16906
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The primitive simples of arithmetic are the essence, determining the subject, and its boundaries [Frege, by Jeshion]
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Full Idea:
The primitive truths contain the core of arithmetic because their constituents are simples which define the essential boundaries of the subject. …The primitive truths are the most general ones, containing the basic, essence determining elements.
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From:
report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Robin Jeshion - Frege's Notion of Self-Evidence 2
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A reaction:
This presents Frege as explicable in essentialist terms, as identifying the core of an abstract discipline, from which the rest of it is generated. Jeshion says 'simples are the essence'.
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14236
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Each horse doesn't fall under the concept 'horse that draws the carriage', because all four are needed [Oliver/Smiley on Frege]
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Full Idea:
Frege says the number four is assigned to the concept 'horse that draws the Kaiser's carriage', but the four horses that drew the carriage did so together, not separately. No horses, not four, fall under the Fregean concept.
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From:
comment on Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], §46) by Oliver,A/Smiley,T - What are Sets and What are they For? Intro
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A reaction:
They say that Frege stumbles because he is blind to irreducibly plural predicates.
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17624
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To understand axioms you must grasp their logical power and priority [Frege, by Burge]
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Full Idea:
Understanding the axioms depends not only on understanding Frege's elucidatory remarks about the interpretation of his symbols, but also on understanding their logical structure - their power to entail other truths, and their reason-giving priority.
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From:
report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], 4) by Tyler Burge - Frege on Knowing the Foundations 4
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A reaction:
This is a distinctively Burgean spin put on what Frege has to say about axioms, but I like it, and it seems well enough supported in Frege's writings (e.g. 1914).
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