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All the ideas for 'Frege's Theory of Numbers', 'works' and 'Logicism and Ontological Commits. of Arithmetic'

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39 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
Truth in a model is more tractable than the general notion of truth [Hodes]
     Full Idea: Truth in a model is interesting because it provides a transparent and mathematically tractable model - in the 'ordinary' rather than formal sense of the term 'model' - of the less tractable notion of truth.
     From: Harold Hodes (Logicism and Ontological Commits. of Arithmetic [1984], p.131)
     A reaction: This is an important warning to those who wish to build their entire account of truth on Tarski's rigorously formal account of the term. Personally I think we should start by deciding whether 'true' can refer to the mental state of a dog. I say it can.
Truth is quite different in interpreted set theory and in the skeleton of its language [Hodes]
     Full Idea: There is an enormous difference between the truth of sentences in the interpreted language of set theory and truth in some model for the disinterpreted skeleton of that language.
     From: Harold Hodes (Logicism and Ontological Commits. of Arithmetic [1984], p.132)
     A reaction: This is a warning to me, because I thought truth and semantics only entered theories at the stage of 'interpretation'. I must go back and get the hang of 'skeletal' truth, which sounds rather charming. [He refers to set theory, not to logic.]
5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
Higher-order logic may be unintelligible, but it isn't set theory [Hodes]
     Full Idea: Brand higher-order logic as unintelligible if you will, but don't conflate it with set theory.
     From: Harold Hodes (Logicism and Ontological Commits. of Arithmetic [1984], p.131)
     A reaction: [he gives Boolos 1975 as a further reference] This is simply a corrective, because the conflation of second-order logic with set theory is an idea floating around in the literature.
5. Theory of Logic / D. Assumptions for Logic / 4. Identity in Logic
Identity is a level one relation with a second-order definition [Hodes]
     Full Idea: Identity should he considered a logical notion only because it is the tip of a second-order iceberg - a level 1 relation with a pure second-order definition.
     From: Harold Hodes (Logicism and Ontological Commits. of Arithmetic [1984])
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]
     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
'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
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 / I. Semantics of Logic / 1. Semantics of Logic
When an 'interpretation' creates a model based on truth, this doesn't include Fregean 'sense' [Hodes]
     Full Idea: A model is created when a language is 'interpreted', by assigning non-logical terms to objects in a set, according to a 'true-in' relation, but we must bear in mind that this 'interpretation' does not associate anything like Fregean senses with terms.
     From: Harold Hodes (Logicism and Ontological Commits. of Arithmetic [1984], p.131)
     A reaction: This seems like a key point (also made by Hofweber) that formal accounts of numbers, as required by logic, will not give an adequate account of the semantics of number-terms in natural languages.
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / a. Numbers
Mathematics is higher-order modal logic [Hodes]
     Full Idea: I take the view that (agreeing with Aristotle) mathematics only requires the notion of a potential infinity, ...and that mathematics is higher-order modal logic.
     From: Harold Hodes (Logicism and Ontological Commits. of Arithmetic [1984])
     A reaction: Modern 'modal' accounts of mathematics I take to be heirs of 'if-thenism', which seems to have been Russell's development of Frege's original logicism. I'm beginning to think it is right. But what is the subject-matter of arithmetic?
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
Parsons says counting is tagging as first, second, third..., and converting the last to a cardinal [Parsons,C, by Heck]
     Full Idea: In Parsons's demonstrative model of counting, '1' means the first, and counting says 'the first, the second, the third', where one is supposed to 'tag' each object exactly once, and report how many by converting the last ordinal into a cardinal.
     From: report of Charles Parsons (Frege's Theory of Numbers [1965]) by Richard G. Heck - Cardinality, Counting and Equinumerosity 3
     A reaction: This sounds good. Counting seems to rely on that fact that numbers can be both ordinals and cardinals. You don't 'convert' at the end, though, because all the way you mean 'this cardinality in this order'.
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / f. Arithmetic
Arithmetic must allow for the possibility of only a finite total of objects [Hodes]
     Full Idea: Arithmetic should be able to face boldly the dreadful chance that in the actual world there are only finitely many objects.
     From: Harold Hodes (Logicism and Ontological Commits. of Arithmetic [1984], p.148)
     A reaction: This seems to be a basic requirement for any account of arithmetic, but it was famously a difficulty for early logicism, evaded by making the existence of an infinity of objects into an axiom of the system.
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
It is claimed that numbers are objects which essentially represent cardinality quantifiers [Hodes]
     Full Idea: The mathematical object-theorist says a number is an object that represents a cardinality quantifier, with the representation relation as the entire essence of the nature of such objects as cardinal numbers like 4.
     From: Harold Hodes (Logicism and Ontological Commits. of Arithmetic [1984])
     A reaction: [compressed] This a classic case of a theory beginning to look dubious once you spell it our precisely. The obvious thought is to make do with the numerical quantifiers, and dispense with the objects. Do other quantifiers need objects to support them?
Numerical terms can't really stand for quantifiers, because that would make them first-level [Hodes]
     Full Idea: The dogmatic Frege is more right than wrong in denying that numerical terms can stand for numerical quantifiers, for there cannot be a language in which object-quantifiers and objects are simultaneously viewed as level zero.
     From: Harold Hodes (Logicism and Ontological Commits. of Arithmetic [1984], p.142)
     A reaction: Subtle. We see why Frege goes on to say that numbers are level zero (i.e. they are objects). We are free, it seems, to rewrite sentences containing number terms to suit whatever logical form appeals. Numbers are just quantifiers?
7. Existence / D. Theories of Reality / 7. Fictionalism
Talk of mirror images is 'encoded fictions' about real facts [Hodes]
     Full Idea: Talk about mirror images is a sort of fictional discourse. Statements 'about' such fictions are not made true or false by our whims; rather they 'encode' facts about the things reflected in mirrors.
     From: Harold Hodes (Logicism and Ontological Commits. of Arithmetic [1984], p.146)
     A reaction: Hodes's proposal for how we should view abstract objects (c.f. Frege and Dummett on 'the equator'). The facts involved are concrete, but Hodes is offering 'encoding fictionalism' as a linguistic account of such abstractions. He applies it to numbers.
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
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).
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].
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
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
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
     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.