This paper gives two complete and elementary proofs that if the speed of light over closed paths has a universal value c, then it is possible to synchronize clocks in such a way that the one-way speed of light is c. The first proof is an elementary version of a recent proof. The second provides high precision experimental evidence that it is possible to synchronize clocks in such a way that the one-way speed of light has a universal value. We (...) also discuss an old incomplete proof by Weyl which is important from an historical perspective. (shrink)

Would the existence of extraterrestrial intelligent life conflict in any way with Christian belief? We identify six areas of potential conflict. If there be no conflict in any of these areas—and we argue ultimately there is not—we are confident in declaring that there is no conflict, period. This conclusion underwrites the integrity of theological explorations into the existence of ETI, which has become a topic of increasing interest among theologians in recent years.

Many philosophers have appealed to the PSR in arguments for a being that exists a se, a being whose explanation is in itself. But what does it mean, exactly, for something to have its explanation ‘in itself’? Contemporary philosophers have said next to nothing about this, relying instead on phrases plucked from the accounts of various historical figures. In this article, I analyse five such accounts – those of Anselm, Aquinas, Descartes, Spinoza, and Leibniz – and argue that none are (...) satisfactory. Should we abandon or restrict the PSR, then? I think that would be hasty, for many reasons. I therefore consider the prospects of explaining everything, including God, given the constraints of certain features of good explanations, and conclude with several observations about future approaches. (shrink)

I explore the view that the imago Dei is essential to us as humans but accidental to us as persons. To image God is to resemble God, and resemblance comes in degrees. This has the straightforward—and perhaps disturbing—implication that we can be more or less human, and possibly cease to be human entirely. Hence, I call it the spectrum view. I argue that the spectrum view is complementary to the Biblical data, helps explain the empirical reality of horrendous evil, and (...) offers an elegant rapprochement between the traditional view of hell and its rivals. (shrink)

I argue that Social Trinitarians can and should conceive of God as a group person. They can by drawing on recent theories of group agency realism that show how groups can be not just agents but persons distinct from their members – albeit, I argue, persons of a different kind. They should because the resultant novel view of the Trinity – that God is three ‘intrinsicist’ persons in one ‘functional’ person – is theologically sound, effectively counters the most trenchant criticisms (...) of Social Trinitarianism, and enjoys independent theological support from the biblical notion of ‘corporate personality’. (shrink)

The question I wish to explore is this: Does idealism conflict with common sense? Unfortunately, the answer I give may seem like a rather banal one: It depends. What do we mean by ‘idealism’ and ‘common sense?’ I distinguish three main varieties of idealism: absolute idealism, Berkeleyan idealism, and dualistic idealism. After clarifying what is meant by common sense, I consider whether our three idealisms run afoul of it. The first does, but the latter two don’t. I conclude that while (...) Moore’s famous common sense critique is sound against external world skepticism, against Berkeleyan idealism and dualist idealism it is unavailing. (shrink)

Linda Zagzebski’s book on epistemic authority is an impressive and stimulating treatment of an important topic. 1 I admire the way she manages to combine imagination, originality and argumentative control. Her work has the further considerable merit of bringing analytic thinking and abstract theory to bear upon areas of concrete human concern, such as the attitudes one should have towards moral and religious authority. The book is stimulating in a way good philosophy should be -- provoking both disagreement and emulation. (...) I agree with much of what she says, and have been instructed by it, but it will be of more interest and relevance here if I concentrate upon areas of disagreement. Perhaps they are better seen as areas, at least some of them, where her emphases suggest a position that seems to me untenable, but that she may not really intend. In that event, I will be happy to have provoked a clarification or the dispelling of my misunderstanding. My focus will be upon problems in her account of communal authority and autonomy, especially with respect to religious and political authority. Here my worry is that she places too much trust in trust and not enough in what I call selective mistrust. (shrink)

Whenever science returns a confident and univocal answer to a question, Trumping Naturalism enjoins us to accept it. The majority of contemporary philosophers are sympathetic to this sort of position. Indeed, several have endorsed it or something very close to it. Arguments for Trumping Naturalism, however, are scant, the principal one being the Track Record Argument. The argument is based on the fact that in cases of conflict, science has a better track record than non-scientific forms of inquiry such as (...) philosophy. My chapter investigates this argument. I enumerate and assess several objections to the argument, from footling objections to stronger ones. My conclusion is that the Track Record Argument is not as strong as imagined. (shrink)

In this article, I outline a strategy for challenging J.L. Schellenberg’s hiddenness argument, and specifically the premise within the argument that asserts the existence of what Schellenberg calls nonresistant nonbelief. Drawing on some of the philosophical resources of skeptical theism, I show how this premise is based on a particular “noseeum assumption”—what I call Schellenberg’s Noseeum Assumption—that underwrites a particular “noseeum argument.” This assumption is that, regarding putative nonresistant nonbelievers, more likely than not we’d detect these nonbelievers’ resistance toward God (...) if there were any. I give reasons for thinking that it is not more reasonable to affirm than to refrain from affirming Schellenberg’s Noseeum Assumption, and so reason to think that the hiddenness argument is not a good argument for atheism. I also defend the strategy I outline against several objections. (shrink)

What are we to make of the cultural nonconformity of hardcore/punks? Is there any ethical value in the pursuit of cultural nonconformity? Distinct moral justifications can be teased from the lyrics of the hardcore/punk bands that we have grown up with and still love. The best explanation of what makes cultural nonconformity morally valuable, we believe, comes from John Stuart Mill: that it opens up new cultural space to oneself and to others, permitting "new and original experiments of living.".

A graph-theoretic account of logics is explored based on the general notion of m-graph (that is, a graph where each edge can have a finite sequence of nodes as source). Signatures, interpretation structures and deduction systems are seen as m-graphs. After defining a category freely generated by a m-graph, formulas and expressions in general can be seen as morphisms. Moreover, derivations involving rule instantiation are also morphisms. Soundness and completeness theorems are proved. As a consequence of the generality of the (...) approach our results apply to very different logics encompassing, among others, substructural logics as well as logics with nondeterministic semantics, and subsume all logics endowed with an algebraic semantics. (shrink)

This article is part of a For-Discussion-Section of Methods of Information in Medicine about the paper "Biomedical Informatics: We Are What We Publish", written by Peter L. Elkin, Steven H. Brown, and Graham Wright. It is introduced by an editorial. This article contains the combined commentaries invited to independently comment on the Elkin et al. paper. In subsequent issues the discussion can continue through letters to the editor.

In 2020, an international team of intercultural philosophers and African linguists created a multilinguistic game named Adinkra. This name refers to a medieval rooted symbolic language in Ghana that is actively used by the Akan and especially the Asante among them to communicate indirectly. The Akan is both the meta-ethnic name of the largest Ghanaian cultural-linguistic group of which the Asante is an Akan cultural subgroup and of a Central Tano language of which Asante-Twi is a dialect. The Adinkra symbols, (...) which have permeated Akan life and the arts, can be found e.g. on Asante royal staffs and gold weights. They are also loosely connected to Akan proverbs. The game Adinkra aims to enhance its players’ intercultural communicative, and moral philosophical understanding by matching Adinkra symbols with Akan proverbs. It was created for educational and therapeutical purposes. This article focusses on the rules, the making of Adinkra, its aims and objectives. The objective of this article is twofold. First, it focusses on the game itself. It elaborates on what its rules are and the content of the game. It also focusses on how playing the multilinguistic game, Adinkra can enhance intercultural understanding and communication. It, furthermore, concentrates on the results of a pilot reception study of this game in the Netherlands among intercultural groups of players. This study has proven that the Adinkra game stimulates creative thinking, engagement in dialogue and reflective ethical thinking. For this reason, the authors believe that it has a lot to contribute to intercultural educational programs with a focus on intercultural communication, philosophy and arts in both Africa and the global North. Finally, a section is devoted to the question of how the Adinkra game was developed and methodologically grounded in Gadamer’s playful hermeneutics, and the theories of the Wheel of the Intercultural Art of living and (African) Indigenous Religions. Secondly, the article focusses on the game’s oral-literary storytelling context and Akan moral ideas. It then throws the searchlight on the creative, therapeutic value and its potential to serve as a ‘cultural detox’. The authors and game makers think that being introduced to an African communitarian ethos hidden in the Adinkra symbols and Akan proverbs can help its players to develop a critical eye for the highly individualistic ethos of Western culture that, among others, is promoted by neoliberal thinking and praxis. The word praxis is used by the authors in the meaning found in educational contexts. Adinkra’s players are stimulated to reflect upon a different moral idea, which can change their mindset and put them into action to contribute to social awareness and societal change. (shrink)

In mathematics, the deductive method reigns. Without proof, a claim remains unsolved, a mere conjecture, not something that can be simply assumed; when a proof is found, the problem is solved, it turns into a “result,” something that can be relied on. So mathematicians think. But is there more to mathematical justification than proof? -/- The answer is an emphatic yes, as I explain in this article. I argue that non-deductive justification is in fact pervasive in mathematics, and that it (...) is in good epistemic standing. (shrink)

Visual imagery is a form of sensory imagination, involving subjective experiences typically described as similar to perception, but which occur in the absence of corresponding external stimuli. We used the Activation Likelihood Estimation algorithm (ALE) to identify regions consistently activated by visual imagery across 40 neuroimaging studies, the first such meta-analysis. We also employed a recently developed multi-modal parcellation of the human brain to attribute stereotactic co-ordinates to one of 180 anatomical regions, the first time this approach has been combined (...) with the ALE algorithm. We identified a total 634 foci, based on measurements from 464 participants. Our overall comparison identified activation in the superior parietal lobule, particularly in the left hemisphere, consistent with the proposed ‘top-down’ role for this brain region in imagery. Inferior premotor areas and the inferior frontal sulcus were reliably activated, a finding consistent with the prominent semantic demands made by many visual imagery tasks. We observed bilateral activation in several areas associated with the integration of eye movements and visual information, including the supplementary and cingulate eye fields (SCEFs) and the frontal eye fields (FEFs), suggesting that enactive processes are important in visual imagery. V1 was typically activated during visual imagery, even when participants have their eyes closed, consistent with influential depictive theories of visual imagery. Temporal lobe activation was restricted to area PH and regions of the fusiform gyrus, adjacent to the fusiform face complex (FFC). These results provide a secure foundation for future work to characterise in greater detail the functional contributions of specific areas to visual imagery. (shrink)

The revival of the philosophy of mathematics in the 60s following its post-1931 slump left us with two conflicting positions on arithmetic’s ontological relationship to set theory. W.V. Quine’s view, presented in 'Word and Object' (1960), was that numbers are sets. The opposing view was advanced in another milestone of twentieth-century philosophy of mathematics, Paul Benacerraf’s 'What Numbers Could Not Be' (1965): one of the things numbers could not be, it explained, was sets; the other thing numbers could not be, (...) even more dramatically, was objects. Curiously, although Benacerraf’s article appeared in the heyday of Quine’s influence, it declined to engage the Quinean position squarely, even seemed to think it was not its business to do so. Despite that, in my experience, most philosophers believe that Benacerraf’s article put paid to the reductionist view that numbers are sets (though perhaps not the view that numbers are objects). My chapter will attempt to overturn this orthodoxy. (shrink)

Background If trials of therapeutic interventions are to serve society's interests, they must be of high methodological quality and must satisfy moral commitments to human subjects. The authors set out to develop a clinical - trials compendium in which standards for the ethical treatment of human subjects are integrated with standards for research methods. Methods The authors rank-ordered the world's nations and chose the 31 with >700 active trials as of 24 July 2008. Governmental and other authoritative entities of the (...) 31 countries were searched, and 1004 English-language documents containing ethical and/or methodological standards for clinical trials were identified. The authors extracted standards from 144 of those: 50 designated as ‘core’, 39 addressing trials of invasive procedures and a 5% sample of the remainder. As the integrating framework for the standards we developed a coherent taxonomy encompassing all elements of a trial's stages. Findings Review of the 144 documents yielded nearly 15 000 discrete standards. After duplicates were removed, 5903 substantive standards remained, distributed in the taxonomy as follows: initiation, 1401 standards, 8 divisions; design, 1869 standards, 16 divisions; conduct, 1473 standards, 8 divisions; analysing and reporting results, 997 standards, four divisions; and post-trial standards, 168 standards, 5 divisions. Conclusions The overwhelming number of source documents and standards uncovered in this study was not anticipated beforehand and confirms the extraordinary complexity of the clinical trials enterprise. This taxonomy of multinational ethical and methodological standards may help trialists and overseers improve the quality of clinical trials, particularly given the globalisation of clinical research. (shrink)

Euclid’s Elements inspired a number of foundationalist accounts of mathematics, which dominated the epistemology of the discipline for many centuries in the West. Yet surprisingly little has been written by recent philosophers about this conception of mathematical knowledge. The great exception is Imre Lakatos, whose characterisation of the Euclidean Programme in the philosophy of mathematics counts as one of his central contributions. In this essay, we examine Lakatos’s account of the Euclidean Programme with a critical eye, and suggest an alternative (...) picture which builds on his work, but differs in a number of important respects. (shrink)

How did I raise my arm? The simple answer is that I raised it as a consequence of intending to raise it. A slightly more complicated response would mention the absence of any factors which would inhibit the execution of the intention- and a more complicated one still would specify the intention in terms of a goal (say, drinking a beer) which requires arm-raising as a means towards that end. Whatever the complications, the simple answer appears to be on the (...) right track. (shrink)

A graph-theoretic account of fibring of logics is developed, capitalizing on the interleaving characteristics of fibring at the linguistic, semantic and proof levels. Fibring of two signatures is seen as a multi-graph (m-graph) where the nodes and the m-edges include the sorts and the constructors of the signatures at hand. Fibring of two models is a multi-graph (m-graph) where the nodes and the m-edges are the values and the operations in the models, respectively. Fibring of two deductive systems is an (...) m-graph whose nodes are language expressions and the m-edges represent the inference rules of the two original systems. The sobriety of the approach is confirmed by proving that all the fibring notions are universal constructions. This graph-theoretic view is general enough to accommodate very different fibrings of propositional based logics encompassing logics with non-deterministic semantics, logics with an algebraic semantics, logics with partial semantics and substructural logics, among others. Soundness and weak completeness are proved to be preserved under very general conditions. Strong completeness is also shown to be preserved under tighter conditions. In this setting, the collapsing problem appearing in several combinations of logic systems can be avoided. (shrink)

We can see mereology as a theory of parthood and topology as a theory of wholeness. How can these be combined to obtain a unified theory of parts and wholes? This paper examines various non-equivalent ways of pursuing this task, with specific reference to its relevance to spatio-temporal reasoning. In particular, three main strategies are compared: (i) mereology and topology as two independent (though mutually related) chapters; (ii) mereology as a general theory subsuming topology; (iii) topology as a general theory (...) subsuming mereology. Some more speculative strategies and directions for further research are also considered. (shrink)

The concept of niche (setting, context, habitat, environment) has been little studied by ontologists, in spite of its wide application in a variety of disciplines from evolutionary biology to economics. What follows is a first formal theory of this concept, a theory of the relations between objects and their niches. The theory builds upon existing work on mereology, topology, and the theory of spatial location as tools of formal ontology. It will be illustrated above all by means of simple biological (...) examples, but the concept of niche should be understood as being, like concepts such as part, boundary, and location, a structural concept that is applicable in principle to a wide range of different domains. (shrink)

There are conflicting intuitions concerning the status of a boundary separating two adjacent entities (or two parts of the same entity). The boundary cannot belong to both things, for adjacency excludes overlap; and it cannot belong to neither, for nothing lies between two adjacent things. Yet how can the dilemma be avoided without assigning the boundary to one thing or the other at random? Some philosophers regard this as a reductio of the very notion of a boundary, which should accordingly (...) be treated a mere façon de parler. In this paper I resist this temptation and examine some ways of taking the puzzle at face value within a realist perspective—treating boundaries as ontologically on a par with (albeit parasitic upon) extended parts. (shrink)

This short article discusses the fact that the word ‘ancestor’ features in certain arguments that a) are apparently logically valid, b) contain infinitely many premises, and c) are such that none of their finite sub-arguments are logically valid. The article's aim is to motivate, within its brief compass, the study of infinitary logics.

The paper is an introduction to geometric algebra and geometric calculus for those with a knowledge of undergraduate mathematics. No knowledge of physics is required. The section Further Study lists many papers available on the web.

Are there any bona fide boundaries, i.e., boundaries that carve at the joints? Or is any boundary —hence any object—the result of a fiat articulation reflecting our cognitive biases and our so-cial practices and conventions? Does the choice between these two options amount to a choice between realism and wholesome relativism?

Hans C. Ohanian 1 claims to “defeat” the conventionalist thesis of clock synchronization using an argument based on dynamics. My aim here is to show that his argument does not succeed.

Recent research has relied on trolley-type sacrificial moral dilemmas to study utilitarian versus nonutili- tarian modes of moral decision-making. This research has generated important insights into people’s attitudes toward instrumental harm—that is, the sacrifice of an individual to save a greater number. But this approach also has serious limitations. Most notably, it ignores the positive, altruistic core of utilitarianism, which is characterized by impartial concern for the well-being of everyone, whether near or far. Here, we develop, refine, and validate a (...) new scale—the Oxford Utilitarianism Scale—to dissociate individual differences in the ‘negative’ (permissive attitude toward instrumental harm) and ‘positive’ (impartial concern for the greater good) dimensions of utilitarian thinking as manifested in the general population. We show that these are two independent dimensions of proto-utilitarian tendencies in the lay population, each exhibiting a distinct psychological profile. Empathic concern, identification with the whole of humanity, and concern for future generations were positively associated with impartial beneficence but negatively associated with instrumental harm; and although instrumental harm was associated with subclinical psychopathy, impartial beneficence was associated with higher religiosity. Importantly, although these two dimensions were independent in the lay population, they were closely associated in a sample of moral philosophers. Acknowledging this dissociation between the instrumental harm and impartial beneficence components of utilitarian thinking in ordinary people can clarify existing debates about the nature of moral psychology and its relation to moral philosophy as well as generate fruitful avenues for further research. (shrink)

Genetic testing in the workplace is a technology both full of promise and fraught with ethical peril. Though not yet common, it is likely to become increasingly so. We survey the key arguments in favour of such testing, along with the most significant ethical worries. We further propose a set of pragmatic criteria, which, if met, would make it permissible for employers to offer (but not to require) workplace genetic testing.

A brief article introducing *One True Logic*. The book argues that there is one correct foundational logic and that it is highly infinitary.

Peter Simons has argued that the expression ‘the universe’ is not a genuine singular term: it can name neither a single, completely encompassing individual, nor a collection of individuals. (It is, rather, a semantically plural term standing equally for every existing object.) I offer reasons for resisting Simons’s arguments on both scores.

What is knowledge of one's own current, consciously entertained intentional states a form of inner awareness? If so, what form? In this paper I explore the prospects for a quasi-observational account of a certain class of cases where subjects appear to have self-knowledge, namely, the so-called cogito-like cases. In section one I provide a rationale for the claim that we need an epistemology of self-knowledge, and specifically, an epistemology of the cogito-like cases. In section two I argue that contentful properties (...) in such cases have two features in common with observational properties of objects. In section three, I develop a quasi-observational account of self-knowledge for the cogito-like cases by considering various accounts of the nature of observational properties and by applying them to these cases. I conclude by addressing some important objections to the account. (shrink)

Margaret Macdonald was at the institutional heart of analytic philosophy in Britain in the mid-twentieth century. However, her views on the nature of philosophical theories diverge quite considerably from those of many of her contemporaries. In this article, I focus on Macdonald’s provocative 1953 paper, “Linguistic Philosophy and Perception,” in which she argues that the value of philosophical theories is more akin to that of poetry or art than science or mathematics. I do so for two reasons. First, (...) it reveals just how far Macdonald’s metaphilosophical views diverged from those of many of her contemporaries. Second, the discussion in her article preempts recent literature on the nature of philosophical inquiry and the efficacy of philosophical arguments. Indeed, Macdonald’s paper is just as likely to provoke discussion today as it was in the 1950s. (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)

The paper investigates the link between the theory of modal occurrents (where individuals are allowed to stretch across possible worlds) and Lewis’s counterpart theory (where all individuals are world-bound but have counterparts in other worlds). First I show how to interpret modal talk extensionally within the theory of modal occurrents. Then I show that the assumption that worlds be pairwise discrete is all that is needed to reconstruct the bulk of counterpart theory (i.e., to define the concept of a counterpart (...) and to derive the standard postulates governing that concept) in terms of the theory of modal occurrents. Finally, I argue that this reconstruction allows us to view the indeterminacy of our modal intuitions as being part and parcel with the indeterminacy of our criteria for individuating modal occurrents, and that this indeterminacy is naturally explained in terms of linguistic (as opposed to ontic) vagueness. (shrink)

REMARKS ON EVOLUTION AND TIME-SCALES, Graham Cairns-Smith; HODGSON'S BLACK BOX, Thomas Clark; DO HODGSON'S PROPOSITIONS UNIQUELY CHARACTERIZE FREE WILL?, Ravi Gomatam; WHAT SHOULD WE RETAIN FROM A PLAIN PERSON'S CONCEPT OF FREE WILL?, Gilberto Gomes; ISOLATING DISPARATE CHALLENGES TO HODGSON'S ACCOUNT OF FREE WILL, Liberty Jaswal; FREE AGENCY AND LAWS OF NATURE, Robert Kane; SCIENCE VERSUS REALIZATION OF VALUE, NOT DETERMINISM VERSUS CHOICE, Nicholas Maxwell; COMMENTS ON HODGSON, J.J.C. Smart; THE VIEW FROM WITHIN, Sean Spence; COMMENTARY ON HODGSON, Henry Stapp.

A focussed issue of The Reasoner on the topic of 'Infinitary Reasoning'. Owen Griffiths and A.C. Paseau were the guest editors.

ABSTRACT This essay focuses on two underlying presumptions that impinge on the effort of UNESCO to engender universal agreement on a set of bioethical norms: the conception of universality that pervades much of the document, and its disregard of structural inequalities that significantly impact health. Drawing on other UN system documents and recent feminist bioethics scholarship, we argue that the formulation of universal principles should not rely solely on shared ethical values, as the draft document affirms, but also on differences (...) in ethical values that obtain across cultures. UNESCO's earlier work on gender mainstreaming illustrates the necessity of thinking from multiple perspectives in generating universal norms. The declaration asserts the ‘fundamental equality of all human beings in dignity and rights’1 and insists that ‘the highest attainable standard of health is one of the fundamental rights of every human being without distinction of race, religion, political belief, economic or social condition’2 yet it does not explicitly recognize disparities of power and wealth that deny equal dignity and rights to many. Without attention to structural (as opposed to merely accidental) inequities, UNESCO's invocation of rights is so abstract as to be incompatible with its avowed intention. (shrink)

Since its first appearance in 1966, the notion of a supervaluation has been regarded by many as a powerful tool for dealing with semantic gaps. Only recently, however, applications to semantic gluts have also been considered. In previous work I proposed a general framework exploiting the intrinsic gap/glut duality. Here I also examine an alternative account where gaps and gluts are treated on a par: although they reflect opposite situations, the semantic upshot is the same in both cases--the value of (...) some expressions is not uniquely defined. Other strategies for generalizing supervaluations are considered and some comparative facts are discussed. (shrink)

O artigo oferece uma breve exposição da biografia e do contexto histórico do filósofo neoplatônico Damáscio (c. 458 - c. 538) para, na sequência, apresentar a tradução de um dos seus poemas líricos do período final de sua vida. O procedimento adotado justifica-se pelo caráter lutuoso e decididamente pessoal dos versos, nos quais Damáscio lamenta consigo próprio as perdas sofridas no decorrer de sua longa e fascinante vida. Como veremos, tais perdas estão, em verdade, diretamente ligadas ao colapso do mundo (...) antigo e ao derradeiro golpe proferido por Justiniano contra a filosofia helênica pagã. (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)

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)

An important source of doubt about our knowledge of the "external world" is the thought that all of our sensory experience could be delusive without our realizing it. Such wholesale questioning of the deliverances of all forms of perception seems to leave no resources for successfully justifying our belief in the existence of an objective world beyond our subjective experiences. I argue that there is there is a fatal flaw in the very expression of philosophical doubt about the "external world." (...) Therefore, no such justification is necessary. The feature of skepticism which I believe renders it vulnerable is the assumption that each of us has a right to be certain of his own existence as a subject of conscious experience even in the face of comprehensive doubt about our empirical beliefs. (shrink)