Combining Texts

All the ideas for 'fragments/reports', 'Investigations in the Foundations of Set Theory I' and 'In a Critical Condition'

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57 ideas

1. Philosophy / F. Analytic Philosophy / 4. Conceptual Analysis
It seems likely that analysis of concepts is impossible, but justification can survive without it [Fodor]
1. Philosophy / F. Analytic Philosophy / 7. Limitations of Analysis
Despite all the efforts of philosophers, nothing can ever be reduced to anything [Fodor]
2. Reason / A. Nature of Reason / 8. Naturalising Reason
Turing invented the idea of mechanical rationality (just based on syntax) [Fodor]
2. Reason / D. Definition / 8. Impredicative Definition
Predicative definitions are acceptable in mathematics if they distinguish objects, rather than creating them? [Zermelo, by Lavine]
2. Reason / E. Argument / 2. Transcendental Argument
Transcendental arguments move from knowing Q to knowing P because it depends on Q [Fodor]
4. Formal Logic / F. Set Theory ST / 1. Set Theory
We take set theory as given, and retain everything valuable, while avoiding contradictions [Zermelo]
Set theory investigates number, order and function, showing logical foundations for mathematics [Zermelo]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
ZFC: Existence, Extension, Specification, Pairing, Unions, Powers, Infinity, Choice [Zermelo, by Clegg]
Zermelo published his axioms in 1908, to secure a controversial proof [Zermelo, by Maddy]
Set theory can be reduced to a few definitions and seven independent axioms [Zermelo]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / c. Axiom of Pairing II
Zermelo introduced Pairing in 1930, and it seems fairly obvious [Zermelo, by Maddy]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / i. Axiom of Foundation VIII
Zermelo used Foundation to block paradox, but then decided that only Separation was needed [Zermelo, by Maddy]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / m. Axiom of Separation
Not every predicate has an extension, but Separation picks the members that satisfy a predicate [Zermelo, by Hart,WD]
The Axiom of Separation requires set generation up to one step back from contradiction [Zermelo, by Maddy]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
In ZF, the Burali-Forti Paradox proves that there is no set of all ordinals [Zermelo, by Hart,WD]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / f. Zermelo numbers
For Zermelo the successor of n is {n} (rather than n U {n}) [Zermelo, by Maddy]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
Zermelo believed, and Von Neumann seemed to confirm, that numbers are sets [Zermelo, by Maddy]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
Different versions of set theory result in different underlying structures for numbers [Zermelo, by Brown,JR]
8. Modes of Existence / B. Properties / 7. Emergent Properties
The world is full of messy small things producing stable large-scale properties (e.g. mountains) [Fodor]
8. Modes of Existence / D. Universals / 6. Platonic Forms / b. Partaking
Don't define something by a good instance of it; a good example is a special case of the ordinary example [Fodor]
11. Knowledge Aims / A. Knowledge / 4. Belief / e. Belief holism
How do you count beliefs? [Fodor]
11. Knowledge Aims / C. Knowing Reality / 3. Idealism / c. Empirical idealism
Berkeley seems to have mistakenly thought that chairs are the same as after-images [Fodor]
12. Knowledge Sources / B. Perception / 6. Inference in Perception
Maybe explaining the mechanics of perception will explain the concepts involved [Fodor]
12. Knowledge Sources / C. Rationalism / 1. Rationalism
Rationalism can be based on an evolved computational brain with innate structure [Fodor]
12. Knowledge Sources / D. Empiricism / 2. Associationism
According to empiricists abstraction is the fundamental mental process [Fodor]
12. Knowledge Sources / D. Empiricism / 5. Empiricism Critique
Rationalists say there is more to a concept than the experience that prompts it [Fodor]
15. Nature of Minds / A. Nature of Mind / 1. Mind / b. Purpose of mind
The function of a mind is obvious [Fodor]
Empirical approaches see mind connections as mirrors/maps of reality [Fodor]
15. Nature of Minds / B. Features of Minds / 4. Intentionality / a. Nature of intentionality
Do intentional states explain our behaviour? [Fodor]
16. Persons / B. Nature of the Self / 6. Self as Higher Awareness
If I have a set of mental modules, someone had better be in charge of them! [Fodor]
17. Mind and Body / C. Functionalism / 1. Functionalism
Functionalists see pains as properties involving relations and causation [Fodor]
17. Mind and Body / D. Property Dualism / 3. Property Dualism
Why bother with neurons? You don't explain bird flight by examining feathers [Fodor]
17. Mind and Body / E. Mind as Physical / 1. Physical Mind
Type physicalism is a stronger claim than token physicalism [Fodor]
17. Mind and Body / E. Mind as Physical / 4. Connectionism
Modern connectionism is just Hume's theory of the 'association' of 'ideas' [Fodor]
18. Thought / A. Modes of Thought / 1. Thought
The goal of thought is to understand the world, not instantly sort it into conceptual categories [Fodor]
18. Thought / B. Mechanics of Thought / 3. Modularity of Mind
Babies talk in consistent patterns [Fodor]
Rationality rises above modules [Fodor]
Modules have encapsulation, inaccessibility, private concepts, innateness [Fodor]
Something must take an overview of the modules [Fodor]
Obvious modules are language and commonsense explanation [Fodor]
Modules analyse stimuli, they don't tell you what to do [Fodor]
Modules make the world manageable [Fodor]
Blindness doesn't destroy spatial concepts [Fodor]
Modules have in-built specialist information [Fodor]
18. Thought / B. Mechanics of Thought / 4. Language of Thought
Language is ambiguous, but thought isn't [Fodor]
Mentalese doesn't require a theory of meaning [Fodor]
Mentalese may also incorporate some natural language [Fodor]
18. Thought / C. Content / 9. Conceptual Role Semantics
Content can't be causal role, because causal role is decided by content [Fodor]
18. Thought / D. Concepts / 2. Origin of Concepts / c. Nativist concepts
Experience can't explain itself; the concepts needed must originate outside experience [Fodor]
18. Thought / D. Concepts / 3. Ontology of Concepts / b. Concepts as abilities
Are concepts best seen as capacities? [Fodor]
For Pragmatists having a concept means being able to do something [Fodor]
19. Language / A. Nature of Meaning / 3. Meaning as Speaker's Intention
It seems unlikely that meaning can be reduced to communicative intentions, or any mental states [Fodor]
19. Language / A. Nature of Meaning / 7. Meaning Holism / b. Language holism
If to understand "fish" you must know facts about them, where does that end? [Fodor]
19. Language / E. Analyticity / 3. Analytic and Synthetic
Analysis is impossible without the analytic/synthetic distinction [Fodor]
19. Language / F. Communication / 4. Private Language
The theory of the content of thought as 'Mentalese' explains why the Private Language Argument doesn't work [Fodor]
26. Natural Theory / A. Speculations on Nature / 5. Infinite in Nature
Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius]
27. Natural Reality / G. Biology / 3. Evolution
Archelaus said life began in a primeval slime [Archelaus, by Schofield]