Combining Texts

All the ideas for 'In a Critical Condition', 'On Formally Undecidable Propositions' and 'Plural Quantification Exposed'

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64 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 / E. Argument / 2. Transcendental Argument
Transcendental arguments move from knowing Q to knowing P because it depends on Q [Fodor]
3. Truth / F. Semantic Truth / 1. Tarski's Truth / a. Tarski's truth definition
Prior to Gödel we thought truth in mathematics consisted in provability [Gödel, by Quine]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
Gödel show that the incompleteness of set theory was a necessity [Gödel, by Hallett,M]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / n. Axiom of Comprehension
A comprehension axiom is 'predicative' if the formula has no bound second-order variables [Linnebo]
5. Theory of Logic / A. Overview of Logic / 4. Pure Logic
A 'pure logic' must be ontologically innocent, universal, and without presuppositions [Linnebo]
5. Theory of Logic / G. Quantification / 6. Plural Quantification
Plural quantification depends too heavily on combinatorial and set-theoretic considerations [Linnebo]
Can second-order logic be ontologically first-order, with all the benefits of second-order? [Linnebo]
5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
The limitations of axiomatisation were revealed by the incompleteness theorems [Gödel, by Koellner]
5. Theory of Logic / K. Features of Logics / 2. Consistency
Second Incompleteness: nice theories can't prove their own consistency [Gödel, by Smith,P]
5. Theory of Logic / K. Features of Logics / 3. Soundness
If soundness can't be proved internally, 'reflection principles' can be added to assert soundness [Gödel, by Halbach/Leigh]
5. Theory of Logic / K. Features of Logics / 5. Incompleteness
Gödel's First Theorem sabotages logicism, and the Second sabotages Hilbert's Programme [Smith,P on Gödel]
The undecidable sentence can be decided at a 'higher' level in the system [Gödel]
6. Mathematics / A. Nature of Mathematics / 1. Mathematics
There can be no single consistent theory from which all mathematical truths can be derived [Gödel, by George/Velleman]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
Gödel showed that arithmetic is either incomplete or inconsistent [Gödel, by Rey]
First Incompleteness: arithmetic must always be incomplete [Gödel, by Smith,P]
Arithmetical truth cannot be fully and formally derived from axioms and inference rules [Gödel, by Nagel/Newman]
Gödel's Second says that semantic consequence outruns provability [Gödel, by Hanna]
First Incompleteness: a decent consistent system is syntactically incomplete [Gödel, by George/Velleman]
Second Incompleteness: a decent consistent system can't prove its own consistency [Gödel, by George/Velleman]
There is a sentence which a theory can show is true iff it is unprovable [Gödel, by Smith,P]
'This system can't prove this statement' makes it unprovable either way [Gödel, by Clegg]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / d. Predicativism
Realists are happy with impredicative definitions, which describe entities in terms of other existing entities [Gödel, by Shapiro]
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]
9. Objects / A. Existence of Objects / 1. Physical Objects
The modern concept of an object is rooted in quantificational logic [Linnebo]
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
Empirical approaches see mind connections as mirrors/maps of reality [Fodor]
The function of a mind is obvious [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 / C. Functionalism / 2. Machine Functionalism
Basic logic can be done by syntax, with no semantics [Gödel, by Rey]
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
Modules analyse stimuli, they don't tell you what to do [Fodor]
Blindness doesn't destroy spatial concepts [Fodor]
Something must take an overview of the modules [Fodor]
Modules have in-built specialist information [Fodor]
Modules have encapsulation, inaccessibility, private concepts, innateness [Fodor]
Obvious modules are language and commonsense explanation [Fodor]
Modules make the world manageable [Fodor]
Babies talk in consistent patterns [Fodor]
Rationality rises above modules [Fodor]
18. Thought / B. Mechanics of Thought / 4. Language of Thought
Language is ambiguous, but thought isn't [Fodor]
Mentalese may also incorporate some natural language [Fodor]
Mentalese doesn't require a theory of meaning [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]