{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T00:14:11Z","timestamp":1777421651587,"version":"3.51.4"},"reference-count":56,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":12611,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1979,9]]},"abstract":"<jats:p>We are often told, correctly, that modern logic originated with Frege. For Frege clearly depicted polyadic predication, negation, the conditional, and the quantifier as the bases of logic; moreover, he introduced the idea of a formal system, and argued that mathematical demonstrations, to be fully precise, must be carried out within a formal language by means of explicitly formulated syntactic rules.<\/jats:p><jats:p>Consequently Frege has often been read as providing<jats:italic>all<\/jats:italic>the central notions that constitute our current understanding of quantification. For example, in his recent book on Frege [1973], Michael Dummett speaks of \u201dthe semantics which [Frege] introduced for formulas of the language of predicate logic.\u201d That is, \u201cAn interpretation of such a formula \u2026 is obtained by assigning entities of suitable kinds to the primitive nonlogical constants occurring in the formula \u2026 [T]his procedure is exactly the same as the modern semantic treatment of predicate logic\u201d (pp. 89\u201390). Indeed, \u201cFrege would therefore have had within his grasp the concepts necessary to frame the notion of the completeness of a formalization of logic as well as its soundness \u2026 but he did not do so\u201d (p. 82).<\/jats:p><jats:p>This common appraisal of Frege's work is, I think, quite misleading. Even given Frege's tremendous achievements, the road to an understanding of quantification theory was an arduous one. Obtaining such understanding and formulating those notions which are now common coin in the discussion of logical systems were the tasks of much of the work in logic during the nineteen-twenties.<\/jats:p>","DOI":"10.2307\/2273128","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T21:50:56Z","timestamp":1146952256000},"page":"351-368","source":"Crossref","is-referenced-by-count":140,"title":["Logic in the twenties: the nature of the quantifier"],"prefix":"10.1017","volume":"44","author":[{"given":"Warren D.","family":"Goldfarb","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200048271_ref056","volume-title":"Tractatus logico-philosophicus","author":"Wittgenstein","year":"1922"},{"key":"S0022481200048271_ref055","volume-title":"Principia mathematica","volume":"1","author":"Whitehead","year":"1925"},{"key":"S0022481200048271_ref054","volume-title":"Principia mathematica","volume":"3","author":"Whitehead","year":"1913"},{"key":"S0022481200048271_ref053","volume-title":"Principia mathematica","volume":"2","author":"Whitehead","year":"1912"},{"key":"S0022481200048271_ref051","doi-asserted-by":"publisher","DOI":"10.1007\/BF01475439"},{"key":"S0022481200048271_ref050","doi-asserted-by":"crossref","first-page":"219","DOI":"10.1515\/crll.1925.154.219","article-title":"Eine Axiomatisierung der Mengenlehre","volume":"154","author":"Von Neumann","year":"1925","journal-title":"Journal f\u00fcr die reine und angewandte Mathematik"},{"key":"S0022481200048271_ref048","volume-title":"Prace Towarzystwa Naukowego Warsqawskiego","author":"Tarski","year":"1933"},{"key":"S0022481200048271_ref047","volume-title":"Selected works in logic","author":"Skolem","year":"1970"},{"key":"S0022481200048271_ref046","first-page":"25","volume-title":"Les Entretiens de Zurich sur les Fondements et la M\u00e9thode des Sciences Math\u00e9matiques, 6\u20139 D\u00e9cembre 1938","author":"Skolem","year":"1938"},{"key":"S0022481200048271_ref043","first-page":"125","article-title":"\u00dcber die mathematische Logik","volume":"10","author":"Skolem","year":"1928","journal-title":"Norsk matematisk tidsskrift"},{"key":"S0022481200048271_ref042","volume-title":"Videnskapsselskapets skrifter. 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