3 ideas
| 17619 | We renounce all abstract entities [Goodman/Quine] |
| Full Idea: We do not believe in abstract entities..... We renounce them altogether. | |
| From: Goodman,N/Quine,W (Steps Towards a Constructive Nominalism [1947], p.105), quoted by Penelope Maddy - Defending the Axioms | |
| A reaction: Goodman always kept the faith here, but Quine decided to embrace sets, as a minimal commitment to abstracta needed for mathematics, which was needed for science. My sympathies are with Goodman. This is the modern form of 'nominalism'. |
| 13166 | 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. |
| 14080 | 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. |