Ignacio Angelelli

The author distinguishes three views of negation: 1) term-negation ; 2) predicate-negation ; 3) sentence-negation. Strictly, however, he thinks there is no genuine sentential negation; sentential negation is reducible to the denial of a predicate. The author claims to have shown this in the present book. If sentential negation is regarded as "external" and predicate negation as "internal" to sentences, the reduction of sentential negation to predicate negation is an "internalization" of negation. The author envisages a more general reductionism for logical symbols: "the internalization of negation seems to be the first and most important step [in Englebretsen's program of viewing all sentences as logically categorical]. The internalization of other operations, including modality, should follow".

After presenting the ordinary and the Fregean formulations of the ancestral, I raise the question of what is their relationship, the natural candidate being that the Fregean version is an analysans intended to improve upon, and replace, the common notion of ancestral (the analysandum). Next, two types of circles that arise in connection with the Fregean ancestral are presented, and it is claimed that one of the circles makes it impossible to maintain the just described (“replacement”) interpretation. A reference is made to Kerry, who was the first to point out a circularity in Frege’s ancestral. Some of Frege’s remarks are examined in order to tentatively sketch, an answer to the issue of the relationship between ordinary and Fregean ancestral; the latter, if not as an analysans replacing the common notion, can still be seen as a profound enrichment of the former

In lieu of an abstract, here is a brief excerpt of the content:Journal of the History of Philosophy 41.1 (2003) 138-139 [Access article in PDF] Erich H. Reck, editor. From Frege to Wittgenstein: Perspectives on Early Analytic Philosophy. New York: Oxford University Press, 2002. Pp. xv + 470. Cloth, $65.00. The volume is divided into four main parts: I: "Background and general themes," II: "Frege," III: "Frege to early Wittgenstein," and IV: "Early Wittgenstein." Part I includes the following essays: Erich H. Reck, "Wittgenstein's 'great debt' to Frege: biographical traces and philosophical themes"; Gottfried Gabriel, "Frege, Lotze, and the continental roots of early analytic philosophy"; and Steven Gerrard, "One Wittgenstein?". Part II includes: Hans Sluga, "Frege on the indefinability of truth"; Sanford Shieh, "On interpreting Frege on truth and logic"; Marco Ruffino, "Logical objects in Frege's Grundgesetze, section 10"; and Joan Weiner, "Section 31 revisited: Frege's elucidations." Part III includes: Warren Goldfarb, "Wittgenstein's understanding of Frege: the pre-tractarian evidence"; Danielle Machbeth, "Frege and early Wittgenstein on logic and language"; Thomas Ricketts, "Wittgenstein against Frege and Russell"; and Cora Diamond, "Truth before Tarski: after Sluga, after Ricketts, after Geach, after Goldfarb, Hylton, Floyd, and Van Heijenoort." Part IV includes: Ian Proops, "The Tractatus on inference and entailment"; Juliet Floyd, "Number and ascriptions of number in Wittgenstein's Tractatus"; Matthew B. Ostrow, "Wittgenstein and the liberating word"; and James Conant, "The method of the Tractatus."Reck, while opposing the "widespread view" that Wittgenstein's "debt" to Frege was "rather minimal," warns the reader against going too far in the contrary direction (exemplified by Geach). Gabriel maintains (39) the thesis that "at least early analytic philosophy has its roots in the tradition of continental philosophy, especially in the philosophy of Hermann Lotze" (the founder of neo-Kantianism). Gerrard argues against the common distinction of an "early" and a "late" Wittgenstein.Sluga writes in favor of the significance of Frege's remark (rather neglected in the Fregean literature) that "the content of the word 'true' is altogether unique and indefinable." Shieh's "principal question," observing that Frege's philosophy of logic has been interpreted in two opposite ways: "semantical" (Dummett), and "antisemantical" (Ricketts), is: "Did Frege provide an explanatory justification of logical laws in semantic terms?" The "central result" of the essay is that "the substance of the disagreements between the antisemantical interpreters and their perceived opponents is not what they suggest it to be" (97). Ruffino focuses on the Fregean attempt to determine the nature of the extensions introduced by his (in)famous Axiom V, and compares Frege's handling of this issue with the seemingly analogous issue of determining the nature of numbers introduced by what is nowadays called "Hume's principle." Weiner attacks another crucial portion of Frege's work: Grundgesetze I §31, and proposes to read it as "elucidation" rather than as proof.Goldfarb intends to "cast doubt on the assessment of Frege's influence on Wittgenstein" expressed by several scholars. Goldfarb holds that Frege and Wittgenstein arrive at views that "have many similarities" but that they do it independently (187). Rather, in Wittgenstein "the basic framework and the basic stance are thoroughly inherited from Russell" (197). Macbeth argues that Frege and Wittgenstein have radically different conceptions of meaning: inferentialist and representative respectively. Ricketts argues that Wittgenstein's critique of Frege "is mounted from within his own distinctive approach to language and logic," so that "while Wittgenstein does not meet Frege on Frege's own terms, neither does he straightforwardly misunderstand Frege" (228). The content of Diamond's paper is more than hinted at by its long title.Proops aims at investigating "Wittgenstein's well-known, yet obscure, objection to the views of Frege and Russell on deductive inference and its justification," (283) an objection set out in Tractatus5.132: laws of inference are senseless, superfluous. Floyd intends to highlight the philosophy of arithmetic found in the Tractatus against a "tendency to pass over the Tractatus remarks on arithmetic in silence" (309). Ostrow points out that "it is not at once apparent" how the "Wittgensteinian liberation" is to be conceived (353), and his...

For centuries abstraction was understood as an operation according to which, from a given phenomenon, something is kept, but something else is not paid attention to, is ”abstracted from”. This notion of abstraction not only has been rejected by the mainstream of analytic philosophy and logic as worthless psychologism but, moreover, largely replaced by a new conception of abstraction in which the allegedly ”psychological” feature of ”not paying attention to”, or ”abstracting from”, is no longer visible. Psychologism has been overcome, of course, but at the expense of removing any genuine abstraction from the new notion. This is the ”trouble” in the history of abstraction

I wish to express, first of all, my profound gratitude to Professor J. M. Bochenski, without whose assistance the present work would have not been possible. To be concise, I would like to state that his contribution to this book may be viewed at three levels: (1) that of the general spirit, (2) that of the specific ideas, theses or approaches which are expressed in its pages, (3) that of this work qua doctoral dissertation. The general spirit which has guided my research coincides with that underlying Professor :Oochenski's own works, in particular his Formale Logik (Munchen 1956). Moreover, the particular occasion which suggested my investigation was a statement included in that book according to which the literature in the field still lacked a detailed work on Frege (p. 317). I wish, likewise, to express my gratitude to other professors of the University of Fribourg for their generous help. I mention especially Professors P. Wyser, M. D. Philippe, N. Luyten, and V. Kuiper. I have also benefited from Professor E. Specker's lectures at the Eidge nossische Technische Hochschule (ZUrich) and from Professor Olof Gigon's lectures at the University of Bern. From an earlier period I wish to express my gratitude to the professors of the philosophy department of the Universidad Nacional de Buenos Aires, especially the late Professor Francisco Romero. The Swiss National Library (Bern) has greatly facilitated access to bibliographical sources, and the library of the University of Munster (Westphalien) has kindly provided microfilms of Frege's Nachlap.