This distinguished collection of essays has been produced to honour Donald McKinnon, who retired from the Norris-Hulse Professorship of Divinity in the ...

In this paper, we delve into the significant impact of recent advancements in Artificial Intelligence (AI) on the future landscape of work. We discuss the looming possibility of mass unemployment triggered by AI and the societal repercussions of this transition. Despite the challenges this shift presents, we argue that it also unveils opportunities to mitigate social inequalities, combat global poverty, and empower individuals to follow their passions. Amidst this discussion, we also touch upon the existential question of the purpose of (...) human life in a world where machines predominantly perform work. Additionally, we explore the contentious issue of the moral status and rights of AI entities, contemplating the scenario where machines evolve to become sapient and sentient. The paper concludes with a call to action, emphasizing the necessity to acknowledge these potential outcomes and proactively seek solutions, as part of an inevitable journey through the evolution of human society shared with intelligent machines. (shrink)

The subject of this paper is the philosophical problem of accounting for the relationship between mathematics and non-mathematical reality. The first section, devoted to the importance of the problem, suggests that many of the reasons for engaging in philosophy at all make an account of the relationship between mathematics and reality a priority, not only in philosophy of mathematics and philosophy of science, but also in general epistemology/metaphysics. This is followed by a (rather brief) survey of the major, traditional philosophies (...) of mathematics indicating how each is prepared to deal with the present problem. It is shown that (the standard formulations of) some views seem to deny outright that there is a relationship between mathematics and any non-mathematical reality; such philosophies are clearly unacceptable. Other views leave the relationship rather mysterious and, thus, are incomplete at best. The final, more speculative section provides the direction of a positive account. A structuralist philosophy of mathematics is outlined and it is proposed that mathematics applies to reality though the discovery of mathematical structures underlying the non-mathematical universe. (shrink)

Meaning, Understanding, and Practice is a selection of the most notable essays of an eminent contemporary philosopher on a set of central topics in analytic philosophy. Barry Stroud offers penetrating studies of meaning, understanding, necessity, and the intentionality of thought, with particular reference to the thought of Wittgenstein.

Graham Priest's In Contradiction (Dordrecht: Martinus Nijhoff Publishers, 1987, chapter 3) contains an argument concerning the intuitive, or ‘naïve’ notion of (arithmetic) proof, or provability. He argues that the intuitively provable arithmetic sentences constitute a recursively enumerable set, which has a Gödel sentence which is itself intuitively provable. The incompleteness theorem does not apply, since the set of provable arithmetic sentences is not consistent. The purpose of this article is to sharpen Priest's argument, avoiding reference to informal notions, consensus, or (...) Church's thesis. We add Priest's dialetheic semantics to ordinary Peano arithmetic PA, to produce a recursively axiomatized formal system PA★ that contains its own truth predicate. Whether one is a dialetheist or not, PA★ is a legitimate, rigorously defined formal system, and one can explore its proof‐theoretic properties. The system is inconsistent (but presumably non‐trivial), and it proves its own Gödel sentence as well as its own soundness. Although this much is perhaps welcome to the dialetheist, it has some untoward consequences. There are purely arithmetic (indeed, Π0) sentences that are both provable and refutable in PA★. So if the dialetheist maintains that PA★ is sound, then he must hold that there are true contradictions in the most elementary language of arithmetic. Moreover, the thorough dialetheist must hold that there is a number g which both is and is not the code of a derivation of the indicated Gödel sentence of PA★. For the thorough dialetheist, it follows ordinary PA and even Robinson arithmetic are themselves inconsistent theories. I argue that this is a bitter pill for the dialetheist to swallow. (shrink)

Ethics of Artificial Intelligence This article provides a comprehensive overview of the main ethical issues related to the impact of Artificial Intelligence on human society. AI is the use of machines to do things that would normally require human intelligence. In many areas of human life, AI has rapidly and significantly affected human society … Continue reading Ethics of Artificial Intelligence →.

§1. Overview. Philosophers and mathematicians have drawn lots of conclusions from Gödel's incompleteness theorems, and related results from mathematical logic. Languages, minds, and machines figure prominently in the discussion. Gödel's theorems surely tell us something about these important matters. But what?A descriptive title for this paper would be “Gödel, Lucas, Penrose, Turing, Feferman, Dummett, mechanism, optimism, reflection, and indefinite extensibility”. Adding “God and the Devil” would probably be redundant. Despite the breath-taking, whirlwind tour, I have the modest aim of forging (...) connections between different parts of this literature and clearing up some confusions, together with the less modest aim of not introducing any more confusions.I propose to focus on three spheres within the literature on incompleteness. The first, and primary, one concerns arguments that Gödel's theorem refutes the mechanistic thesis that the human mind is, or can be accurately modeled as, a digital computer or a Turing machine. The most famous instance is the much reprinted J. R. Lucas [18]. To summarize, suppose that a mechanist provides plans for a machine,M, and claims that the output ofMconsists of all and only the arithmetic truths that a human, or the totality of human mathematicians, will ever or can ever know. We assume that the output ofMis consistent. (shrink)

A number of authors have recently weighed in on the issue of whether it is coherent to have bound variables that range over absolutely everything. Prima facie, it is difficult, and perhaps impossible, to coherently state the “relativist” position without violating it. For example, the relativist might say, or try to say, that for any quantifier used in a proposition of English, there is something outside of its range. What is the range of this quantifier? Or suppose we ask the (...) relativist if there are some things that cannot appear in the range of any bound variable. The likely response would be along these lines: “No. For each object o, it possible to include o in the range of quantifiers, but one cannot quantify over everything at once.” This sentence contains unrestricted quantifiers, or so it seems, pending some clever move from a relativist. On the other hand, in the context of set theory, the reasoning behind the Burali-Forti paradox strongly suggests that there are well-orderings strictly longer than the collection of all ordinals. And set theorists regularly do transfinite recursions and transfinite reductions along such well-orderings. The relativist simply points out that one can always define new ordinals, and thus expand the range of one’s bound variables. The purpose of this paper is to explore the iterative framework, proposed in Zermelo’s 1930 paper, “Über Grenzzahlen und Mengenbereiche” (“On boundary numbers and domains of sets”), in order to shed light on these issues, and see what is involved in resolving them. (shrink)

This book discusses five philosophers and writers, Hume, Kierkegaar, Camus, Simone Weil and Dostoevsky, who represents different strands of our cultural inheritance which are all theologically and religiously alive today. What they have in common is willingness to explore the borderlands between belief and unbelief and to review their own position in the light of what those coming from the opposite direction may have to teach them. What they each reject is the sort of caricature which assumes that belief an (...) unbelief and to review their own position in the light of what those coming from the opposite direction may have to teach them. What they each reject is the sort of caricature which assumes that belief and unbelief are two homogeneous wholes which have nothing to say to each other and no ground for common discussion other that that of agnosticism. Equally, however, they disdain the implications that the only possibility of dialogue is a marshmallow middle ground where the only rule is that you avoid saying what you really think. Theologians and believers have often stood back from exploration on this middle ground. Encounters with secular philosophies or systems of belief are risky and dangerous. On the other hand, a theology which avoids such encounters is a much impoverished theology. Professor Sutherland's discussion considers the nature and extent of the risk, and the title of his book indicates where the believers who live close to the boundaries often share more with neighbourly unbelievers than they do with fellow believers who view the pastures of unbelief as far distant and dangerou lands from which they will for ever remain separated. (shrink)

My dissertation consists of two main parts. In the first part, I begin by assuming the plausibility of the libertarian thesis that agents sometimes could have done otherwise than they did given the very same history of the world. In light of this assumption, I undertake to develop a model of agency which does not employ the concept of agent-causation. My agency theory is developed in three main stages: I suggest that any agency theory must satisfy four desiderata: It must (...) adequately account for the freedom and responsibility of human agents. It must provide an adequate answer to the question of what distinguishes human actions from mere happenings. It must adequately account for the epistemological fact that human agents have an immediate and nonobservational awareness of their actions. It should have the support of a respectable philosophical tradition. I argue that agent-causation provides a theory of agency which fails adequately to satisfy these four desiderata. I claim both that human actions are uncaused exercisings by agents of their powers and that human agents typically act for reasons. I maintain that the central issue dividing agency theorists and nonagency theorists is whether reasons for performing actions cause the latter. I maintain that the sense of 'because' in 'I did x because...' is not causal in nature, but teleological. ;Having developed my model of agency, in the second part of my dissertation I investigate what are some of the paradigmatic actions human agents perform. I claim that bodily actions, such as moving an arm, are psychological in nature. Essential to my argument is the concept of a body-image. A normal agent 'feels' as if she is present in her physical arm. The way a normal agent feels is revealed in the case of a phantom limb. The subject of a phantom arm feels as if her amputated physical arm is still there and she can move while feeling armishly. I maintain that the bodily action of moving an arm is the agent's movement as a psychological arm-image of her physical arm, whether the physical arm is present or not. (shrink)

A team of two brothers enters a baking contest. Their cake wins the first-place prize of £500. Will they demand £500 each? Of course not. Winners must split the prize. We often ignore this when we claim credit for team accomplishments. We take more credit than we deserve. I apply this idea to baking competitions and academic production but it applies equally to other arenas with teams of varying sizes.Export citation.

This essay concerns Adorno's articulation of an idea of philosophy as it is developed through his considerations of philosophy's form or mode of presentation. It hereby attempts to illuminate some of what remains obscure about Adorno's understanding of a renewal of philosophy after Marx and the crisis of German Idealism. Various forms–from "anti-system" and "constellation" to "essay," "fragment," "encyclopaedia" and "dictionary"–are examined for what they contribute to an idea of philosophy. This focus distinguishes this essay from other studies of form (...) in Adorno that have predominantly literary or musical concerns. (shrink)

The purpose of this paper is to present a thought experiment and argument that spells trouble for “radical” deflationism concerning meaning and truth such as that advocated by the staunch nominalist Hartry Field. The thought experiment does not sit well with any view that limits a truth predicate to sentences understood by a given speaker or to sentences in (or translatable into) a given language, unless that language is universal. The scenario in question concerns sentences that are not understood but (...) are known to be logical consequences of known and understood sentences. Ultimately, the issue turns on the notion of logical consequence that is available to various versions of deflationism. (shrink)

In this paper, I develop a noncausal view of agency. I defend the thesis that choices are uncaused mental actions and maintain, contrary to causal theorists of action, that choices differ intrinsically or inherently from nonactions. I explain how they do by placing them in an ontology favored by causal agency theorists (agent-causationists). This ontology is one of powers and liabilities.After explicating how a choice is an uncaused event, I explain how an adequate account of freedom involves the concept of (...) choosing for a reason. Choosing for a reason is a teleological notion, and I set forth what is involved in making a choice for a purpose. (shrink)

Argues against naturalism, or the idea that natural physical processes explain everything, the mind and soul do not exist, and consciousness and causality may have no basis, and suggests that it does not account for human--or any--action.

The purpose of this article is to delimit what can and cannot be claimed on behalf of second-order logic. The starting point is some of the discussions surrounding my Foundations without Foundationalism: A Case for Secondorder Logic.