Combining Texts

All the ideas for 'Structures and Structuralism in Phil of Maths', 'The Source of Necessity' and 'works'

unexpand these ideas     |    start again     |     specify just one area for these texts


51 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
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]
3. Truth / F. Semantic Truth / 2. Semantic Truth
While true-in-a-model seems relative, true-in-all-models seems not to be [Reck/Price]
     Full Idea: While truth can be defined in a relative way, as truth in one particular model, a non-relative notion of truth is implied, as truth in all models.
     From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §4)
     A reaction: [The article is actually discussing arithmetic] This idea strikes me as extremely important. True-in-all-models is usually taken to be tautological, but it does seem to give a more universal notion of truth. See semantic truth, Tarski, Davidson etc etc.
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
ZFC set theory has only 'pure' sets, without 'urelements' [Reck/Price]
     Full Idea: In standard ZFC ('Zermelo-Fraenkel with Choice') set theory we deal merely with pure sets, not with additional urelements.
     From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §2)
     A reaction: The 'urelements' would the actual objects that are members of the sets, be they physical or abstract. This idea is crucial to understanding philosophy of mathematics, and especially logicism. Must the sets exist, just as the urelements do?
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
5. Theory of Logic / G. Quantification / 5. Second-Order Quantification
Three types of variable in second-order logic, for objects, functions, and predicates/sets [Reck/Price]
     Full Idea: In second-order logic there are three kinds of variables, for objects, for functions, and for predicates or sets.
     From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §5)
     A reaction: It is interesting that a predicate seems to be the same as a set, which begs rather a lot of questions. For those who dislike second-order logic, there seems nothing instrinsically wicked in having variables ranging over innumerable multi-order types.
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
'Analysis' is the theory of the real numbers [Reck/Price]
     Full Idea: 'Analysis' is the theory of the real numbers.
     From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §2)
     A reaction: 'Analysis' began with the infinitesimal calculus, which later built on the concept of 'limit'. A continuum of numbers seems to be required to make that work.
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / a. Axioms for numbers
Mereological arithmetic needs infinite objects, and function definitions [Reck/Price]
     Full Idea: The difficulties for a nominalistic mereological approach to arithmetic is that an infinity of physical objects are needed (space-time points? strokes?), and it must define functions, such as 'successor'.
     From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §4)
     A reaction: Many ontologically austere accounts of arithmetic are faced with the problem of infinity. The obvious non-platonist response seems to be a modal or if-then approach. To postulate infinite abstract or physical entities so that we can add 3 and 2 is mad.
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / e. Peano arithmetic 2nd-order
Peano Arithmetic can have three second-order axioms, plus '1' and 'successor' [Reck/Price]
     Full Idea: A common formulation of Peano Arithmetic uses 2nd-order logic, the constant '1', and a one-place function 's' ('successor'). Three axioms then give '1 is not a successor', 'different numbers have different successors', and induction.
     From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §2)
     A reaction: This is 'second-order' Peano Arithmetic, though it is at least as common to formulate in first-order terms (only quantifying over objects, not over properties - as is done here in the induction axiom). I like the use of '1' as basic instead of '0'!
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
Set-theory gives a unified and an explicit basis for mathematics [Reck/Price]
     Full Idea: The merits of basing an account of mathematics on set theory are that it allows for a comprehensive unified treatment of many otherwise separate branches of mathematics, and that all assumption, including existence, are explicit in the axioms.
     From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §4)
     A reaction: I am forming the impression that set-theory provides one rather good model (maybe the best available) for mathematics, but that doesn't mean that mathematics is set-theory. The best map of a landscape isn't a landscape.
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
Structuralism emerged from abstract algebra, axioms, and set theory and its structures [Reck/Price]
     Full Idea: Structuralism has emerged from the development of abstract algebra (such as group theory), the creation of axiom systems, the introduction of set theory, and Bourbaki's encyclopaedic survey of set theoretic structures.
     From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §2)
     A reaction: In other words, mathematics has gradually risen from one level of abstraction to the next, so that mathematical entities like points and numbers receive less and less attention, with relationships becoming more prominent.
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / b. Varieties of structuralism
Relativist Structuralism just stipulates one successful model as its arithmetic [Reck/Price]
     Full Idea: Relativist Structuralism simply picks one particular model of axiomatised arithmetic (i.e. one particular interpretation that satisfies the axioms), and then stipulates what the elements, functions and quantifiers refer to.
     From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §4)
     A reaction: The point is that a successful model can be offered, and it doesn't matter which one, like having any sort of aeroplane, as long as it flies. I don't find this approach congenial, though having a model is good. What is the essence of flight?
There are 'particular' structures, and 'universal' structures (what the former have in common) [Reck/Price]
     Full Idea: The term 'structure' has two uses in the literature, what can be called 'particular structures' (which are particular relational systems), but also what can be called 'universal structures' - what particular systems share, or what they instantiate.
     From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §6)
     A reaction: This is a very helpful distinction, because it clarifies why (rather to my surprise) some structuralists turn out to be platonists in a new guise. Personal my interest in structuralism has been anti-platonist from the start.
Pattern Structuralism studies what isomorphic arithmetic models have in common [Reck/Price]
     Full Idea: According to 'pattern' structuralism, what we study are not the various particular isomorphic models of arithmetic, but something in addition to them: a corresponding pattern.
     From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §7)
     A reaction: Put like that, we have to feel a temptation to wield Ockham's Razor. It's bad enough trying to give the structure of all the isomorphic models, without seeking an even more abstract account of underlying patterns. But patterns connect to minds..
There are Formalist, Relativist, Universalist and Pattern structuralism [Reck/Price]
     Full Idea: There are four main variants of structuralism in the philosophy of mathematics - formalist structuralism, relativist structuralism, universalist structuralism (with modal variants), and pattern structuralism.
     From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §9)
     A reaction: I'm not sure where Chihara's later book fits into this, though it is at the nominalist end of the spectrum. Shapiro and Resnik do patterns (the latter more loosely); Hellman does modal universalism; Quine does the relativist version. Dedekind?
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / c. Nominalist structuralism
Formalist Structuralism says the ontology is vacuous, or formal, or inference relations [Reck/Price]
     Full Idea: Formalist Structuralism endorses structural methodology in mathematics, but rejects semantic and metaphysical problems as either meaningless, or purely formal, or as inference relations.
     From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §3)
     A reaction: [very compressed] I find the third option fairly congenial, certainly in preference to rather platonist accounts of structuralism. One still needs to distinguish the mathematical from the non-mathematical in the inference relations.
Maybe we should talk of an infinity of 'possible' objects, to avoid arithmetic being vacuous [Reck/Price]
     Full Idea: It is tempting to take a modal turn, and quantify over all possible objects, because if there are only a finite number of actual objects, then there are no models (of the right sort) for Peano Arithmetic, and arithmetic is vacuously true.
     From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §5)
     A reaction: [compressed; Geoffrey Hellman is the chief champion of this view] The article asks whether we are not still left with the puzzle of whether infinitely many objects are possible, instead of existent.
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / d. Platonist structuralism
Universalist Structuralism is based on generalised if-then claims, not one particular model [Reck/Price]
     Full Idea: Universalist Structuralism is a semantic thesis, that an arithmetical statement asserts a universal if-then statement. We build an if-then statement (using quantifiers) into the structure, and we generalise away from any one particular model.
     From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §5)
     A reaction: There remains the question of what is distinctively mathematical about the highly generalised network of inferences that is being described. Presumable the axioms capture that, but why those particular axioms? Russell is cited as an originator.
Universalist Structuralism eliminates the base element, as a variable, which is then quantified out [Reck/Price]
     Full Idea: Universalist Structuralism is eliminativist about abstract objects, in a distinctive form. Instead of treating the base element (say '1') as an ambiguous referring expression (the Relativist approach), it is a variable which is quantified out.
     From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §5)
     A reaction: I am a temperamental eliminativist on this front (and most others) so this is tempting. I am also in love with the concept of a 'variable', which I take to be utterly fundamental to all conceptual thought, even in animals, and not just a trick of algebra.
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
The existence of an infinite set is assumed by Relativist Structuralism [Reck/Price]
     Full Idea: Relativist Structuralism must first assume the existence of an infinite set, otherwise there would be no model to pick, and arithmetical terms would have no reference.
     From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §4)
     A reaction: See Idea 10169 for Relativist Structuralism. They point out that ZFC has an Axiom of Infinity.
8. Modes of Existence / E. Nominalism / 6. Mereological Nominalism
A nominalist might avoid abstract objects by just appealing to mereological sums [Reck/Price]
     Full Idea: One way for a nominalist to reject appeal to all abstract objects, including sets, is to only appeal to nominalistically acceptable objects, including mereological sums.
     From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §4)
     A reaction: I'm suddenly thinking that this looks very interesting and might be the way to go. The issue seems to be whether mereological sums should be seen as constrained by nature, or whether they are unrestricted. See Mereology in Ontology...|Intrinsic Identity.
10. Modality / C. Sources of Modality / 1. Sources of Necessity
Explanation of necessity must rest on something necessary or something contingent [Hale]
     Full Idea: The dilemma is that to give the ultimate source of any necessity, we must either appeal to something which could not have been otherwise (i.e. is itself necessary), or advert to something which could have been otherwise (i.e. is itself merely contingent).
     From: Bob Hale (The Source of Necessity [2002], p.301)
     A reaction: [Hale is summarising Blackburn's view, and going on to disagree with it] Hale looks for a third way, but Blackburn seems to face us with quite a plausible dilemma.
Why is this necessary, and what is necessity in general; why is this necessary truth true, and why necessary? [Hale]
     Full Idea: We must distinguish between explaining particular necessities and explaining necessity in general; and we ought to distinguish between explaining, in regard to any necessary truth, why it is true, and explaining why it is necessary.
     From: Bob Hale (The Source of Necessity [2002], p.308)
     A reaction: Useful. The pluralist view I associate with Fine says we can explain types of necessity, but not necessity in general. If we seek truthmakers, there is a special case of what adds the necessity to the truth.
The explanation of a necessity can be by a truth (which may only happen to be a necessary truth) [Hale]
     Full Idea: My claim is that there are non-transitive explanations of necessities, where what explains is indeed necessary, but what explains the necessity of the explanandum is not the explanation's necessity, but its truth simpliciter.
     From: Bob Hale (The Source of Necessity [2002], p.311)
     A reaction: The big idea is to avoid a regress of necessities. The actual truths he proposes are essentialist. An interesting proposal. It might depend on how one views essences (as giving identity, or causal power)
10. Modality / C. Sources of Modality / 3. Necessity by Convention
If necessity rests on linguistic conventions, those are contingent, so there is no necessity [Hale]
     Full Idea: If the alleged necessity, e,g, 2+2=4, really does depend upon a convention governing the use of the words in which we state it, and the existence of that convention is merely a contingent matter, then it can't after all be necessary.
     From: Bob Hale (The Source of Necessity [2002], p.302)
     A reaction: [Hale is citing Blackburn for this claim] Hale suggests replies, by keeping truth and meaning separate, and involving laws of logic. Blackburn clearly has a good point.
10. Modality / C. Sources of Modality / 4. Necessity from Concepts
Concept-identities explain how we know necessities, not why they are necessary [Hale]
     Full Idea: It seems to me that identity-relations among concepts have more to do with explaining how we know that vixens are female foxes etc., than with explaining why it is necessary, and, more generally, with explaining why some necessities are knowable a priori.
     From: Bob Hale (The Source of Necessity [2002], P.313)
     A reaction: Hale rejects the conceptual and conventional accounts of necessity, in favour of the essentialist view. This strikes me as a good suggestion of Hale's, since I agree with him about the essentialism.
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.
19. Language / A. Nature of Meaning / 1. Meaning
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.
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
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