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All the ideas for 'works', 'Knowledge:Readings in Cont.Epist' and 'Investigations in the Foundations of Set Theory I'

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52 ideas

1. Philosophy / D. Nature of Philosophy / 1. Philosophy
Derrida focuses on other philosophers, rather than on science [Derrida]
     Full Idea: We should focus on other philosophers, and not on science.
     From: Jacques Derrida (works [1990]), quoted by Barry Stocker - Derrida on Deconstruction
1. Philosophy / D. Nature of Philosophy / 3. Philosophy Defined
Philosophy is just a linguistic display [Derrida]
     Full Idea: Philosophy is entirely linguistic, and is a display.
     From: Jacques Derrida (works [1990]), quoted by Barry Stocker - Derrida on Deconstruction
1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / e. Philosophy as reason
Philosophy aims to build foundations for thought [Derrida, by May]
     Full Idea: Derrida points out that the project of philosophy consists largely in attempting to build foundations for thought.
     From: report of Jacques Derrida (works [1990]) by Todd May - Gilles Deleuze 1.04
     A reaction: You would first need to be convinced that there could be such a thing as foundations for thinking. Derrida thinks the project is hopeless. I think of it more as building an ideal framework for thought.
1. Philosophy / D. Nature of Philosophy / 7. Despair over Philosophy
Philosophy is necessarily metaphorical, and its writing is aesthetic [Derrida]
     Full Idea: All of philosophy is necessarily metaphorical, and hence aesthetic.
     From: Jacques Derrida (works [1990]), quoted by Barry Stocker - Derrida on Deconstruction
1. Philosophy / H. Continental Philosophy / 3. Hermeneutics
Interpretations can be interpreted, so there is no original 'meaning' available [Derrida]
     Full Idea: Because interpretations of texts can be interpreted, they can therefore have no 'original meaning'.
     From: Jacques Derrida (works [1990]), quoted by Barry Stocker - Derrida on Deconstruction
Hermeneutics blunts truth, by conforming it to the interpreter [Derrida, by Zimmermann,J]
     Full Idea: Derrida worried that hermeneutics blunts the disruptive power of truth by forcing it conform to the interpreter's mental horizon.
     From: report of Jacques Derrida (works [1990]) by Jens Zimmermann - Hermeneutics: a very short introduction 3 'The heart'
     A reaction: Good heavens - I agree with Derrida. Very French, though, to see the value of truth in its disruptiveness. I tend to find the truth reassuring, but then I'm English.
Hermeneutics is hostile, trying to overcome the other person's difference [Derrida, by Zimmermann,J]
     Full Idea: Derrida described the hermeneutic impulse to understand another as a form of violence that seeks to overcome the other's particularity and unique difference.
     From: report of Jacques Derrida (works [1990]) by Jens Zimmermann - Hermeneutics: a very short introduction App 'Derrida'
     A reaction: I'm not sure about 'violence', but Derrida was on to somethng here. The 'hermeneutic circle' sounds like a creepy process of absorption, where the original writer disappears in a whirlpool of interpretation.
1. Philosophy / H. Continental Philosophy / 4. Linguistic Structuralism
Structuralism destroys awareness of dynamic meaning [Derrida]
     Full Idea: Structuralism destroys awareness of dynamic meaning.
     From: Jacques Derrida (works [1990]), quoted by Barry Stocker - Derrida on Deconstruction
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]
     Full Idea: The tradition of conceiving being in terms of persisting presence, and meaning in terms of pure intelligibility or logos potentially present to the mind, finds itself dismantled by resources internal to its own construction.
     From: report of Jacques Derrida (works [1990]) by Simon Glendinning - Derrida: A Very Short Introduction 6
     A reaction: [compressed] Glendinning says this is the basic meaning of de-construction. My personal reading of this is that Aristotle is right, and grand talk of Being is hopeless, so we should just aim to understand objects. I also believe in propositions.
Sincerity can't be verified, so fiction infuses speech, and hence reality also [Derrida]
     Full Idea: Sincerity can never be verified, so fiction infuses all speech, which means that reality is also fictional.
     From: Jacques Derrida (works [1990]), quoted by Barry Stocker - Derrida on Deconstruction
Sentences are contradictory, as they have opposite meanings in some contexts [Derrida]
     Full Idea: Sentences are implicitly contradictory, because they can be used differently in different contexts (most obviously in 'I am ill').
     From: Jacques Derrida (works [1990]), quoted by Barry Stocker - Derrida on Deconstruction
We aim to explore the limits of expression (as in Mallarmé's poetry) [Derrida]
     Full Idea: The aim is to explore the limits of expression (which is what makes the poetry of Mallarmé so important).
     From: Jacques Derrida (works [1990]), quoted by Barry Stocker - Derrida on Deconstruction
2. Reason / D. Definition / 8. Impredicative Definition
Predicative definitions are acceptable in mathematics if they distinguish objects, rather than creating them? [Zermelo, by Lavine]
     Full Idea: On Zermelo's view, predicative definitions are not only indispensable to mathematics, but they are unobjectionable since they do not create the objects they define, but merely distinguish them from other objects.
     From: report of Ernst Zermelo (Investigations in the Foundations of Set Theory I [1908]) by Shaughan Lavine - Understanding the Infinite V.1
     A reaction: This seems to have an underlying platonism, that there are hitherto undefined 'objects' lying around awaiting the honour of being defined. Hm.
3. Truth / A. Truth Problems / 9. Rejecting Truth
Derrida says that all truth-talk is merely metaphor [Derrida, by Engel]
     Full Idea: Derrida's view is that every discourse is metaphorical, and there is no difference between truth-talk and metaphor.
     From: report of Jacques Derrida (works [1990]) by Pascal Engel - Truth §2.5
     A reaction: Right. Note that this is a Frenchman's summary. How would one define metaphor, without mentioning that it is parasitic on truth? Certainly some language tries to be metaphor, and other language tries not to be.
True thoughts are inaccessible, in the subconscious, prior to speech or writing [Derrida]
     Full Idea: 'True' thoughts are inaccessible, buried in the subconscious, long before they get to speech or writing.
     From: Jacques Derrida (works [1990]), quoted by Barry Stocker - Derrida on Deconstruction
     A reaction: [My reading of some Derrida produced no quotations. I've read two commentaries, which were obscure. The Derrida ideas in this db are my simplistic tertiary summaries. Experts can chuckle over my failure]
4. Formal Logic / F. Set Theory ST / 1. Set Theory
We take set theory as given, and retain everything valuable, while avoiding contradictions [Zermelo]
     Full Idea: Starting from set theory as it is historically given ...we must, on the one hand, restrict these principles sufficiently to exclude as contradiction and, on the other, take them sufficiently wide to retain all that is valuable in this theory.
     From: Ernst Zermelo (Investigations in the Foundations of Set Theory I [1908], Intro)
     A reaction: Maddy calls this the one-step-back-from-disaster rule of thumb. Zermelo explicitly mentions the 'Russell antinomy' that blocked Frege's approach to sets.
Set theory investigates number, order and function, showing logical foundations for mathematics [Zermelo]
     Full Idea: Set theory is that branch whose task is to investigate mathematically the fundamental notions 'number', 'order', and 'function', taking them in their pristine, simple form, and to develop thereby the logical foundations of all of arithmetic and analysis.
     From: Ernst Zermelo (Investigations in the Foundations of Set Theory I [1908], Intro)
     A reaction: At this point Zermelo seems to be a logicist. Right from the start set theory was meant to be foundational to mathematics, and not just a study of the logic of collections.
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]
     Full Idea: Zermelo-Fraenkel axioms: Existence (at least one set); Extension (same elements, same set); Specification (a condition creates a new set); Pairing (two sets make a set); Unions; Powers (all subsets make a set); Infinity (set of successors); Choice
     From: report of Ernst Zermelo (Investigations in the Foundations of Set Theory I [1908]) by Brian Clegg - Infinity: Quest to Think the Unthinkable Ch.15
Zermelo published his axioms in 1908, to secure a controversial proof [Zermelo, by Maddy]
     Full Idea: Zermelo proposed his listed of assumptions (including the controversial Axiom of Choice) in 1908, in order to secure his controversial proof of Cantor's claim that ' we can always bring any well-defined set into the form of a well-ordered set'.
     From: report of Ernst Zermelo (Investigations in the Foundations of Set Theory I [1908]) by Penelope Maddy - Believing the Axioms I §1
     A reaction: This is interesting because it sometimes looks as if axiom systems are just a way of tidying things up. Presumably it is essential to get people to accept the axioms in their own right, the 'old-fashioned' approach that they be self-evident.
Set theory can be reduced to a few definitions and seven independent axioms [Zermelo]
     Full Idea: I intend to show how the entire theory created by Cantor and Dedekind can be reduced to a few definitions and seven principles, or axioms, which appear to be mutually independent.
     From: Ernst Zermelo (Investigations in the Foundations of Set Theory I [1908], Intro)
     A reaction: The number of axioms crept up to nine or ten in subsequent years. The point of axioms is maximum reduction and independence from one another. He says nothing about self-evidence (though Boolos claimed a degree of that).
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]
     Full Idea: Zermelo's Pairing Axiom superseded (in 1930) his original 1908 Axiom of Elementary Sets. Like Union, its only justification seems to rest on 'limitations of size' and on the 'iterative conception'.
     From: report of Ernst Zermelo (Investigations in the Foundations of Set Theory I [1908]) by Penelope Maddy - Believing the Axioms I §1.3
     A reaction: Maddy says of this and Union, that they seem fairly obvious, but that their justification is of prime importance, if we are to understand what the axioms should be.
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]
     Full Idea: Zermelo used a weak form of the Axiom of Foundation to block Russell's paradox in 1906, but in 1908 felt that the form of his Separation Axiom was enough by itself, and left the earlier axiom off his published list.
     From: report of Ernst Zermelo (Investigations in the Foundations of Set Theory I [1908]) by Penelope Maddy - Believing the Axioms I §1.2
     A reaction: Foundation turns out to be fairly controversial. Barwise actually proposes Anti-Foundation as an axiom. Foundation seems to be the rock upon which the iterative view of sets is built. Foundation blocks infinite descending chains of sets, and circularity.
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / m. Axiom of Separation
The Axiom of Separation requires set generation up to one step back from contradiction [Zermelo, by Maddy]
     Full Idea: The most characteristic Zermelo axiom is Separation, guided by a new rule of thumb: 'one step back from disaster' - principles of set generation should be as strong as possible short of contradiction.
     From: report of Ernst Zermelo (Investigations in the Foundations of Set Theory I [1908]) by Penelope Maddy - Believing the Axioms I §1.4
     A reaction: Why is there an underlying assumption that we must have as many sets as possible? We are then tempted to abolish axioms like Foundation, so that we can have even more sets!
Not every predicate has an extension, but Separation picks the members that satisfy a predicate [Zermelo, by Hart,WD]
     Full Idea: Zermelo assumes that not every predicate has an extension but rather that given a set we may separate out from it those of its members satisfying the predicate. This is called 'separation' (Aussonderung).
     From: report of Ernst Zermelo (Investigations in the Foundations of Set Theory I [1908]) by William D. Hart - The Evolution of Logic 3
5. Theory of Logic / F. Referring in Logic / 1. Naming / b. Names as descriptive
'I' is the perfect name, because it denotes without description [Derrida]
     Full Idea: 'I' is the perfect name, because it denotes without description.
     From: Jacques Derrida (works [1990]), quoted by Barry Stocker - Derrida on Deconstruction
Names have a subjective aspect, especially the role of our own name [Derrida]
     Full Idea: We can give a subjective account of names, by considering our own name.
     From: Jacques Derrida (works [1990]), quoted by Barry Stocker - Derrida on Deconstruction
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]
     Full Idea: Even Kripke can't explain names, because the word is the thing, and also the thing is the word.
     From: Jacques Derrida (works [1990]), quoted by Barry Stocker - Derrida on Deconstruction
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]
     Full Idea: In Zermelo's set theory, the Burali-Forti Paradox becomes a proof that there is no set of all ordinals (so 'is an ordinal' has no extension).
     From: report of Ernst Zermelo (Investigations in the Foundations of Set Theory I [1908]) by William D. Hart - The Evolution of Logic 3
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]
     Full Idea: For Zermelo the successor of n is {n} (rather than Von Neumann's successor, which is n U {n}).
     From: report of Ernst Zermelo (Investigations in the Foundations of Set Theory I [1908]) by Penelope Maddy - Naturalism in Mathematics I.2 n8
     A reaction: I could ask some naive questions about the comparison of these two, but I am too shy about revealing my ignorance.
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]
     Full Idea: Zermelo was a reductionist, and believed that theorems purportedly about numbers (cardinal or ordinal) are really about sets, and since Von Neumann's definitions of ordinals and cardinals as sets, this has become common doctrine.
     From: report of Ernst Zermelo (Investigations in the Foundations of Set Theory I [1908]) by Penelope Maddy - Believing the Axioms I §1.8
     A reaction: Frege has a more sophisticated take on this approach. It may just be an updating of the Greek idea that arithmetic is about treating many things as a unit. A set bestows an identity on a group, and that is all that is needed.
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]
     Full Idea: In Zermelo's set-theoretic definition of number, 2 is a member of 3, but not a member of 4; in Von Neumann's definition every number is a member of every larger number. This means they have two different structures.
     From: report of Ernst Zermelo (Investigations in the Foundations of Set Theory I [1908]) by James Robert Brown - Philosophy of Mathematics Ch. 4
     A reaction: This refers back to the dilemma highlighted by Benacerraf, which was supposed to be the motivation for structuralism. My intuition says that the best answer is that they are both wrong. In a pattern, the nodes aren't 'members' of one another.
11. Knowledge Aims / A. Knowledge / 1. Knowledge
Perception, introspection, testimony, memory, reason, and inference can give us knowledge [Bernecker/Dretske]
     Full Idea: The basic sources of knowledge and justification are perception, introspection, testimony, memory, reason, and inference.
     From: Bernecker / Dretske (Knowledge:Readings in Cont.Epist [2000], Pt.V Int)
12. Knowledge Sources / B. Perception / 7. Causal Perception
Causal theory says true perceptions must be caused by the object perceived [Bernecker/Dretske]
     Full Idea: The causal theory of perceptions says that to perceive an object is to have a sense-datum caused by that object; it is not enough for the world to be the way we perceive it; the world must cause the perception.
     From: Bernecker / Dretske (Knowledge:Readings in Cont.Epist [2000], Pt.V Int)
     A reaction: All causal theories seem dubious to me; what causes something is not the same was what it means, or refers to, or what justifies it. The hallmark of successful perception is truth. I would perceive a tree if God planted the perception in me.
12. Knowledge Sources / E. Direct Knowledge / 4. Memory
You can acquire new knowledge by exploring memories [Bernecker/Dretske]
     Full Idea: You can first come to know by remembering, as in learning how many windows there were in your childhood home by imagining a tour.
     From: Bernecker / Dretske (Knowledge:Readings in Cont.Epist [2000], Pt.V Int)
13. Knowledge Criteria / A. Justification Problems / 1. Justification / a. Justification issues
Justification can be of the belief, or of the person holding the belief [Bernecker/Dretske]
     Full Idea: There is a distinction between a person being justified in holding a belief, and the belief itself being justified.
     From: Bernecker / Dretske (Knowledge:Readings in Cont.Epist [2000], Pt.II Int)
     A reaction: This is the crucial and elementary distinction which even the most sophisticated of epistemologists keep losing sight of. Epistemology is about persons. All true beliefs are justified - by the facts!
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / a. Foundationalism
Foundationalism aims to avoid an infinite regress [Bernecker/Dretske]
     Full Idea: The driving force behind foundationalism has always been the threat of an infinite regress.
     From: Bernecker / Dretske (Knowledge:Readings in Cont.Epist [2000], Pt.III Int)
     A reaction: You could just live with the regress (Peter Klein), or say that the regress fades away, or that it is cut off by social epistemological convention, or the regress circles round and rejoins.
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / f. Foundationalism critique
Infallible sensations can't be foundations if they are non-epistemic [Bernecker/Dretske]
     Full Idea: If sense experiences are non-epistemic they may be infallible, but they are unsuitable for providing the foundations for other beliefs.
     From: Bernecker / Dretske (Knowledge:Readings in Cont.Epist [2000], Pt.III Int)
     A reaction: If we experience flashing lights in the retina, or an afterimage, we don't think we are seeing objects, so why is normal perception different? Ans: because it is supported by judgement.
13. Knowledge Criteria / C. External Justification / 1. External Justification
Justification is normative, so it can't be reduced to cognitive psychology [Bernecker/Dretske]
     Full Idea: The concept of justification is absolutely central to epistemology; but this concept is normative (i.e. it lays down norms), so epistemology can't be reduced to factual cognitive psychology.
     From: Bernecker / Dretske (Knowledge:Readings in Cont.Epist [2000], Pt.III Int)
     A reaction: A simple rejection of the 'epistemology naturalised' idea. Best to start with slugs rather than people. You can confuse a slug, so it has truth or falsehood, but what is slug normativity? This is an interesting discussion point, not an argument.
13. Knowledge Criteria / D. Scepticism / 6. Scepticism Critique
Modern arguments against the sceptic are epistemological and semantic externalism, and the focus on relevance [Bernecker/Dretske]
     Full Idea: In modern epistemology the three strategies to rebut the sceptic are 1) epistemological externalism, 2) the 'relevant alternative account of knowledge' (that scepticism is too extreme to be relevant), and 3) semantic externalism.
     From: Bernecker / Dretske (Knowledge:Readings in Cont.Epist [2000], Pt.IV Int)
14. Science / C. Induction / 5. Paradoxes of Induction / a. Grue problem
Predictions are bound to be arbitrary if they depend on the language used [Bernecker/Dretske]
     Full Idea: The new riddle of induction ('grue') seems to demonstrate that sound inductive inferences are arbitrary because they depend on the actual language people use to formulate predictions.
     From: Bernecker / Dretske (Knowledge:Readings in Cont.Epist [2000], Pt.V Int)
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]
     Full Idea: Heidegger showed us the importance of transient time for consciousness.
     From: Jacques Derrida (works [1990]), quoted by Barry Stocker - Derrida on Deconstruction
18. Thought / A. Modes of Thought / 1. Thought
'Tacit theory' controls our thinking (which is why Freud is important) [Derrida]
     Full Idea: All thought is controlled by tacit theory (which is why Freud is so important).
     From: Jacques Derrida (works [1990]), quoted by Barry Stocker - Derrida on Deconstruction
     A reaction: This idea is said to be the essential thought of Derrida's Deconstruction. The aim is liberation of thought, by identifying and bypassing these tacit metaphysical schemas.
18. Thought / C. Content / 6. Broad Content
Semantic externalism ties content to the world, reducing error [Bernecker/Dretske]
     Full Idea: Semantic externalism ties our mental content down to our actual environment so there is no possibility of massive error.
     From: Bernecker / Dretske (Knowledge:Readings in Cont.Epist [2000], Pt.V Int)
     A reaction: This sounds more prescriptive than descriptive. People do make massive errors in their concepts. Maybe educated people are more externalist (respectful of experts) than uneducated people?
19. Language / A. Nature of Meaning / 1. Meaning
Madness and instability ('the demonic hyperbole') lurks in all language [Derrida]
     Full Idea: Madness and instability ('the demonic hyperbole') lurks behind all language.
     From: Jacques Derrida (works [1990]), quoted by Barry Stocker - Derrida on Deconstruction
Meanings depend on differences and contrasts [Derrida]
     Full Idea: Meaning depends on 'differences' (contrasts).
     From: Jacques Derrida (works [1990]), quoted by Barry Stocker - Derrida on Deconstruction
For Aristotle all proper nouns must have a single sense, which is the purpose of language [Derrida]
     Full Idea: A noun [for Aristotle] is proper when it has but a single sense. Better, it is only in this case that it is properly a noun. Univocity is the essence, or better, the telos of language.
     From: Jacques Derrida (works [1990]), quoted by Simon Glendinning - Derrida: A Very Short Introduction 5
     A reaction: [no ref given] His target seem to be Aristotelian definition, and also formal logic, which usually needs unambiguous meanings. {I'm puzzled that he thinks 'telos' is simply better than 'essence', since it is quite different].
Capacity for repetitions is the hallmark of language [Derrida]
     Full Idea: The capacity for repetitions is the hallmark of language.
     From: Jacques Derrida (works [1990]), quoted by Barry Stocker - Derrida on Deconstruction
The sign is only conceivable as a movement between elusive presences [Derrida]
     Full Idea: The sign is conceivable only on the basis of the presence that it defers, and moving toward the deferred presence that it aims to reappropriate.
     From: Jacques Derrida (works [1990]), quoted by Simon Glendinning - Derrida: A Very Short Introduction 6
     A reaction: [Glendinning gives no source for this] I take the fundamental idea to be that meanings are dynamic, when they are traditionally understood as static (and specifiable in dictionaries).
Writing functions even if the sender or the receiver are absent [Derrida, by Glendinning]
     Full Idea: Writing can and must be able to do without the presence of the sender. ...Also writing can and must he able to do without the presence of the receiver.
     From: report of Jacques Derrida (works [1990]) by Simon Glendinning - Derrida: A Very Short Introduction 6
     A reaction: In simple terms, one of them could die during the transmission. This is the grounds for the assertion of the primacy of writing. It opposes orthodox views which define language in terms of sender and receiver.
19. Language / A. Nature of Meaning / 9. Ambiguity
'Dissemination' is opposed to polysemia, since that is irreducible, because of multiple understandings [Derrida, by Glendinning]
     Full Idea: The intention to oppose polysemia with dissemination does not aim to affirm that everything we say is ambiguous, but that polysemia is irreducible in the sense that each and every 'meaning' is itself subject to more than one understanding.
     From: report of Jacques Derrida (works [1990]) by Simon Glendinning - Derrida: A Very Short Introduction 5
     A reaction: The key point, I think, is that ambiguity and polysemia are not failures of language (which is the way most logicians see it), but part of the essential and irreducible nature of language. Nietzsche started this line of thought.
19. Language / A. Nature of Meaning / 10. Denial of Meanings
Words exist in 'spacing', so meanings are never synchronic except in writing [Derrida]
     Full Idea: Words only exist is 'spacings' (of time and space), so there are no synchronic meanings (except perhaps in writing).
     From: Jacques Derrida (works [1990]), quoted by Barry Stocker - Derrida on Deconstruction
22. Metaethics / C. The Good / 1. Goodness / a. Form of the Good
The good is implicitly violent (against evil), so there is no pure good [Derrida]
     Full Idea: Even the good is implicitly violent (against evil), so there can be no 'pure' good.
     From: Jacques Derrida (works [1990]), quoted by Barry Stocker - Derrida on Deconstruction