81 ideas
| 21887 | 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 |
| 21888 | 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 |
| 21896 | 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. |
| 21893 | 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 |
| 21892 | 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 |
| 20934 | 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. |
| 20925 | 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. |
| 21895 | 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 |
| 21934 | 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. |
| 21881 | 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 |
| 21883 | 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 |
| 21882 | 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 |
| 18137 | Impredicative definitions are wrong, because they change the set that is being defined? [Bostock] |
| Full Idea: Poincaré suggested that what is wrong with an impredicative definition is that it allows the set defined to alter its composition as more sets are added to the theory. | |
| From: David Bostock (Philosophy of Mathematics [2009], 8.3) |
| 4756 | 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. |
| 21877 | 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] |
| 18122 | Classical interdefinitions of logical constants and quantifiers is impossible in intuitionism [Bostock] |
| Full Idea: None of the classical ways of defining one logical constant in terms of others is available in intuitionist logic (and this includes the two quantifiers). | |
| From: David Bostock (Philosophy of Mathematics [2009], 7.2) |
| 18114 | There is no single agreed structure for set theory [Bostock] |
| Full Idea: There is so far no agreed set of axioms for set theory which is categorical, i.e. which does pick just one structure. | |
| From: David Bostock (Philosophy of Mathematics [2009], 6.4) | |
| A reaction: This contrasts with Peano Arithmetic, which is categorical in its second-order version. |
| 18107 | A 'proper class' cannot be a member of anything [Bostock] |
| Full Idea: A 'proper class' cannot be a member of anything, neither of a set nor of another proper class. | |
| From: David Bostock (Philosophy of Mathematics [2009], 5.4) |
| 18115 | We could add axioms to make sets either as small or as large as possible [Bostock] |
| Full Idea: We could add the axiom that all sets are constructible (V = L), making the universe of sets as small as possible, or add the axiom that there is a supercompact cardinal (SC), making the universe as large as we no know how to. | |
| From: David Bostock (Philosophy of Mathematics [2009], 6.4) | |
| A reaction: Bostock says most mathematicians reject the first option, and are undecided about the second option. |
| 18139 | The Axiom of Choice relies on reference to sets that we are unable to describe [Bostock] |
| Full Idea: The usual accounts of ZF are not restricted to subsets that we can describe, and that is what justifies the axiom of choice. | |
| From: David Bostock (Philosophy of Mathematics [2009], 8.4 n36) | |
| A reaction: This contrasts interestingly with predicativism, which says we can only discuss things which we can describe or define. Something like verificationism hovers in the background. |
| 18105 | Replacement enforces a 'limitation of size' test for the existence of sets [Bostock] |
| Full Idea: The Axiom of Replacement (or the Axiom of Subsets, 'Aussonderung', Fraenkel 1922) in effect enforces the idea that 'limitation of size' is a crucial factor when deciding whether a proposed set or does not not exist. | |
| From: David Bostock (Philosophy of Mathematics [2009], 5.4) |
| 18108 | First-order logic is not decidable: there is no test of whether any formula is valid [Bostock] |
| Full Idea: First-order logic is not decidable. That is, there is no test which can be applied to any arbitrary formula of that logic and which will tell one whether the formula is or is not valid (as proved by Church in 1936). | |
| From: David Bostock (Philosophy of Mathematics [2009], 5.5) |
| 18109 | The completeness of first-order logic implies its compactness [Bostock] |
| Full Idea: From the fact that the usual rules for first-level logic are complete (as proved by Gödel 1930), it follows that this logic is 'compact'. | |
| From: David Bostock (Philosophy of Mathematics [2009], 5.5) | |
| A reaction: The point is that the completeness requires finite proofs. |
| 18812 | Split out the logical vocabulary, make an assignment to the rest. It's logical if premises and conclusion match [Tarski, by Rumfitt] |
| Full Idea: Tarski made a division of logical and non-logical vocabulary. He then defined a model as a non-logical assignment satisfying the corresponding sentential function. Then a conclusion follows logically if every model of the premises models the conclusion. | |
| From: report of Alfred Tarski (The Concept of Logical Consequence [1936]) by Ian Rumfitt - The Boundary Stones of Thought 3.2 | |
| A reaction: [compressed] This is Tarski's account of logical consequence, which follows on from his account of truth. 'Logical validity' is then 'true in every model'. Rumfitt doubts whether Tarski has given the meaning of 'logical consequence'. |
| 13344 | X follows from sentences K iff every model of K also models X [Tarski] |
| Full Idea: The sentence X follows logically from the sentences of the class K if and only if every model of the class K is also a model of the sentence X. | |
| From: Alfred Tarski (The Concept of Logical Consequence [1936], p.417) | |
| A reaction: [see Idea 13343 for his account of a 'model'] He is offering to define logical consequence in general, but this definition fits what we now call 'semantic consequence', written |=. This it is standard practice to read |= as 'models'. |
| 21878 | 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 |
| 21889 | '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 |
| 21879 | 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 |
| 18123 | Substitutional quantification is just standard if all objects in the domain have a name [Bostock] |
| Full Idea: Substitutional quantification and quantification understood in the usual 'ontological' way will coincide when every object in the (ontological) domain has a name. | |
| From: David Bostock (Philosophy of Mathematics [2009], 7.3 n23) |
| 18120 | The Deduction Theorem is what licenses a system of natural deduction [Bostock] |
| Full Idea: The Deduction Theorem is what licenses a system of 'natural deduction' in the first place. | |
| From: David Bostock (Philosophy of Mathematics [2009], 7.2) |
| 13343 | A 'model' is a sequence of objects which satisfies a complete set of sentential functions [Tarski] |
| Full Idea: An arbitrary sequence of objects which satisfies every sentential function of the sentences L' will be called a 'model' or realization of the class L of sentences. There can also be a model of a single sentence is this way. | |
| From: Alfred Tarski (The Concept of Logical Consequence [1936], p.417) | |
| A reaction: [L' is L with the constants replaced by variables] Tarski is the originator of model theory, which is central to modern logic. The word 'realization' is a helpful indicator of what he has in mind. A model begins to look like a possible world. |
| 18125 | Berry's Paradox considers the meaning of 'The least number not named by this name' [Bostock] |
| Full Idea: Berry's Paradox can be put in this form, by considering the alleged name 'The least number not named by this name'. | |
| From: David Bostock (Philosophy of Mathematics [2009], 8.1) |
| 18101 | Each addition changes the ordinality but not the cardinality, prior to aleph-1 [Bostock] |
| Full Idea: If you add to the ordinals you produce many different ordinals, each measuring the length of the sequence of ordinals less than it. They each have cardinality aleph-0. The cardinality eventually increases, but we can't say where this break comes. | |
| From: David Bostock (Philosophy of Mathematics [2009], 4.5) |
| 18100 | ω + 1 is a new ordinal, but its cardinality is unchanged [Bostock] |
| Full Idea: If we add ω onto the end of 0,1,2,3,4..., it then has a different length, of ω+1. It has a different ordinal (since it can't be matched with its first part), but the same cardinal (since adding 1 makes no difference). | |
| From: David Bostock (Philosophy of Mathematics [2009], 4.5) | |
| A reaction: [compressed] The ordinals and cardinals coincide up to ω, but this is the point at which they come apart. |
| 18102 | A cardinal is the earliest ordinal that has that number of predecessors [Bostock] |
| Full Idea: It is the usual procedure these days to identify a cardinal number with the earliest ordinal number that has that number of predecessors. | |
| From: David Bostock (Philosophy of Mathematics [2009], 4.5) | |
| A reaction: This sounds circular, since you need to know the cardinal in order to decide which ordinal is the one you want, but, hey, what do I know? |
| 18106 | Aleph-1 is the first ordinal that exceeds aleph-0 [Bostock] |
| Full Idea: The cardinal aleph-1 is identified with the first ordinal to have more than aleph-0 members, and so on. | |
| From: David Bostock (Philosophy of Mathematics [2009], 5.4) | |
| A reaction: That is, the succeeding infinite ordinals all have the same cardinal number of members (aleph-0), until the new total is triggered (at the number of the reals). This is Continuum Hypothesis territory. |
| 18095 | Instead of by cuts or series convergence, real numbers could be defined by axioms [Bostock] |
| Full Idea: In addition to cuts, or converging series, Cantor suggests we can simply lay down a set of axioms for the real numbers, and this can be done without any explicit mention of the rational numbers [note: the axioms are those for a complete ordered field]. | |
| From: David Bostock (Philosophy of Mathematics [2009], 4.4) | |
| A reaction: It is interesting when axioms are best, and when not. Set theory depends entirely on axioms. Horsten and Halbach are now exploring treating truth as axiomatic. You don't give the 'nature' of the thing - just rules for its operation. |
| 18099 | The number of reals is the number of subsets of the natural numbers [Bostock] |
| Full Idea: It is not difficult to show that the number of the real numbers is the same as the number of all the subsets of the natural numbers. | |
| From: David Bostock (Philosophy of Mathematics [2009], 4.5) | |
| A reaction: The Continuum Hypothesis is that this is the next infinite number after the number of natural numbers. Why can't there be a number which is 'most' of the subsets of the natural numbers? |
| 18093 | For Eudoxus cuts in rationals are unique, but not every cut makes a real number [Bostock] |
| Full Idea: As Eudoxus claimed, two distinct real numbers cannot both make the same cut in the rationals, for any two real numbers must be separated by a rational number. He did not say, though, that for every such cut there is a real number that makes it. | |
| From: David Bostock (Philosophy of Mathematics [2009], 4.4) | |
| A reaction: This is in Bostock's discussion of Dedekind's cuts. It seems that every cut is guaranteed to produce a real. Fine challenges the later assumption. |
| 18110 | Infinitesimals are not actually contradictory, because they can be non-standard real numbers [Bostock] |
| Full Idea: Non-standard natural numbers will yield non-standard rational and real numbers. These will include reciprocals which will be closer to 0 than any standard real number. These are like 'infinitesimals', so that notion is not actually a contradiction. | |
| From: David Bostock (Philosophy of Mathematics [2009], 5.5) |
| 18156 | Modern axioms of geometry do not need the real numbers [Bostock] |
| Full Idea: A modern axiomatisation of geometry, such as Hilbert's (1899), does not need to claim the existence of real numbers anywhere in its axioms. | |
| From: David Bostock (Philosophy of Mathematics [2009], 9.B.5.ii) | |
| A reaction: This is despite the fact that geometry is reduced to algebra, and the real numbers are the equivalent of continuous lines. Bostock votes for a Greek theory of proportion in this role. |
| 18097 | The Peano Axioms describe a unique structure [Bostock] |
| Full Idea: The Peano Axioms are categorical, meaning that they describe a unique structure. | |
| From: David Bostock (Philosophy of Mathematics [2009], 4.4 n20) | |
| A reaction: So if you think there is nothing more to the natural numbers than their structure, then the Peano Axioms give the essence of arithmetic. If you think that 'objects' must exist to generate a structure, there must be more to the numbers. |
| 18148 | Hume's Principle is a definition with existential claims, and won't explain numbers [Bostock] |
| Full Idea: Hume's Principle will not do as an implicit definition because it makes a positive claim about the size of the universe (which no mere definition can do), and because it does not by itself explain what the numbers are. | |
| From: David Bostock (Philosophy of Mathematics [2009], 9.A.2) |
| 18145 | Many things will satisfy Hume's Principle, so there are many interpretations of it [Bostock] |
| Full Idea: Hume's Principle gives a criterion of identity for numbers, but it is obvious that many other things satisfy that criterion. The simplest example is probably the numerals (in any notation, decimal, binary etc.), giving many different interpretations. | |
| From: David Bostock (Philosophy of Mathematics [2009], 9.A.2) |
| 18149 | There are many criteria for the identity of numbers [Bostock] |
| Full Idea: There is not just one way of giving a criterion of identity for numbers. | |
| From: David Bostock (Philosophy of Mathematics [2009], 9.A.2) |
| 18143 | Frege makes numbers sets to solve the Caesar problem, but maybe Caesar is a set! [Bostock] |
| Full Idea: The Julius Caesar problem was one reason that led Frege to give an explicit definition of numbers as special sets. He does not appear to notice that the same problem affects his Axiom V for introducing sets (whether Caesar is or is not a set). | |
| From: David Bostock (Philosophy of Mathematics [2009], 9.A.2) | |
| A reaction: The Julius Caesar problem is a sceptical acid that eats into everything in philosophy of mathematics. You give all sorts of wonderful accounts of numbers, but at what point do you know that you now have a number, and not something else? |
| 18116 | Numbers can't be positions, if nothing decides what position a given number has [Bostock] |
| Full Idea: There is no ground for saying that a number IS a position, if the truth is that there is nothing to determine which number is which position. | |
| From: David Bostock (Philosophy of Mathematics [2009], 6.4) | |
| A reaction: If numbers lose touch with the empirical ability to count physical objects, they drift off into a mad world where they crumble away. |
| 18117 | Structuralism falsely assumes relations to other numbers are numbers' only properties [Bostock] |
| Full Idea: Structuralism begins from a false premise, namely that numbers have no properties other than their relations to other numbers. | |
| From: David Bostock (Philosophy of Mathematics [2009], 6.5) | |
| A reaction: Well said. Describing anything purely relationally strikes me as doomed, because you have to say why those things relate in those ways. |
| 18141 | Nominalism about mathematics is either reductionist, or fictionalist [Bostock] |
| Full Idea: Nominalism has two main versions, one which tries to 'reduce' the objects of mathematics to something simpler (Russell and Wittgenstein), and another which claims that such objects are mere 'fictions' which have no reality (Field). | |
| From: David Bostock (Philosophy of Mathematics [2009], 9) |
| 18157 | Nominalism as based on application of numbers is no good, because there are too many applications [Bostock] |
| Full Idea: The style of nominalism which aims to reduce statements about numbers to statements about their applications does not work for the natural numbers, because they have many applications, and it is arbitrary to choose just one of them. | |
| From: David Bostock (Philosophy of Mathematics [2009], 9.B.5.iii) |
| 18150 | Actual measurement could never require the precision of the real numbers [Bostock] |
| Full Idea: We all know that in practice no physical measurement can be 100 per cent accurate, and so it cannot require the existence of a genuinely irrational number, rather than some of the rational numbers close to it. | |
| From: David Bostock (Philosophy of Mathematics [2009], 9.A.3) |
| 18158 | Ordinals are mainly used adjectively, as in 'the first', 'the second'... [Bostock] |
| Full Idea: The basic use of the ordinal numbers is their use as ordinal adjectives, in phrases such as 'the first', 'the second' and so on. | |
| From: David Bostock (Philosophy of Mathematics [2009], 9.5.iii) | |
| A reaction: That is because ordinals seem to attach to particulars, whereas cardinals seem to attach to groups. Then you say 'three is greater than four', it is not clear which type you are talking about. |
| 18127 | Simple type theory has 'levels', but ramified type theory has 'orders' [Bostock] |
| Full Idea: The simple theory of types distinguishes sets into different 'levels', but this is quite different from the distinction into 'orders' which is imposed by the ramified theory. | |
| From: David Bostock (Philosophy of Mathematics [2009], 8.1) | |
| A reaction: The ramified theory has both levels and orders (p.235). Russell's terminology is, apparently, inconsistent. |
| 18147 | Neo-logicists meet the Caesar problem by saying Hume's Principle is unique to number [Bostock] |
| Full Idea: The response of neo-logicists to the Julius Caesar problem is to strengthen Hume's Principle in the hope of ensuring that only numbers will satisfy it. They say the criterion of identity provided by HP is essential to number, and not to anything else. | |
| From: David Bostock (Philosophy of Mathematics [2009], 9.A.2) |
| 18144 | Neo-logicists agree that HP introduces number, but also claim that it suffices for the job [Bostock] |
| Full Idea: The neo-logicists take up Frege's claim that Hume's Principle introduces a new concept (of a number), but unlike Frege they go on to claim that it by itself gives a complete account of that concept. | |
| From: David Bostock (Philosophy of Mathematics [2009], 9.A.2) | |
| A reaction: So the big difference between Frege and neo-logicists is the Julius Caesar problem. |
| 18111 | Treating numbers as objects doesn't seem like logic, since arithmetic fixes their totality [Bostock] |
| Full Idea: If logic is neutral on the number of objects there are, then logicists can't construe numbers as objects, for arithmetic is certainly not neutral on the number of numbers there are. They must be treated in some other way, perhaps as numerical quantifiers. | |
| From: David Bostock (Philosophy of Mathematics [2009], 5.5) |
| 18146 | If Hume's Principle is the whole story, that implies structuralism [Bostock] |
| Full Idea: If Hume's Principle is all we are given, by way of explanation of what the numbers are, the only conclusion to draw would seem to be the structuralists' conclusion, ...studying all systems that satisfy that principle. | |
| From: David Bostock (Philosophy of Mathematics [2009], 9.A.2) | |
| A reaction: Any approach that implies a set of matching interpretations will always imply structuralism. To avoid it, you need to pin the target down uniquely. |
| 18129 | Many crucial logicist definitions are in fact impredicative [Bostock] |
| Full Idea: Many of the crucial definitions in the logicist programme are in fact impredicative. | |
| From: David Bostock (Philosophy of Mathematics [2009], 8.2) |
| 18159 | Higher cardinalities in sets are just fairy stories [Bostock] |
| Full Idea: In its higher reaches, which posit sets of huge cardinalities, set theory is just a fairy story. | |
| From: David Bostock (Philosophy of Mathematics [2009], 9.5.iii) | |
| A reaction: You can't say the higher reaches are fairy stories but the lower reaches aren't, if the higher is directly derived from the lower. The empty set and the singleton are fairy stories too. Bostock says the axiom of infinity triggers the fairy stories. |
| 18155 | A fairy tale may give predictions, but only a true theory can give explanations [Bostock] |
| Full Idea: A common view is that although a fairy tale may provide very useful predictions, it cannot provide explanations for why things happen as they do. In order to do that a theory must also be true (or, at least, an approximation to the truth). | |
| From: David Bostock (Philosophy of Mathematics [2009], 9.B.5) | |
| A reaction: Of course, fictionalism offers an explanation of mathematics as a whole, but not of the details (except as the implications of the initial fictional assumptions). |
| 18140 | The best version of conceptualism is predicativism [Bostock] |
| Full Idea: In my personal opinion, predicativism is the best version of conceptualism that we have yet discovered. | |
| From: David Bostock (Philosophy of Mathematics [2009], 8.4) | |
| A reaction: Since conceptualism is a major player in the field, this makes predicativism a very important view. I won't vote Predicativist quite yet, but I'm tempted. |
| 18138 | Conceptualism fails to grasp mathematical properties, infinity, and objective truth values [Bostock] |
| Full Idea: Three simple objections to conceptualism in mathematics are that we do not ascribe mathematical properties to our ideas, that our ideas are presumably finite, and we don't think mathematics lacks truthvalue before we thought of it. | |
| From: David Bostock (Philosophy of Mathematics [2009], 8.4) | |
| A reaction: [compressed; Bostock refers back to his Ch 2] Plus Idea 18134. On the whole I sympathise with conceptualism, so I will not allow myself to be impressed by any of these objections. (So, what's actually wrong with them.....?). |
| 18131 | If abstracta only exist if they are expressible, there can only be denumerably many of them [Bostock] |
| Full Idea: If an abstract object exists only when there is some suitable way of expressing it, then there are at most denumerably many abstract objects. | |
| From: David Bostock (Philosophy of Mathematics [2009], 8.2) | |
| A reaction: Fine by me. What an odd view, to think there are uncountably many abstract objects in existence, only a countable portion of which will ever be expressed! [ah! most people agree with me, p.243-4] |
| 18134 | Predicativism makes theories of huge cardinals impossible [Bostock] |
| Full Idea: Classical mathematicians say predicative mathematics omits areas of great interest, all concerning non-denumerable real numbers, such as claims about huge cardinals. There cannot be a predicative version of this theory. | |
| From: David Bostock (Philosophy of Mathematics [2009], 8.3) | |
| A reaction: I'm not sure that anyone will really miss huge cardinals if they are prohibited, though cryptography seems to flirt with such things. Are we ever allowed to say that some entity conjured up by mathematicians is actually impossible? |
| 18135 | If mathematics rests on science, predicativism may be the best approach [Bostock] |
| Full Idea: It has been claimed that only predicative mathematics has a justification through its usefulness to science (an empiricist approach). | |
| From: David Bostock (Philosophy of Mathematics [2009], 8.3) | |
| A reaction: [compressed. Quine is the obvious candidate] I suppose predicativism gives your theory roots, whereas impredicativism is playing an abstract game. |
| 18136 | If we can only think of what we can describe, predicativism may be implied [Bostock] |
| Full Idea: If we accept the initial idea that we can think only of what we ourselves can describe, then something like the theory of predicativism quite naturally results | |
| From: David Bostock (Philosophy of Mathematics [2009], 8.3) | |
| A reaction: I hate the idea that we can only talk of what falls under a sortal, but 'what we can describe' is much more plausible. Whether or not you agree with this approach (I'm pondering it), this makes predicativism important. |
| 18133 | The usual definitions of identity and of natural numbers are impredicative [Bostock] |
| Full Idea: The predicative approach cannot accept either the usual definition of identity or the usual definition of the natural numbers, for both of these definitions are impredicative. | |
| From: David Bostock (Philosophy of Mathematics [2009], 8.3) | |
| A reaction: [Bostock 237-8 gives details] |
| 18132 | The predicativity restriction makes a difference with the real numbers [Bostock] |
| Full Idea: It is with the real numbers that the restrictions imposed by predicativity begin to make a real difference. | |
| From: David Bostock (Philosophy of Mathematics [2009], 8.3) |
| 21890 | 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 |
| 21880 | '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. |
| 21884 | 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 |
| 21935 | 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). |
| 21930 | 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]. |
| 21933 | 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. |
| 21894 | 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 |
| 21886 | 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 |
| 21931 | '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. |
| 21885 | 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 |
| 13345 | Sentences are 'analytical' if every sequence of objects models them [Tarski] |
| Full Idea: A class of sentences can be called 'analytical' if every sequence of objects is a model of it. | |
| From: Alfred Tarski (The Concept of Logical Consequence [1936], p.418) | |
| A reaction: See Idea 13344 and Idea 13343 for the context of this assertion. |
| 18121 | In logic a proposition means the same when it is and when it is not asserted [Bostock] |
| Full Idea: In Modus Ponens where the first premise is 'P' and the second 'P→Q', in the first premise P is asserted but in the second it is not. Yet it must mean the same in both premises, or it would be guilty of the fallacy of equivocation. | |
| From: David Bostock (Philosophy of Mathematics [2009], 7.2) | |
| A reaction: This is Geach's thought (leading to an objection to expressivism in ethics, that P means the same even if it is not expressed). |
| 21891 | 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 | |
| A reaction: Is good implicitly non-violent? Appropriate anger seems to be good behaviour, and I can't see why it is impure. Maybe anger and violence lack the control needed for pure goodness. |