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All the ideas for 'Lysis', 'works' and 'Naturalism in Mathematics'

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56 ideas

1. Philosophy / D. Nature of Philosophy / 1. Philosophy
Derrida focuses on other philosophers, rather than on science [Derrida]
1. Philosophy / D. Nature of Philosophy / 3. Philosophy Defined
Philosophy is just a linguistic display [Derrida]
1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / e. Philosophy as reason
Philosophy aims to build foundations for thought [Derrida, by May]
1. Philosophy / D. Nature of Philosophy / 7. Despair over Philosophy
Philosophy is necessarily metaphorical, and its writing is aesthetic [Derrida]
1. Philosophy / H. Continental Philosophy / 3. Hermeneutics
Interpretations can be interpreted, so there is no original 'meaning' available [Derrida]
Hermeneutics blunts truth, by conforming it to the interpreter [Derrida, by Zimmermann,J]
Hermeneutics is hostile, trying to overcome the other person's difference [Derrida, by Zimmermann,J]
1. Philosophy / H. Continental Philosophy / 4. Linguistic Structuralism
Structuralism destroys awareness of dynamic meaning [Derrida]
1. Philosophy / H. Continental Philosophy / 6. Deconstruction
The idea of being as persistent presence, and meaning as conscious intelligibility, are self-destructive [Derrida, by Glendinning]
Sincerity can't be verified, so fiction infuses speech, and hence reality also [Derrida]
Sentences are contradictory, as they have opposite meanings in some contexts [Derrida]
We aim to explore the limits of expression (as in Mallarmé's poetry) [Derrida]
3. Truth / A. Truth Problems / 9. Rejecting Truth
Derrida says that all truth-talk is merely metaphor [Derrida, by Engel]
True thoughts are inaccessible, in the subconscious, prior to speech or writing [Derrida]
4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / b. Terminology of ST
'Forcing' can produce new models of ZFC from old models [Maddy]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
A Large Cardinal Axiom would assert ever-increasing stages in the hierarchy [Maddy]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / f. Axiom of Infinity V
Axiom of Infinity: completed infinite collections can be treated mathematically [Maddy]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / i. Axiom of Foundation VIII
The Axiom of Foundation says every set exists at a level in the set hierarchy [Maddy]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / p. Axiom of Reducibility
Axiom of Reducibility: propositional functions are extensionally predicative [Maddy]
5. Theory of Logic / E. Structures of Logic / 1. Logical Form
'Propositional functions' are propositions with a variable as subject or predicate [Maddy]
5. Theory of Logic / F. Referring in Logic / 1. Naming / b. Names as descriptive
Names have a subjective aspect, especially the role of our own name [Derrida]
'I' is the perfect name, because it denotes without description [Derrida]
5. Theory of Logic / F. Referring in Logic / 1. Naming / c. Names as referential
Even Kripke can't explain names; the word is the thing, and the thing is the word [Derrida]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / d. Actual infinite
Completed infinities resulted from giving foundations to calculus [Maddy]
Cantor and Dedekind brought completed infinities into mathematics [Maddy]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / i. Cardinal infinity
Infinity has degrees, and large cardinals are the heart of set theory [Maddy]
For any cardinal there is always a larger one (so there is no set of all sets) [Maddy]
An 'inaccessible' cardinal cannot be reached by union sets or power sets [Maddy]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / l. Limits
Theorems about limits could only be proved once the real numbers were understood [Maddy]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers
The extension of concepts is not important to me [Maddy]
In the ZFC hierarchy it is impossible to form Frege's set of all three-element sets [Maddy]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / e. Caesar problem
Frege solves the Caesar problem by explicitly defining each number [Maddy]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
Making set theory foundational to mathematics leads to very fruitful axioms [Maddy]
Unified set theory gives a final court of appeal for mathematics [Maddy]
Set theory brings mathematics into one arena, where interrelations become clearer [Maddy]
Identifying geometric points with real numbers revealed the power of set theory [Maddy]
The line of rationals has gaps, but set theory provided an ordered continuum [Maddy]
Mathematics rests on the logic of proofs, and on the set theoretic axioms [Maddy]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / b. Indispensability of mathematics
Maybe applications of continuum mathematics are all idealisations [Maddy]
Scientists posit as few entities as possible, but set theorist posit as many as possible [Maddy]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / c. Neo-logicism
We can get arithmetic directly from HP; Law V was used to get HP from the definition of number [Maddy]
7. Existence / D. Theories of Reality / 11. Ontological Commitment / e. Ontological commitment problems
The theoretical indispensability of atoms did not at first convince scientists that they were real [Maddy]
15. Nature of Minds / B. Features of Minds / 1. Consciousness / b. Essence of consciousness
Heidegger showed that passing time is the key to consciousness [Derrida]
15. Nature of Minds / C. Capacities of Minds / 6. Idealisation
Science idealises the earth's surface, the oceans, continuities, and liquids [Maddy]
18. Thought / A. Modes of Thought / 1. Thought
'Tacit theory' controls our thinking (which is why Freud is important) [Derrida]
19. Language / A. Nature of Meaning / 1. Meaning
Meanings depend on differences and contrasts [Derrida]
For Aristotle all proper nouns must have a single sense, which is the purpose of language [Derrida]
Capacity for repetitions is the hallmark of language [Derrida]
The sign is only conceivable as a movement between elusive presences [Derrida]
Writing functions even if the sender or the receiver are absent [Derrida, by Glendinning]
Madness and instability ('the demonic hyperbole') lurks in all language [Derrida]
19. Language / A. Nature of Meaning / 9. Ambiguity
'Dissemination' is opposed to polysemia, since that is irreducible, because of multiple understandings [Derrida, by Glendinning]
19. Language / A. Nature of Meaning / 10. Denial of Meanings
Words exist in 'spacing', so meanings are never synchronic except in writing [Derrida]
22. Metaethics / C. The Good / 1. Goodness / a. Form of the Good
The good is beautiful [Plato]
The good is implicitly violent (against evil), so there is no pure good [Derrida]
23. Ethics / C. Virtue Theory / 4. External Goods / d. Friendship
People say that friendship exists only between good men [Plato]