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All the ideas for 'Explanation in Mathematics', 'Dthat' and 'Russell's Ontological Development'

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5 ideas

2. Reason / D. Definition / 12. Paraphrase
Russell offered a paraphrase of definite description, to avoid the commitment to objects [Quine]
     Full Idea: Russell's theory involved defining a term not by presenting a direct equivalent of it, but by 'paraphrasis', providing equivalents of the sentences. In this way, reference to fictitious objects can be simulated without our being committed to the objects.
     From: Willard Quine (Russell's Ontological Development [1966], p.75)
     A reaction: I hadn't quite grasped that the modern strategy of paraphrase tracks back to Russell - though it now looks obvious, thanks to Quine. Paraphrase is a beautiful way of sidestepping ontological problems. See Frege on the moons of Jupiter.
9. Objects / D. Essence of Objects / 7. Essence and Necessity / b. Essence not necessities
Essences are no use in mathematics, if all mathematical truths are necessary [Mancosu]
     Full Idea: Essences and essential properties do not seem to be useful in mathematical contexts, since all mathematical truths are regarded as necessary (though Kit Fine distinguishes between essential and necessary properties).
     From: Paolo Mancosu (Explanation in Mathematics [2008], §6.1)
     A reaction: I take the proviso in brackets to be crucial. This represents a distortion of notion of an essence. There is a world of difference between the central facts about the nature of a square and the peripheral inferences derivable from it.
19. Language / A. Nature of Meaning / 7. Meaning Holism / a. Sentence meaning
Taking sentences as the unit of meaning makes useful paraphrasing possible [Quine]
     Full Idea: The new freedom that Russell confers by paraphrasis (of definite descriptions) is our reward for recognising that the unit of communication is the sentence and not the word.
     From: Willard Quine (Russell's Ontological Development [1966], p.75)
     A reaction: Since many people hardly ever speak a properly formed sentence, I take propositions to be better candidates for this. However, I don't see how we can reject the compositional view (the meanings are assembled).
Knowing a word is knowing the meanings of sentences which contain it [Quine]
     Full Idea: We can say that knowing words is knowing how to work out the meanings of sentences containing them. Dictionary definitions are mere clauses in a recursive definition of the meanings of sentences.
     From: Willard Quine (Russell's Ontological Development [1966], p.76)
     A reaction: Do you have to recursively define all the sentences that might contain the word, before you can fully know the meaning of the word? He seems to credit Russell with the holistic view of sentences (though I think that starts with Frege).
19. Language / B. Reference / 3. Direct Reference / b. Causal reference
Are causal descriptions part of the causal theory of reference, or are they just metasemantic? [Kaplan, by Schaffer,J]
     Full Idea: Kaplan notes that the causal theory of reference can be understood in two quite different ways, as part of the semantics (involving descriptions of causal processes), or as metasemantics, explaining why a term has the referent it does.
     From: report of David Kaplan (Dthat [1970]) by Jonathan Schaffer - Deflationary Metaontology of Thomasson 1
     A reaction: [Kaplan 'Afterthought' 1989] The theory tends to be labelled as 'direct' rather than as 'causal' these days, but causal chains are still at the heart of the story (even if more diffused socially). Nice question. Kaplan takes the meta- version as orthodox.