Frege’s logicist program is a program of scientific unification of arithmetic and logic via the reduction of arithmetic to logic. Logic on this view is the prior science, indeed, the most fundamental of all sciences. The coherence of this picture has been questioned, based on the claim that the Basic Laws of logic are not justifiable as judgements. That Frege’s conception of logic suffers from this fatal flaw is incorrect, and in this paper I explore why. The discussion has three (...) primary parts. The first explores Frege’s view of logic, distinguishing pure from applied logic. The second delves into Frege’s conception of science as applications of logic, and how arithmetic is understood as such an application. The third concerns Frege’s account of judgement, and how it carefully distinguishes a judgement from judging, the cognitive act of recognizing truths. The final section turns to how on Frege’s account of judgement, the Basic Laws of logic are in fact justified as judgements, and accordingly can serve as the axioms of the science of arithmetic. The paper concludes with reflections on Frege’s understanding of scientific unification and reduction, and its relation to his logical realism. (shrink)

The essay addresses the well‐known idea that there has to be a place for intuition, thought of as a kind of non‐inferential rational insight, in the epistemology of basic logic if our knowledge of its principles is non‐empirical and is to allow of any finite, non‐circular reconstruction. It is argued that the error in this idea consists in its overlooking the possibility that there is, properly speaking, no knowledge of the validity of principles of basic logic. When certain important distinctions (...) are observed, for instance that between recognising that Modus Ponenes is sound and recognising that it is proof against the competent discovery of basic counterexamples, the case for thinking that there is indeed no space for genuine recognition of the validity of Modus Ponens becomes increasingly impressive. It is argued however that, the impossibility of knowledge notwithstanding, we are, in an important sense, entitled to take it that Modus Ponens is sound and that this notion of entitlement can help break the trichotomy ‐ intuition, inference, experience ‐ which imprisons our ordinary thinking about logical knowledge. (shrink)

Does Frege have a metatheory for his logic? There is an obvious and uncontroversial sense in which he does. Frege introduces and discusses his new logic in natural language; he argues, in response to criticisms of Begriffsschrift, that his logic is superior to Boole's by discussing formal features of both systems. In so far as the enterprise of using natural language to introduce, discuss, and argue about features of a formal system is metatheoretic, there can be no doubt: Frege has (...) a metatheory. There is also an obvious and uncontroversial sense in which Frege does not have a metatheory for his logic. The model theoretic semantics with which we are familiar today are a post-Fregean development. The question I address in this paper is, does Frege have a metatheory in the following sense: do his justifications of his basic laws and rules of inference employ, or even require, ineliminable use of a truth predicate and metalinguistic variables? My answer is ‘no’ on both counts. I argue that Frege neither uses, nor has any need to use, a truth predicate or metalinguistic variables in his justifications of his basic laws and rules of inference. Quine's famous explanation of the need for semantic ascent simply does not apply to Frege's logic. The purpose of the discussions that are typically understood as constituting Frege's metatheory is, rather, elucidatory. And once we see what the aim of these particular elucidations is, we can explain Frege's otherwise puzzling eschewal of the truth predicate in his discussions of the justification of the laws and rules of inference. (shrink)

In the opening to his late essay, Der Gedanke, Frege asserts without qualification that the word "true" points the way for logic. But in a short piece from his Nachlass entitled "My Basic Logical Insights", Frege writes that the word true makes an unsuccessful attempt to point to the essence of logic, asserting instead that "what really pertains to logic lies not in the word "true" but in the assertoric force with which the sentence is uttered". Properly understanding what Frege (...) takes to be at issue here is crucial for understanding his conception of logic and, in particular, what he takes to be its normative status vis-à-vis judgement, assertion, and inference. In this paper, I focus my attention on clarifying the latter claim and Frege's motivations for making it, exposing what I take to be a fundamental tension in Frege's conception of logic. Finally, I discuss whether Frege's deployment of the horizontal in his mature Begriffsschrift helps to resolve this tension. (shrink)

In this paper I examine the question of logic’s normative status in the light of Carnap’s Principle of Tolerance. I begin by contrasting Carnap’s conception of the normativity of logic with that of his teacher, Frege. I identify two core features of Frege’s position: first, the normative force of the logical laws is grounded in their descriptive adequacy; second, norms implied by logic are constitutive for thinking as such. While Carnap breaks with Frege’s absolutism about logic and hence with the (...) notion that any system of logic should have a privileged claim to correctness, I argue that there is a sense in which Carnap’s framework-relative conception of logical norms has a constitutive role to play: though they are not constitutive for the conceptual activity for thinking, they do nevertheless set the ground rules that make certain forms of scientific inquiry possible in the first place. I conclude that Carnap’s principle of tolerance is tamer than one might have thought and that, despite remaining differences, Frege’s and Carnap’s conceptions of logic have more in common than one might have thought. (shrink)

In this paper it is contended, against a challenging recent interpretation of Frege, that Frege should be credited with the first semirigorous formulation of semantic theory. It is argued that the considerations advanced against this contention suffer from two kinds of error. The first involves the attribution to Frege of a skeptical attitude towards the truth-predicate. The second involves the sort of justification which these arguments assume a classical semantic theory attempts to provide. Finally, it is shown that Frege was (...) in fact mindful of the need for the relevant sort of justification. (shrink)

(2012). Gingerbread Nuts and Pebbles: Frege and the Neo-Kantians – Two Recently Discovered Documents. British Journal for the History of Philosophy. ???aop.label???. doi: 10.1080/09608788.2012.692665.

H. Sluga (Inquiry, Vol. 18 [1975], No. 4) has criticized me for representing Frege as a realist. He holds that, for Frege, abstract objects were not real: this rests on a mistranslation and a neglect of Frege's contextual principle. The latter has two aspects: as a thesis about sense, and as one about reference. It is only under the latter aspect that there is any tension between it and realism: Frege's later silence about the principle is due, not to his (...) realism, but to his assimilating sentences to proper names. Contrary to what Sluga thinks, the conception of the Bedeutung of a name as its bearer is an indispensable ingredient of Frege's notion of Bedeutung, as also is the fact that it is in the stronger of two possible senses that Frege held that Sinn determines Bedeutung. The contextual principle is not to be understood as meaning that thoughts are not, in general, complex; Frege's idea that the sense of a sentence is compounded out of the senses of its component words is an essential component of his theory of sense. Frege's realism was not the most important ingredient in his philosophy: but the attempt to interpret him otherwise than as a realist leads only to misunderstanding and confusion. (shrink)

Let me start with a well-known story. Kant held that logic and conceptual analysis alone cannot account for our knowledge of arithmetic: “however we might turn and twist our concepts, we could never, by the mere analysis of them, and without the aid of intuition, discover what is the sum [7+5]” (KrV, B16). Frege took himself to have shown that Kant was wrong about this. According to Frege’s logicist thesis, every arithmetical concept can be defined in purely logical terms, and (...) every theorem of arithmetic can be proved using only the basic laws of logic. Hence, Kant was wrong to think that our grasp of arithmetical concepts and our knowledge of arithmetical truth depend on an extralogical source—the pure intuition of time (Frege 1884, §89, §109). Arithmetic, properly understood, is just a part of logic. (shrink)

Controversy remains over exactly why Frege aimed to estabish logicism. In this essay, I argue that the most influential interpretations of Frege's motivations fall short because they misunderstand or neglect Frege's claims that axioms must be self-evident. I offer an interpretation of his appeals to self-evidence and attempt to show that they reveal a previously overlooked motivation for establishing logicism, one which has roots in the Euclidean rationalist tradition. More specifically, my view is that Frege had two notions of self-evidence. (...) One notion is that of a truth being foundationally secure, yet not grounded on any other truth. The second notion is that of a truth that requires only clearly grasping its content for rational, a priori justified recognition of its truth. The overarching thesis I develop is that Frege required that axioms be self-evident in both senses, and he relied on judging propositions to be self-evident as part of his fallibilist method for identifying a foundation of arithmetic. Consequently, we must recognize both notions in order to understand how Frege construes ultimate foundational proofs, his methodology for discovering and identifying such proofs, and why he thought the propositions of arithmetic required proof. (shrink)

Frege claims that the laws of logic are characterized by their “generality,” but it is hard to see how this could identify a special feature of those laws. I argue that we must understand this talk of generality in normative terms, but that what Frege says provides a normative demarcation of the logical laws only once we connect it with his thinking about truth and science. He means to be identifying the laws of logic as those that appear in every (...) one of the scientific systems whose construction is the ultimate aim of science, and in which all truths have a place. Though an account of logic in terms of scientific systems might seem hopelessly antiquated, I argue that it is not: a basically Fregean account of the nature of logic still looks quite promising. (shrink)

Michael Dummett has shown that the fragment ‘17 Kernsätze zur Logik’ is evidence that Frege knew Lotze's Logik Dummett’s dating of this fragment prior to 1879, however, must be rejected.The present paper shows that there are other articles of Frege’s which bear clear traces of Lotze's LogikFirst of all, the expressions Vorstellungsverlauf from ‘Über die wissenschaftliche Berechtigung einer Begriffsschrift’, and veranlassenden Ursachen, from ‘Logik’, certainly are borrowed from Lotze.Second, there are links between ‘Booles rechnende Logik und die Begriffsschrift’ and Lotze's (...) Logik. Furthermore, it is shown that Frege’s ‘Kernsätze’, the ‘Dialog mit Pünjer über Existenz’, and his ‘Logik’ are intimately connected.All of this indicates that these texts were written in roughly the same period, namely the early 1880s.Conclusive evidence for this is that the terms Vorstellung and Vorstellungsverbindung are used indiscriminately in both a psychological and a logical sense in the ‘Begriffsschrift’, a fact which contradicts the ‘Kernsätze’. (shrink)

According to Kant, “mathematical knowledge is the knowledge gained by reason from the construction of concepts.” In this paper, I shall make a few suggestions as to how this characterization of the mathematical method is to be understood.

Joan Weiner has recently claimed that Frege neither uses, nor has any need to use, a truth-predicate in his justification of the logical laws. She argues that because of the assimilation of sentences to proper names in his system, Frege does not need to make use of the Quinean device of semantic ascent in order to formulate the logical laws, and that the predicate ‘is the True’, which is used in Frege's justification, is not to be considered as a truth-predicate, (...) because it does not apply to true sentences or true thoughts. The present paper aims to show that Frege needs to use, and does use, a truth-predicate in this context. It is argued, first, that Frege needs to use a truthpredicate in order to show that the truth of the logical laws is evident from the senses of the sentences by means of which they are formulated, and second, that the predicate that he actually uses, ‘is the True’, must be considered as a truth-predicate in the relevant sense, because it can be used and is actually used by Frege to explain the truth-conditions of thoughts. To defend this interpretation, it is discussed whether the explanatory use of ‘is the True’ in Frege's system is compatible with his deflationary analysis of ‘true’. The paper's conclusion is that there is indeed a conflict here; but, from Frege's point of view, this conflict is due merely to the logical imperfection of natural language and does not affect the proper system but only its propaedeutic. (shrink)

Translation of Frege's 'Über Begriff und Gegenstand' (1892). Translation by Peter Geach, revised by Max Black.

In this paper, we develop an account of the justification thinkers have for employing certain basic belief-forming methods. The guiding idea is inspired by Reichenbach's work on induction. There are certain projects in which thinkers are rationally required to engage. Thinkers are epistemically justified in employing any belief-forming method such that "if it doesn't work, nothing will" for successfully engaging in such a project. We present a detailed account based on this intuitive thought and address objections to it. We conclude (...) by commenting on the implications that our account may have for other important epistemological issues and debates. (shrink)

This paper examines the anti-psychologism of Paul Natorp, a Marburg School Neo-Kantian. It identifies both Natorp’s principle argument against psychologism and the views underlying the argument that give it its force. Natorp’s argument depends for its success on his view that certain scientific laws constitute the intersubjective content of knowledge. That view in turn depends on Natorp’s conception of subjectivity, so it is only against the background of his conception of subjectivity that his reasons for rejecting psychologism make sense. This (...) interpretation of Natorp suggests that attention paid to late nineteenth century theories of subjectivity and philosophy of psychology could improve our understanding of the emergence of anti-psychologism in that period.Keywords: Paul Natorp; Marburg School; Neo-Kantianism; Psychologism; Subjectivity. (shrink)

The short fragment of Frege's Nachlass which bears the above title, given to it by the editors, is in fact a sequence of connected comments by him on the Introduction to Lotze's Logik, or, more exactly, a response by him to that Introduction. It is thus very probably the earliest piece of writing from Frege's pen on the philosophy of logic surviving to us, and, when it is read in this light, the motivation for its author's puzzling selection of remarks (...) and the turns of phrase he employs become intelligible. We see here an early attempt by Frege to attain clarity about a topic that was to preoccupy him throughout his entire philosophical career, the nature of thoughts. (shrink)

In this paper, we present an account of in virtue of what thinkers are justified in employing certain basic belief‐forming methods. The guiding idea is inspired by Reichenbach’s work on induction. There are certain projects in which thinkers are rationally required to engage. Thinkers are epistemically justified in employing a belief‐forming method that is indispensable for successfully engaging in such a project. We present a detailed account based on this intuitive thought, and address objections to it. We conclude by commenting (...) on the implications that our account may have for other important epistemological debates. (shrink)

The Principle of Sufficient Reason states that everything has an explanation. But different notions of explanation yield different versions of this principle. Here a version is formulated in terms of the notion of a “grounding” explanation. Its consequences are then explored, with particular emphasis on the fact that it implies necessitarianism, the view that every truth is necessarily true. Finally, the principle is defended from a number of objections, including objections to necessitarianism. The result is a defense of a “rationalist” (...) metaphysics, one that constitutes an alternative to the contemporary dogmas that some aspects of the world are “metaphysically brute” and that the world could in so many ways have been different. (shrink)

The paper scrutinizes Frege's Euclideanism - his view of arithmetic and geometry as resting on a small number of self-evident axioms from which non-self-evident theorems can be proved. Frege's notions of self-evidence and axiom are discussed in some detail. Elements in Frege's position that are in apparent tension with his Euclideanism are considered - his introduction of axioms in The Basic Laws of Arithmetic through argument, his fallibilism about mathematical understanding, and his view that understanding is closely associated with inferential (...) abilities. The resolution of the tensions indicates that Frege maintained a sophisticated and challenging form of rationalism, one relevant to current epistemology and parts of the philosophy of mathematics. (shrink)

That there are analytic truths may challenge a principle of the homogeneity of truth. Unlike standard conceptions, in which analyticity is couched in terms of "truth in virtue of meanings", Frege's notions of analytic and a priori concern justification, respecting a principle of the homogeneity of truth. Where there is no justification these notions do not apply, Frege insists. Basic truths and axioms may be analytic (or a priori), though unprovable, which means there is a form of justification which is (...) not (deductive) proof. This is also required for regarding singular factual propositions as a posteriori. A Fregean direction for explicating this wider notion of justification is suggested in terms of his notion of sense (Sinn)—modes in which what the axioms are about are given—and its general epistemological significance is sketched. (shrink)

This paper presents an argument for the Principle of Sufficient Reason, the PSR, the principle according to which each thing that exists has an explanation. I begin with several widespread and extremely plausible arguments that I call explicability arguments in which a certain situation is rejected precisely because it would be arbitrary. Building on these plausible cases, I construct a series of explicability arguments that culminates in an explicability argument concerning existence itself. This argument amounts to the claim that the (...) PSR is true. The plausibility of the initial cases in the series provides the basis of an argument for the PSR, an argument that can be rebutted only by drawing a line between the plausible early cases in the series and the apparently unacceptable later cases. I argue that no principled reason for drawing this line has been found and that one cannot draw an unprincipled or arbitrary line without begging the question. The paper concludes that, therefore, this defense of the PSR remains unrebutted and that we have a powerful, new reason to embrace the PSR. (shrink)