind / 8. Brain
4902 Pain doesn't have one brain location, but is linked to attention and emotion [Carter,R]
4915 In primates, brain size correlates closely with size of social group [Carter,R]
4904 Proper brains appear at seven weeks, and neonates have as many neurons as adults do [Carter,R]
15. Nature of Minds / B. Features of Minds / 1. Consciousness / c. Parts of consciousness
4917 Consciousness involves awareness, perception, self-awareness, attention and reflection [Carter,R]
15. Nature of Minds / B. Features of Minds / 1. Consciousness / e. Cause of consciousness
4916 There is enormous evidence that consciousness arises in the frontal lobes of the brain [Carter,R]
15. Nature of Minds / B. Features of Minds / 5. Qualia / a. Nature of qualia
4905 Normal babies seem to have overlapping sense experiences [Carter,R]
15. Nature of Minds / B. Features of Minds / 7. Blindsight
4918 In blindsight V1 (normal vision) is inactive, but V5 (movement) lights up [Carter,R]
17. Mind and Body / A. Mind-Body Dualism / 8. Dualism of Mind Critique
4912 Out-of-body experiences may be due to temporary loss of proprioception [Carter,R]
17. Mind and Body / E. Mind as Physical / 2. Reduction of Mind
4920 Thinking takes place on the upper side of the prefrontal cortex [Carter,R]
4903 Scans of brains doing similar tasks produce very similar patterns of activation [Carter,R]
18. Thought / A. Modes of Thought / 3. Emotions / a. Nature of emotions
4906 Babies show highly emotional brain events, but may well be unaware of them [Carter,R]
18. Thought / A. Modes of Thought / 3. Emotions / g. Controlling emotions
4909 The only way we can control our emotions is by manipulating the outside world that influences them [Carter,R]
18. Thought / A. Modes of Thought / 5. Rationality / c. Animal rationality
4914 A frog will starve to death surrounded by dead flies [Carter,R]
22. Metaethics / C. The Good / 3. Pleasure / d. Sources of pleasure
4907 The 'locus coeruleus' is one of several candidates for the brain's 'pleasure centre' [Carter,R]