Combining Texts

All the ideas for 'Thinking About Mathematics', 'Does Conceivability Entail Possibility?' and 'Mind, Brain and the Quantum'

expand these ideas     |    start again     |     specify just one area for these texts


37 ideas

1. Philosophy / D. Nature of Philosophy / 7. Despair over Philosophy
There is nothing so obvious that a philosopher cannot be found to deny it [Lockwood]
1. Philosophy / F. Analytic Philosophy / 3. Analysis of Preconditions
There may only be necessary and sufficient conditions (and counterfactuals) because we intervene in the world [Lockwood]
1. Philosophy / F. Analytic Philosophy / 7. Limitations of Analysis
No one has ever succeeded in producing an acceptable non-trivial analysis of anything [Lockwood]
3. Truth / C. Correspondence Truth / 3. Correspondence Truth critique
If something is described in two different ways, is that two facts, or one fact presented in two ways? [Lockwood]
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]
7. Existence / D. Theories of Reality / 2. Realism
How does a direct realist distinguish a building from Buckingham Palace? [Lockwood]
10. Modality / D. Knowledge of Modality / 4. Conceivable as Possible / a. Conceivable as possible
Modal Rationalism: conceivability gives a priori access to modal truths [Chalmers, by Stalnaker]
Evaluate primary possibility from some world, and secondary possibility from this world [Chalmers, by Vaidya]
11. Knowledge Aims / A. Knowledge / 4. Belief / f. Animal beliefs
Dogs seem to have beliefs, and beliefs require concepts [Lockwood]
12. Knowledge Sources / C. Rationalism / 1. Rationalism
Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro]
12. Knowledge Sources / D. Empiricism / 1. Empiricism
Empiricism is a theory of meaning as well as of knowledge [Lockwood]
12. Knowledge Sources / E. Direct Knowledge / 1. Common Sense
Commonsense realism must account for the similarity of genuine perceptions and known illusions [Lockwood]
15. Nature of Minds / A. Nature of Mind / 8. Brain
A 1988 estimate gave the brain 3 x 10-to-the-14 synaptic junctions [Lockwood]
15. Nature of Minds / B. Features of Minds / 2. Unconscious Mind
How come unconscious states also cause behaviour? [Lockwood]
Could there be unconscious beliefs and desires? [Lockwood]
15. Nature of Minds / B. Features of Minds / 7. Blindsight
Fish may operate by blindsight [Lockwood]
16. Persons / C. Self-Awareness / 1. Introspection
We might even learn some fundamental physics from introspection [Lockwood]
17. Mind and Body / A. Mind-Body Dualism / 3. Panpsychism
Can phenomenal qualities exist unsensed? [Lockwood]
17. Mind and Body / A. Mind-Body Dualism / 8. Dualism of Mind Critique
If mental events occur in time, then relativity says they are in space [Lockwood]
17. Mind and Body / B. Behaviourism / 4. Behaviourism Critique
Only logical positivists ever believed behaviourism [Lockwood]
17. Mind and Body / E. Mind as Physical / 3. Eliminativism
Identity theory likes the identity of lightning and electrical discharges [Lockwood]
19. Language / A. Nature of Meaning / 5. Meaning as Verification
Perhaps logical positivism showed that there is no dividing line between science and metaphysics [Lockwood]
26. Natural Theory / C. Causation / 9. General Causation / b. Nomological causation
Maybe causation is a form of rational explanation, not an observation or a state of mind [Lockwood]
27. Natural Reality / D. Time / 1. Nature of Time / b. Relative time
We have the confused idea that time is a process of change [Lockwood]