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All the ideas for 'Explanation in Mathematics', 'Dthat' and 'Could a computer ever understand?'

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3 ideas

9. Objects / D. Essence of Objects / 7. Essence and Necessity / b. Essence not necessities
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.
15. Nature of Minds / B. Features of Minds / 1. Consciousness / e. Cause of consciousness
4921 Quantum states in microtubules could bind brain activity to produce consciousness [Penrose]
     Full Idea: I propose that microtubules in nerve cells could give rise to a stable quantum state that would bind the activity of brain cells throughout the cerebrum and in doing so give rise to consciousness.
     From: Roger Penrose (Could a computer ever understand? [1998], p.329)
     A reaction: This seems to offer a physical theory to account for the 'unity' of the mind (which so impressed Descartes), but I don't quite see why being aware of things would ensue from some 'quantum binding'. I daresay 'quantum binding' occurs in the Sun.
19. Language / B. Reference / 3. Direct Reference / b. Causal reference
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.