Combining Texts

All the ideas for 'Explanation in Mathematics', 'Dthat' and 'Knowledge'

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3 ideas

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.
13. Knowledge Criteria / C. External Justification / 3. Reliabilism / a. Reliable knowledge
Belief is knowledge if it is true, certain, and obtained by a reliable process [Ramsey]
     Full Idea: I have always said that a belief was knowledge if it was (i) true, (ii) certain, (iii) obtained by a reliable process.
     From: Frank P. Ramsey (Knowledge [1929]), quoted by Juan Comesaņa - Reliabilism 2
     A reaction: Remarkable to be addressing the Gettier problem at that date, but Russell had flirted with the problem. Ramsey says the production of the belief must be reliable, rather than the justification for the belief. Note that he wants certainty.
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.