In the early 1900s, Russell began to recognize that he, and many other mathematicians, had been using assertions like the Axiom of Choice implicitly, and without explicitly proving them. In working with the Axioms of Choice, Infinity, and Reducibility, and his and Whitehead’s Multiplicative Axiom, Russell came to take the position that some axioms are necessary to recovering certain results of mathematics, but may not be proven to be true absolutely. The essay traces historical roots of, and motivations for, Russell’s (...) method of analysis, which are intended to shed light on his view about the status of mathematical axioms. I describe the position Russell develops in consequence as “immanent logicism,” in contrast to what Irving (1989) describes as “epistemic logicism.” Immanent logicism allows Russell to avoid the logocentric predicament, and to propose a method for discovering structural relationships of dependence within mathematical theories. (shrink)

Hilbert’s choice operators τ and ε, when added to intuitionistic logic, strengthen it. In the presence of certain extensionality axioms they produce classical logic, while in the presence of weaker decidability conditions for terms they produce various superintuitionistic intermediate logics. In this thesis, I argue that there are important philosophical lessons to be learned from these results. To make the case, I begin with a historical discussion situating the development of Hilbert’s operators in relation to his evolving program in the (...) foundations of mathematics and in relation to philosophical motivations leading to the development of intuitionistic logic. This sets the stage for a brief description of the relevant part of Dummett’s program to recast debates in metaphysics, and in particular disputes about realism and anti-realism, as closely intertwined with issues in philosophical logic, with the acceptance of classical logic for a domain reflecting a commitment to realism for that domain. Then I review extant results about what is provable and what is not when one adds epsilon to intuitionistic logic, largely due to Bell and DeVidi, and I give several new proofs of intermediate logics from intuitionistic logic+ε without identity. With all this in hand, I turn to a discussion of the philosophical significance of choice operators. Among the conclusions I defend are that these results provide a finer-grained basis for Dummett’s contention that commitment to classically valid but intuitionistically invalid principles reflect metaphysical commitments by showing those principles to be derivable from certain existence assumptions; that Dummett’s framework is improved by these results as they show that questions of realism and anti-realism are not an “all or nothing” matter, but that there are plausibly metaphysical stances between the poles of anti-realism and realism, because different sorts of ontological assumptions yield intermediate rather than classical logic; and that these intermediate positions between classical and intuitionistic logic link up in interesting ways with our intuitions about issues of objectivity and reality, and do so usefully by linking to questions around intriguing everyday concepts such as “is smart,” which I suggest involve a number of distinct dimensions which might themselves be objective, but because of their multivalent structure are themselves intermediate between being objective and not. Finally, I discuss the implications of these results for ongoing debates about the status of arbitrary and ideal objects in the foundations of logic, showing among other things that much of the discussion is flawed because it does not recognize the degree to which the claims being made depend on the presumption that one is working with a very strong logic. (shrink)

Everyday reasoning is replete with arguments which, though not logically valid, nonetheless harbor a measure of credibility in their own right. Here the claim that such arguments force us to acknowledge material validity, in addition to logical validity, is advanced, and criteria that attempt to unpack this concept are examined in detail. Of special concern is the effort to model these criteria on explications of logical validity that rely on notions of substitutivity and logical form. It is argued, however, that (...) such a parallel is not easily located and that it is uncertain that a construal of material validity can be fashioned after traditional accounts of logical validity. Attention is also given to the topics of enthymemes and to the proper domain of logic. (shrink)

Narrowly speaking, the correspondence theory of truth is the view that truth is correspondence to a fact -- a view that was advocated by Russell and Moore early in the 20 th century. But the label is usually applied much more broadly to any view explicitly embracing the idea that truth consists in a relation to reality, i.e., that truth is a relational property involving a characteristic relation (to be specified) to some portion of reality (to be specified). During the (...) last 2300 years this basic idea has been expressed in many ways, resulting in a rather extended family of views, theories, and theory sketches. The members of the family employ various concepts for the relevant relation (correspondence, conformity, congruence, agreement, accordance, copying, picturing, signification, representation, reference, satisfaction) and/or various concepts for the relevant portion of reality (facts, states of affairs, situations, events, objects, sequences of objects, sets, properties, tropes). The resulting multiplicity of versions and reformulations of the theory is due to a blend of substantive and terminological differences. (shrink)

Immediate knowledge is here construed as true belief that does not owe its status as knowledge to support by other knowledge (or justified belief) of the same subject. The bulk of the paper is devoted to a criticism of attempts to show the impossibility of immediate knowledge. I concentrate on attempts by Wilfrid Sellars and Laurence Bonjour to show that putative immediate knowledge really depends on higher-level knowledge or justified belief about the status of the beliefs involved in the putative (...) immediate knowledge. It is concluded that their arguments are lacking in cogency. (shrink)

Do the same epistemic standards govern scientific and religious belief? Or should science and religion operate in completely independent epistemic spheres? Commentators have recently been divided on William James’s answer to this question. One side depicts “The Will to Believe” as offering a separate-spheres defense of religious belief in the manner of Galileo. The other contends that “The Will to Believe” seeks to loosen the usual epistemic standards so that religious and scientific beliefs can both be justified by a unitary (...) set of evidentiary rules. I argue that James did build a unitary epistemology but not by loosening cognitive standards. In his psychological research, he had adopted the Comtian view that hypotheses and regulative assumptions play a crucial role in the context of discovery even though they must be provisionally adopted before they can be supported by evidence. “The Will to Believe” relies on this methodological point to achieve a therapeutic goal—to convince despairing Victorians that religious faith can be reconciled with a scientific epistemology. James argues that the prospective theist is in the same epistemic situation with respect to the “religious hypothesis” as the scientist working in the context of discovery. (shrink)

The ontological proof became something of a signature argument for the British Idealist movement and this paper examines how and why that was so. Beginning with an account of Hegel's understanding of the argument, it looks at how the thesis was picked up, developed and criticized by the Cairds, Bradley, Pringle-Pattison and others. The importance of Bradley's reading in particular is stressed. Lastly, consideration is given to Collingwood's lifelong interest in the proof and it is argued that his attention is (...) best understood as a direct continuation of theirs. In view of the fact that recent commentators have tried to draw a sharp line between Collingwood's approach to metaphysics and ontology and that of his predecessors, the establishment of this connection calls for a measure of reassessment on both sides. (shrink)

Abstract It is sometimes thought that Absolute Idealism was undermined by its inability to deal with science. Through a critical discussion of F. H. Bradley's philosophy of science, this idea is challenged. His views on science are divided into a positive and a negative part, and it is argued that, although he found the scientific world view to be essentially false, he was nonetheless able to develop a sympathetic and intelligent philosophy of science. This was basically pragmatic and instrumental in (...) tone, and gave to science a large measure of autonomy from philosophy. His doctrine is connected with certain contemporary ideas in the philosophy of science. (shrink)

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.

The goal of this paper is to provide a detailed reading of John Venn's Logic of Chance as a work of logic or, more specifically, as a specific portion of the general system of so-called ‘material’ logic developed in his Principles of Empirical or Inductive Logic and to discuss it against the background of his Boolean-inspired views on the connection between logic and mathematics. It is by means of this situating of Venn 1866 [The Logic of Chance. An Essay on (...) the Foundations and Province of the Theory of Probability. With Especial Reference to Its Application to Moral and Social Science, London: Macmillan] within the entirety of his oeuvre that it becomes both possible to revisit and necessary to re-articulate its place in the history of the frequency interpretation of probability. For it is clear that if Venn's approach to logic not only allowed him to establish its foundations on the basis of a process of idealization and define it as consisting of so-called hypothetical infinite series, bu.. (shrink)

Does (affirmative) judgement have a logical dual, negative judgement? Whether there is such a logical dualism was hotly debated at the beginning of the twentieth century. Frege argued in ?Negation? (1918/9) that logic can dispense with negative judgement. Frege's arguments shaped the views of later generations of analytic philosophers, but they will not have convinced such opponents as Brentano or Windelband. These philosophers believed in negative judgement for psychological, not logical, reasons. Reinach's ?On the Theory of Negative Judgement? (1911) spoke (...) to the concerns of these philosophers. While Frege took the distinction between affirmative and negative judgement to be logically redundant, Reinach argued that it is the result of confusing judgement with a different mental act. In this article, I present Reinach's arguments against the ?old logical dualism? in context, analyse them and discuss Reinach's innovative use of the notion of focus in the theory of judgement. Recently, there has been a revival of the view that sentential negation is grounded in a prior mental act of rejection. In the final section, I argue that Reinach's analysis of rejection poses a challenge for the revivalists. (shrink)

This article puts forward a revisionary reading of Hegel's reception in Britain at the turn of the nineteenth century, in suggesting that the stance of the British Hegelians is very close to the sort of non-metaphysical or category theory interpretations that have been in vogue amongst contemporary commentators. It is shown that the British Hegelians arrived at this position as a way of responding to the hostile existentialist reaction to Hegel begun by Schelling in the 1840s, which led them to (...) abandon the standard Neoplatonic reading of his idealism, and arrive at the sort of non- metaphysical account which is most fully developed by J M E McTaggart in his interpretation of Hegel's Logic. (shrink)

The disciplined investigation of consciousness is of three main types: eidetic, anthropological , and psychophysical. The first concerns the essence of consciousness in general and of its main modes. Its method involves introspection, empathy, and insight into necessities present in what these reveal. As the study of the essence of that which is the locus of all value it is of unique importance, and it is also essential as a foundation of the other inquiries. Such inquiry has been the main (...) task set for itself by phenomenology as a philosophical school, but engagement in it need not imply acceptance of distinctive doctrines of this school. English language?philosophy has developed in ways which discourage the eidetic investigation of consciousness, especially through insistence that modes of consciousness, conceived as a private possession, cannot be the referent of socially shared meanings. Its great mistake has been to expect ?consciousness? to refer to some elusive phenomenon to be looked for in the world and able to be studied as a distinctive reality only if conceptually isolable from what it reveals. Study of consciousness, however, is not primarily study of a phenomenon to be found within the world, but of the variety of ways in which the world can be present to us. (shrink)

Among fundamental metaphysical quests, one might wonder: Why is there anything at all rather than just nothing? Many reject that question because they think it is meaningless, trivial, or necessarily unanswerable. But I provide reasons for thinking that the Why question could make sense and one might even expect an answer to it. I begin by asking why the world is not empty of all concrete things. One might regard this question as important if one accepts that it is, in (...) some sense, possible for all concrete things to vanish, one-by-one. I argue finally that possible replies to the Why question concerning concrete things might point to realities that are abstract instead of concrete. Abstract realities might be explanatorily powerful without their power being guaranteed by Logic. (shrink)

In this paper I attempt to show how Moore’s early emancipation from Bradley’s absolute idealism presupposes a fundamental adherence to certain theses of absolute idealism itself. In particular, I argue that the idea of an immediate epistemic access to concepts and propositions that Moore endorses in his platonic atomism is a reworking of a form of epistemic realism already present in Bradley. Epistemic realism is the conjunction of two theses: i) reality is independent of any constructive work of the human (...) mind; ii) reality is immediately accessible to knowledge. In this paper I first focus on Moore’s early idealist phase, suggesting that it should be understood as an attempt at isolating this thesis in Bradley against Kant’s transcendental idealism. I then suggest that it is on the background of an invariant adherence to it that we should understand Moore’s later rejection of monism and idealism through his anti-psychologism. I hence explore how epistemic realism is at work in Moore’s platonic atomism and conclude with some remarks about the further significance of Moore’s rejection of Kant. (shrink)