Combining Texts

All the ideas for 'The Elm and the Expert', 'Philosophy as a way of life' and 'Nature and Meaning of Numbers'

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


56 ideas

1. Philosophy / D. Nature of Philosophy / 6. Hopes for Philosophy
It is no longer possible to be a sage, but we can practice the exercise of wisdom [Hadot]
2. Reason / A. Nature of Reason / 2. Logos
The logos represents a demand for universal rationality [Hadot]
2. Reason / A. Nature of Reason / 8. Naturalising Reason
A standard naturalist view is realist, externalist, and computationalist, and believes in rationality [Fodor]
2. Reason / D. Definition / 9. Recursive Definition
Dedekind proved definition by recursion, and thus proved the basic laws of arithmetic [Dedekind, by Potter]
3. Truth / A. Truth Problems / 5. Truth Bearers
Psychology has to include the idea that mental processes are typically truth-preserving [Fodor]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / d. Infinite Sets
An infinite set maps into its own proper subset [Dedekind, by Reck/Price]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / f. Axiom of Infinity V
We have the idea of self, and an idea of that idea, and so on, so infinite ideas are available [Dedekind, by Potter]
4. Formal Logic / G. Formal Mereology / 1. Mereology
Dedekind originally thought more in terms of mereology than of sets [Dedekind, by Potter]
5. Theory of Logic / A. Overview of Logic / 4. Pure Logic
Inferences are surely part of the causal structure of the world [Fodor]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / a. Numbers
Numbers are free creations of the human mind, to understand differences [Dedekind]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / c. Priority of numbers
Dedekind defined the integers, rationals and reals in terms of just the natural numbers [Dedekind, by George/Velleman]
Order, not quantity, is central to defining numbers [Dedekind, by Monk]
Ordinals can define cardinals, as the smallest ordinal that maps the set [Dedekind, by Heck]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
Dedekind's ordinals are just members of any progression whatever [Dedekind, by Russell]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / i. Reals from cuts
Dedekind's axiom that his Cut must be filled has the advantages of theft over honest toil [Dedekind, by Russell]
Dedekind says each cut matches a real; logicists say the cuts are the reals [Dedekind, by Bostock]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
In counting we see the human ability to relate, correspond and represent [Dedekind]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / b. Mark of the infinite
A system S is said to be infinite when it is similar to a proper part of itself [Dedekind]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / a. Axioms for numbers
Dedekind gives a base number which isn't a successor, then adds successors and induction [Dedekind, by Hart,WD]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
Zero is a member, and all successors; numbers are the intersection of sets satisfying this [Dedekind, by Bostock]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / e. Peano arithmetic 2nd-order
Categoricity implies that Dedekind has characterised the numbers, because it has one domain [Rumfitt on Dedekind]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / f. Mathematical induction
Induction is proved in Dedekind, an axiom in Peano; the latter seems simpler and clearer [Dedekind, by Russell]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
Dedekind originated the structuralist conception of mathematics [Dedekind, by MacBride]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / b. Varieties of structuralism
Dedekindian abstraction talks of 'positions', where Cantorian abstraction talks of similar objects [Dedekind, by Fine,K]
9. Objects / A. Existence of Objects / 3. Objects in Thought
A thing is completely determined by all that can be thought concerning it [Dedekind]
13. Knowledge Criteria / C. External Justification / 5. Controlling Beliefs
Control of belief is possible if you know truth conditions and what causes beliefs [Fodor]
14. Science / A. Basis of Science / 3. Experiment
An experiment is a deliberate version of what informal thinking does all the time [Fodor]
Participation in an experiment requires agreement about what the outcome will mean [Fodor]
We can deliberately cause ourselves to have true thoughts - hence the value of experiments [Fodor]
Interrogation and experiment submit us to having beliefs caused [Fodor]
14. Science / B. Scientific Theories / 1. Scientific Theory
Theories are links in the causal chain between the environment and our beliefs [Fodor]
15. Nature of Minds / A. Nature of Mind / 1. Mind / e. Questions about mind
I say psychology is intentional, semantics is informational, and thinking is computation [Fodor]
15. Nature of Minds / B. Features of Minds / 1. Consciousness / f. Higher-order thought
We are probably the only creatures that can think about our own thoughts [Fodor]
17. Mind and Body / A. Mind-Body Dualism / 2. Interactionism
Semantics v syntax is the interaction problem all over again [Fodor]
Cartesians consider interaction to be a miracle [Fodor]
17. Mind and Body / E. Mind as Physical / 1. Physical Mind
Type physicalism equates mental kinds with physical kinds [Fodor]
17. Mind and Body / E. Mind as Physical / 4. Connectionism
Hume has no theory of the co-ordination of the mind [Fodor]
18. Thought / A. Modes of Thought / 2. Propositional Attitudes
Propositional attitudes are propositions presented in a certain way [Fodor]
18. Thought / A. Modes of Thought / 5. Rationality / a. Rationality
Rationality has mental properties - autonomy, productivity, experiment [Fodor]
18. Thought / C. Content / 5. Twin Earth
XYZ (Twin Earth 'water') is an impossibility [Fodor]
18. Thought / C. Content / 6. Broad Content
Truth conditions require a broad concept of content [Fodor]
18. Thought / C. Content / 7. Narrow Content
Concepts aren't linked to stuff; they are what is caused by stuff [Fodor]
18. Thought / C. Content / 10. Causal Semantics
Knowing the cause of a thought is almost knowing its content [Fodor]
18. Thought / C. Content / 12. Informational Semantics
Is content basically information, fixed externally? [Fodor]
18. Thought / D. Concepts / 3. Ontology of Concepts / b. Concepts as abilities
In the information view, concepts are potentials for making distinctions [Fodor]
18. Thought / E. Abstraction / 3. Abstracta by Ignoring
Dedekind said numbers were abstracted from systems of objects, leaving only their position [Dedekind, by Dummett]
We derive the natural numbers, by neglecting everything of a system except distinctness and order [Dedekind]
18. Thought / E. Abstraction / 8. Abstractionism Critique
Dedekind has a conception of abstraction which is not psychologistic [Dedekind, by Tait]
19. Language / A. Nature of Meaning / 1. Meaning
Semantic externalism says the concept 'elm' needs no further beliefs or inferences [Fodor]
If meaning is information, that establishes the causal link between the state of the world and our beliefs [Fodor]
19. Language / A. Nature of Meaning / 4. Meaning as Truth-Conditions
To know the content of a thought is to know what would make it true [Fodor]
19. Language / A. Nature of Meaning / 7. Meaning Holism / b. Language holism
For holists no two thoughts are ever quite the same, which destroys faith in meaning [Fodor]
19. Language / B. Reference / 4. Descriptive Reference / a. Sense and reference
It is claimed that reference doesn't fix sense (Jocasta), and sense doesn't fix reference (Twin Earth) [Fodor]
19. Language / C. Assigning Meanings / 2. Semantics
Broad semantics holds that the basic semantic properties are truth and denotation [Fodor]
19. Language / C. Assigning Meanings / 6. Truth-Conditions Semantics
Externalist semantics are necessary to connect the contents of beliefs with how the world is [Fodor]
22. Metaethics / C. The Good / 3. Pleasure / b. Types of pleasure
The pleasure of existing is the only genuine pleasure [Hadot]