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9283
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Our ancient beliefs can never be overthrown by subtle arguments [Euripides]
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Full Idea:
Teiresias: We have no use for theological subtleties./ The beliefs we have inherited, as old as time,/ Cannot be overthrown by any argument,/ Nor by the most inventive ingenuity.
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From:
Euripides (The Bacchae [c.407 BCE], 201)
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A reaction:
[trans. Philip Vellacott (Penguin)] Compare Idea 8243. While very conservative societies have amazing resilience in maintaining traditional beliefs, modern culture eats into them, not directly by argument, but by arguments at fifth remove.
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10529
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If Hume's Principle can define numbers, we needn't worry about its truth [Fine,K]
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Full Idea:
Neo-Fregeans have thought that Hume's Principle, and the like, might be definitive of number and therefore not subject to the usual epistemological worries over its truth.
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From:
Kit Fine (Precis of 'Limits of Abstraction' [2005], p.310)
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A reaction:
This seems to be the underlying dream of logicism - that arithmetic is actually brought into existence by definitions, rather than by truths derived from elsewhere. But we must be able to count physical objects, as well as just counting numbers.
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10530
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Hume's Principle is either adequate for number but fails to define properly, or vice versa [Fine,K]
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Full Idea:
The fundamental difficulty facing the neo-Fregean is to either adopt the predicative reading of Hume's Principle, defining numbers, but inadequate, or the impredicative reading, which is adequate, but not really a definition.
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From:
Kit Fine (Precis of 'Limits of Abstraction' [2005], p.312)
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A reaction:
I'm not sure I understand this, but the general drift is the difficulty of building a system which has been brought into existence just by definition.
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16369
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There is a single file per object, memorised, reactivated, consolidated and expanded [Papineau, by Recanati]
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Full Idea:
For Papineau there is just one file, which is initialised on the first encounter with the object, stored in memory, reactivated on further encounters, and consolidated with familiarity. Accumulation of information shows it is the same file.
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From:
report of David Papineau (Phenomenal and Perceptual Concepts [2006]) by François Recanati - Mental Files 7.2
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A reaction:
Recanati attempts to refute this view, defending a more complex taxonomy of files. I'm sympathetic to Papineau, as distinct shift in file type doesn't sound very plausible. Simplicity suggests Papineau as a better starting-point.
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10527
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An abstraction principle should not 'inflate', producing more abstractions than objects [Fine,K]
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Full Idea:
If an abstraction principle is going to be acceptable, then it should not 'inflate', i.e. it should not result in there being more abstracts than there are objects. By this mark Hume's Principle will be acceptable, but Frege's Law V will not.
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From:
Kit Fine (Precis of 'Limits of Abstraction' [2005], p.307)
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A reaction:
I take this to be motivated by my own intuition that abstract concepts had better be rooted in the world, or they are not worth the paper they are written on. The underlying idea this sort of abstraction is that it is 'shared' between objects.
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