Atheism is skeptical towards gods, and atheology advances philosophical positions defending the reasonableness of that rejection. The history of philosophy encompasses many unorthodox and irreligious movements of thought, and these varieties of unbelief deserve more exegesis and analysis than presently available. Going back to philosophy’s origins, two primary types of atheology have dominated the advancement of atheism, yet they have not cooperated very well. Materialist philosophies assemble cosmologies that leave nothing for gods to do, while skeptical philosophies find conceptions of (...) god to be too unintelligible or unsupported by evidence to warrant credibility. The origins and genealogies of these two atheologies are sketched and compared over many centuries down to present-day atheism, which still displays signs of this internecine divide between confident naturalists and agnostic skeptics. (shrink)

In writings prior to the publication of The Principles of Mathematics (PoM), Russell denies that relations “in the abstract” ever relate and holds instead that only particularized relations, or relational tropes, do so; however, in PoM section 55, he argues against his former view and adopts the view that relations “in the abstract” are capable of a “twofold use” – either as “relations in themselves” or as “actually relating”. I argue that while Russell rightly came to recognize that rejecting his (...) earlier view is necessary for avoiding the Bradleyan view that complex wholes are unanalyzable, his later view can appear as an ad hoc means of avoiding Bradley's argument against “relational thought”. (shrink)

I interpret the philosophical views of Werner Heisenberg as a pragmatism and non-metaphysical realism of a Wittgensteinian kind. The “closed theory” is a Wittgensteinian rule/concept.

Different interpretations of Bradley’s regress argument are considered. On the basis of textual evidences, it is argued that the most persuasive is the one that sees the argument as primarily addressing the general issue of unity or connectedness.

According to some critics, traditional armchair philosophical methodology relies in an illicit way on intuitions. But the particular structure of the critique is not often carefully articulated—a significant omission, since some of the critics’ arguments for skepticism about philosophy threaten to generalize to skepticism in general. More recently, some experimentalist critics have attempted to articulate a critique that is especially tailored to affect traditional methods, without generalizing too widely. Such critiques are more reasonable, and more worthy of serious consideration, than (...) are blunter critiques that generalize far too widely. I argue that a careful (empirical!) examination of extant philosophical practices shows that traditional philosophical methods can meet these more reasonable challenges. (shrink)

This paper offers an interpretation of Russell's multiple-relation theory of judgment which characterizes it as direct application of the 1905 theory of definite descriptions. The paper maintains that it was by regarding propositional symbols (when occurring as subordinate clauses) as disguised descriptions of complexes, that Russell generated the philosophical explanation of the hierarchy of orders and the ramified theory of types of _Principia mathematica (1910). The interpretation provides a new understanding of Russell's abandoned book _Theory of Knowledge (1913), the 'direction (...) problems' and Wittgenstein's criticisms. (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)

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)

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)

This bulletin contains a summary of the main topics of discussion in truthmaker theory, namely: the definition of truthmakers, problems with Truthmaker Necessitarianism and Truthmaker Maximalism, the ontological burden of truthmakers and the recalcitrant topic of truthmakers for negative truths.

The paper critically scrutinizes the widespread idea that Russell subscribes to a "Universalist Conception of Logic." Various glosses on this somewhat under-explained slogan are considered, and their fit with Russell's texts and logical practice examined. The results of this investigation are, for the most part, unfavorable to the Universalist interpretation.

As is widely appreciated and easily demonstrated, the notion that we are essentially experiential (or conscious) beings has a good deal of appeal; what is less obvious, and more controversial, is whether it is possible to devise a viable account of the self along such lines within the confines of a broadly naturalistic metaphysical framework. There are many avenues to explore, but here I confine myself to outlining the case for one particular approach. I suggest that we should think of (...) ourselves (or our essential cores) as being composed of experience-producing systems, and that such systems belong to the same self when they have the capacity to contribute to unified streams of consciousness. The viability of this proposal rests in turn on a particular conception of the structure of consciousness, both at and over time; this conception is defended in the first part of the paper.. (shrink)

The ‘Private Language’ sections of the Philosophical Investigations §§ 243–315 serve to undermine the idea that our ordinary felt sensations, e.g., of heat, or cold, or pain, together with our experienced impressions of colour or of sound, are ‘private’ or ‘inner’ objects, where an object mirrors in the mental realm what we associate with that of the physical. This paper explores Wittgenstein's method in these sections, together with the work of several of his commentators who agree with his ‘therapeutic’ approach (...) to the denial of a possible private language. More significantly, however, it discovers a paradox in the fact that a number of philosophers who claim that his ‘Argument Against Private Language’ is unsuccessful point in reaching this conclusion to the very features concerning first-person sensation ascription that Wittgenstein employs to reveal that our ordinary sensations are not ‘private’ to us in that sense identified in § 243, which talks of ‘a language used to refer to what only its speaker can know’, viz, ‘his immediate private sensations’. This helps to explain why there is still no general agreement on the significance of §§ 243–315. (shrink)

Scientific anti-realists who appeal to the pessimistic induction (PI) claim that the theoretical terms of past scientific theories often fail to refer to anything. But on standard views in philosophy of language, such reference failures prima facie lead to certain sentences being neither true nor false. Thus, if these standard views are correct, then the conclusion of the PI should be that significant chunks of current theories are truth-valueless. But that is semantic anti-realism about scientific discourse—a position most philosophers of (...) science, anti-realists included, consider anathema today. Therefore, proponents of the PI confront a dilemma: either accept semantic anti-realism or reject common semantic views. I examine strategies (with particular emphasis on supervaluations) for the PI proponent to either lessen the sting of this argument, or learn to live with it. 1 Introduction2 Designation Failure 2.1 Designation failure leads to truth-valueless sentences2.1.1 Direct reference theory2.1.2 Fregeanism2.1.3 Accounts of reference-fixing: why ‘phlogiston’ fails to designate 2.2 Objection: sentences exhibiting designation failure are false not truth-valueless 2.3 Avoiding truth-valuelessness via controversial semantic positions3 What to do? Closing the Gaps4 Conclusion. (shrink)

I argue that Beall and Restall's logical pluralism fails. Beall–Restall pluralism is the claim that there are different, equally correct logical consequence relations in a single language. Their position fails for two, related, reasons: first, it relies on an unmotivated conception of the ‘settled core’ of consequence: they believe that truth-preservation, necessity, formality and normativity are ‘settled’ features of logical consequence and that any relation satisfying these criteria is a logical consequence relation. I consider historical evidence and argue that their (...) position relies on an unmotivated conception of the settled features of logical consequence. There are many features that are just as settled but which are inconsistent with pluralism. Second, I argue that Beall–Restall pluralism fails to hold in a single language with a single selection of logical constants, which they require for the position to be distinct from Carnap's. I consider various ways in which Beall and Restall can resist this meaning variance, particularly for negation, but argue that the strongest way relies on an unmotivated conception of the settled features of the logical constants. (shrink)

This article is an attempt to present Gödel's discussion on concepts, from 1944 to the late 1970s, in particular relation to the thought of Frege and Russell. The discussion takes its point of departure from Gödel's claim in notes on Bernay's review of ?Russell's mathematical logic?. It then retraces the historical background of the notion of intension which both Russell and Gödel use, and offers some grounds for claiming that Gödel consistently considered logic as a free-type theory of concepts, called (...) intensions, considered as the denotations of predicate names. (shrink)

Context: The infinite has long been an area of philosophical and mathematical investigation. There are many puzzles and paradoxes that involve the infinite. Problem: The goal of this paper is to answer the question: Which objects are the infinite numbers (when order is taken into account)? Though not currently considered a problem, I believe that it is of primary importance to identify properly the infinite numbers. Method: The main method that I employ is conceptual analysis. In particular, I argue that (...) the infinite numbers should be as much like the finite numbers as possible. Results: Using finite numbers as our guide to the infinite numbers, it follows that infinite numbers are of the structure w + (w* + w) a + w*. This same structure also arises when a large finite number is under investigation. Implications: A first implication of the paper is that infinite numbers may be large finite numbers that have not been investigated fully. A second implication is that there is no number of finite numbers. Third, a number of paradoxes of the infinite are resolved. One change that should occur as a result of these findings is that “infinitely many” should refer to structures of the form w + (w* + w) a + w*; in contrast, there are “indefinitely many” natural numbers. Constructivist content: The constructivist perspective of the paper is a form of strict finitism. (shrink)

In his recent book, "The Metaphysicians of Meaning" (2000), Gideon Makin argues that in the so-called "Gray's Elegy" argument (the GEA) in "On Denoting", Russell provides decisive arguments against not only his own theory of denoting concepts but also Frege's theory of sense. I argue that by failing to recognize fundamental differences between the two theories, Makin fails to recognize that the GEA has less force against Frege's theory than against Russell's own earlier theory. While I agree with many aspects (...) of Makin's interpretation of the GEA, I differ with him regarding some significant details and present an interpretation according to which the GEA emerges as simpler, stronger, and more integrated. (shrink)

What makes it true when we say that something is not the case? Truthmaker maximalists think that every truth has a truthmaker—some fact in the world—that makes it true. No such facts can be found for the socalled negative truths. If a proposition is true when it has a truthmaker, then it would be false when it has no truthmaker. I therefore argue that negative truths, such as t<p>, are best understood as falsehoods, f<p>.

Although for a couple of centuries empiricism was prevalent in physics circles, the development of various schools of philosophy of science, during the second half of the twentieth century, made it clear we do not encounter nature with empty minds and that scientists always use some assumptions in their scientific work. In this article. We argue that metaphysical assumptions play an important role at various stages of science activity. But these assumptions are usually taken from various schools of philosophy or (...) religions. Monotheistic religions can provide such principles. Thus, metaphysics works as a bridge between science and religion. (shrink)

Reply to Beaney: the closing of the historical mindIn his comments, Michael Beaney sets himself up as the arbiter of what is genuine history and what isn’t. While celebrating the outpouring of specialized scholarship on Frege, he has no patience with the enterprise outlined in the Précis, which attempts to construct a large-scale picture of the richness of the analytic tradition. That enterprise is one in which great figures of our recent past are challenged by aspects of contemporary thought, and (...) our current struggles are enriched by insights of theirs that haven’t been fully absorbed. Although some work of this sort can be done piecemeal, one historical figure at a time, there is much to be learned from a more encompassing perspective. While no picture constructed by a single author can be authoritative about everything, the attempt to give informative, connected assessments of major milestones in the tradition is our best hope of understanding who we are and where we have come from. (shrink)

We can anticipate what is yet to happen, remember what has already happened, but our immediate experience is confined to the present, the here and now. So much seems common sense. So much so that it is no surprise to see Thomas Reid, that pre-eminent champion of common sense in philosophy, advocating precisely this position.

In this article, I show and discuss the relevance of Wittgenstein's arguments as to the spatial structure of sight to recent issues in the philosophy of mind. The first, bearing upon the dimensionality of the manifolds at play in depiction, plays a critical role in Clark's attempt to provide an independent account ofqualiaand of their differentiative properties. The second, pertaining to the properly spatial structure formed by the data of sight, is explicitly appealed to in the debate on the realistic (...) character of any genuinely spatial scheme. I argue that if Wittgenstein rightly assumes that the simultaneous presence of sensible places in vision is a key condition for objectivity, he fails nevertheless to warrant the allegedly realistic character of the scheme employed in his own search for a phenomenological description of the visual field. (shrink)

Some descriptivists reply to the modal argument by appealing to scope ambiguities. In this paper, we argue that those replies don’t work in the case of apparently empty names like ‘Sherlock Holmes’.

This paper is about one of Arthur Prior’s earliest publications in philosophy, “The Nation and the Individual”. Its aims are to show that Prior made a remarkable contribution to social ontology in the 1930s which should be read with some attention to its historical background, which closely follows John Wisdom as to its theoretical elements, in particular the notion of a “logical construction”, but which is more clearly eliminativist with regard to nations and which is original in terms of rather (...) bold ethical consequences; to interpret Prior’s/Wisdom’s proposal as a promise of reduction by translation and to connect Prior’s/Wisdom’s ideas with John Searle’s recent work on social ontology. (shrink)

La théorie russellienne des relations est ordinairement conçue comme le résultat d'une réflexion logique et ontologique sur l'ordre et l'asymétrie. Le présent article vise à présenter une autre généalogie, centrée sur les concepts de grandeur et de vecteur. Nous montrons en premier lieu que la thèse de l'irréductibilité des relations est avancée pour la première fois en 1897, à l'occasion d'une reformulation de la dialectique hégélienne de la quantité. Nous soulignons, en second lieu, que la notion de grandeur fait, autour (...) des années 1898-1899, l'objet d'une formalisation mathématique, complètement indépendante de la théorie des relations et fondée exclusivement sur les algèbres vectorielles. Nous montrons enfin que Russell, en possession de sa nouvelle doctrine logique, développe dès 1901 une théorie relationnelle des grandeurs vectorielles. Tout se passe donc comme si un des intérêts de la nouvelle théorie était, pour le philosophe, de permettre la substitution des relations aux grandeurs. (shrink)

This paper is concerned with the status of a symbol in Wittgenstein’s Tractatus. It is claimed in the first section that a Tractarian symbol, whilst essentially a syntactic entity to be distinguished from the mark or sound that is its sign, bears its semantic significance only inessentially. In the second and third sections I pursue this point of exegesis through the Tractarian discussions of nonsense and the context principle respectively. The final section of the paper places the forgoing work in (...) a secondary context, addressing in particular a debate regarding the realism of the Tractatus. (shrink)

This paper examines Russell's substitutional theory of classes and relations, and its influence on the development of the theory of logical types between the years 1906 and the publication of Principia Mathematica (volume I) in 1910. The substitutional theory proves to have been much more influential on Russell's writings than has been hitherto thought. After a brief introduction, the paper traces Russell's published works on type-theory up to Principia. Each is interpreted as presenting a version or modification of the substitutional (...) theory. New motivations for Russell's 1908 axiom of infinity and axiom of reducibility are revealed. (shrink)