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2011, Noûs
nor even to make us more certain of what we are proving (Gl, §2), but rather to force every assumption on which a given proof depends to be made explicit, so that the grounds on which the result rests can be reliably ascertained . This is what Frege intends by his insistence that proofs must be rigorous and 'gap-free'. Only then can we be certain that we have shown how a truth follows from other truths. Given Frege's perspective, what makes formalization possible is thus the fact that, in Begriffsschrift, the logical properties of contents are made visible in the signs that express those contents. And that, Frege seems to have understood from the start, is because these signs-the sentences of Begriffsschrift-are composed of parts that have their own contents, contents that together determine the content of the sentence. The expression '2 2 = 4', for example, occurs in the expression '2 2 = 4 → 2 4 = 16', and, as a part of the latter sentence, it has the very same content it has when...
American Philosophical Quarterly
The Problem of the Essential Icon2008 •
Charles Peirce famously divided all signs into icons, indices and symbols. The past few decades have seen mainstream analytic philosophy broaden its traditional focus on symbols to recognise the so-called essential indexical. Can the moral now be extended to icons? Is there an “essential icon”? And if so, what exactly would be essential about it? It is argued that there is and it consists in logical form. Danielle Macbeth’s radical new “expressivist” interpretation of Frege’s logic and Charles Peirce’s existential graphs are mobilized in support of this claim.
History and Philosophy of Logic
Frege: Two Theses, Two Senses - 20032003 •
One particular topic in the literature on Frege’s conception of sense relates to two apparently contradictory theses held by Frege: the isomorphism of thought and language on one hand and the expressibility of a thought by different sentences on the other. I will divide the paper into five sections. In (1) I introduce the problem of the tension in Frege’s thought. In (2) I discuss the main attempts to resolve the conflict between Frege’s two contradictory claims, showing what is wrong with some of them. In (3), I analyze where, in Frege’s writings and discussions on sense identity, one can find grounds for two different conceptions of sense. In (4) I show how the two contradictory theses held by Frege are connected with different concerns, compelling Frege to a constant oscillation in terminology. In (5) I summarize two further reasons that prevented Frege from making the distinction between two conceptions of sense clear: (i) the antipsychologism problem and (ii) the overlap of traditions in German literature contemporary to Frege about the concept of value. I conclude with a hint for a reconstruction of the Fregean notion of ‘thought’ which resolves the contradiction between his two theses
Grazer Philosophische Studien
Striving for Truth in the Practice of Mathematics: Kant and Frege2007 •
Dialectica
Caesar from Frege's Perspective2005 •
I attempt to explain Frege's handling of the Julius Caesar issue in terms of his more general philosophical commitments. These only became fully explicit in his middle-period writings, but his earlier moves are best explained, I suggest, if we suppose them to be implicit in his earlier thinking. These commitments conditionally justify Frege in rejecting Hume's Principle as either a definition or axiom but in accepting Axiom V. However, the general epistemological picture they constitute has serious problems in accounting for how knowledge is possible at all of such propositions as that Julius Caesar is not a number.

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