Combining Texts

All the ideas for 'fragments/reports', 'In a Critical Condition' and 'Philosophy of Mathematics'

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76 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 / 2. Aims of Definition
Definitions should be replaceable by primitives, and should not be creative [Brown,JR]
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 / 3. Types of Set / d. Infinite Sets
Set theory says that natural numbers are an actual infinity (to accommodate their powerset) [Brown,JR]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / d. Naïve logical sets
Naïve set theory assumed that there is a set for every condition [Brown,JR]
Nowadays conditions are only defined on existing sets [Brown,JR]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / e. Iterative sets
The 'iterative' view says sets start with the empty set and build up [Brown,JR]
4. Formal Logic / F. Set Theory ST / 7. Natural Sets
A flock of birds is not a set, because a set cannot go anywhere [Brown,JR]
5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
If a proposition is false, then its negation is true [Brown,JR]
5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
Axioms are either self-evident, or stipulations, or fallible attempts [Brown,JR]
5. Theory of Logic / L. Paradox / 4. Paradoxes in Logic / c. Berry's paradox
Berry's Paradox finds a contradiction in the naming of huge numbers [Brown,JR]
6. Mathematics / A. Nature of Mathematics / 1. Mathematics
Mathematics is the only place where we are sure we are right [Brown,JR]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / a. Numbers
'There are two apples' can be expressed logically, with no mention of numbers [Brown,JR]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / n. Pi
π is a 'transcendental' number, because it is not the solution of an equation [Brown,JR]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / g. Applying mathematics
Mathematics represents the world through structurally similar models. [Brown,JR]
6. Mathematics / B. Foundations for Mathematics / 2. Proof in Mathematics
There is no limit to how many ways something can be proved in mathematics [Brown,JR]
Computers played an essential role in proving the four-colour theorem of maps [Brown,JR]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / b. Mathematics is not set theory
Set theory may represent all of mathematics, without actually being mathematics [Brown,JR]
When graphs are defined set-theoretically, that won't cover unlabelled graphs [Brown,JR]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / d. Platonist structuralism
To see a structure in something, we must already have the idea of the structure [Brown,JR]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
Sets seem basic to mathematics, but they don't suit structuralism [Brown,JR]
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
The irrationality of root-2 was achieved by intellect, not experience [Brown,JR]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism
There is an infinity of mathematical objects, so they can't be physical [Brown,JR]
Numbers are not abstracted from particulars, because each number is a particular [Brown,JR]
6. Mathematics / C. Sources of Mathematics / 5. Numbers as Adjectival
Empiricists base numbers on objects, Platonists base them on properties [Brown,JR]
6. Mathematics / C. Sources of Mathematics / 7. Formalism
Does some mathematics depend entirely on notation? [Brown,JR]
For nomalists there are no numbers, only numerals [Brown,JR]
The most brilliant formalist was Hilbert [Brown,JR]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / a. Constructivism
There are no constructions for many highly desirable results in mathematics [Brown,JR]
Constructivists say p has no value, if the value depends on Goldbach's Conjecture [Brown,JR]
7. Existence / C. Structure of Existence / 7. Abstract/Concrete / a. Abstract/concrete
David's 'Napoleon' is about something concrete and something abstract [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
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 / 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
Mentalese doesn't require a theory of meaning [Fodor]
Language is ambiguous, but thought isn't [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]
18. Thought / E. Abstraction / 1. Abstract Thought
'Abstract' nowadays means outside space and time, not concrete, not physical [Brown,JR]
The older sense of 'abstract' is where 'redness' or 'group' is abstracted from particulars [Brown,JR]
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 / A. Nature of Meaning / 7. Meaning Holism / c. Meaning by Role
A term can have not only a sense and a reference, but also a 'computational role' [Brown,JR]
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
Given atomism at one end, and a finite universe at the other, there are no physical infinities [Brown,JR]
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]