Abstract
In “Function and Concept” and “On Concept and Object”, Frege argued that certain differences between dependent and independent meanings were inviolable and “founded deep in the nature of things” but, in those articles, he was not explicit about the actual consequences of violating such differences. However, since by creating a law that permitted one to pass from a concept to its extension, he himself mixed dependent and independent meanings, we are in a position to study some of the actual consequences of his having done so. To make certain of Frege’s ideas about the inviolability of logical form more tangible, I describe a string of very interrelated consequences that his attempt to transform dependent meanings into independent meanings actually brought in its wake.
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Notes
In “Incomplete Symbols, Dependent Meanings, and Paradox”, in Husserl’s Logical Investigations, D. Dahlstrom (ed.), Dordrecht: Kluwer, 2003, 69–93, I connect Husserl’s reflections in the 4th Logical Investigation with some of Frege’s and Russell’s ideas on this matter (Hill 2003).
In Frege’s special vocabulary, functions, concepts, predicates were ungesättigt, which has usually been translated as ‘unsaturated’. Here I translate ungesättigt as ‘unfilled’, which I find clearer in meaning and more natural. According to my Random House College Dictionary, ‘to saturate’ means 1. to cause (a substance) to unite with the greatest possible amount of another substance through solution, chemical combination, or the like. 2. to charge to the utmost, as with magnetism. 3. to soak, impregnate, or imbue thoroughly or completely. 4. to destroy (a target) completely with many bombs or missiles. 5. to furnish (a market) with goods to the point of oversupply. None of these meanings speak to Frege’s concerns. I have also modified the published translations.
For example, in my “Reference and Paradox”, Synthese 138, 2004, 207–32.
J. L. Austin chose to translate ‘selbständiger’ as ‘self-subsistent’ rather than using the more common translation ‘independent”, which better serves the purposes of the present essay.
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Hill, C.O. On Fundamental Differences between Dependent and Independent Meanings. Axiomathes 20, 313–332 (2010). https://doi.org/10.1007/s10516-010-9104-1
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DOI: https://doi.org/10.1007/s10516-010-9104-1