Artykuł dotyczy dwóch bardzo mało znanych utworów słynnych twórców literatury niemieckiej. Johann Wolfgang von Goethe, twórca Fausta, ma w swym dorobku moralizatorski wiersz pt. Dziennik. Jednak z obawy o posądzenie go o niemoralne treści, nigdy za życia poety utwór ten nie został opublikowany. Również Siedem wierszy Rainera Marii Rilkego jest bardzo rzadko drukowanych. Mimo, iż Rilke długo wzbraniał się przed lekturą utworów niemieckiego wieszcza, to jednak Dziennik stanowił wyjątek. Wiersz Goethego poświęcony jest kryzysowi seksualnemu i twórczemu bohatera, za którym kryje (...) się sam poeta. Wiersze Rilkego stanowią cykl poświęcony aktowi miłosnemu dwojga kochanków. Artykuł stara się przeanalizować wzajemne związki obu tych tak różnych dzieł i odpowiedzieć na pytanie, czy R. M. Rilke wzorował się na twórczości J. W. Goethego. (shrink)

The lectures on Heidegger‘s Being and Time held at a congress in Siegen (by Charles Bambach, Dieter Thomä, Johannes Fritsche, Rainer Marten et al.) and published in a book in the spring of 2019, are subject to a revision here. In particular, the works of the group around Emmanuel Faye are considered sect-like sessions of the intention to interpret Being and Time by the later Nazi identity of its author. Due to the dominance of these interpretations, the conference (...) is criticized under this aspect as „Congress of Braunfärber“ (i.e. those who dye it brown). Die auf einem Kongress in Siegen gehaltenen Vorträge zu Heideggers Sein und Zeit (von Charles Bambach, Dieter Thomä, Johannes Fritsche, Rainer Marten u.a.), im Frühling 2019 in Buchform publiziert, werden hier einer Revision unterzogen. Insbesondere die Arbeiten der Gruppe um Emmanuel Faye werden dabei als sektenhafte Sessionen des Unternehmen bewertet, „Sein und Zeit von der späteren nazistischen Mission seines Verfassers her zu lesen“. Aufgrund der Dominanz dieser Deutung wird die Tagung in Siegen wird unter diesem Gesichtspunkt als “Kongress der Braunfärber“ kritisiert. (shrink)

This book aims to develop certain aspects of Gottlob Frege’s theory of meaning, especially those relevant to intensional logic. It offers a new interpretation of the nature of senses, and attempts to devise a logical calculus for the theory of sense and reference that captures as closely as possible the views of the historical Frege. (The approach is contrasted with the less historically-minded Logic of Sense and Denotation of Alonzo Church.) Comparisons of Frege’s theory with those of Russell and others (...) are given. It is in the end shown that developing Frege’s theory in these ways reveals serious problems hitherto largely unnoticed, including those possibly rendering a Fregean intensional logic inconsistent even if his naïve class theory is excluded. (shrink)

Bertrand Russell was one of the best-known proponents of logicism: the theory that mathematics reduces to, or is an extension of, logic. Russell argued for this thesis in his 1903 The Principles of Mathematics and attempted to demonstrate it formally in Principia Mathematica (PM 1910–1913; with A. N. Whitehead). Russell later described his work as a further “regressive” step in understanding the foundations of mathematics made possible by the late 19th century “arithmetization” of mathematics and Frege’s logical definitions of arithmetical (...) concepts. The logical system of PM sought to improve on earlier attempts by solving the contradictions found in, e.g., Frege’s system, by employing a theory of types. In this article, I also consider and critically evaluate the most common objections to Russell’s logicism, including the claim that it is undermined by Gödel’s incompleteness results, and Putnam's charge of “if-thenism”. I suggest that if we are willing to accept a slightly revisionist account of what counts as a mathematical truth, these criticisms do not obviously refute Russell’s claim to have established that mathematical truths generally are a species of logical truth. (shrink)

It would be an understatement to say that Russell was interested in Cantorian diagonal paradoxes. His discovery of the various versions of Russell’s paradox—the classes version, the predicates version, the propositional functions version—had a lasting effect on his views in philosophical logic. Similar Cantorian paradoxes regarding propositions—such as that discussed in §500 of The Principles of Mathematics—were surely among the reasons Russell eventually abandoned his ontology of propositions.1 However, Russell’s reasons for abandoning what he called “denoting concepts”, and his rejection (...) of similar “semantic dualisms” such as Frege’s theory of sense and reference—at least in “On Denoting”—made no explicit mention of any Cantorian paradox. My aim in this paper is to argue that such paradoxes do pose a problem for certain theories such as Frege’s, and early Russell’s, about how definite descriptions are meaningful. My first aim is simply to lay out the problem I have in mind. Next, I shall turn to arguing that the theories of descriptions endorsed by Frege and by Russell prior to “On Denoting” are susceptible to the problem. Finally, I explore what responses a.. (shrink)

Review essay covering Godehard Link, ed. One Hundred Years of Russell’s Paradox (de Gruyter 2004).

Along with offering an historically-oriented interpretive reconstruction of the syntax of PM ( rst ed.), I argue for a certain understanding of its use of propositional function abstracts formed by placing a circum ex on a variable. I argue that this notation is used in PM only when de nitions are stated schematically in the metalanguage, and in argument-position when higher-type variables are involved. My aim throughout is to explain how the usage of function abstracts as “terms” (loosely speaking) is (...) not inconsistent with a philosophy of types that does not think of propositional functions as mind- and language-independent objects, and adopts a nominalist/substitutional semantics instead. I contrast PM’s approach here both to function abstraction found in the typed λ-calculus, and also to Frege’s notation for functions of various levels that forgoes abstracts altogether, between which it is a kind of intermediary. (shrink)

Logicism is the view that mathematical truths are logical truths. But a logical truth is commonly thought to be one with a universally valid form. The form of “7 > 5” would appear to be the same as “4 > 6”. Yet one is a mathematical truth, and the other not a truth at all. To preserve logicism, we must maintain that the two either are different subforms of the same generic form, or that their forms are not at all (...) what they appear. The historical record shows that Russell pursued both these options, but that the struggle with the logical paradoxes pushed him away from the first kind of response and toward the second. An object cannot itself have a kind of inner logical complexity that makes a proposition have a different logical form merely in virtue of being about it, nor can their representatives in logical forms be single things different for different forms, at least not without postulating too many such objects and thereby creating Cantorian diagonal paradoxes. There are only apparent objects which are actually fragments of logical forms, different in different cases. (shrink)

In this paper, I counter arguments to the effect that pacifism must be irrational which cite hypothetical situations in which violence is necessary to prevent a far greater evil. I argue that for persons similar to myself, for whom such scenarios are extremely unlikely, promoting in oneself the disposition to avoid violence in any circumstances is more likely to lead to better results than not cultivating such a disposition just for the sake of such unlikely eventualities.

The positions of Frege, Russell and Wittgenstein on the priority of complexes over (propositional) functions are sketched, challenging those who take the "judgment centered" aspects of the Tractatus to be inherited from Frege not Russell. Frege's views on the priority of judgments are problematic, and unlike Wittgenstein's. Russell's views on these matters, and their development, are discussed in detail, and shown to be more sophisticated than usually supposed. Certain misreadings of Russell, including those regarding the relationship between propositional functions and (...) universals, are exposed. Wittgenstein's and Russell's views on logical grammar are shown to be very similar. Russell's type theory does not countenance types of genuine entities nor metaphysical truths that cannot be put into words, contrary to conventional wisdom. I relate this to the debate over "inexpressible truths" in the Tractatus. I lastly comment on the changes to Russell's views brought about by Wittgenstein's influence. (shrink)

This chapter clarifies that it was the works Giuseppe Peano and his school that first led Russell to embrace symbolic logic as a tool for understanding the foundations of mathematics, not those of Frege, who undertook a similar project starting earlier on. It also discusses Russell’s reaction to Peano’s logic and its influence on his own. However, the chapter also seeks to clarify how and in what ways Frege was influential on Russell’s views regarding such topics as classes, functions, meaning (...) and denotation, etc., and summarizes the correspondence between Frege and Russell and the light it sheds on the philosophical logic of both. (shrink)

In this article, I propose a formal criterion that distinguishes between deductively valid arguments that do and do not beg the question. I define the concept of a Never-failing Minimally Competent Knower (NMCK) and suggest that an argument begs the question just in case it cannot possibly assist an NMCK in extending his or her knowledge.

The chapter argues from an ethology-inspired internalist perspective that ‘colour’ is not a homogeneous and autonomous attribute, but rather plays different roles in different conceptual forms underlying perception. It discusses empirical and theoretical evidence that indicates that core assumptions underlying orthodox conceptions are grossly inadequate. The assumptions pertain to the idea that colour is a kind of autonomous and unitary attribute. It is regarded as unitary or homogeneous by assuming that its core properties do not depend on the type of (...) ‘perceptual object’ to which it pertains and that‘colour per se’ constitutes a natural attribute in the functional architecture of the perceptual system. It is regarded as autonomous by assuming that it can be studied in isolation of other perceptual attributes. More generally, the chapter argues on the bases of corresponding empirical and theoretical evidence that perception cannot be understood as the ‘recovery’ of physical world structure from sensory structure by input-based computational processes. Rather, the sensory input serves as a kind of sign for biologically relevant aspects of the external world that activates biologically given conceptual forms with their internal parameters. Although the sensory input is a causally necessary requirement for the activation of conceptual forms, the perceptual computations triggered are under the control of an internal programme based on a set of conceptual forms. (shrink)

Russell is often taken as a forerunner of the Quinean position that “to be is to be the value of a bound variable”, whereupon the ontological commitment of a theory is given by what it quantifies over. Among other reasons, Russell was among the first to suggest that all existence statements should be analyzed by means of existential quantification. That there was more to Russell’s metaphysics than what existential quantifications come out as true is obvious in the earlier period where (...) Russell still made a distinction between existence and being/subsistence. But even the later Russell, including that of the Logical Atomism lectures period, would not have understood ontological questions to be first and foremost questions of quantification. He would take fundamentality to be important too, which explains in part his assertions to the effect the the values of individual variables have a reality not attributable to values of higher-order variables, even ineliminable higher-order variables. (shrink)

In he Problems of Philosophy and other works of the same period, Russell claims that every proposition must contain at least one universal. Even fully general propositions of logic are claimed to contain “abstract logical universals”, and our knowledge of logical truths claimed to be a species of a priori knowledge of universals. However, these views are in considerable tension with Russell’s own philosophy of logic and mathematics as presented in Principia Mathematica. Universals generally are qualities and relations, but if, (...) for example, PM’s disjunction (∨) is a relation, what is it a relation between? There is no obvious answer to this given Russell’s other philosophical commitments at this time, although hints are left in some of the pre-PM manuscripts. In this paper, I explore this tension in Russell's philosophy and relate it to developments both before and after Problems. (shrink)

Interactive social cognition theory and approaches of developmental psychology widely agree that central aspects of emotional and social experience arise in the unfolding of processes of embodied social interaction. Bi-directional dynamical couplings of bodily displays such as facial expressions, gestures, and vocalizations have repeatedly been described in terms of coordination, synchrony, mimesis, or attunement. In this paper, I propose conceptualizing such dynamics rather as processes of affective resonance. Starting from the immediate phenomenal experience of being immersed in interaction, I develop (...) the philosophical notion of affective resonance to refer to a dynamic entanglement of moving and being-moved in relation. The concept of affective resonance makes visible that the interaction dynamic itself creates an affective experience rather than transmitting internal feeling states between pre-existent individuals. This leads to a philosophical framework in which relationality and ontogeny are primary over separate individuals, and in which the naturalistic distinction of a fundamental physical level versus an emerging level of social processes has to be given up. (shrink)

This article connects value-sensitive design to Gibson’s affordance theory: the view that we perceive in terms of the ease or difficulty with which we can negotiate space. Gibson’s ideas offer a nonsubjectivist way of grasping culturally relative values, out of which we develop a concept of political affordances, here understood as openings or closures for social action, often implicit. Political affordances are equally about environments and capacities to act in them. Capacities and hence the severity of affordances vary with age, (...) health, social status and more. This suggests settings are selectively permeable, or what postphenomenologists call multistable. Multistable settings are such that a single physical location shows up differently – as welcoming or hostile – depending on how individuals can act on it. In egregious cases, authoritarian governments redesign politically imbued spaces to psychologically cordon both them and the ideologies they represent. Selective permeability is also orchestrated according to business interests, which is symptomatic of commercial imperatives increasingly dictating what counts as moral and political goods. (shrink)

This chapter explores the metaphysical views about higher-order logic held by two individuals responsible for introducing it to philosophy: Gottlob Frege (1848–1925) and Bertrand Russell (1872–1970). Frege understood a function at first as the remainder of the content of a proposition when one component was taken out or seen as replaceable by others, and later as a mapping between objects. His logic employed second-order quantifiers ranging over such functions, and he saw a deep division in nature between objects and functions. (...) Russell understood propositional functions as what is obtained when constituents of propositions are replaced by variables, but eventually denied that they were entities in their own right. Both encountered contradictions when supposing there to exist as many objects as functions, and both adopted views about the meaningfulness of higher-order discourse that were difficult to state from within their own strictures. (shrink)

The chapter deals with misconceptions in perception theory that are based on the idea of slicing the nature of perception along the joints of physics and on corresponding ill-conceived ʹpurposesʹ and ʹgoalsʹ of the perceptual system. It argues that the conceptual structure underlying the percept cannot be inferentially attained from the sensory input. The output of the perceptual system, namely meaningful categories, is evidently vastly underdetermined by the sensory input, namely physico-geometric energy patterns. Thus, the core task of perception theory (...) is to understand the internal conceptual structure with which our perceptual system is endowed. The conceptual structure underlying the semantic distinctions that characterise the output of the perceptual system can, by conceptual necessity, only be expressed by a logical language that is strictly more powerful than the logical language by which sensory notions can be expressed. Consequently, the internal structure underlying perceptual meaning – including core notions such as ‘Gestalt’ or ‘perceptual object’ – cannot be derived, by whatever kind of general inductive machinery, from the sensory input, or, more generally, from experience. (shrink)

This article investigates what constitutes good reason, in particular in scientific communication. I will start out with a general description of what scientists do and will identify the good argument as an integral part of all science. Employing some simple examples, I will then move on to derive some necessary conditions for the goodness of an argument. Along the way, I will introduce various basic concepts in logic and briefly talk about the nature of human knowledge. I will conclude by (...) relating my discussion of good reasoning in science to critical thinking in general and explain why I believe that critical thinking is at the heart of a well-functioning liberal democracy. (shrink)

The chapter outlines an abstract theoretical framework that is currently (re-)emerging in the course of a theoretical convergence of several disciplines. In the first section, the fundamental problem of perception theory is formulated, namely, the generation, by the perceptual system, of meaningful categories from physicogeometric energy patterns. In the second section, it deals with basic intuitions and assumptions underlying what can be regarded as the current Standard Model of Perceptual Psychology and points out why this model is profoundly inadequate for (...) dealing with the fundamental problem of perception theory. In the third section, it discusses a level of analysis that promises to be fruitful for dealing, in conformity with established procedures of the natural sciences, with the problem of perceptual “meaning” and the problem of what constitutes a “perceptual object.” In the fourth section, it outlines a theoretical perspective on basic principles of the perceptual system which centers on the notions of complex data types and conceptual forms, and draws an entirely different theoretical picture of the role of the sensory input than traditional accounts. The final section focusses on the issue of material qualities and discusses, within the general theoretical framework outlined, some observations and results on the perception of certain material properties, namely, lustrous and glassy appearances. (shrink)

For a long time, academic institutes stigmatized activism and dissociated it from academic practice. It was looked down upon and considered to be disruptive and western institutes continued silencing critical thinking and practice, and encouraged what they named 'critical distance'. These practices of exclusion must push us, city inhabitants, to ask: what is the point of excluding activism from academic practice? How can we bridge between theory and activism? How can we decenter city planning? If cities belong to the people, (...) why are public authorities trying to erase the public's print in the urban realm? Who gets to speak and why? In our group as the ‘Radicals’, we discussed the gap between urban theory and practice, while encouraging the audience to reflect on how urban concepts adopt multiple definitions within different geographies and communities. (shrink)

Russell corresponded with Sir Michael Dummett (1925–2011) between 1953 and 1963 while the latter was working on a book on Frege, eventually published as Frege: Philosophy of Language (1973). In their letters they discuss Russell’s correspondence with Frege, translating it into English, as well as Frege’s attempted solution to Russell’s paradox in the appendix to vol. 2 of his Grundgesetze der Arithmetik. After Dummett visited the University of Münster to view Frege’s Nachlaß, he sent reports back to Russell concerning both (...) the philosophical materials Frege left behind, as well as information from Frege’s journal revealing his anti-semitic political opinions. Their interaction contains interpretive conjectures and insights on Dummett’s side, and some dark humor on Russell’s. (shrink)

Frege developed the theory of sense and reference while composing his Grundgesetze and considering its philosophical implications. The Grundgesetze is thus the most important test case for the application of this theory of meaning. I argue that evidence internal and external to the Grundgesetze suggests that he thought of senses as having a structure isomorphic to the Grundgesetze expressions that would be used to express them, which entails a theory about the identity conditions of senses that is relatively fine-grained, though (...) still coarser than some other commentators have suggested. While this interpretation does not make Frege’s ontological commitment to the denizens of a “third realm” as profligate as some have alleged, it is sufficiently bloated to lead to Cantorian paradoxes and diagonal contradictions independent of his Basic Law V. (shrink)

Debates on Nietzsche’s naturalism usually posit nature and culture as competing principles to understand the contingent genesis of humanity. In contrast to this polarizing tendency, I argue that Nietzsche focuses on the cultural characteristics of humanity because of his naturalistic framework. Moreover, I submit that Nietzsche’s conceptualization of the entanglement of nature and culture contains important insights for critically understanding the challenges of the Anthropocene today.

Certain commentators on Russell's “no class” theory, in which apparent reference to classes or sets is eliminated using higher-order quantification, including W. V. Quine and (recently) Scott Soames, have doubted its success, noting the obscurity of Russell’s understanding of so-called “propositional functions”. These critics allege that realist readings of propositional functions fail to avoid commitment to classes or sets (or something equally problematic), and that nominalist readings fail to meet the demands placed on classes by mathematics. I show that Russell (...) did thoroughly explore these issues, and had good reasons for rejecting accounts of propositional functions as extra-linguistic entities. I argue in favor of a reading taking propositional functions to be nothing over and above open formulas which addresses many such worries, and in particular, does not interpret Russell as reducing classes to language. (shrink)

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 therein. (shrink)

Certain advocates of the so-called “neo-logicist” movement in the philosophy of mathematics identify themselves as “neo-Fregeans” (e.g., Hale and Wright), presenting an updated and revised version of Frege’s form of logicism. Russell’s form of logicism is scarcely discussed in this literature and, when it is, often dismissed as not really logicism at all (in light of its assumption of axioms of infinity, reducibility and so on). In this paper I have three aims: firstly, to identify more clearly the primary meta-ontological (...) and methodological differences between Russell’s logicism and the more recent forms; secondly, to argue that Russell’s form of logicism offers more elegant and satisfactory solutions to a variety of problems that continue to plague the neo-logicist movement (the bad company objection, the embarrassment of richness objection, worries about a bloated ontology, etc.); thirdly, to argue that neo-Russellian forms of logicism remain viable positions for current philosophers of mathematics. (shrink)

There are few moral convictions that enjoy the same intuitive plausibility and level of acceptance both within and across nations, cultures, and traditions as the conviction that, normally, it is morally wrong to kill people. Attempts to provide a philosophical explanation of why that is so broadly fall into three groups: Consequentialists argue that killing is morally wrong, when it is wrong, because of the harm it inflicts on society in general, or the victim in particular, whereas personhood and human (...) dignity accounts see the wrongness of killing people in its typically involving a failure to show due respect for the victim and his or her intrinsic moral worth. I argue that none of these attempts to explain the wrongness of killing is successful. Consequentialism generates too many moral reasons to kill, cannot account for deeply felt and widely shared intuitions about the comparative wrongness of killing, and gives the wrong kind of explanation of the wrongness of killing. Personhood and human dignity accounts each draw a line that is arbitrary and entirely unremarkable in terms of empirical reality, and hence ill-suited to carry the moral weight of the difference in moral status between the individuals below and above it. Paying close attention to the different ways in which existing accounts fail to convince, I identify a number of conditions that any plausible account of the wrongness of killing must meet. I then go on to propose an account that does. I suggest that the reason that typically makes killing normal human adults wrong equally applies to atypical human beings and a wide range of non-human animals, and hence challenge the idea that killing a non-human animal is normally easier to justify than killing a human being. This idea has persisted in Western philosophy from Aristotle to the present, and even progressive moral thinkers and animal advocates such as Peter Singer and Tom Regan are committed to it. I conclude by discussing some important practical implications of my account. (shrink)

In 1903, in _The Principles of Mathematics_ (_PoM_), Russell endorsed an account of classes whereupon a class fundamentally is to be considered many things, and not one, and used this thesis to explicate his first version of a theory of types, adding that it formed the logical justification for the grammatical distinction between singular and plural. The view, however, was short-lived; rejected before _PoM_ even appeared in print. However, aside from mentions of a few misgivings, there is little evidence about (...) why he abandoned this view. In this paper, I speculate as to what those reasons were, and evaluate them in light of recent work and interest in plural logic. (shrink)

Sequel to Part I. In these articles, I describe Cantor’s power-class theorem, as well as a number of logical and philosophical paradoxes that stem from it, many of which were discovered or considered (implicitly or explicitly) in Bertrand Russell’s work. These include Russell’s paradox of the class of all classes not members of themselves, as well as others involving properties, propositions, descriptive senses, class-intensions and equivalence classes of coextensional properties. Part II addresses Russell’s own various attempts to solve these paradoxes, (...) including strategies that he considered and rejected (limitation of size, the zigzag theory, etc.), as well as his own final views whereupon many purported entities that, if reified, lead to these contradictions, must not be genuine entities, but ‘logical fictions’ or ‘logical constructions’ instead. (shrink)

The chapter deals with the notion of phenomenal realness, which was first systematically explored by Albert Michotte. Phenomenal realness refers to the impression that a perceptual object is perceived to have an autonomous existence in our mind-independent world. Perceptual psychology provides an abundance of phenomena, ranging from amodal completion to picture perception, that indicate that phenomenal realness is an independent perceptual attribute that can be conferred to perceptual objects in different degrees. The chapter outlines a theoretical framework that appears particularly (...) well-suited for dealing with corresponding phenomena. According to this framework, perception can be understood as a triggering of conceptual forms by sensor inputs. It is argued that the attribute of phenomenal realness is based on specific types of internal evaluation functions which deal with the segregation of causes conceived as ‘external’ from those conceived as ‘internal’. These evaluation functions integrate different internal sources of ‘knowledge’ about the potential causes for the activation of conceptual forms and provide markers by which conceptual forms can be tagged as ‘external world objects’. (shrink)

In these articles, I describe Cantor’s power-class theorem, as well as a number of logical and philosophical paradoxes that stem from it, many of which were discovered or considered (implicitly or explicitly) in Bertrand Russell’s work. These include Russell’s paradox of the class of all classes not members of themselves, as well as others involving properties, propositions, descriptive senses, class-intensions, and equivalence classes of coextensional properties. Part I focuses on Cantor’s theorem, its proof, how it can be used to manufacture (...) paradoxes, Frege’s diagnosis of the core difficulty, and several broad categories of strategies for offering solutions to these paradoxes. (shrink)

Attempts to evaluate a belief or argument on the basis of its cause or origin are usually condemned as committing the genetic fallacy. However, I sketch a number of cases in which causal or historical factors are logically relevant to evaluating a belief, including an interesting abductive form that reasons from the best explanation for the existence of a belief to its likely truth. Such arguments are also susceptible to refutation by genetic reasoning that may come very close to the (...) standard examples given of supposedly fallacious genetic reasoning. (shrink)

It is well known that the circumflex notation used by Russell and Whitehead to form complex function names in Principia Mathematica played a role in inspiring Alonzo Church's “lambda calculus” for functional logic developed in the 1920s and 1930s. Interestingly, earlier unpublished manuscripts written by Russell between 1903–1905—surely unknown to Church—contain a more extensive anticipation of the essential details of the lambda calculus. Russell also anticipated Schönfinkel's combinatory logic approach of treating multiargument functions as functions having other functions as value. (...) Russell’s work in this regard seems to have been largely inspired by Frege’s theory of functions and “value-ranges”. This system was discarded by Russell due to his abandonment of propositional functions as genuine entities as part of a new tack for solving Russell’s paradox. In this article, I explore the genesis and demise of Russell’s early anticipation of the lambda calculus. (shrink)

Many philosophers still countenance senses or meanings in the broadly Fregean vein. However, it is difficult to posit the existence of senses without positing quite a lot of them, including at least one presenting every entity in existence. I discuss a number of Cantorian paradoxes that seem to result from an overly large metaphysics of senses, and various possible solutions. Certain more deflationary and nontraditional understanding of senses, and to what extent they fare better in solving the problems, are also (...) discussed. In the end, it is concluded that one must divide senses into various ramified-orders in order to avoid antinomy, but that the philosophical justification of such orders is, as yet, still somewhat problematic. (shrink)

I trace changes to Frege's understanding of numbers, arguing in particular that the view of arithmetic based in geometry developed at the end of his life (1924–1925) was not as radical a deviation from his views during the logicist period as some have suggested. Indeed, by looking at his earlier views regarding the connection between numbers and second-level concepts, his understanding of extensions of concepts, and the changes to his views, firstly, in between Grundlagen and Grundgesetze, and, later, after learning (...) of Russell's paradox, this position is a natural position for him to have retreated to, when properly understood. (shrink)

Russell discovered the classes version of Russell's Paradox in spring 1901, and the predicates version near the same time. There is a problem, however, in dating the discovery of the propositional functions version. In 1906, Russell claimed he discovered it after May 1903, but this conflicts with the widespread belief that the functions version appears in _The Principles of Mathematics_, finished in late 1902. I argue that Russell's dating was accurate, and that the functions version does not appear in the (...) _Principles_. I distinguish the functions and predicates versions, give a novel reading of the _Principles_, section 85, as a paradox dealing with what Russell calls _assertions_, and show that Russell's logical notation in 1902 had no way of even formulating the functions version. The propositional functions version had its origins in the summer of 1903, soon after Russell's notation had changed in such a way as to make a formulation possible. (shrink)

It is a characteristic feature of our mental make-up that the same perceptual input situation can simultaneously elicit conflicting mental perspectives. This ability pervades our perceptual and cognitive domains. Striking examples are the dual character of pictures in picture perception, pretend play, or the ability to employ metaphors and allegories. I will argue that traditional approaches, beyond being inadequate on principle grounds, are theoretically ill-equipped to deal with these achievements. I will then outline a theoretical perspective that has been emerging (...) from a theoretical convergence of perceptual psychology, ethology, linguistics, and developmental research. On the basis of this framework, I will argue that corresponding achievements are brought forth by a specific type of functional architecture whose core features are: (i) a perceptual system that is biologically furnished with a rich system of conceptual forms, (ii) a triggering relation between the sensory input and conceptual forms by which the same sensory input can be exploited by different types or systems of conceptual forms, and (iii) computational principles for handling semantically underspecified conceptual forms. Characteristic features of the proposed theoretical framework will be pointed out using the Heider-Simmel phenomenon as an example. (shrink)

In this paper I explore a position on which it is possible to eliminate the need for postulating abstract objects through abstraction principles by treating terms for abstracta as ‘incomplete symbols’, using Russell's no-classes theory as a template from which to generalize. I defend views of this stripe against objections, most notably Richard Heck's charge that syntactic forms of nominalism cannot correctly deal with non-first-orderizable quantifcation over apparent abstracta. I further discuss how number theory may be developed in a system (...) treating apparent terms for numbers using these definitions. (shrink)

This is a big-picture discussion of an important implication of Darwinism for ethics. I argue that there is a misfit between our scientific view of the natural world and the view, still dominant in academic philosophy and wider society alike, that there is a discrete hierarchy of moral status among conscious beings. I will suggest that the clear line of traditional morality – between human beings and other animals – is a remnant of an obsolete moral outlook, not least because (...) it has no counterpart in empirical reality, and I will invite the reader to think, with me, about tenable alternatives. (shrink)

Analytic philosophy has been perhaps the most successful philosophical movement of the twentieth century. While there is no one doctrine that defines it, one of the most salient features of analytic philosophy is its reliance on contemporary logic, the logic that had its origin in the works of George Boole and Gottlob Frege and others in the mid‐to‐late nineteenth century. Boolean algebra, the heart of Boole's contributions to logic, has also come to represent a cornerstone of modern computing. Frege had (...) broad philosophical interests, and his writings on the nature of logical form, meaning and truth remain the subject of intense theoretical discussion, especially in the analytic tradition. Frege's works, and the powerful new logical calculi developed at the end of the nineteenth century, influenced many of its most seminal figures, such as Bertrand Russell, Ludwig Wittgenstein and Rudolf Carnap. (shrink)

Russell claims in his autobiography and elsewhere that he discovered his 1905 theory of descriptions while attempting to solve the logical and semantic paradoxes plaguing his work on the foundations of mathematics. In this paper, I hope to make the connection between his work on the paradoxes and the theory of descriptions and his theory of incomplete symbols generally clearer. In particular, I argue that the theory of descriptions arose from the realization that not only can a class not be (...) thought of as a single thing, neither can the meaning/intension of any expression capable of singling out one collection (class) of things as opposed to another. If this is right, it shows that Russell’s method of solving the logical paradoxes is wholly incompatible with anything like a Fregean dualism between sense and reference or meaning and denotation. I also discuss how this realization lead to modifications in his understanding of propositions and propositional functions, and suggest that Russell’s confrontation with these issues may be instructive for ongoing research. (shrink)

This paper discusses certain problems arising within the treatment of the senses of functions in Alonzo Church's Logic of Sense and Denotation. Church understands such senses themselves to be "sense-functions," functions from sense to sense. However, the conditions he lays out under which a sense-function is to be regarded as a sense presenting another function as denotation allow for certain undesirable results given certain unusual or "deviant" sense-functions. Certain absurdities result, e.g., an argument can be found for equating any two (...) senses of the same type. An alternative treatment of the senses of functions is discussed, and is thought to do better justice to Frege's original theory. (shrink)

When does opinion formation within an interacting group lead to consensus, polarization or fragmentation? The article investigates various models for the dynamics of continuous opinions by analytical methods as well as by computer simulations. Section 2 develops within a unified framework the classical model of consensus formation, the variant of this model due to Friedkin and Johnsen, a time-dependent version and a nonlinear version with bounded confidence of the agents. Section 3 presents for all these models major analytical results. Section (...) 4 gives an extensive exploration of the nonlinear model with bounded confidence by a series of computer simulations. An appendix supplies needed mathematical definitions, tools, and theorems. (shrink)

This paper continues a thread in Analysis begun by Adam Rieger and Nicholas Denyer. Rieger argued that Frege’s theory of thoughts violates Cantor’s theorem by postulating as many thoughts as concepts. Denyer countered that Rieger’s construction could not show that the thoughts generated are always distinct for distinct concepts. By focusing on universally quantified thoughts, rather than thoughts that attribute a concept to an individual, I give a different construction that avoids Denyer’s problem. I also note that this problem for (...) Frege’s philosophy was discovered by Bertrand Russell as early as 1902 and has been discussed intermittently since. (shrink)