Frege: two theses,two senses

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 analyse where, in Frege'ps 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.     

The Middle Wittgenstein’s Critique of Frege

ABSTRACT

This article aims to analyse Wittgenstein’s 1929–1932 notes concerning Frege’s critique of what is referred to as old formalism in the philosophy of mathematics. Wittgenstein disagreed with Frege’s critique and, in his notes, outlined his own assessment of formalism. First of all, he approvingly foregrounded its mathematics-game comparison and insistence that rules precede the meanings of expressions. In this article, I recount Frege’s critique of formalism and address Wittgenstein’s assessment of it to show that his remarks are not so much a critique of Frege as rather a defence of the formalist anti-metaphysical investment.     

Frege on Syntax,Ontology, and Truth's Pride of Place

Frege's strict alignment between his syntactic and ontological categories is not, as is commonly assumed, some kind of a philosophical thesis. There is no thesis that proper names refer only to objects, say, or that what refers to an object is a proper name. Rather, the alignment of categories is internal to Frege's conception of what syntax and ontology are. To understand this, we need to recognise the pride of place Frege assigns within his theorising to the notion of truth. For both language and the world, the Fregean categories are logical categories, categories, that is, of truth. The elaboration of this point makes clear the incoherence of supposing that they might not align.     

SYSTEMS OF MEASUREMENT

Wittgenstein and Kripke disagree about the status of the proposition: the Standard Metre is one metre long. Wittgenstein believes it is necessary. Kripke argues that it is contingent. Kripke's argument depends crucially on a certain sort of thought‐experiment with which we are invited to test our intuitions about what is and isn’t necessary. In this paper I argue that, while Kripke's conclusion is strictly correct, nevertheless similar Kripke‐style thought experiments indicate that the metric system of measurement is after all relative in something like the way Wittgenstein seems to think. Central to this paper is a thought‐experiment I call The Smedlium Case.     

Frege on the generality of logical laws

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.     

Beltrami's model and the independence of the parallel postulate

In their correspondence in 1902 and 1903, after discussing the Russell paradox, Russell and Frege discussed the paradox of propositions considered informally in Appendix B of Russell's Principles of Mathematics. It seems that the proposition, p, stating the logical product of the class w, namely, the class of all propositions stating the logical product of a class they are not in, is in w if and only if it is not. Frege believed that this paradox was avoided within his philosophy due to his distinction between sense (Sinn) and reference (Bedeutung). However, I show that while the paradox as Russell formulates it is ill-formed with Frege's extant logical system, if Frege's system is expanded to contain the commitments of his philosophy of language, an analogue of this paradox is formulable. This and other concerns in Fregean intensional logic are discussed, and it is discovered that Frege's logical system, even without its naive class theory embodied in its infamous Basic Law V, leads to inconsistencies when the theory of sense and reference is axiomatized therin. therein.     

Kant,wittgenstein and the limits of logic

This paper has two purposes. (1) To justify the claim that there is an important distinction underlying the saying/showing distinction of the Tractatus; the distinction which Kant characterises as that between historical and rational knowledge. (2) To argue that it is because the Tractatus accepts Frege/Russell logic as a complete representation of all thought according to laws, that what is shown cannot be recognised as knowledge. This is done by interpolating Frege's logical innovations between the views of Kant and Wittgenstein on logic and mathematics.     

Tractarian objects and logical categories

It has been much debated whether Tractarian objects are what Russell would have called particulars or whether they include also properties and relations. This paper claims that the debate is misguided: there is no logical category such that Wittgenstein intended the reader of the Tractatus to understand his objects either as providing examples of or as not providing examples of that category. This is not to say that Wittgenstein set himself against the very idea of a logical category: quite the contrary. However, where Russell presents his logical variety of particulars and the various types of universal, and Frege presents his of objects and the various types of function, Wittgenstein denies the propriety of such a priori expositions. Wittgenstein envisages a variety of logical types of entity but insists that the nature of these types is something to be discovered only through analysis. This research was conducted whilst holding a Jacobsen Research Fellowship at the University of London.     

Categorial Indeterminacy,Generality and Logical Form in Wittgenstein's Tractatus

Many commentators have attempted to say, more clearly than Wittgenstein did in his Tractatus logico‐philosophicus, what sort of things the ‘simple objects’ spoken of in that book are. A minority approach, but in my view the correct one, is to reject all such attempts as misplaced. The Tractarian notion of an object is categorially indeterminate: in contrast with both Frege's and Russell's practice, it is not the logician's task to give a specific categorial account of the internal structure of elementary propositions or atomic facts, nor, correlatively, to give an account of the forms of simple objects. The few commentators who have hitherto maintained this view have mainly devoted themselves to establishing that this was Wittgenstein's intention, and do not much address the question why Wittgenstein held that it is not the logician's business to say what the objects are. The present paper means to fill this lacuna by placing this view in the context of the Tractatus's treatment of logic generally, and in particular by connecting it with Wittgenstein's treatment of generality and with his reaction to Russell's approach to logical form.     

HOW DID FREGE FALL INTO THE CONTRADICTION?

Quine made it conventional to portray the contradiction that destroyed Frege's logicism as some kind of act of God, a thunderbolt that descended from a clear blue sky. This portrayal suited the moral Quine was antecedently inclined to draw, that intuition is bankrupt, and that reliance on it must therefore be replaced by a pragmatic methodology. But the portrayal is grossly misleading, and Quine's moral simply false. In the person of others – Cantor, Dedekind, and Zermelo – intuition was working pretty well. It was in Frege that it suffered a local and temporary blindness. The question to ask, then, is not how Frege was overtaken by the contradiction, but how it is that he didn't see it coming. The paper offers one kind of answer to that question. Starting from the very close similarity between Frege's proof of infinity and the reasoning that leads to the contradiction, it asks: given his understanding of the first, why did Frege did not notice the second? The reason is traced, first, to a faulty generalization Frege made from the case of directions and parallel lines; and, through that, to Frege's having retained, and attempted incoherently to combine with his own, aspects of a pre‐Fregean understanding of the generality of logical principles.     

The Content of Emotional Thoughts

Abstract

In this paper I examine Peter Goldie's theory of emotional thoughts and feelings, offered in his recent book The Emotions and subsequent articles. Goldie argues that emotional thoughts cannot be assimilated to belief or judgment, together with some added-on phenomenological component, and on this point I agree with him. However, he also argues that emotionally-laden thoughts, thoughts had, as he puts it, ‘with feeling,’ in part differ from unemotional thoughts in their content. The thought ‘the gorilla is dangerous’ when thought with an emotional feeling of fear differs in its content from the thought ‘the gorilla is dangerous’ when thought without actually feeling fear. I argue that Goldie offers no good reason to think that the difference between emotional and unemotional thoughts is found in their contents. In fact, the analogies Goldie presents to help make his case actually suggest that the contribution feelings make to the distinctive role played by emotional thoughts consists solely in their influencing the way we think emotional thoughts. However, this position is consistent with Goldie's broader point: that theories which treat emotional feelings as phenomenological afterthoughts should be rejected.     

Wittgenstein on Scepticism and Nonsense

In the Tractatus Wittgenstein wrote: “Skepticism is not irrefutable, but obviously nonsensical when it tries to raise doubts where no questions can be asked.” In this paper I show how Wittgenstein developed this insight in On Certainty. My principal aim is to show that this is a logical insight, that it is bound up with the distinction between saying and showing, and that one misses the point of On Certainty if one reads it, as some commentators have, in epistemological terms. Throughout all of this I pay special attention to why Wittgenstein thought that skepticism is nonsensical, and what it might mean to say that philosophy is a logical investigation.     

Propositions,Properties and Relations: Wittgenstein's “Notes on Logic” and the Tractatus

Frege famously argued that truth is not a property or relation. In the “Notes on Logic” Wittgenstein emphasised the bi‐polarity of propositions which he called their sense. He argued that “propositions by virtue of sense cannot have predicates or relations.” This led to his fundamental thought that the logical constants do not represent predicates or relations. The idea, however, has wider ramifications than that. It is not just that propositions cannot have relations to other propositions but also that they cannot have relations to anything at all. The paper explores the consequences of this insight for the way in which we should read the Tractatus. In the “Notes on Logic” the insight led to Wittgenstein's emphasis on “facts” in any attempt to understand the nature of symbolism. This emphasis is continued in the Tractatus. It is central to his view that propositions are facts which picture facts which prevent us from construing such picturing as a relation between what pictures and what is pictured. It illuminates the importance of context principle with regard to the distinction between showing and saying to which Wittgenstein attached so much importance and it underlies the non‐relational view of psychological propositions which he advocates. Finally, if propositions by virtue of sense cannot have predicates or relations the paradox at the end of a work which consist largely of propositions about propositions becomes intelligible.     

The philosophy of science at the turn of the millenium

Abstract

Central to a new, or ‘resolute’, reading of Wittgenstein’s Tractatus LogicoPhilosophicus is the idea that Wittgenstein held there an ‘austere’ view of nonsense: the view, that is, that nonsense is only ever a matter of our failure to give words a meaning, and so that there are no logically distinct kinds of nonsense. Resolute readers tend not only to ascribe such a view to Wittgenstein, but also to subscribe to it themselves; and it is also a feature of some readings which in other respects are clearly not Resolute. This paper forms part of a reply to Hans-Johann Glock’s work in which he argues (in part) that Wittgenstein in the Tractatus held a view of nonsense other than the austere view. Instead, Glock argues, Wittgenstein there held that there are many logically distinct kinds of nonsense. Here, I outline and defend the austere view, together with its attribution to the early Wittgenstein, against a number of Glock’s criticisms, and focussing especially on Wittgenstein’s reformulation in the Tractatus of Frege’s context-principle.     

Kripke's Second Paragraph of Philosophical Investigations 201

The received view of Kripke's Wittgenstein on Rules and Private Language is that it fails as an interpretation because, inter alia, it ignores or overlooks what Wittgenstein has to say in the second paragraph of Philosophical Investigations (PI) 201. In this paper, I demonstrate that the paragraph in question is in fact fully accommodated within Kripke's reading, and cannot therefore be reasonably utilised to object to it. In part one I characterise the objection; in part two I explain why it fails; in part three I suggest why commentators might have been motivated to offer it; and in part four I claim that two commentators who have offered it also imply otherwise.     

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.     

It's a Wonderful Life: Reflections on Wittgenstein's Last Words

On his deathbed, Wittgenstein is reported to have said, upon hearing that his friends were coming for a visit, “Tell them I've had a wonderful life.” Malcolm found this puzzling, given that Wittgenstein seemed to be fiercely unhappy. I find my way into these words against the backdrop of the Hollywood film It's a Wonderful Life and Wittgenstein's famous remark, to wit, “Man has to awaken to wonder . . . Science is a way of sending him to sleep again.” Along the way I discuss Plato's praise of wonder, Nietzsche's attack on science, and Kierkegaard's remark about finding the sublime in the pedestrian. I conclude that Wittgenstein did have a wonderful life insofar as he was fully awake to wonder, what I call the wonder of our words.     

The Unity of a Tractarian Fact

It is not immediately clear from Wittgenstein’s Tractatus how to connect his idea there of an object with the logical ontologies of Frege and Russell. Toward clarification on this matter, this paper compares Russell’s and Wittgenstein’s versions of the thesis of an atomic fact that it is a complex composition. The claim arrived at is that whilst Russell (at times at least) has one particular of the elements of a fact – the relation – responsible for the unity of the whole, for Wittgenstein the unity of a fact is the product of copulative powers inherent in all its elements. All kinds of constituents of Tractarian facts – all kinds (forms) of object – are, to use Fregean terminology, unsaturated.