Kant’s teleology as presented in the Critique of Judgment is commonly interpreted in relation to the late eighteenth-century biological research of Johann Friedrich Blumenbach. In the present paper, I show that this interpretative perspective is incomplete. Understanding Kant’s views on teleology and biology requires a consideration of the teleological and biological views of Christian Wolff and his rationalist successors. By reconstructing the Wolffian roots of Kant’s teleology, I identify several little known sources of Kant’s views on biology. I argue that (...) one of Kant’s main contributions to eighteenth-century debates on biology consisted in demarcating biology from metaphysics. Kant rejected Wolffian views on the hierarchy of sciences, according to which propositions specifying the functions of organisms are derived from theological truths. In addition, Kant argued that organic self-organization necessitates a teleological description in order to show that self-organization does not support materialism. By demarcating biology and metaphysics, Kant made a small yet important contribution to establishing biology as a science. (shrink)

Ernst Mayr argued that the emergence of biology as a special science in the early nineteenth century was possible due to the demise of the mathematical model of science and its insistence on demonstrative knowledge. More recently, John Zammito has claimed that the rise of biology as a special science was due to a distinctive experimental, anti-metaphysical, anti-mathematical, and anti-rationalist strand of thought coming from outside of Germany. In this paper we argue that this narrative neglects the important role played (...) by the mathematical and axiomatic model of science in the emergence of biology as a special science. We show that several major actors involved in the emergence of biology as a science in Germany were working with an axiomatic conception of science that goes back at least to Aristotle and was popular in mid-eighteenth-century German academic circles due to its endorsement by Christian Wolff. More specifically, we show that at least two major contributors to the emergence of biology in Germany—Caspar Friedrich Wolff and Gottfried Reinhold Treviranus—sought to provide a conception of the new science of life that satisfies the criteria of a traditional axiomatic ideal of science. Both C.F. Wolff and Treviranus took over strong commitments to the axiomatic model of science from major philosophers of their time, Christian Wolff and Friedrich Wilhelm Joseph Schelling, respectively. The ideal of biology as an axiomatic science with specific biological fundamental concepts and principles thus played a role in the emergence of biology as a special science. (shrink)

Kant’s views on animals have received much attention in recent years. According to some, Kant attributed the capacity for objective perceptual awareness to non-human animals, even though he denied that they have concepts. This position is difficult to square with a conceptualist reading of Kant, according to which objective perceptual awareness requires concepts. Others take Kant’s views on animals to imply that the mental life of animals is a blooming, buzzing confusion. In this article I provide a historical reconstruction of (...) Kant’s views on animals, relating them to eighteenth-century debates on animal cognition. I reconstruct the views of Buffon and Reimarus and show that (i) both Buffon and Reimarus adopted a conceptualist position, according to which concepts structure the cognitive experience of adult humans, and (ii) that both described the mental life of animals as a blooming, buzzing confusion. Kant’s position, I argue, is virtually identical to that of Reimarus. Hence Kant’s views on animals support a conceptualist reading of Kant. The article further articulates the historical antecedents of the Kantian idea that concepts structure human cognitive experience and provides a novel account of how the ideas of similarity and difference were conceptualized in eighteenth-century debates on animal cognition. (shrink)

This paper aims to evaluate the relevance of Kant’s much discussed essentialism and mechanism for present-day philosophy of psychiatry. Kendler et al (2011) have argued that essentialism is inadequate for conceptualizing psychiatric disorders. In this paper, I develop this argument in detail by highlighting a variety of essentialism that differs from the one rejected by Kendler et al. I show that Kant’s essentialism is not directly affected by the argument of Kendler et al (2011), and that Kendler et al’s (2011) (...) argument also does not affect other essentialist positions in psychiatry. Hence, the rejection of essentialism in psychiatry needs more arguments than the one supplied by Kendler et al. Nevertheless, the study of current psychiatry also provides reasons to reject Kant’s essentialism and his transcendental project. I argue that Kant’s theory of mechanical explanation is more relevant for analyzing present-day philosophy of psychiatry, insofar as (a) modern psychiatric research into the causes of psychiatric disorders fits the mechanist paradigm, (b) Kant’s theory of mechanical explanation is importantly similar to modern theories of mechanical explanation applicable to psychiatry, such as those of Bechtel and associates, and (c) Kant’s stance that mechanism constitutes a regulative ideal points to useful arguments for the pursuit of mechanical explanations in psychiatry. (shrink)

This paper presents the first bibliometric mapping analysis of the field of computer and information ethics (C&IE). It provides a map of the relations between 400 key terms in the field. This term map can be used to get an overview of concepts and topics in the field and to identify relations between information and communication technology concepts on the one hand and ethical concepts on the other hand. To produce the term map, a data set of over thousand articles (...) published in leading journals and conference proceedings in the C&IE field was constructed. With the help of various computer algorithms, key terms were identified in the titles and abstracts of the articles and co-occurrence frequencies of these key terms were calculated. Based on the co-occurrence frequencies, the term map was constructed. This was done using a computer program called VOSviewer. The term map provides a visual representation of the C&IE field and, more specifically, of the organization of the field around three main concepts, namely privacy, ethics, and the Internet. (shrink)

In this paper, I investigate the relation of Kant's theory of biology to epigenetic accounts of organic generation and development. In the literature, a dispute about similarities between Blumenbach's epigenetic account and Kant dominated the debate for many years (see Lenoir 1980, 1981, and 1982, 17–34, Richards 2000; 2002, 207–37; Look 2006, and van den Berg 2009). Some more recent interpreters claim that Wolff's, more than Blumenbach's account plays the pivotal role in the development of a vitalistic conception of (...) epigenesis in Kant (see Dupont 2007 and Huneman 2007). Although I myself hold the view that Kant's position contains preformistic and epigenetic characteristics, in the current paper I focus solely on an investigation of epigenetic elements in Kant's account and compare them to the corresponding epigenetic elements in Wolff's theory. Section I of the paper is devoted to an analysis of Wolff's most important epigenetic theorems: the notion of the essential power (vis essentialis) and the conception of the part-whole composition of organized matter. Although Wolff describes the essential power vitalisticly, as a principle of life, he understands it as the cause of mechanical motions explaining the generation, nourishment, and the growth of an organism. Wolff's model of the part-whole composition of organic matter is subtle, but committed to fundamental mechanistic assumptions, such as that the organism as a whole is composed of inorganic parts. In section II, I analyze the corresponding elements in Kant's theory: the notion of the formative power and the conception of the whole-part composition of organized materials. Kant describes the formative power as a principle that causes the purposive form of an organized being such that matter and mechanism are the means to the purpose of the being as their end. The purpose of the whole is a functional unit which is in principle superior to the form and matter of the subordinate parts. The parts are combined into such a whole in being mutually cause and effect of each other and in being related to the superior whole. In section III, I respond to the debate in the literature. Against Dupont (2007) and Huneman (2007) I argue that, according to Wolff, the vis essentialis accounts for mechanic effects in matter, whereas, according to Kant, the formative power explains the intentional order (form, end, purpose) of an individual organized being, its parts, and its species. Since this view is closer to Blumenbach than to Wolff, the ongoing comparison between Kant and Blumenbach in the literature is justified. However, the emphasis on the specific part-whole composition that Kant considers to be the determining feature of an organized being can be found only in Wolff and not in Blumenbach—though Wolff and Kant describe it in opposing ways. This increases the systematic importance of Wolff for Kant. Thus, a fresh look on the historical debate is required. (shrink)

In this paper, I offer a close reading of Wittgenstein's remarks on inconsistency, mostly as they appear in the Lectures on the Foundations of Mathematics. I focus especially on an objection to Wittgenstein's view given by Alan Turing, who attended the lectures, the so-called ‘falling bridges’-objection. Wittgenstein's position is that if contradictions arise in some practice of language, they are not necessarily fatal to that practice nor necessitate a revision of that practice. If we then assume that we have adopted (...) a paraconsistent logic, Wittgenstein's answer to Turing is that if we run into trouble building our bridge, it is either because we have made a calculation mistake or our calculus does not actually describe the phenomenon it is intended to model. The possibility of either kind of error is not particular to contradictions nor inconsistency, and thus contradictions do not have any special status as a thing to be avoided. (shrink)

Mary Wollstonecraft argues that women must be independent citizens, but that they cannot be that unless they fulfill certain duties as mothers. This is problematic in a number of ways, as argued by Laura Brace in a 2000 article. However, I argue that if we understand Wollstonecraft's concept of independence in a republican, rather than a liberal context, and at the same time pay close attention to her discussion of motherhood, a feminist reading of Wollstonecraft is not only possible but (...) enriching. I will attempt to show, in particular, that the seeds of a feminist argument for co-parenting are to be found in the Vindication of the Rights of Woman. (shrink)

Artificial intelligence research and regulation seek to balance the benefits of innovation against any potential harms and disruption. However, one unintended consequence of the recent surge in AI research is the potential re-orientation of AI technologies to facilitate criminal acts, term in this article AI-Crime. AIC is theoretically feasible thanks to published experiments in automating fraud targeted at social media users, as well as demonstrations of AI-driven manipulation of simulated markets. However, because AIC is still a relatively young and inherently (...) interdisciplinary area—spanning socio-legal studies to formal science—there is little certainty of what an AIC future might look like. This article offers the first systematic, interdisciplinary literature analysis of the foreseeable threats of AIC, providing ethicists, policy-makers, and law enforcement organisations with a synthesis of the current problems, and a possible solution space. (shrink)

A self-fulfilling prophecy is, roughly, a prediction that brings about its own truth. Although true predictions are hard to fault, self-fulfilling prophecies are often regarded with suspicion. In this article, we vindicate this suspicion by explaining what self-fulfilling prophecies are and what is problematic about them, paying special attention to how their problems are exacerbated through automated prediction. Our descriptive account of self-fulfilling prophecies articulates the four elements that define them. Based on this account, we begin our critique by showing (...) that typical self-fulfilling prophecies arise due to mistakes about the relationship between a prediction and its object. Such mistakes—along with other mistakes in predicting or in the larger practical endeavor—are easily overlooked when the predictions turn out true. Thus we note that self-fulfilling prophecies prompt no error signals; truth shrouds their mistakes from humans and machines alike. Consequently, self-fulfilling prophecies create several obstacles to accountability for the outcomes they produce. We conclude our critique by showing how failures of accountability, and the associated failures to make corrections, explain the connection between self-fulfilling prophecies and feedback loops. By analyzing the complex relationships between accuracy and other evaluatively significant features of predictions, this article sheds light both on the special case of self-fulfilling prophecies and on the ethics of prediction more generally. (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)

This article argues that a person’s well-being at a time and the goodness of her life are two distinct values. It is commonly accepted as platitudinous that well-being is what makes a life good for the person who lives it. Even philosophers who distinguish between well-being at a time and the goodness of a life still typically assume that increasing a person’s well-being at some particular moment, all else equal, necessarily improves her life on the whole. I develop a precise (...) statement of this standard assumption, and then show that it is subject to counterexamples. The possibility of such counterexamples depends only on premises similar to those sometimes invoked to argue that a person’s well-being over a long period is not simply the aggregate well-being of the shorter periods that compose the long period. The refutation of the standard assumption linking well-being and life-goodness entails that these are distinct and sometimes divergent values. As an alternative to the standard assumption, it is proposed that well-being is best understood as an ingredient in a good life. (shrink)

These essays draw on work in the history and philosophy of science, the philosophy of mind and language, the development of concepts in children, conceptual..

This article addresses three questions about well-being. First, is well-being future-sensitive? I.e., can present well-being depend on future events? Second, is well-being recursively dependent? I.e., can present well-being depend on itself? Third, can present and future well-being be interdependent? The third question combines the first two, in the sense that a yes to it is equivalent to yeses to both the first and second. To do justice to the diverse ways we contemplate well-being, I consider our thought and discourse about (...) well-being in three domains: everyday conversation, social science, and philosophy. This article’s main conclusion is that we must answer the third question with no. Present and future well-being cannot be interdependent. The reason, in short, is that a theory of well-being that countenances both future-sensitivity and recursive dependence would have us understand a person’s well-being at a time as so intricately tied to her well-being at other times that it would not make sense to consider her well-being an aspect of her state at particular times. It follows that we must reject either future-sensitivity or recursive dependence. I ultimately suggest, especially in light of arguments based on assumptions of empirical research on well-being, that the balance of reasons favors rejecting future-sensitivity. (shrink)

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)

Imagine you are casually browsing an online bookstore, looking for an interesting novel. Suppose the store predicts you will want to buy a particular novel: the one most chosen by people of your same age, gender, location, and occupational status. The store recommends the book, it appeals to you, and so you choose it. Central to this scenario is an automated prediction of what you desire. This article raises moral concerns about such predictions. More generally, this article examines the ethics (...) of artificial social cognition—the ethical dimensions of attribution of mental states to humans by artificial systems. The focus is presumptuous aim attributions, which are defined here as aim attributions based crucially on the premise that the person in question will have aims like superficially similar people. Several everyday examples demonstrate that this sort of presumptuousness is already a familiar moral concern. The scope of this moral concern is extended by new technologies. In particular, recommender systems based on collaborative filtering are now commonly used to automatically recommend products and information to humans. Examination of these systems demonstrates that they naturally attribute aims presumptuously. This article presents two reservations about the widespread adoption of such systems. First, the severity of our antecedent moral concern about presumptuousness increases when aim attribution processes are automated and accelerated. Second, a foreseeable consequence of reliance on these systems is an unwarranted inducement of interpersonal conformity. (shrink)

The effective altruism movement (EA) is one of the most influential philosophically savvy movements to emerge in recent years. Effective Altruism has historically been dedicated to finding out what charitable giving is the most overall-effective, that is, the most effective at promoting or maximizing the impartial good. But some members of EA want the movement to be more inclusive, allowing its members to give in the way that most effectively promotes their values, even when doing so isn’t overall-effective. When we (...) examine what it means to give according to one’s values, I argue, we will see that this is both inconsistent with what EA is like now and inconsistent with its central philosophical commitment to an objective standard that can be used to critically analyze one’s giving. While EA is not merely synonymous with act utilitarianism, it cannot be much more inclusive than it is right now. (shrink)

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)

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)

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)

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)

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)

Just as humans can draw conclusions responsibly or irresponsibly, so too can computers. Machine learning systems that have been trained on data sets that include irresponsible judgments are likely to yield irresponsible predictions as outputs. In this paper I focus on a particular kind of inference a computer system might make: identification of the intentions with which a person acted on the basis of photographic evidence. Such inferences are liable to be morally objectionable, because of a way in which they (...) are presumptuous. After elaborating this moral concern, I explore the possibility that carefully procuring the training data for image recognition systems could ensure that the systems avoid the problem. The lesson of this paper extends beyond just the particular case of image recognition systems and the challenge of responsibly identifying a person’s intentions. Reflection on this particular case demonstrates the importance (as well as the difficulty) of evaluating machine learning systems and their training data from the standpoint of moral considerations that are not encompassed by ordinary assessments of predictive accuracy. (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)

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)

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)

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)

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)

When we can’t live up to the ultimate standards of morality, how can moral theory give us guidance? We can distinguish between ideal and non-ideal theory to see that there are different versions of the voluntarist constraint, ‘ought implies can.’ Ideal moral theory identifies the best standard, so its demands are constrained by one version. Non-ideal theory tells us what to do given our psychological and motivational shortcomings and so is constrained by others. Moral theory can now both provide an (...) ultimate standard and give us guidance; this view also gives us new insights into demandingness and blame. (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)

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)

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)

What is the best way to make sustained societal progress over time? Non-ideal theory done on its own faces the problem of second best, but ideal theory seems unable to cope with disagreement about how to make progress. If ideal theory gives up its claims to completeness, then we can use the method of incompletely theorized agreements to make progress over time.

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)

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)

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)

Fregeans face the difficulty finding a notation for distinguishing statements about the sense or meaning of an expression as opposed to its reference or denotation. Famously, in "On Denoting", Russell rejected methods that begin with an expression designating its denotation, and then alter it with a "the meaning of" operator to designate the meaning. Such methods attempt an impossible "backward road" from denotation to meaning. Contemporary neo-Fregeans, however, have suggested that we can disambiguate _with_, rather than _against_, the grain, by (...) using a notation that begins with expressions designating senses or meanings, and then alters them with a "the denotation of" operator to designate the denotation. I show that in his manuscripts of 1903–05, Russell both considered and rejected a similar notation along with the metaphysical suppositions underlying it. This discussion sheds light on the evolution of Russell's thought, and may yet be instructive for ongoing debates. (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)

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)

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)

ABSTRACT Objectives There is little research on moral uncertainties and distress of palliative and hospice care providers (PHCPs) working in jurisdictions anticipating legalising voluntary assisted dying (VAD). This study examines the perception and anticipated concerns of PHCPs in providing VAD in the State of Queensland, Australia prior to legalisation of the practice in 2021. The findings help inform strategies to facilitate training and support the health and well-being of healthcare workers involved in VAD. Design The study used a qualitative approach (...) to examine and analyse the perception and anticipated concerns of PHCPs regarding challenges of providing assisted dying in Queensland. Fourteen PHCPs were recruited using a purposive sampling strategy to obtain a broad representation of perspectives including work roles, geographical locations and workplace characteristics. Data were collected via one in-depth interview per participant. The transcripts were coded for patterns and themes using an inductive analysis approach following the tradition of Grounded Theory. Setting The study was conducted in hospital, hospice, community and residential aged care settings in Queensland, Australia. These included public and private facilities, secular and faith-based facilities, and regional/rural and urban facilities. Participants Interviews were conducted with fourteen PHCPs: 10 nurses and 4 physicians; 11 female and 3 male. The median number of years of palliative care practice was 17, ranging from 2 to 36 years. For inclusion, participants had to be practising palliative and hospice care providers. Results PHCPs are divided on whether VAD should be considered part of palliative care. Expectations of moral distress and uncertainty about practising VAD were identified in five areas: handling requests, assessing patient capacity, arranging patient transfers and logistical issues, managing unsuccessful attempts, and dealing with team conflicts and stigma. Conclusions The possibility of having to practise VAD causes moral distress and uncertainty for some PHCPs. Procedural clarity can address some uncertainties; moral and psychological distress, however, remains a source of tension that needs support to ensure ongoing care of both patients and PHCPs. The introduction of VAD post-legalisation may present an occasion for further moral education and development of PHCPs. (shrink)

This paper proposes to reconstruct Boaventura de Sousa Santos' conception of "epistemologies of the south" both (a) as a critical theory aiming at denouncing the impoverishment of the epistemic field entailed by the normative imposition of a certain model of knowledge (what we call "the monoculture of reason"), and (b) as a long-term political project of a harmonic coexistence of different epistemologies ("an ecology of knowledges").

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)

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)

Several interesting themes emerge from G. E. Moore’s previously unpub­lished review of _The Principles of Mathematics_. These include a worry concerning whether mathematical notions are identical to purely logical ones, even if coextensive logical ones exist. Another involves a conception of infinity based on endless series neglected in the Principles but arguably involved in Zeno’s paradox of Achilles and the Tortoise. Moore also questions the scope of Russell’s notion of material implication, and other aspects of Russell’s claim that mathematics reduces (...) to logic. (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.