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All the ideas for 'The Rationality of Science', 'Mapping the Mind' and 'Structures and Structuralism in Phil of Maths'

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54 ideas

1. Philosophy / G. Scientific Philosophy / 1. Aims of Science
For science to be rational, we must explain scientific change rationally [Newton-Smith]
We do not wish merely to predict, we also want to explain [Newton-Smith]
The real problem of science is how to choose between possible explanations [Newton-Smith]
1. Philosophy / G. Scientific Philosophy / 2. Positivism
Critics attack positivist division between theory and observation [Newton-Smith]
Positivists hold that theoretical terms change, but observation terms don't [Newton-Smith]
3. Truth / A. Truth Problems / 6. Verisimilitude
More truthful theories have greater predictive power [Newton-Smith]
Theories generate infinite truths and falsehoods, so they cannot be used to assess probability [Newton-Smith]
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]
7. Existence / E. Categories / 2. Categorisation
Brain lesions can erase whole categories of perception, suggesting they are hard-wired [Carter,R]
8. Modes of Existence / E. Nominalism / 6. Mereological Nominalism
A nominalist might avoid abstract objects by just appealing to mereological sums [Reck/Price]
10. Modality / C. Sources of Modality / 1. Sources of Necessity
De re necessity arises from the way the world is [Newton-Smith]
11. Knowledge Aims / A. Knowledge / 4. Belief / a. Beliefs
We must assess the truth of beliefs in identifying them [Newton-Smith]
12. Knowledge Sources / B. Perception / 5. Interpretation
Sense organs don't discriminate; they reduce various inputs to the same electrical pulses [Carter,R]
The recognition sequence is: classify, name, locate, associate, feel [Carter,R, by PG]
12. Knowledge Sources / E. Direct Knowledge / 4. Memory
There seems to be no dividing line between a memory and a thought [Carter,R]
13. Knowledge Criteria / E. Relativism / 6. Relativism Critique
Defeat relativism by emphasising truth and reference, not meaning [Newton-Smith]
14. Science / A. Basis of Science / 1. Observation
A full understanding of 'yellow' involves some theory [Newton-Smith]
14. Science / A. Basis of Science / 5. Anomalies
All theories contain anomalies, and so are falsified! [Newton-Smith]
The anomaly of Uranus didn't destroy Newton's mechanics - it led to Neptune's discovery [Newton-Smith]
Anomalies are judged against rival theories, and support for the current theory [Newton-Smith]
14. Science / B. Scientific Theories / 1. Scientific Theory
Why should it matter whether or not a theory is scientific? [Newton-Smith]
14. Science / B. Scientific Theories / 5. Commensurability
If theories are really incommensurable, we could believe them all [Newton-Smith]
15. Nature of Minds / A. Nature of Mind / 7. Animal Minds
No one knows if animals are conscious [Carter,R]
15. Nature of Minds / A. Nature of Mind / 8. Brain
Pain doesn't have one brain location, but is linked to attention and emotion [Carter,R]
Proper brains appear at seven weeks, and neonates have as many neurons as adults do [Carter,R]
In primates, brain size correlates closely with size of social group [Carter,R]
15. Nature of Minds / B. Features of Minds / 1. Consciousness / c. Parts of consciousness
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
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
Normal babies seem to have overlapping sense experiences [Carter,R]
15. Nature of Minds / B. Features of Minds / 7. Blindsight
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
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
Scans of brains doing similar tasks produce very similar patterns of activation [Carter,R]
Thinking takes place on the upper side of the prefrontal cortex [Carter,R]
18. Thought / A. Modes of Thought / 3. Emotions / a. Nature of emotions
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
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
A frog will starve to death surrounded by dead flies [Carter,R]
20. Action / C. Motives for Action / 3. Acting on Reason / c. Reasons as causes
Explaining an action is showing that it is rational [Newton-Smith]
22. Metaethics / C. The Good / 3. Pleasure / d. Sources of pleasure
The 'locus coeruleus' is one of several candidates for the brain's 'pleasure centre' [Carter,R]