In the 1920s, David Hilbert proposed a research program with the aim of providing mathematics with a secure foundation. This was to be accomplished by first formalizing logic and mathematics in their entirety, and then showing---using only so-called finitistic principles---that these formalizations are free of contradictions. ;In the area of logic, the Hilbert school accomplished major advances both in introducing new systems of logic, and in developing central metalogical notions, such as completeness and decidability. The analysis of unpublished material presented (...) in Chapter 2 shows that a completeness proof for propositional logic was found by Hilbert and his assistant Paul Bernays already in 1917--18, and that Bernays's contribution was much greater than is commonly acknowledged. Aside from logic, the main technical contribution of Hilbert's Program are the development of formal mathematical theories and proof-theoretical investigations thereof, in particular, consistency proofs. In this respect Wilhelm Ackermann's 1924 dissertation is a milestone both in the development of the Program and in proof theory in general. Ackermann gives a consistency proof for a second-order version of primitive recursive arithmetic which, surprisingly, explicitly uses a finitistic version of transfinite induction up to www . He also gave a faulty consistency proof for a system of second-order arithmetic based on Hilbert's &egr;-substitution method. Detailed analyses of both proofs in Chapter 3 shed light on the development of finitism and proof theory in the 1920s as practiced in Hilbert's school. ;In a series of papers, Charles Parsons has attempted to map out a notion of mathematical intuition which he also brings to bear on Hilbert's finitism. According to him, mathematical intuition fails to be able to underwrite the kind of intuitive knowledge Hilbert thought was attainable by the finitist. It is argued in Chapter 4 that the extent of finitistic knowledge which intuition can provide is broader than Parsons supposes. According to another influential analysis of finitism due to W. W. Tait, finitist reasoning coincides with primitive recursive reasoning. The acceptance of non-primitive recursive methods in Ackermann's dissertation presented in Chapter 3, together with additional textual evidence presented in Chapter 4, shows that this identification is untenable as far as Hilbert's conception of finitism is concerned. Tait's conception, however, differs from Hilbert's in important respects, yet it is also open to criticisms leading to the conclusion that finitism encompasses more than just primitive recursive reasoning. (shrink)

In 1947 Quine wrote one of the most important and influential articles in the twentieth century philosophy - "On What There Is". One of the aims of this article was a critique of Meinong's Theory of Object. The critique was especially focused upon nonactual possibilities, which (according to Meinong) are some kinds of nonexistent objects. In my paper I want to present Neo-Meinongian refutations of Quine's critique. In order to do this I discuss: (i) the main thesis of "On What (...) There Is" ,(ii) premises of Meinongian Theory, (iii) views of proponents and opponents of the idea of nonexistent objects, (iv) Quine's critique aimed at nonactual possibilities, (v) Terence Parsons' theory, based on the distinction between nuclear and extranucler properties, and (vi) noneism, defended by Richard Routley. I also try to give a reply to the most popular critiques aimed at both Neo-Meinongian theories. The main conclusion is that Quine's critique and his arguments against nonactual possibilities aren't dangerous for theories endorsing Meinong's Theory of Object. Contrary to what Gilbert Ryle once claimed (If Meinongianism isn't dead, nothing is), Meinongian theories are still alive and doing well. (shrink)

Reading Putnam consists largely of papers from the fantastic ‘Putnam @80’ conference (organised by Maria Baghramian in 2007) together with replies from Hilary Putnam. Given the diversity of Putnam’s work, the papers in this collection cover many different topics. This makes the collection difficulty to read but, ultimately, extremely rewarding. In this review, I focus on the contributions from Michael Devitt, Charles Parsons, Richard Boyd, Ned Block, Charles Travis and John McDowell, together with Putnam’s responses. My aim is (...) to highlight some connections between Putnam’s (evolving) views on ontology, conceptual relativism, and perception. (shrink)

Our culture praises—indeed revels in—the beauty of the human form. And yet, in the midst of this exuberant celebration of corporeal beauty, not even the most unreflective can be unaware of the problems that have been laid at its feet. The philosopher Kathleen Higgins notes a “pervasive impression that is widespread in our culture: that beauty, or some near kin of it, is unsavory, a temptation that might get the soul off-track” (2000, 89). In response to this suspicion, some have (...) argued that beauty is in desperate need of reform or redefinition in our time. In this essay, I attempt to analyze and evaluate this counsel. How should these claims be understood? Would we be wise to follow them? (shrink)

Whilst media and political rhetoric in Britain is sceptical and often outright damning of the (presumed) morals and behaviours of the White marginalized poor, our aim is to explore the conditions under which successful communities are nevertheless built. Specifically, we examine the features of community and stress its importance both for belonging and bonding around shared norms and practices and for fostering the necessary bridging essential for interacting and cooperating with others. In considering what it means to foster a community (...) that acts as a breakwater against the tides of stigma or disadvantage, we pay special attention to what we will call enabling conditions – essential features that communities either can or should be able to provide or that exist independent of communities and are indispensable for accessing opportunities in the wider society. We detail the dynamics of White poverty and exclusion before turning our attention to possible responses to these challenges. In searching for viable responses to stigma and disadvantage, we compare some different typologies of community presently available to the White poor in Britain and examine whether these are sufficient to satisfy the enabling conditions associated with more robust forms of group membership. (shrink)

Alongside existing research into the social, political and economic impacts of the Web, there is a need to study the Web from a cognitive and epistemic perspective. This is particularly so as new and emerging technologies alter the nature of our interactive engagements with the Web, transforming the extent to which our thoughts and actions are shaped by the online environment. Situated and ecological approaches to cognition are relevant to understanding the cognitive significance of the Web because of the emphasis (...) they place on forces and factors that reside at the level of agent–world interactions. In particular, by adopting a situated or ecological approach to cognition, we are able to assess the significance of the Web from the perspective of research into embodied, extended, embedded, social and collective cognition. The results of this analysis help to reshape the interdisciplinary configuration of Web Science, expanding its theoretical and empirical remit to include the disciplines of both cognitive science and the philosophy of mind. (shrink)

Scientific cognitivism is the idea that nature must be aesthetically appreciated in light of scientific information about it. I defend Carlson's traditional formulation of scientific cognitivism from some recent criticisms. However, I also argue that if we employ this formulation it is difficult to uphold two claims that Carlson makes about scientific cognitivism: (i) it is the correct analysis of the notion of appropriate aesthetic appreciation of nature, and (ii) it justifies the idea that nature, seen aright, is always beautiful (...) (that is, positive aesthetics about nature). I attempt to find a revised formulation of scientific cognitivism that can support both of these claims. I argue that to do this we must rethink the notion of positive aesthetics and its place in our theorizing about the appropriate aesthetic appreciation of nature. Specifically, I propose that positive aesthetics be made ‘internal’ to the theory of appropriate aesthetic appreciation, in the sense that this theory determines the correct scientific categories for appreciating a natural object, in part, in virtue of a ‘beauty-making’ criterion. I argue that this sort of formulation of scientific cognitivism can support both of Carlson's claims and does not compromise the objectivist scruples that motivate the view. (shrink)

Normally this is not how we think material objects work. I, for example, am a material object that is located in multiple places: this place to my left where my left arm is, and this, distinct, place to my right, where my right arm is. But I am only partially located in each place. My left arm is a part of me that fills exactly the place to my left, and my right arm is a distinct part of me that (...) fills exactly the place to my right. I am located in multiple places by virtue of having distinct parts in those places. So entension is not happening to me — I do not entend. (shrink)

Truthmaker theorists typically claim not only that all truths have truthmakers (Truthmaker Maximalism), but also that there is some enlightening metaphysical theory to be given of the nature of those truthmakers (e.g. that they are Armstrongian states of affairs, or tropes, or concrete individuals). Call this latter thesis the "Material Theory Thesis" (it is the thesis that there is some true material theory of truthmakers). I argue that the Material Theory Thesis is inconsistent with Truthmaker Maximalism.

The aim of this paper is to emphasize the fact that for all finitely-many-valued logics there is a completely systematic relation between sequent calculi and tableau systems. More importantly, we show that for both of these systems there are al- ways two dual proof sytems (not just only two ways to interpret the calculi). This phenomenon may easily escape one’s attention since in the classical (two-valued) case the two systems coincide. (In two-valued logic the assignment of a truth value and (...) the exclusion of the opposite truth value describe the same situation.). (shrink)

A construction principle for natural deduction systems for arbitrary, finitely-many-valued first order logics is exhibited. These systems are systematically obtained from sequent calculi, which in turn can be automatically extracted from the truth tables of the logics under consideration. Soundness and cut-free completeness of these sequent calculi translate into soundness, completeness, and normal-form theorems for natural deduction systems.

All disciplines must define their basic units and core processes. In evolutionary biology, the core process is natural selection and the basic unit of selection and adaptation is the individual. To operationalize the theory of natural selection we must count individuals, as they are the bearers of fitness. While canonical individuals have often been taken to be multicellular organisms, the hierarchy of life shows that new kinds of individuals have evolved. A variety of criteria have been used to define biological (...) individuality. Some criteria rely on the presence/absence of a particular property while others advocate an approach that reflects the process of natural selection. The plethora of approaches to classifying individuality has resulted in confusion regarding how to study individuality in a given taxon. (shrink)

Assessing the success or failure of a work of architecture typically requires determining its function. However, architectural criticism often founders on apparently intractable disputes concerning the 'true' function of particular works. In this essay, I propose that the proper function of an architectural work is a matter of empirical fact, and can be determined by examining the history of the relevant architectural type. I develop this claim by appeal to the so-called 'etiological theory of function'.

Religion, especially Western religion, calls upon us to 'believe' on the basis of 'faith.' But in what way can faith serve as a justification for belief? In this essay, I distinguish between 'belief in' and 'belief that' and argue that faith, properly understood, entails the former, not the latter.

Aesthetic preservation is the idea of sparing natural areas from development because of their aesthetic value. In this article I discuss a problem for aesthetic preservation that I call the ‘hidden gems problem’: in certain cases, the natural area under consideration is so remote and/or fragile that few people can actually experience it. In these cases, it becomes unclear how nature's aesthetic value can justify its preservation when development promises practical human benefits. After rejecting some potential responses to the hidden (...) gems problem, I offer a different solution. I argue that we have an aesthetic reason to preserve nature's hidden gems because they are required to produce ‘true judges’ of aesthetic value, who are capable of improving the general quality of taste for landscape. I develop this argument using the example of recent preservationist efforts to save the isolated landscape of Sable Island, Nova Scotia. (shrink)

An imperative conditional is a conditional in the imperative mood (by analogy with “indicative conditional”, “subjunctive conditional”). What, in general, is the meaning and the illocutionary effect of an imperative conditional? I survey four answers: the answer that imperative conditionals are commands to the effect that an indicative conditional be true; two versions of the answer that imperative conditionals express irreducibly conditional commands; and finally, the answer that imperative conditionals express a kind of hybrid speech act between command and assertion.

In Mind and World, John McDowell argues against the view that perceptual representation is non-conceptual. The central worry is that this view cannot offer any reasonable account of how perception bears rationally upon belief. I argue that this worry, though sensible, can be met, if we are clear that perceptual representation is, though non-conceptual, still in some sense 'assertoric': Perception, like belief, represents things as being thus and so.

Paper begins: I have two gloves, a left glove and a right glove. I can fit the left glove onto my left hand, but not the right glove. Why? Because the right glove is the wrong shape to go on my left hand. So the two gloves are different shapes….

It’s now commonplace — since Korsgaard (1996) — in ethical theory to distinguish between two distinctions: on the one hand, the distinction between value an object has in virtue of its intrinsic properties vs. the value it has in virtue of all its properties, intrinsic or extrinsic; and on the other hand, the distinction between the value has an object as an end, vs. the value it has as a means to something else. I’ll call the former distinction the distinction (...) between intrinsic and nonintrinsic value; the latter is between value as-an-end and instrumental value. (shrink)

A letter to The Times of London, May 9, 1992 protesting the Cambridge University proposal to award an honorary degree to M. Jacques Derrida.

In Natural Beauty, Ronald Moore presents a novel account of our aesthetic encounters with the natural world. In this essay, I consider the relation between Moore's 'syncretic aesthetic' and rival views of the aesthetics of nature, particularly the view sometimes called 'scientific cognitivism'. After discussing Moore's characterization of rival views in general, and scientific cognitivism in particular, I rehearse his reasons for rejecting the latter view. I critique these arguments, but also suggest that scientific cognitivism and the syncretic aesthetic need (...) not, after all, be viewed as incompatible notions. (shrink)

Analytic philosophers usually think about modality in terms of possible worlds. According to the possible worlds framework, a proposition is necessary if it is true according to all possible worlds; it is possible if it is true according to some possible world. There are as many possible worlds as there are ways the actual world might be. Only one world is actual.

This paper began life as a short section of a more general paper about non-classical mereologies. In that paper I had a mereological theory that I wanted to show could be applied to all sorts of different metaphysical positions — notably, to those positions that believe in mereological vagueness in re — in “vague individuals”. To do that I felt I first had to dispatch the leading rival theory of vague individuals, which is due to Peter van Inwa-gen, and holds (...) that the part-whole relation admits of degrees. It seemed to me that this theory had a serious technical problem, or at best a serious gap. I sat down to write a paragraph or two highlighting the gap, preferably showing that it couldn’t be filled. This paper is the result. (shrink)

What we value, like, endorse, want, and prefer changes over the course of our lives. Richard Pettigrew presents a theory of rational decision making for agents who recognise that their values will change over time and whose decisions will affect those future times.

The problem of imperative consequence consists in the fact that theses (i) through (iii) are inconsistent; but yet all three are attractive (for the reasons sketched above). A solution to the problem consists in the denial of one of the three theses; I describe solutions as belonging to type 1, type 2, or type 3, depending on which thesis they deny. For the purposes of this paper, I would like to focus on a certain variety of type 3 solution – (...) a solution that offers a revised criterion of validity of a particular kind. (shrink)

This logic has a standard one-dimensional possible worlds semantics with an accessibility relation (I will call this, for short, the accessibility semantics for KDDc4, contrasting with the preposcription semantics given in “Command and consequence”). In the accessibility semantics, the semantic value of a sentence is a world (rather than a pair of worlds).

It is shown that Gqp↑, the quantified propositional Gödel logic based on the truth-value set V↑ = {1 - 1/n : n≥1}∪{1}, is decidable. This result is obtained by reduction to Büchi's theory S1S. An alternative proof based on elimination of quantifiers is also given, which yields both an axiomatization and a characterization of Gqp↑ as the intersection of all finite-valued quantified propositional Gödel logics.

The first-order temporal logics with □ and ○ of time structures isomorphic to ω (discrete linear time) and trees of ω-segments (linear time with branching gaps) and some of its fragments are compared: the first is not recursively axiomatizable. For the second, a cut-free complete sequent calculus is given, and from this, a resolution system is derived by the method of Maslov.

In an earlier paper, "Non-conceptual Content and the 'Space of Reasons'", I distinguished two forms of the view that perceptual content is non-conceptual, which I called the 'state view' and the 'content view'. On the latter, but not the former, perceptual states have a different kind of content than do cognitive states. Many have found it puzzling why anyone would want to make this claim and, indeed, what it might mean. This paper attempts to address these questions.

It is shown that the infinite-valued first-order Gödel logic G° based on the set of truth values {1/k: k ε w {0}} U {0} is not r.e. The logic G° is the same as that obtained from the Kripke semantics for first-order intuitionistic logic with constant domains and where the order structure of the model is linear. From this, the unaxiomatizability of Kröger's temporal logic of programs (even of the fragment without the nexttime operator O) and of the authors' temporal (...) logic of linear discrete time with gaps follows. (shrink)

Frege held that referring expressions in general, and demonstratives and indexicals in particular, contribute more than just their reference to what is expressed by utterances of sentences containing them. Heck first attempts to get clear about what the essence of the Fregean view is, arguing that it rests upon a certain conception of linguistic communication that is ultimately indefensible. On the other hand, however, he argues that understanding a demonstrative (or indexical) utterance requires one to think of the object denoted (...) in an appropriate way. This fact makes it difficult to reconcile the view that referring expressions are "directly referential" with any view that seeks (as Grice's does) to ground meaning in facts about communication. (shrink)

Co-authored letter to the APA to take a lead role in the recognition of teaching in the classroom, based on the participation in an interdisciplinary Conference on the Role of Advocacy in the Classroom back in 1995. At the time of this writing, the late Myles Brand was the President of Indiana University and a member of the IU Department of Philosophy.

Effective altruism sounds so innocuous—who could possibly be opposed to doing good more effectively? Yet it has inspired significant backlash in recent years. This paper addresses some common misconceptions and argues that the core “beneficentric” ideas of effective altruism are both excellent and widely neglected. Reasonable people may disagree on details of implementation, but all should share the basic goals or values underlying effective altruism.

This Element, written for researchers and students in philosophy and the behavioral sciences, reviews and critically assesses extant work on number concepts in developmental psychology and cognitive science. It has four main aims. First, it characterizes the core commitments of mainstream number cognition research, including the commitment to representationalism, the hypothesis that there exist certain number-specific cognitive systems, and the key milestones in the development of number cognition. Second, it provides a taxonomy of influential views within mainstream number cognition research, (...) along with the central challenges these views face. Third, it identifies and critically assesses a series of core philosophical assumptions often adopted by number cognition researchers. Finally, the Element articulates and defends a novel version of pluralism about number concepts. (shrink)

This paper analyses the phenomenology and epistemology of chatbots such as ChatGPT and Bard. The computational architecture underpinning these chatbots are large language models (LLMs), which are generative artificial intelligence (AI) systems trained on a massive dataset of text extracted from the Web. We conceptualise these LLMs as multifunctional computational cognitive artifacts, used for various cognitive tasks such as translating, summarizing, answering questions, information-seeking, and much more. Phenomenologically, LLMs can be experienced as a “quasi-other”; when that happens, users anthropomorphise them. (...) For most users, current LLMs are black boxes, i.e., for the most part, they lack data transparency and algorithmic transparency. They can, however, be phenomenologically and informationally transparent, in which case there is an interactional flow. Anthropomorphising and interactional flow can, in some users, create an attitude of (unwarranted) trust towards the output LLMs generate. We conclude this paper by drawing on the epistemology of trust and testimony to examine the epistemic implications of these dimensions. Whilst LLMs generally generate accurate responses, we observe two epistemic pitfalls. Ideally, users should be able to match the level of trust that they place in LLMs to the degree that LLMs are trustworthy. However, both their data and algorithmic opacity and their phenomenological and informational transparency can make it difficult for users to calibrate their trust correctly. The effects of these limitations are twofold: users may adopt unwarranted attitudes of trust towards the outputs of LLMs (which is particularly problematic when LLMs hallucinate), and the trustworthiness of LLMs may be undermined. (shrink)

The primary goal of this essay is to provide a comprehensive overview and analysis of the various relations between material artifacts and the embodied mind. A secondary goal of this essay is to identify some of the trends in the design and use of artifacts. First, based on their functional properties, I identify four categories of artifacts co-opted by the embodied mind, namely (1) embodied artifacts, (2) perceptual artifacts, (3) cognitive artifacts, and (4) affective artifacts. These categories can overlap and (...) so some artifacts are members of more than one category. I also identify some of the techniques (or skills) we use when interacting with artifacts. Identifying these categories of artifacts and techniques allows us to map the landscape of relations between embodied minds and the artifactual world. Second, having identified categories of artifacts and techniques, this essay then outlines some of the trends in the design and use of artifacts, focussing on neuroprosthetics, brain-computer interfaces, and personalisation algorithms nudging their users towards particular epistemic paths of information consumption. (shrink)

This article provides an overview and analysis of recent work on the extended self, demonstrating that the boundaries of selves are fluid, shifting across biological, artifactual, and sociocultural structures. First, it distinguishes the notions of minimal self, person, and narrative self. Second, it surveys how philosophers, psychologists, and cognitive scientists argue that embodiment, cognition, emotion, consciousness, and moral character traits can be extended and what that implies for the boundaries of selves. It also reviews and responds to various criticisms and (...) counterarguments against the extended self. The main focus is on the link between the extended mind and extended self, which has received the most attention in recent literature. But accounts of the extended self developed independently of the extended mind are also briefly discussed. This article ends by drawing out some of the conceptual, methodological, and normative implications of the extended self and suggesting some directions for future research. (shrink)

In this paper, we seek a reliabilist account of justified credence. Reliabilism about justified beliefs comes in two varieties: process reliabilism (Goldman, 1979, 2008) and indicator reliabilism (Alston, 1988, 2005). Existing accounts of reliabilism about justified credence comes in the same two varieties: Jeff Dunn (2015) proposes a version of process reliabilism, while Weng Hong Tang (2016) offers a version of indicator reliabilism. As we will see, both face the same objection. If they are right about what justification is, it (...) is mysterious why we care about justification, for neither of the accounts explains how justification is connected to anything of epistemic value. We will call this the Connection Problem. I begin by describing Dunn’s process reliabilism and Tang’s indicator reliabilism. I argue that, understood correctly, they are, in fact, extensionally equivalent. That is, Dunn and Tang reach the top of the same mountain, albeit by different routes. However, I argue that both face the Connection Problem. In response, I offer my own version of reliabilism, which is both process and indicator, and I argue that it solves that problem. Furthermore, I show that it is also extensionally equivalent to Dunn’s reliabilism and Tang’s. Thus, I reach the top of the same mountain as well. (shrink)

Rescorla (Erkenntnis, 2020) has recently pointed out that the standard arguments for Bayesian Conditionalization assume that whenever I become certain of something, it is true. Most people would reject this assumption. In response, Rescorla offers an improved Dutch Book argument for Bayesian Conditionalization that does not make this assumption. My purpose in this paper is two-fold. First, I want to illuminate Rescorla’s new argument by giving a very general Dutch Book argument that applies to many cases of updating beyond those (...) covered by Conditionalization, and then showing how Rescorla’s version follows as a special case of that. Second, I want to show how to generalise R. A. Briggs and Richard Pettigrew’s Accuracy Dominance argument to avoid the assumption that Rescorla has identified (Briggs and Pettigrew in Noûs, 2018). In both cases, these arguments proceed by first establishing a very general reflection principle. (shrink)

Hartry Field has suggested that we should adopt at least a methodological deflationism: [W]e should assume full-fledged deflationism as a working hypothesis. That way, if full-fledged deflationism should turn out to be inadequate, we will at least have a clearer sense than we now have of just where it is that inflationist assumptions ... are needed. I argue here that we do not need to be methodological deflationists. More pre-cisely, I argue that we have no need for a disquotational truth-predicate; (...) that the word true, in ordinary language, is not a disquotational truth-predicate; and that it is not at all clear that it is even possible to introduce a disquotational truth-predicate into ordinary language. If so, then we have no clear sense how it is even possible to be a methodological deflationist. My goal here is not to convince a committed deflationist to abandon his or her position. My goal, rather, is to argue, contrary to what many seem to think, that reflection on the apparently trivial character of T-sentences should not incline us to deflationism. (shrink)

Critics have often misunderstood the higher-order theory (HOT) of consciousness. Here we clarify its position on several issues, and distinguish it from other views such as the global The higher-order theory (HOT) of consciousness has often been misunderstood by critics. Here we clarify its position on several issues, and distinguish it from other views such as the global workspace theory (GWT) and early sensory models (e.g. first-order local recurrency theories). For example, HOT has been criticized for over-intellectualizing consciousness. We show (...) that while higher-order states are cognitively assembled, the requirements are actually considerably less than often presumed. In this sense HOT may be viewed as an intermediate position between GWT and early sensory views. Also, we clarify that most proponents of HOT do not stipulate consciousness as equivalent to metacognition or confidence. Further, compared to other existing theories, HOT can arguably account better for complex everyday experiences, such as of emotions and episodic memories. This makes HOT particularly useful as a framework for conceptualizing pathological mental states. (shrink)

According to certain normative theories in epistemology, rationality requires us to be logically omniscient. Yet this prescription clashes with our ordinary judgments of rationality. How should we resolve this tension? In this paper, I focus particularly on the logical omniscience requirement in Bayesian epistemology. Building on a key insight by Hacking :311–325, 1967), I develop a version of Bayesianism that permits logical ignorance. This includes: an account of the synchronic norms that govern a logically ignorant individual at any given time; (...) an account of how we reduce our logical ignorance by learning logical facts and how we should update our credences in response to such evidence; and an account of when logical ignorance is irrational and when it isn’t. At the end, I explain why the requirement of logical omniscience remains true of ideal agents with no computational, processing, or storage limitations. (shrink)

Conditionalization is one of the central norms of Bayesian epistemology. But there are a number of competing formulations, and a number of arguments that purport to establish it. In this paper, I explore which formulations of the norm are supported by which arguments. In their standard formulations, each of the arguments I consider here depends on the same assumption, which I call Deterministic Updating. I will investigate whether it is possible to amend these arguments so that they no longer depend (...) on it. As I show, whether this is possible depends on the formulation of the norm under consideration. (shrink)

William Alston has written that religious belief is justifiable because it is based upon epistemic practices similar to those justifying belief in sensory facts. In this paper I argue for a different understanding of religious belief. What is called for in religious belief is not affirmation of factual truth-claims but devotion to God. The significance and validity of creedal formulae lie in their capacity to elicit and express such devotion, not in their factual and/or informational character. My paper considers four (...) fundamental questions with respect to religious belief: 1. What is a religious belief? 2. What is the basis upon which one should adopt a religious belief? 3. What is the relation between belief and salvation/sanctification? 4. What attitude should one adopt toward alternate belief systems? I argue that these questions are best answered when we recognize the radical dissimilarity of creedal formulae to empirical truth-claims. (shrink)

Logic has pride of place in mathematics and its 20th century offshoot, computer science. Modern symbolic logic was developed, in part, as a way to provide a formal framework for mathematics: Frege, Peano, Whitehead and Russell, as well as Hilbert developed systems of logic to formalize mathematics. These systems were meant to serve either as themselves foundational, or at least as formal analogs of mathematical reasoning amenable to mathematical study, e.g., in Hilbert’s consistency program. Similar efforts continue, but have been (...) expanded by the development of sophisticated methods to study the properties of such systems using proof and model theory. In parallel with this evolution of logical formalisms as tools for articulating mathematical theories (broadly speaking), much progress has been made in the quest for a mechanization of logical inference and the investigation of its theoretical limits, culminating recently in the development of new foundational frameworks for mathematics with sophisticated computer-assisted proof systems. In addition, logical formalisms developed by logicians in mathematical and philosophical contexts have proved immensely useful in describing theories and systems of interest to computer scientists, and to some degree, vice versa. Three examples of the influence of logic in computer science are automated reasoning, computer verification, and type systems for programming languages. (shrink)

This work is the transcript of a theological dialogue I had with ChatGPT that spanned a couple of days. I began it merely out of curiosity over how ChatGPT might respond to questions and challenges I posed. As it progressed, I became increasingly impressed with the nuance, depth, and relevance of its responses. The dialogue became, for me, something of a contemplative exercise. I still don’t know quite how to understand the ability of generative A.I. to respond with such (apparent) (...) understanding and even insight. -/- I’ve decided to post this dialogue, not only because of the puzzle it poses concerning A.I, but even more, because I believe that the theological conclusions ‘we’ arrived at have real merit. -/- In the end, the theological views expressed here echo those that I’ve expressed in other works of mine, but the expression of these views are enhanced by the way ChatGPT picks up on them, rephrases them, elaborates upon them, and often places them in the context of the classical theological tradition. -/- I might add that I have been an A.I. skeptic for some time now, concerned over the potential dangers of A.I. in general. But this dialogue, anyway, reveals its potential use as a vehicle for reflection, even profound reflection. -/- . (shrink)