Frege on Truth,Assertoric Force and the Essence of Logic

In a posthumous text written in 1915, Frege makes some puzzling remarks about the essence of logic, arguing that the essence of logic is indicated, properly speaking, not by the word ‘true’, but by the assertoric force. William Taschek has recently shown that these remarks, which have received only little attention, are very important for understanding Frege's conception of logic. On Taschek's reconstruction, Frege characterizes logic in terms of assertoric force in order to stress the normative role that the logical laws play vis-à-vis judgement, assertion and inference. My aim in this paper is to develop and defend an alternative reconstruction according to which Frege stresses that logic is not only concerned with ‘how thoughts follow from other thoughts’, but also with the ‘step from thought to truth-value’. Frege considers logic as a branch of the theory of justification. To justify a conclusion by means of a logical inference, the ‘step from thought to truth-value’ must be taken, that is, the premises must be asserted as true. It is for this reason that, in the final analysis, the assertoric force indicates the essence of logic, for Frege.     

A CRITIQUE OF FREGE ON COMMON NOUNS

Frege analyzed the grammatical subject‐term ‘S’ in quantified subject‐predicate sentences, ‘q S are P’, as being logically predicative. This is in contrast to Aristotelian Logic, according to which it is a logical subject‐term, like the proper name ‘a’ in ‘a is P’– albeit a plural one, designating many particulars. I show that Frege’s arguments for his analysis are unsound, and explain how he was misled to his position by the mathematical concept of function. If common nouns in this grammatical subject position are indeed logical subject‐terms, this should require a thorough reevaluation of the adequacy of Frege’s predicate calculus as a tool for the analysis of the logic and semantics of natural language.     

Formality of logic and Frege’s Begriffsschrift

This paper challenges a standard interpretation according to which Frege’s conception of logic (early and late) is at odds with the contemporary one, because on the latter’s view logic is formal, while on Frege’s view it is not, given that logic’s subject matter is reality’s most general features. I argue that Frege – in Begriffsschrift – retained the idea that logic is formal; Frege sees logic as providing the ‘logical cement’ that ties up together the contentful concepts of specific sciences, not the most general truths. Finally, I discuss how Frege conceives of the application of Begriffsschrift, and of its status as a ‘lingua characteristica’.     

Responding to N.T. Wright's Rejection of the Soul

At a 2011 meeting of the Society of Christian Philosophers, N. T. Wright offered four reasons for rejecting the existence of soul. This was surprising, as many Christian philosophers had previously taken Wright's defense of a disembodied intermediate state as a defense of a substance dualist view of the soul. In this paper, I offer responses to each of Wright's objections, demonstrating that Wright's arguments fail to undermine substance dualism. In so doing, I expose how popular arguments against dualism fail, such as (1) dualism is merely an unwarranted influence of Greek culture on Christianity, and (2) substance dualism is merely a soul‐of‐the‐gaps hypothesis. Moreover, I demonstrate that Wright himself has offered a powerful reason for adopting substance dualism in his previous works. In conclusion I offer a view that explains why the human soul needs a resurrected body.     

Relying on Intuitions: Where Cappelen and Deutsch Go Wrong

Abstract

In Philosophy without Intuitions (Oxford: Oxford University Press, 2012), Herman Cappelen challenges the ‘almost universally accepted’ thesis of ‘Centrality’: ‘philosophers rely on intuitions as evidence (or as a source of evidence) for philosophical theories’. Cappelen takes there to be two arguments for Centrality and rejects both. According to the first, Centrality is supported by the way philosophers characterize key premises in their arguments as ‘intuitive’. Central to Cappelen’s rejection of this is his lengthy argument that philosophers’ ‘intuition’-talk is very hard to interpret, indeed often ‘meaningless’. I argue, in contrast, that this talk is easy to interpret. The great mass of philosophers who would endorse Centrality mean by ‘intuition’ just what it ordinarily means: ‘immediate judgment, without reasoning or inference’. Cappelen claims further that philosophers’ ‘intuition’-talk, however it is interpreted, does not support Centrality. I argue that this talk, interpreted in the ordinary way, does indeed support Centrality. According to the second argument, Centrality is supported by the very practice of philosophy. Cappelen rejects this with a thorough examination of several philosophical arguments. Deutsch has attacked Centrality similarly, in effect, with a thorough examination of one famous argument from Kripke. How are we to tell whether philosophical practice relies on intuitions? Cappelen, and Deutsch to some extent, answer by looking to the opinions of intuition-theorists about the nature of intuitions. This approach is quite mistaken. Rather, we should look to our ordinary ability to recognize intuitions. Adopting this approach, and discussing Deutsch’s Kripke example in most detail, I argue that Centrality gets support from all of these examples of philosophical practice.     

Gottlob Frege und Rudolf Eucken—Gesprächspartner in der Herausbildungsphase der modernen Logik

Frege and Eucken were colleagues in the faculty of philosophy at Jena University for more than 40 years. At times they had close scientific contacts. Eucken promoted Frege's career at the university. A comparison of Eucken's writings between 1878 and 1880 with Frege's writings shows Eucken to have had an important philosophical influence on Frege's philosophical development between 1879 and 1885. In particular the classification of the Begriffsschrift in the tradition of Leibniz is influenced by Eucken. Eucken also influenced Frege's choice of philosophical and logical terms. Finally, there are analogous positions concerning relations between concepts and their expressions in natural language, Frege was probably also influenced by Eucken's use of the term ‘tone’. Eucken used Frege's arguments in his own fight against psychologism and empiricism.     

A Perennial Illusion? Wittgenstein,Quentin Skinner's Contextualism and the Possibility of Refuting Past Philosophers

Contemporary philosophers often purport to ‘borrow’ or ‘refute’ claims made by past philosophers. In doing so they contravene a contextualist methodological prohibition once defended by Quentin Skinner in his seminal paper “Meaning and Understanding in the History of Ideas”. Skinner's methodology has been much debated by theorists of textual meaning and interpretation, and yet the precise nature of the logical path from his premises to his prohibitory conclusion remains elusive. This paper seeks to refute two of the most promising variants of an argument for his methodological prohibition on ‘refutation’, one of which draws on his appeal to Wittgenstein's conception of ‘meaning as use’, and the other of which draws on his appeal to speech act theory.     

Demythologizing intuition

Max Deutsch’s new book argues against the commonly held ‘myth’ that philosophical methodology characteristically employs intuitions as evidence. While I am sympathetic to the general claim that philosophical methodology has been grossly oversimplified in the intuition literature, the particular claim that it is a myth that philosophers rely on intuitions as evidence is open to several very different interpretations. The plausibility and consequences of a rejection of the ‘myth’ will depend on the notion of evidence one employs, the notion of intuition one holds, and how one understands the idea of ‘relying on’ or ‘employing’ something as evidence. I describe what I take to be the version of The Myth which is most plausibly undermined by Deutsch’s arguments; however, I also argue that the falsity of this myth has only minimal consequences for the viability of the experimental philosophy research project.     

Dummett and Frege on sense and Selbständigkeit

As part of his attack on Frege’s ‘myth’ that senses reside in the third realm, Dummett alleges that Frege’s view that all objects are selbständig (‘self-subsistent’, ‘independent’) is an underlying mistake, since some objects depend upon others. Whatever the merits of Dummett’s other arguments against Frege’s conception of sense, this objection fails. First, Frege’s view that senses are third-realm entities is not traceable to his view that all objects are selbständig. Second, while Frege recognizes that there are objects that are dependent upon other objects, he does not take this to compromise the Selbständigkeit of any objects. Thus, Frege’s doctrine that objects are selbständig does not make the claim of absolute independence that Dummett appears to have taken it to make. Nevertheless, in order to make a good case against Frege based on the dependency of senses, Dummett need only establish his claim that senses depend upon expressions: appeal to an absolute conception of independence is unnecessary. However, Dummett’s arguments for the dependency of senses upon expressions are unsuccessful and they show that Dummett’s conception of what it is to be an expression also differs significantly from Frege’s.     

Platonism and metaphor in the texts of mathematics: Gödel and Frege on mathematical knowledge

In this paper, I challenge those interpretations of Frege that reinforce the view that his talk of grasping thoughts about abstract objects is consistent with Russell's notion of acquaintance with universals and with Gödel's contention that we possess a faculty of mathematical perception capable of perceiving the objects of set theory. Here I argue the case that Frege is not an epistemological Platonist in the sense in which Gödel is one. The contention advanced is that Gödel bases his Platonism on a literal comparison between mathematical intuition and physical perception. He concludes that since we accept sense perception as a source of empirical knowledge, then we similarly should posit a faculty of mathematical intuition to serve as the source of mathematical knowledge. Unlike Gödel, Frege does not posit a faculty of mathematical intuition. Frege talks instead about grasping thoughts about abstract objects. However, despite his hostility to metaphor, he uses the notion of ‘grasping’ as a strategic metaphor to model his notion of thinking, i.e., to underscore that it is only by logically manipulating the cognitive content of mathematical propositions that we can obtain mathematical knowledge. Thus, he construes ‘grasping’ more as theoretical activity than as a kind of inner mental ‘seeing’.

     

Lotze and frege: The dating of the ’Kernsätze’ ∗

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’     

Context and consequence. An intercontextual substructural logic

Some apparently valid arguments crucially rely on context change. To take a kind of example first discussed by Frege, ‘Tomorrow, it’ll be sunny’ taken on a day seems to entail ‘Today, it’s sunny’ taken on the next day, but the first sentence taken on a day sadly does not seem to entail the second sentence taken on the second next day. Mid-argument context change has not been accounted for by the tradition that has extensively studied the distinctive logical properties of context-dependent languages, for that tradition has focussed on arguments whose premises and conclusions are taken at the same context. I first argue for the desiderability of having a logic that accounts for mid-argument context change and I explain how one can informally understand such context change in a standard framework in which the relation of logical consequence holds among sentences. I then propose a family of simple temporal “intercontextual” logics that adequately model the validity of certain arguments in which the context changes. In particular, such logics validate the apparently valid argument in the Fregean example. The logics lack many traditional structural properties (reflexivity, contraction, commutativity etc.) as a consequence of the logical significance acquired by the sequence structure of premises and conclusions. The logics are however strong enough to capture in the form of logical truths all the valid arguments of both classical logic and Kaplan-style “intracontextual” logic. Finally, I extend the framework by introducing new operations into the object language, such as intercontextual conjunction, disjunction and implication, which, contrary to intracontextual conjunction, disjunction and implication, perfectly match the metalinguistic, intercontextual notions of premise combination, conclusion combination and logical consequence by representing their respective two operands as taken at different contexts.     

What It Is to Pretend

Pretense is a topic of keen interest to philosophers and psychologists. But what is it, really, to pretend? What features qualify an act as pretense? Surprisingly little has been said on this foundational question. Here I defend an account of what it is to pretend, distinguishing pretense from a variety of related but distinct phenomena, such as (mere) copying and practicing. I show how we can distinguish pretense from sincerity by sole appeal to a person's beliefs, desires, and intentions – and without circular recourse to an ‘intention to pretend’ or to a sui generis mental state of ‘imagining.’     

Plato's Revenge: Moral Deliberation As Dialogical Activity

In this article I offer an account of normative thought inspired by Plato's proposal in the Theaetetus that judgement is ‘speech spoken … silently.’ After arguing that force conventionalism is the speech act theory best suited for modeling dialogic inner speech, I close the article by sketching the picture of normative thought that results. Though I defend a particular theory of normative speech elsewhere, the core insights of this article can be used by other theorists as well. The arguments offered here also serve as an important step forward for the more general program of using social speech to better understand thought.     

The Role of Structural Reasoning in the Genesis of Graph Theory

The concept of quantity (Größe) plays a key role in Frege's theory of real numbers. Typically enough, he refers to this theory as ‘theory of quantity’ (‘Größenlehre’) in the second volume of his opus magnum Grundgesetze der Arithmetik (Frege 1903). In this essay, I deal, in a critical way, with Frege's treatment of the concept of quantity and his approach to analysis from the beginning of his academic career until Frege 1903. I begin with a few introductory remarks. In Section 2, I first analyze Frege's use of the term ‘source of knowledge’ (‘Erkenntnisquelle’) with particular emphasis on the logical source of knowledge. The analysis includes a brief comparison between Frege and Kant's conceptions of logic and the logical source of knowledge. In a second step, I examine Frege's theory of quantity in Rechnungsmethoden, die sich auf eine Erweiterung des Größenbegriffes gründen (Frege 1874). Section 3 contains a couple of critical observations on Frege's comments on Hankel's theory of real numbers in Die Grundlagen der Arithmetik (Frege 1884). In Section 4, I consider Frege's discussion of the concept of quantity in Frege 1903. Section 5 is devoted to Cantor's theory of irrational numbers and the critique deployed by Frege. In Section 6, I return to Frege's own constructive treatment of analysis in Frege 1903 and succinctly describe what I take to be the quintessence of his account.     

ANALYSIS,ABSTRACTION PRINCIPLES,AND SLINGSHOT ARGUMENTS

Frege's views regarding analysis and synomymy have long been the subject of critical discussion. Some commentators, led by Dummett, have argued that Frege was committed to the view that each thought admits of a unique ultimate analysis. However, this interpretation is in apparent conflict with Frege's criterion of synonymy, according to which two sentence express the same thought if one cannot understand them without regarding them as having the same truth–value. In a recent article in this journal, Drai attempts to reconcile Frege's criterion of synonymy with unique ultimate analysis by holding that, for Frege, if two sentences satisfy the criterion without being intensionally isomorphic, at most one of them is a privileged representation of the thought expressed. I argue that this proposal fails, because it conflicts not only with Frege's views of abstraction principles but also with slingshot arguments (including one presented by Drai herself) that accurately reflect Frege's commitment to the view that sentences alike in truth–value have the same Bedeutung. While Drai helpfully connects Frege's views of abstraction principles with such slingshot arguments, this connection cannot become fully clear until we recognise that Frege rejects unique ultimate analysis.     

Indicating a Translation for ‘Bedeutung’

The translation of both ‘bedeuten’ and ‘Bedeutung’ in Frege's works remains sufficiently problematic that some contemporary authors prefer to leave these words untranslated. Here a case is made for returning to Russell's initial choice of ‘to indicate’ and ‘indication’ as better alternatives than the more usual ‘meaning’, ‘reference’, or ‘denotation’. It is argued that this choice has the philosophical payoff that Frege's controversial doctrines concerning the semantic values of sentences and predicative expressions are rendered far more comprehensible by it, and that this translational strategy fulfills the desiderata of offering a translation which is acceptable both before and after Frege introduced the distinction between sense and reference or, as this paper would have it, between the sense of an expression and what it indicates.     

SENSATION,INTENTIONALITY, AND ANIMAL CONSCIOUSNESS: MALEBRANCHE'S THEORY OF THE MIND

In general, seventeenth-century philosophers seem to have assumed that intentionality is an essential characteristic of our mental life. Malebranche is perhaps the only philosopher in the period who stands out clearly against the prevailing orthodoxy; he is committed to the thesis that there is a large class of mental items - sensations - which have no representational content. In this paper I argue that due attention to this fact makes it possible to mount at least a partial defence of his notorious doctrine of ‘the rainbow-coloured soul’; Malebranche's doctrine is a striking anticipation of modern adverbial theories of sensation. I then argue that failure to appreciate the non-intentional character of sensations for Malebranche vitiates one recent attempt to explain why he accepted the Cartesian doctrine of the beastmachine; in contrast to the Radners, I suggest that Malebranche has the philosophical resources to offer an interesting theory of animal consciousness, and that his failure to develop such a theory rests largely on his acceptance of certain theological arguments. The paper ends by speculating about how Malebranche's theological commitments may have encouraged him to adopt the philosophically important thesis that intentionality is not the mark of the mental.