I defend the historical definition of "function" originally given in my Language, Thought and Other Biological Categories (1984a). The definition was not offered in the spirit of conceptual analysis but is more akin to a theoretical definition of "function". A major theme is that nonhistorical analyses of "function" fail to deal adequately with items that are not capable of performing their functions.

Main description: Angesichts der zunehmenden Zerstörung der Natur durch den Menschen und der technischen Fortschritte in den Biowissenschaften ist die Frage nach dem Verhältnis des Menschen zu seiner natürlichen Umwelt von höchster Aktualität. Ausgehend von der Philosophie Kants, nach der die Betrachtung der Natur wesentlich in einer Analogie mit der Vernunft des Menschen gründet, entwickelt Angela Breitenbach einen Ansatz zu einer modernen Umweltphilosophie, die einen wichtigen Beitrag zu aktuellen Debatten in der Umweltethik und der Philosophie der Biologie liefert.

How is Frege able to claim that the notion of judgement is essential to his logic without introducing a form of psychologism? I argue first that Frege’s logical notion of judgement is to be distinguished from an empirical notion of judgement, that it cannot be understood as an abstract, idealized notion, and that there are doubts concerning a transcendental reading of Frege’s writings. Then, I explain that the logical notion of judgement has to be understood from a first-person perspective, to (...) be contrasted with a third-person perspective, in which judgement is understood as an empirical, psychological phenomenon. Frege’s logic is essentially a first-person engagement, as each of us can make use of the ideography as a science of logic only if we ourselves have made the relevant judgements. Finally, I claim that the judging agent as conceived by Frege can, after all, be understood as a transcendental ego. (shrink)

According to Frege, judgement is the ‘logically primitive activity’. So what is judgement? In his mature work, he characterizes judging as ‘acknowledging the truth’ (‘Anerkennen der Wahrheit’). Frege’s remarks about judging as acknowledging the truth of a thought require further elaboration and development. I will argue that the development that best suits his argumentative purposes takes acknowledging the truth of a thought to be a non-propositional attitude like seeing an object; it is a mental relation between a thinker, a thought, (...) and an object, namely a truth-value. (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)

This paper has a two-fold objective: to provide a balanced, multi-faceted account of the origins of logicism; to rehabilitate Richard Dedekind as a main logicist. Logicism should be seen as more deeply rooted in the development of modern mathematics than typically assumed, and this becomes evident by reconsidering Dedekind's writings in relation to Frege's. Especially in its Dedekindian and Fregean versions, logicism constitutes the culmination of the rise of ?pure mathematics? in the nineteenth century; and this rise brought with it (...) an inter-weaving of methodological and epistemological considerations. The latter aspect illustrates how philosophical concerns can grow out of mathematical practice, as opposed to being imposed on it from outside. It also sheds new light on the legacy and the lasting significance of logicism today. (shrink)

A critical discussion of Lu-Adler's chapter on Kant's mature view of pure general logic. I sketch an alternative interpretation of its formality on which Kant would hold no deduction is possible of this logic's laws.

In this essay I examine Kant's analogy with life from §65 of the Critique of the power of Judgment. I argue that this analogy is central for understanding his notion of a natural end, for his account of the formative power of organisms in the third Critique, and for situating Kant's account of this power in relation to the Lebenskräfte of the vitalists.

There are two ways interpreters have tended to understand the nature of the laws of Kant’s pure general logic. On the first, these laws are unconditional norms for how we ought to think, and will govern anything that counts as thinking. On the second, these laws are formal criteria for being a thought, and violating them makes a putative thought not a thought. These traditions are in tension, in so far as the first depends on the possibility of thoughts that (...) violate these laws, and the second makes violation impossible. In this essay I develop an interpretation of Kant’s pure general logic that overcomes this tension. It accounts for the possibility of logical mistakes, as the first tradition does, while still establishing the absolute impossibility of logical aliens, as the second tradition does. I then argue that the formalist insight that illogical exercises of the understanding are not alternative ways coherent thoughts could have been, but are mere confusions, is fundamental for achieving a proper understanding of the absolute normativity of the laws of pure general logic. (shrink)

Contrary to the contemporary view that negation is a logical operation that modifies the mere content of a thought or judgment, but not the act of thinking or judging it, Kant maintains that negation is an act of logical apperception through which I exclude a thought or judgment from what ‘I think.’ In this paper, I argue against two interpretations of Kant’s account of logical negation. According to the first, negation is a subjective psychological act of excluding an erroneous judgment. (...) Against this, I will show that for Kant, negation is an operation of logical, not empirical apperception. The second interpretation views logical negation as an objective representation either of a relation of opposition or of non-being. I argue that, on the contrary, the logical function of negation is merely formal, not material, and therefore does not have semantic content. The paper’s final section develops a positive conception of logical negation as a formal function of judging. (shrink)

For Kant, ‘reflection’ is a technical term with a range of senses. I focus here on the senses of reflection that come to light in Kant's account of logic, and then bring the results to bear on the distinction between ‘logical’ and ‘transcendental’ reflection that surfaces in the Amphiboly chapter of the Critique of Pure Reason. Although recent commentary has followed similar cues, I suggest that it labours under a blind spot, as it neglects Kant's distinction between ‘pure’ and ‘applied’ (...) general logic. The foundational text of existing interpretations is a passage in Logik Jäsche that appears to attribute to Kant the view that reflection is a mental operation involved in the generation of concepts from non-conceptual materials. I argue against the received view by attending to Kant's division between ‘pure’ and ‘applied’ general logic, identifying senses of reflection proper to each, and showing that none accords well with the received view. Finally, to take account of Kant's notio.. (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)

At A71/B96–7 Kant explains that singular judgements are ‘special’ because they stand to the general ones as Einheit to Unendlichkeit. The reference to Einheit brings to mind the category of unity and hence raises a spectre of circularity in Kant’s explanation. I aim to remove this spectre by interpreting the Einheit-Unendlichkeit contrast in light of the logical distinctions among universal, particular and singular judgments shared by Kant and his logician predecessors. This interpretation has a further implication for resolving a controversy (...) over the correlation between the logical moments of quantity (universal, particular, singular) and the categorial ones (unity, plurality, totality). (shrink)

In a famous passage (A68/B93), Kant writes that “the understanding can make no other use of […] concepts than that of judging by means of them.” Kant's thought is often called the thesis of the priority of judgments over concepts. We find a similar sounding priority thesis in Frege: “it is one of the most important differences between my mode of interpretation and the Boolean mode […] that I do not proceed from concepts, but from judgments.” Many interpreters have thought (...) that Frege's priority principle is close to (or at least derivable from) Kant's. I argue that it is not. Nevertheless, there was a gradual historical development that began with Kant's priority thesis and culminated in Frege's new logic. (shrink)

This paper explores a pair of puzzling and controversial topics in the history of late nineteenth-century philosophy: the psychologism debates, and the nature of neo-Kantianism. Each is sufficientl...

This paper explores a pair of puzzling and controversial topics in the history of late nineteenth-century philosophy: the psychologism debates, and the nature of neo-Kantianism. Each is sufficientl...

Officially, for Kant, judgments are analytic iff the predicate is "contained in" the subject. I defend the containment definition against the common charge of obscurity, and argue that arithmetic cannot be analytic, in the resulting sense. My account deploys two traditional logical notions: logical division and concept hierarchies. Division separates a genus concept into exclusive, exhaustive species. Repeated divisions generate a hierarchy, in which lower species are derived from their genus, by adding differentia(e). Hierarchies afford a straightforward sense of containment: (...) genera are contained in the species formed from them. Kant's thesis then amounts to the claim that no concept hierarchy conforming to division rules can express truths like '7+5=12.' Kant is correct. Operation concepts ( ) bear two relations to number concepts: and are inputs, is output. To capture both relations, hierarchies must posit overlaps between concepts that violate the exclusion rule. Thus, such truths are synthetic. (shrink)

According to received wisdom, Kant takes the laws of logic to be normative laws of thought. This has been challenged by Tolley (2006). In this paper, I defend the received wisdom, but with an important modification: Kant's logical laws are constitutive norms for thought. The laws of logic do tell us what thinking is, not because all thoughts are in conformity with logical laws, but because all thoughts are, by nature, subject to the standard of logic.

I shall make two main claims. My first main claim is that Frege started out with a view of logic that is closer to Kant’s than is generally recognized, but that he gradually came to reject this Kantian view, or at least totally to transform it. My second main claim concerns Frege’s reasons for distancing himself from the Kantian conception of logic. It is natural to speculate that this change in Frege’s view of logic may have been spurred by a (...) desire to establish the logicality of the axiom system he needed for his logicist reduction, including the infamous Basic Law V. I admit this may have been one of Frege’s motives. But I shall argue that Frege also had a deeper and more interesting reason to reject his early Kantian view of logic, having to do with his increasingly vehement anti-psychologism. (shrink)