In Wollstonecraft’s early writings, she articulates the foundational theological and philosophical principles that would underpin her work throughout her career. One difference between her early and later work lies in the way that the values to which she refers are combined. Whereas Wollstonecraft at first appeals to the separate ideals of independence, equality, and virtue, from the 1790s onwards she integrates these into a characteristic republican framework that was in common use amongst dissenting theorists at the time. The set of (...) values on which Wollstonecraft draws, and the version of the republican framework that she develops, closely resemble those of Richard Price with whose work she was familiar. Examining the structural similarities between their respective models, I argue, gives us an insight into the systematic manner of aspects of Wollstonecraft’s own thought. It also allows us to see how Wollstonecraft goes beyond the republicanism of Price and others as she develops her own feminist solutions to the problems of structural domination. (shrink)

There are two opposing views concerning intuitive cases of wage exploitation. The first denies that they are cases of exploitation at all. It is based on the nonworseness claim: there is nothing wrong with a discretionary mutually beneficial employment relationship. The second is the reasonable view: some employment relationships can be exploitative even if employers have no duty towards their employees. This article argues that the reasonable view does not completely defeat defences of wage exploitation, because these do not rely (...) solely on the nonworseness claim. They also rely on the idea, popularised by Alan Wertheimer, that exploitation is a form of disequilibrium price occurring in defective markets. The article then proceeds to criticise Wertheimer’s account through neoclassical, new institutional, and Austrian economics. It concludes that considerations for economic efficiency are irrelevant to assessing intuitions regarding exploitation. (shrink)

This paper takes up Huw Price׳s challenge to develop a retrocausal toy model of the Bell-EPR experiment. I develop three such models which show that a consistent, local, hidden-variables interpretation of the EPR experiment is indeed possible, and which give a feel for the kind of retrocausation involved. The first of the models also makes clear a problematic feature of retrocausation: it seems that we cannot interpret the hidden elements of reality in a retrocausal model as possessing determinate dispositions (...) to affect the outcome of experiments. This is a feature which Price has embraced, but Gordon Belot has argued that this feature renders retrocausal interpretations “unsuitable for formal development”, and the lack of such determinate dispositions threatens to undermine the motivation for hidden-variables interpretations in the first place. But Price and Belot are both too quick in their assessment. I show that determinate dispositions are indeed consistent with retrocausation. What is more, I show that the ontological economy allowed by retrocausation holds out the promise of a classical understanding of spin and polarization. (shrink)

This is my Cambridge PhD thesis, written under the supervision of Hugh Mellor and Richard Healey, and examined by Mary Hesse and Simon Blackburn. It addresses what it takes to be the core of the problem of single case probability, namely, the interpretation of claims such as ‘It is probable that P’ (where the probabilistic component occurs as a sentential or propositional operator). I argue that claims of this form are not genuinely truth-apt, and that such operators modify the (...) force, rather than the sense, of sentences or propositions to which they attach. In contemporary terms, I thus defend a version of what Yalcin (2012) has called ‘credal expressivism’. Some of the core arguments were later published in the following papers: (i) ‘Does “Probably” modify sense?’, Australasian Journal of Philosophy 61(1983), 396–408 and (ii) 'Mellor, chance and the single case', British Journal for the Philosophy of Science 35(1984), 11-23. Other arguments, including an attempt at the Frege-Geach problem, form the basis of an unpublished piece 'The use of force in a theory of meaning' (1983), accessible at PhilPapers. (shrink)

The Dutch Book Argument for Probabilism assumes Ramsey's Thesis (RT), which purports to determine the prices an agent is rationally required to pay for a bet. Recently, a new objection to Ramsey's Thesis has emerged (Hedden 2013, Wronski & Godziszewski 2017, Wronski 2018)--I call this the Expected Utility Objection. According to this objection, it is Maximise Subjective Expected Utility (MSEU) that determines the prices an agent is required to pay for a bet, and this often disagrees with Ramsey's Thesis. I (...) suggest two responses to Hedden's objection. First, we might be permissive: agents are permitted to pay any price that is required or permitted by RT, and they are permitted to pay any price that is required or permitted by MSEU. This allows us to give a revised version of the Dutch Book Argument for Probabilism, which I call the Permissive Dutch Book Argument. Second, I suggest that even the proponent of the Expected Utility Objection should admit that RT gives the correct answer in certain very limited cases, and I show that, together with MSEU, this very restricted version of RT gives a new pragmatic argument for Probabilism, which I call the Bookless Pragmatic Argument. (shrink)

Book review of Richard A. Richards' The Species Problem: A Philosophical Analysis.

Pragmatism’s heartening recent revival (spearheaded by Richard Rorty’s bold intervention into analytic philosophy Philosophy and the Mirror of Nature) has coalesced into a distinctive philosophical movement frequently referred to as ‘neopragmatism’. This movement interprets the very meaning of pragmatism as rejection of metaphysical commitments: our words do not primarily serve to represent non-linguistic entities, but are tools to achieve a range of human purposes. A particularly thorough and consistent version of this position is Huw Price’s global expressivism. We (...) here critically appraise Price’s understanding of a commitment to pragmatism as a rejection of metaphysics, and argue that such rejection is not as easy or desirable as Price claims. First we argue that Price’s global expressivism itself draws on significant metaphysical assumptions (a ‘word-world’ dualism, and a nominalism concerning the meaning of general terms). Then we seek to resolve neopragmatist anxieties about metaphysics by arguing that metaphysics is indispensable for pragmatist philosophizing insofar as it seeks ways for human beings to realise themselves through practices of understanding reality and their place in it. If, as we argue, metaphysics consists in a maximally general inquiry into the nature and structure of reality, to try to block it seems a puzzling exercise in epistemic self-harm. (shrink)

This paper is a critique of coercive theories of meaning, that is, theories (or criteria) of meaning designed to do down ones opponents by representing their views as meaningless or unintelligible. Many philosophers from Hobbes through Berkeley and Hume to the pragmatists, the logical positivists and (above all) Wittgenstein have devised such theories and criteria in order to discredit their opponents. I argue 1) that such theories and criteria are morally obnoxious, a) because they smack of the totalitarian linguistic tactics (...) of the Party in Orwell’s 1984 and b) because they dehumanize the opposition by portraying them as mere spouters of gibberish; 2) that they are profoundly illiberal since if true, they would undermine Mill’s arguments for free speech; 3) that such theories are prone to self-contradiction, pragmatic and otherwise; 4) that they often turn against their creators including what they were meant to exclude and excluding what they were meant to include; 5) that such theories are susceptible to a modus tollens pioneered by Richard Price in his Review Concerning the Principle Questions of Morals(1758); and 6) that such theories are prima facie false since they fail to ‘predict’ the data that is it their business to explain (or, in the case of criteria, fail to capture the concept that they allegedly represent). The butcher’s bill is quite considerable: some of Hobbes, a fair bit of Locke, half of Berkeley, large chunks of Hume, Russell's Theory of Types, verificationism in its positivist and Dummettian variants, much of pragmatism and most of Wittgenstein - all these have to be sacrificed if we are to save our souls as philosophic liberals. (shrink)

The article discusses the varying conceptions of the faculty of ‘the understanding’ in 18th-century British philosophy and logic. Topics include the distinction between the understanding and the will, the traditional division of three acts of understanding and its critics, the naturalizing of human understanding, conceiving of the limits of human understanding, British innatism and the critique of empiricist conceptions of the understanding, and reconceiving the understanding and the elimination of scepticism. Authors discussed include Richard Price, James Harris, Zachary (...) Mayne, Edward Bentham, Isaac Watts, Dugald Stewart, John Norris—as well as Locke, Berkeley, Hume and Reid. (shrink)

In their recent paper, “Epistemology for Beginners: Two to Five-Year-Old Children’s Representation of Falsity,” Olivier Mascaro and Olivier Morin study the ontogeny of a naïve understanding of truth in humans. Their paper is fascinating for several reasons, but most striking is their claim (given a rather optimistic reading of epistemology) that toddlers as young as two can, at times, recognize false from true assertions. Their Optimistic Epistemology Hypothesis holds that children seem to have an innate capacity to represent a state (...) of affairs truthfully. In the following paper, I investigate the problems this research poses for deflationist theories of truth. Richard Rorty and Huw Price hold that the best way to understand truth or “the truth” is to understand the necessary conditions required for assertoric practice. Both philosophers present unique and very different deflationary theories when it comes to construing truth. I argue that neither philosopher’s approach is successful because they focus on truth and fail to recognize truthfulness as a norm of assertoric practice. I show that truthfulness is the elusive third norm of claim-based discourse and is consistent with Mascaro and Morin’s findings. (shrink)

Review of: Robert J. Richards and Michael Ruse: Debating Darwin. University of Chicago Press, Chicago. 2016. ISBN: 9780226384429, 320 pages, price: $30.00 (hardcover).

This review of Richard Tuck's Free Riding conveys Tuck's crucial distinction between the logic of collective action which fails due to the problem of causal negligibility, and free riding, which has been modeled as a Prisoner's Dilemma and involves casually impacting another actor in an adverse manner. Tuck also distinguishes the practice of voting which he argues neither fails due to the worry of causal negligibility or due to free riding; instead it represents a problem of achieving sufficiency of (...) votes representing a minimum winning coalition. This article clarifies how the problem of collective action resembles perfect free market competition which is defined to be characterized by a state in which no single agent can impact the price of a good. Similarly, in a large scale collective action, no single actor can have a causal impact on the outcome of the vast enterprise. This inability to make a difference due to the negligibility of each individual's causal power differentiates collective action and the tragedy of the commons from other social problems. (shrink)

Evidentialism as its leading proponents describe it has two distinct senses, these being evidentialism as a conceptual analysis of epistemic justification, and as a prescriptive ethics of belief—an account of what one ‘ought to believe’ under different epistemic circumstances. These two senses of evidentialism are related, but in the work of leading evidentialist philosophers, in ways that I think are deeply problematic. Although focusing on Richard Feldman’s ethics of belief, this chapter is critical of evidentialism in both senses. However, (...) I share with authors like Feldman and Earl Conee, that epistemology has important prescriptive functions, and that a sound, civic ethics of belief is of more than merely philosophic importance. One reason why an ethics of belief might be important to problems of practice is the need we have for tools to more effectively mediate the renewed round of ‘culture wars’ we are experiencing in Anglo-American cultures. I mean especially that grand cultural clash between science and religion, reason and faith, secularist atheism and religious fundamentalism, etc. Let us start with the genealogical question of why there is such a grand cultural debate in the first place, and why the debate especially as played out in public and popular forums and even in the courtrooms seems so volatile and so often to confusedly drag everything—beliefs, values, passions, etc., with it. These are questions that I think Sigmund Freud’s classic Civilization and its Discontents can help us understand. Freud was a major voice in criticism of the stern and often hypocritical Victorian morality, a voice pointing out the price of its sometimes high-handed, guiltinducing curtailments of the satisfactions sought by the individual. But for Freud while there are real differences in the moral demands that different societies or traditions place upon people, there is something inevitable about the conflict itself, for “replacement of the power of the individual by the power of a community constitutes the decisive step of civilization... (shrink)

Propositional temporalism is the view that there are temporary propositions: propositions that are true, but not always true. Factual futurism is the view that there are futurist facts: facts that obtain, but that will at some point not obtain. Most A-theoretic views in the philosophy of time are committed both to propositional temporalism and to factual futurism. Mark Richard, Jeffrey King and others have argued that temporary propositions are not fit to be the contents of propositional attitudes, or to (...) be the semantic values of natural language utterances. But these discussions have overlooked another role that the A-theorist’s posits struggle to play: the role of facts in explaining other facts. Focusing on the case of action explanation by reasons, this paper presents the challenge that explanation poses for factual futurism. It then brings that challenge to bear against propositional temporalism and the A-theory more generally. My argument saddles the factual futurist with surprising commitments concerning reasons, facts and explanation. The futurist might accept those commitments and pay the price. The alternative – which I prefer – is to reject factual futurism, and with it the A-theory. (shrink)

Can new technology enhance purpose-driven, democratic dialogue in groups, governments, and societies? Online Deliberation: Design, Research, and Practice is the first book that attempts to sample the full range of work on online deliberation, forging new connections between academic research, technology designers, and practitioners. Since some of the most exciting innovations have occurred outside of traditional institutions, and those involved have often worked in relative isolation from each other, work in this growing field has often failed to reflect the full (...) set of perspectives on online deliberation. This volume is aimed at those working at the crossroads of information/communication technology and social science, and documents early findings in, and perspectives on, this new field by many of its pioneers. -/- CONTENTS: -/- Introduction: The Blossoming Field of Online Deliberation (Todd Davies, pp. 1-19) -/- Part I - Prospects for Online Civic Engagement -/- Chapter 1: Virtual Public Consultation: Prospects for Internet Deliberative Democracy (James S. Fishkin, pp. 23-35) -/- Chapter 2: Citizens Deliberating Online: Theory and Some Evidence (Vincent Price, pp. 37-58) -/- Chapter 3: Can Online Deliberation Improve Politics? Scientific Foundations for Success (Arthur Lupia, pp. 59-69) -/- Chapter 4: Deliberative Democracy, Online Discussion, and Project PICOLA (Public Informed Citizen Online Assembly) (Robert Cavalier with Miso Kim and Zachary Sam Zaiss, pp. 71-79) -/- Part II - Online Dialogue in the Wild -/- Chapter 5: Friends, Foes, and Fringe: Norms and Structure in Political Discussion Networks (John Kelly, Danyel Fisher, and Marc Smith, pp. 83-93) -/- Chapter 6: Searching the Net for Differences of Opinion (Warren Sack, John Kelly, and Michael Dale, pp. 95-104) -/- Chapter 7: Happy Accidents: Deliberation and Online Exposure to Opposing Views (Azi Lev-On and Bernard Manin, pp. 105-122) -/- Chapter 8: Rethinking Local Conversations on the Web (Sameer Ahuja, Manuel Pérez-Quiñones, and Andrea Kavanaugh, pp. 123-129) -/- Part III - Online Public Consultation -/- Chapter 9: Deliberation in E-Rulemaking? The Problem of Mass Participation (David Schlosberg, Steve Zavestoski, and Stuart Shulman, pp. 133-148) -/- Chapter 10: Turning GOLD into EPG: Lessons from Low-Tech Democratic Experimentalism for Electronic Rulemaking and Other Ventures in Cyberdemocracy (Peter M. Shane, pp. 149-162) -/- Chapter 11: Baudrillard and the Virtual Cow: Simulation Games and Citizen Participation (Hélène Michel and Dominique Kreziak, pp. 163-166) -/- Chapter 12: Using Web-Based Group Support Systems to Enhance Procedural Fairness in Administrative Decision Making in South Africa (Hossana Twinomurinzi and Jackie Phahlamohlaka, pp. 167-169) -/- Chapter 13: Citizen Participation Is Critical: An Example from Sweden (Tomas Ohlin, pp. 171-173) -/- Part IV - Online Deliberation in Organizations -/- Chapter 14: Online Deliberation in the Government of Canada: Organizing the Back Office (Elisabeth Richard, pp. 177-191) -/- Chapter 15: Political Action and Organization Building: An Internet-Based Engagement Model (Mark Cooper, pp. 193-202) -/- Chapter 16: Wiki Collaboration Within Political Parties: Benefits and Challenges (Kate Raynes-Goldie and David Fono, pp. 203-205) -/- Chapter 17: Debian’s Democracy (Gunnar Ristroph, pp. 207-211) -/- Chapter 18: Software Support for Face-to-Face Parliamentary Procedure (Dana Dahlstrom and Bayle Shanks, pp. 213-220) -/- Part V - Online Facilitation -/- Chapter 19: Deliberation on the Net: Lessons from a Field Experiment (June Woong Rhee and Eun-mee Kim, pp. 223-232) -/- Chapter 20: The Role of the Moderator: Problems and Possibilities for Government-Run Online Discussion Forums (Scott Wright, pp. 233-242) -/- Chapter 21: Silencing the Clatter: Removing Anonymity from a Corporate Online Community (Gilly Leshed, pp. 243-251) -/- Chapter 22: Facilitation and Inclusive Deliberation (Matthias Trénel, pp. 253-257) -/- Chapter 23: Rethinking the ‘Informed’ Participant: Precautions and Recommendations for the Design of Online Deliberation (Kevin S. Ramsey and Matthew W. Wilson, pp. 259-267) -/- Chapter 24: PerlNomic: Rule Making and Enforcement in Digital Shared Spaces (Mark E. Phair and Adam Bliss, pp. 269-271) -/- Part VI - Design of Deliberation Tools -/- Chapter 25: An Online Environment for Democratic Deliberation: Motivations, Principles, and Design (Todd Davies, Brendan O’Connor, Alex Cochran, Jonathan J. Effrat, Andrew Parker, Benjamin Newman, and Aaron Tam, pp. 275-292) -/- Chapter 26: Online Civic Deliberation with E-Liberate (Douglas Schuler, pp. 293-302) -/- Chapter 27: Parliament: A Module for Parliamentary Procedure Software (Bayle Shanks and Dana Dahlstrom, pp. 303-307) -/- Chapter 28: Decision Structure: A New Approach to Three Problems in Deliberation (Raymond J. Pingree, pp. 309-316) -/- Chapter 29: Design Requirements of Argument Mapping Software for Teaching Deliberation (Matthew W. Easterday, Jordan S. Kanarek, and Maralee Harrell, pp. 317-323) -/- Chapter 30: Email-Embedded Voting with eVote/Clerk (Marilyn Davis, pp. 325-327) -/- Epilogue: Understanding Diversity in the Field of Online Deliberation (Seeta Peña Gangadharan, pp. 329-358). -/- For individual chapter downloads, go to odbook.stanford.edu. (shrink)

Can the so-ca\led first incompleteness theorem refer to itself? Many or maybe even all the paradoxes in mathematics are connected with some kind of self-reference. Gбdel built his proof on the ground of self-reference: а statement which claims its unprovabllity. So, he demonstrated that undecidaЬle propositions exist in any enough rich axiomatics (i.e. such one which contains Peano arithmetic in some sense). What about the decidabllity of the very first incompleteness theorem? We can display that it fulfills its conditions. That's (...) why it can Ье applied to itself, proving that it is an undecidaЬle statement. It seems to Ье а too strange kind of proposition: its validity implies its undecidabllity. If the validity of а statement implies its untruth, then it is either untruth (reductio ad absurdum) or an antinomy (if also its negation implies its validity). А theory that contains а contradiction implies any statement. Appearing of а proposition, whose validity implies its undecidabllity, is due to the statement that claims its unprovability. Obviously, it is а proposition of self-referential type. Ву Gбdel's words, it is correlative with Richard's or liar paradox, or even with any other semantic or mathematical one. What is the cost, if а proposition of that special kind is used in а proof? ln our opinion, the price is analogous to «applying» of а contradictory in а theory: any statement turns out to Ье undecidaЬ!e. Ifthe first incompleteness theorem is an undecidaЬ!e theorem, then it is impossiЬle to prove that the very completeness of Peano arithmetic is also an tmdecidaЬle statement (the second incompleteness theorem). Hilbert's program for ап arithmetical self-foundation of matheшatics is partly rehabllitated: only partly, because it is not decidaЬ!e and true, but undecidaЬle; that's wby both it and its negation шау Ье accepted as true, however not siшultaneously true. The first incompleteness theoreш gains the statute of axiom of а very special, semi-philosophical kind: it divides mathematics as whole into two parts: either Godel шathematics or Нilbert matheшatics. Нilbert's program of self-foundation ofmatheшatic is valid only as to the latter. (shrink)

The choices we make in our daily lives have consequences that span the oceans: many consumers are not aware that some of the most exotic foods which belong to our breakfast plates every single day, such as coffee or chocolate, have a profound impact on the lives of many people. In Western societies, we are used to eating and consuming fresh ingredients which sprout on a different continent, yet we are unable to see the very hands that carry a simple (...) thing as a banana to our tables, as a consequence of a global supply chain. This alienation from the places and people involved in the supply chain leads consumers to ignore the impact of producing some foods and enabling them to travel all the way to one’s table. What is regarded as a simple commodity, in fact, is a result of the labour and exploitation of many families and crops on the other side of the ocean. Modern slavery comes in many guises and is often obscured by the alienation of modern consumers from their products, an example of which includes the slave system that holds many people tied behind our food chains. As consumers, we unconsciously become commissioners of a system of inequality and exploitation which we ignore. This includes many ‘fair-trade’ certified products, which are employed by multinationals as a psychological marketing tactic. This phenomenon is described by the cultural anthropologist Richard Robbins (2013) as the ‘commodification of morality’, where even commitments to just, fair or sustainable practices have been monopolised by economic agents. Within this framework, our moral choices are put on the market with a price which rarely returns or reflects the true cost of such products. This article begins by defining modern slavery, proceeding with a particular focus on forced labour in the current neoliberal regime. This is then contextualised in the case study of bananas as one of the most consumed, yet furthest grown, items of Western diets. The article then analyses the ethical backdrop of economic practices, using the fair-trade movement as a synecdoche of the moral economy of our day. The main question raised within this analysis is to what extent our moral choices can contribute to exploitation or to social change, and how our way of eating can oppose the great inequalities that still exist in the present context. (shrink)

In connecting embodied, embedded, extended, and enactive (4E) cognition with affectivity and emotions, the framework of “situated affectivity” has recently emerged. This framework emphasizes the interactions between the emoter and the environment in the unfolding of our affective lives (Colombetti and Krueger 2015; Griffiths and Scarantino 2009; Piredda 2022; Stephan and Walter 2020). In the last decades, there has also been a growing interest in the philosophical analysis of technology and artifacts (Houkes and Vermaas 2010; Margolis and Laurence 2007; Preston (...) 2022). The aim of this special issue is to foster the interaction between philosophical reflections on affectivity and those on technology, further developing this fruitful borderland (Clowes et al. 2021; Colombetti 2020; Fasoli 2018; Krueger and Osler 2019; Heersmink 2018; Piredda and Candiotto 2019; Piredda 2020; Viola 2021). -/- . (shrink)

Pragmatist approaches to truth have often been judged in light of a caricature of William James’ claim that, “the ‘true’ is only the expedient in our way of thinking”. This unfortunate caricature, where truth is claimed to be ‘whatever it’s useful to believe’, means pragmatist theories of truth are generally seen as non-starters, or unworthy of serious attention. And even leaving aside stalking-horse versions of classical pragmatism, there is also a view that whatever contemporary pragmatists have been doing with ‘truth’ (...) it bears little resemblance to the projects that concern analytic philosophers. For example, Rorty’s frequent exhortations for pragmatists to turn their back on truth and look... (shrink)

By definition, pain is a sensory and emotional experience that is felt in a particular part of the body. The precise relationship between somatic events at the site where pain is experienced, and central processing giving rise to the mental experience of pain remains the subject of debate, but there is little disagreement in scholarly circles that both aspects of pain are critical to its experience. Recent experimental work, however, suggests a public view that is at odds with this conceptualisation. (...) By demonstrating that the public does not necessarily endorse central tenets of the “mental” view of pain (subjectivity, privacy, and incorrigibility), experimental philosophers have argued that the public holds a more “body-centric” view than most clinicians and scholars. Such a discrepancy would have important implications for how the public interacts with pain science and clinical care. In response, we tested the hypothesis that the public is capable of a more “mind-centric” view of pain. Using a series of vignettes, we demonstrate that in situations which highlight mental aspects of pain the public can, and does, recognize pain as a mental phenomenon. We also demonstrate that the public view is subject to context effects, by showing that the public’s view is modified when situations emphasizing mental and somatic aspects of pain are presented together. (shrink)

A discussion of the recent prominence of 'new atheism' and 'Christian nationalism' in the United States.

This paper discusses the nature of, problems for, and benefits delivered by fictionalist strategies in metaphysics.

Hofweber (Ontology and the ambitions of metaphysics, Oxford University Press, 2016) argues for a thesis he calls “internalism” with respect to natural number discourse: no expressions purporting to refer to natural numbers in fact refer, and no apparent quantification over natural numbers actually involves quantification over natural numbers as objects. He argues that while internalism leaves open the question of whether other kinds of abstracta exist, it precludes the existence of natural numbers, thus establishing what he calls “restricted nominalism” about (...) natural numbers. We argue that Hofweber’s internalism fails to establish restricted nominalism. Not only is his primary argument for restricted nominalism invalid, the analysis of quantification proposed threatens to collapse internalism into either a traditional form of error theory or realism. (shrink)

In his influential book 'Making Things Happen' and in other places, Jim Woodward has noted some affinities between his own account of causation and that of Menzies and Price, but argued that the latter view is implausibly ‘subjective’. In this piece I discuss Woodward’s criticisms. I argue that the Menzies and Price view is not as different from Woodward’s own account as he believes, and that in so far as it is different, it has some advantages whose importance (...) Woodward misses; but also that the Menzies and Price view lacks some elements whose importance Woodward rightly stresses. When properly characterized, however, the ‘subjectivity’ survives unscathed. (shrink)

Three recent research reports by Topping and Trickey, by Fair and colleagues, and by Gorard, Siddiqui and Huat See have produced data that support the conclusion that a Philosophy for Children program of one-hour-per-week structured discussions has a marked positive impact on students. This article presents data from a follow up study done three years after the completion of the study reported in Fair et al.. The data show that the positive gains in scores on the Cognitive Abilities Test were (...) still present and had not faded after three years. Given the strength of these confirmations of the positive durable impact of the P4C program of structured discussions and given the relatively low cost of implementing the P4C program, it is recommended that it become a standard part of the school curriculum. (shrink)

Ethical issues of information and communication technologies (ICTs) are important because they can have significant effects on human liberty, happiness, their ability to lead a good life. They are also of functional interest because they can determine whether technologies are used and whether their positive potential can unfold. For these reasons policy makers are interested in finding out what these issues are and how they can be addressed. The best way of creating ICT policy that is sensitive to ethical issues (...) would be to be proactive and address such issues at early stages of the technology life cycle. The present paper uses this position as a starting point and discusses how knowledge of ethical aspects of emerging ICTs can be gained. It develops a methodology that goes beyond established futures methodologies to cater for the difficult nature of ethical issues. The paper goes on to outline some of the preliminary findings of a European research project that has applied this method. (shrink)

Higher-order theories of consciousness typically account for introspection in terms of one's higher-order thoughts being conscious, which would require a third-order thought — i.e.a thought about a thought about a mental state. In this work, we offer an alternative account of introspection that builds on the recent HigherOrder Representation of a Representation (HOROR) theory of phenomenal consciousness. According to HOROR theory, phenomenal consciousness consists in having the right kind of higher-order representation. We claim that this theory can be extended to (...) introspection by recognizing that there is a distinctive kind of consciousness — i.e. introspective consciousness — which can be accounted for as the theory does for phenomenal consciousness generally. We call this novel view: Higher-Order Representation Intentionally For Introspective Consciousness (HORIFIC). We argue that there are independent reasons for thinking that introspective consciousness can be either 'stimuli-induced' or 'self-triggered' and that one of the benefits of the view we develop is that it can embrace a pluralist approach. Our view also accounts for what specific mental state is represented by a particular higher-order representation, and for the way in which we are aware of changes, transitions, and boundaries between mental states in specific cases of introspective consciousness. (shrink)

This is the second part of my theological dialogue with ChatGPT on the meaning of God. We explore the nature of God's agency, will, goodness, the problem of evil and suffering, the meaning of sin, and the meaning and nature of the redemptive act of Christ.

Some of the most important developments of symbolic logic took place in the 1920s. Foremost among them are the distinction between syntax and semantics and the formulation of questions of completeness and decidability of logical systems. David Hilbert and his students played a very important part in these developments. Their contributions can be traced to unpublished lecture notes and other manuscripts by Hilbert and Bernays dating to the period 1917-1923. The aim of this paper is to describe these results, focussing (...) primarily on propositional logic, and to put them in their historical context. It is argued that truth-value semantics, syntactic ("Post-") and semantic completeness, decidability, and other results were first obtained by Hilbert and Bernays in 1918, and that Bernays's role in their discovery and the subsequent development of mathematical logic is much greater than has so far been acknowledged. (shrink)

我们必须记住的第一件事是，当说中国这样说或中国这样做时，我们不是说中国人民，而是控制中国共产党的社会路径者，即七大社会病态连环杀手。中共常务委员会或中央政治局委员等25人。 中共对三战和全面统治的计划在中国政府的出版物和演讲中已经非常明确地阐述了，这就是习近平的"中国梦"。只有统治中国的少数人（也许只有几十到几百人）的梦想，也是其他人（包括14亿中国人 ）的噩梦。每年100亿美元使他们或他们的傀儡拥有或控制报纸、杂志、电视和广播频道，每天在世界各地的大多数主要媒体上放置假新闻。 此外，他们有一支军队（也许有数百万人），他们滚动所有媒体进行更多的宣传，淹没合法的评论（50美分的军队）。 除了剥夺第三世界的资源外，数万亿美元的"一带一路"倡议的主要主旨是在全世界建立军事基地。他们迫使自由世界陷入大规模的高科技军备竞赛，使得与苏联的冷战看起来像是野餐。 尽管SSSSK和世界上其他的军事国家都在高级硬件上花费巨资，但WW3（或导致它的小型交战）很可能以软件为主。SSSSK，可能有更多的黑客（编码器）为他们工作，然后世界其他国家加起来，通过通过网络瘫痪他 们的敌人，以最小的物理冲突赢得未来的战争。"没有卫星，没有电话，没有通讯，没有金融交易，没有电网，没有互联网，没有先进的武器，没有车辆，火车，船舶和飞机。 罢免中共只有两条主要途径，即释放14亿中国囚犯，结束向第三次世界大战的疯狂进军。 和平的一个方案是发动一场全面的贸易战来摧毁中国经济，直到军方受够了，把中共赶出去。 关闭中国经济的替代方案是一场有限的战争，比如在中共第20届大会上，50架热压无人机进行有针对性的打击，当时所有高层成员都在一个地方，但这种情况要到2022年才会发生。一个可以击中年度全体会议。 袭击发生后，中国人将被告知，他们必须放下武器，准备举行民主选举，否则就要进入石器时代。另一种选择是全面核攻击。 鉴于中共目前的路线，军事对抗是不可避免的。 几十年后，这种情况可能会发生在南中国海或台湾的岛屿上，但随着它们在世界各地建立军事基地，它可能发生在任何地方（见"卧虎藏"等）。 未来的冲突将有硬性与软性方面与中共的既定目标，强调网络战争，通过黑客和瘫痪控制系统的所有军事和工业通信，设备，发电厂，卫星，互联网，银行，以及连接到网络的任何设备或车辆。 SS正在缓慢地部署一系列全球载人和自主水面和水下潜艇或无人驾驶飞机，这些潜艇或无人机能够发射可能处于休眠状态，等待中国发出信号，甚至寻找美国船只或飞机的签名。 在摧毁我们的卫星，从而消除美国和我们全球部队之间的通信的同时，他们将使用他们的卫星，与无人机一起瞄准和摧毁我们目前优越的海军部队。 当然，所有这一切都是越来越多地由AI自动完成的。 到目前为止，中共最大的盟友是美国民主党。 选择是现在停止中共，或者看着他们把中国监狱扩展到全世界。 当然，对我们的生活进行普遍监控和数字化是不可避免的。任何不这么认为的人，都是极度脱节的。 当然，正是那些期待中国社会路径者统治世界的人，而悲观主义者（他们认为自己是现实主义者）则期望AI的社会病态 （或我称之为"假愚蠢"或"人造社会病态"）的选择性。）接管，也许到2030年。 那些有兴趣在现代社会的疯狂道路的进一步细节可能会参考我的其他作品，如自杀的民主-美国和世界第三版2019年和自 杀乌托邦幻想在21日世纪：哲学、人性与文明的崩溃（2019）.

ホフスタッター牧師による原理主義自然主義教会からの最新の説教。彼のはるかに有名な(または容赦ない哲学的誤りで悪名高い)作品ゴーデル、エッシャー、バッハのように、それは表面的な妥当性を持っていますが、こ れが哲学的なものと実際の科学的問題を混ぜ合わせた横行するサイエンティズムであることを理解すれば(つまり、唯一の本当の問題は、私たちがプレイすべき言語ゲームです)、その後、ほとんどすべての関心が消えます 。進化心理学とヴィトゲンシュタインの仕事に基づく分析のフレームワークを提供しています(最近の著作で更新されて以来)。 現代の2つのシス・エムスの見解から人間の行動のための包括的な最新の枠組みを望む人は、私の著書「ルートヴィヒ・ヴィトゲンシュタインとジョン・サールの第2回(2019)における哲学、心理学、ミンと言語の論 理的構造」を参照することができます。私の著作の多くにご興味がある人は、運命の惑星における「話す猿--哲学、心理学、科学、宗教、政治―記事とレビュー2006-2019 第3回(2019)」と21世紀4日(2019年)の自殺ユートピア妄想st Century 4th ed (2019)などを見ることができます .

Wie wäre es mit einer anderen Ausg. der Reichen und Berühmten? Zuerst das Offensichtliche – die Harry-Potter-Romane sind primitiver Aberglaube, der Kinder dazu ermutigt, an Fantasie zu glauben, anstatt Verantwortung für die Welt zu übernehmen – natürlich die Norm. JKR ist genauso ahnungslos über sich und die Welt wie die meisten Menschen,aber etwa 200 Mal so destruktiv wie der durchschnittliche Amerikaner und etwa 800 Mal mehr als der durchschnittliche Chinese. Sie war verantwortlich für die Zerstörung von vielleicht 30.000 Hektar Wald, (...) um diese Müllromane zu produzieren, und die ganze Erosion, die sich daraus ergibt (nicht trivial, da esmindestens 6 und vielleicht 12 Tonnen/Jahr Boden in den Ozean für alle auf der Erde oder vielleicht 100 Tonnen pro Amerikaner ist, und so etwa 5000 Tonnen/Jahr für Rowlings Bücher und Bewegungenundihre 3 Kinder). Die Erde verliert jedes Jahr mindestens 1% ihres Oberbodens, so dass der größte Teil ihrer Nahrungsmittelanbaukapazität weg sein wird, wenn sie sich dem Jahr 2100 nähert. Dann gibt es die riesige Menge an verbranntem Brennstoff und Abfall, die gemacht werden, um die Bücher und Filme, Plastikpuppen usw. herzustellen und zu vertreiben. Sie zeigt ihren Mangel an sozialer Verantwortung, indem sie Kinder hervorbringt, anstatt ihre Millionen zu verwenden, um familienplanerisch zu sein oder den Regenwald aufzukaufen, und indem sie die konventionelle liberale Dummheit der Vorherrschaft der Dritten Welt fördert, die Großbritannien, Amerika, die Welt und die Zukunft ihres Nachkommen zerstört. Natürlich unterscheidet sie sich nicht so sehr von den anderen 7. 8 Milliarden ahnungslos - nur noiser und zerstörerischer.. Es ist das keine kostenlose Mittagessen Problem schreiben groß. Der Mob kann einfach nicht sehen, dass es nichts gibt, wie einer Person zu helfen, ohne anderen zu schaden. Rechte oder Privilegien, die Neuankömmlingen in einer überfüllten Welt gewährt werden, können die Rechte anderer nurvereist enden. Trotz der massiven ökologischen Katastrophen, die sich jeden Tag überall vor ihnen abspielen, können sie sie nicht an die hemmungslose Mutterschaft der "Vielfalt" heften, die für den größten Teil des Bevölkerungszuwachses des letzten Jahrhunderts und all das in diesem jahr erklärt. Ihnen fehlt eine Kombination aus Intelligenz, Bildung, Erfahrung und Gesunden, die erforderlich sind, um die täglichen Angriffe auf die Ressourcen und das Funktionieren der Gesellschaft auf den letztendlichen Zusammenbruch der industriellen Zivilisation zu extrapolieren. Jede Mahlzeit, jede Fahrt mit dem Auto oder Bus, jedes Paar Schuhe ist ein weiterer Nagel im Sarg der Erde. Es ist ihr wahrscheinlich nie in den Sinn gekommen, dass ein Sitz in einem Flugzeug von London nach San Francisco etwa eine Tonne Kohlenstoff produziert, der etwa 3 Quadratmeter Meereis schmilzt, und als eine der Überprivilegierten hat sie wahrscheinlich Hunderte solcher Flüge geflogen. Nicht nur die Reichen und Berühmten, sondern fast jede öffentliche Persönlichkeit überhaupt, einschließlich praktisch aller Lehrer, werden unter Druck gesetzt, politisch korrekt zu sein, was in den westlichen Demokratien heute sozialdemokratisch(neomarxistisch – d.h. verwässerte Kommunisten) bedeutet, dass die Supremacisten der Dritten Welt für die Zerstörung ihrer eigenen Gesellschaften und ihrer eigenen Nachkommen arbeiten. Diejenigen also, deren Bildung,Erfahrung, Intelligenz (und der grundlegende gesunde Menschenverstand), die ihnen verbieten sollten, überhaupt öffentliche Erklärungen abzugeben, völlig alle Medien beherrschen und den Eindruck erwecken, dass die Intelligenten und Zivilisierten Demokratie, Vielfalt und Gleichheit begünstigen müssen, während die Wahrheit ist, dass dies die Probleme und nicht die Lösungen sind und dass sie selbst die Hauptfeinde der Zivilisation sind. Siehe my Suicide by Democracy 2nd ed (2019) und andere. (shrink)

The proof theory of many-valued systems has not been investigated to an extent comparable to the work done on axiomatizatbility of many-valued logics. Proof theory requires appropriate formalisms, such as sequent calculus, natural deduction, and tableaux for classical (and intuitionistic) logic. One particular method for systematically obtaining calculi for all finite-valued logics was invented independently by several researchers, with slight variations in design and presentation. The main aim of this report is to develop the proof theory of finite-valued first order (...) logics in a general way, and to present some of the more important results in this area. In Systems covered are the resolution calculus, sequent calculus, tableaux, and natural deduction. This report is actually a template, from which all results can be specialized to particular logics. (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)

Hilbert’s program was an ambitious and wide-ranging project in the philosophy and foundations of mathematics. In order to “dispose of the foundational questions in mathematics once and for all,” Hilbert proposed a two-pronged approach in 1921: first, classical mathematics should be formalized in axiomatic systems; second, using only restricted, “finitary” means, one should give proofs of the consistency of these axiomatic systems. Although Gödel’s incompleteness theorems show that the program as originally conceived cannot be carried out, it had many partial (...) successes, and generated important advances in logical theory and metatheory, both at the time and since. The article discusses the historical background and development of Hilbert’s program, its philosophical underpinnings and consequences, and its subsequent development and influences since the 1930s. (shrink)

Ich behaupte, dass die Tabelle der Intentionalität (Rationalität, Bewusstein, Geist, Denken, Sprache, Persönlichkeit usw.), die hier prominent dargestellt wird, mehr oder weniger genau beschreibt oder zumindest als Heuristik dient, wie wir denken und uns verhalten, und so umfasst sie nicht nur Philosophie und Psychologie, aber alles andere (Geschichte, Literatur, Mathematik, Politik etc.). Beachten Sie insbesondere, dass Intentionalität und Rationalität, wie ich (zusammen mit Searle, Wittgenstein und anderen) es sehen, sowohl bewusst deliberative linguistische System 2 als auch unbewusste automatisierte prälinguistische System (...) 1 Aktionen oder Reflexe umfasst. Ich mache einen kritischen Überblick über einige der wichtigsten Ergebnisse von zwei der bedeutendsten Studenten des Verhaltens der modernen Zeit, Ludwig Wittgenstein und John Searle, über die logische Struktur der Intentionalität (Geist, Sprache, Verhalten), als Ausgangspunkt wittgensteins grundlegende Entdeckung – dass alle wirklich "philosophischen" Probleme die gleichen sind – Verwirrungen darüber, wie Sprache in einem bestimmten Kontext zu verwenden, und so sind alle Lösungen gleich – blickend, wie Sprache in dem Kontext verwendet werden kann, um die Wahrheitsbedingungen (Bedingungen der Zufriedenheit oder COS) sind klar. Das Grundproblem ist, dass man alles sagen kann, aber man kann keine willkürliche Äußerung und Bedeutung bedeuten (geben, die man klar coS für) willenweise nur in einem ganz bestimmten Kontext möglich ist. Ich analysiere verschiedene Schriften von und über sie aus der modernen Perspektive der beiden Systeme des Denkens (popularisiert als "schnell denken, langsam denken"), mit einer neuen Tabelle der Intentionalität und neue duale Systeme Nomenklatur. Ich zeige, dass dies eine starke Heuristik für die Beschreibung von Verhalten ist. Somit ist jedes Verhalten eng miteinander verbunden, wenn man den richtigen Standpunkt einnimmt. Die phänomenologische Illusion (Vergessen unseres automatisierten Systems 1) ist universell und erstreckt sich nicht nur über die gesamte Philosophie, sondern über das ganze Leben hinweg. Ich bin sicher, dass Chomsky, Obama, Zuckerberg und der Papst ungläubig wären, wenn man ihnen sagen würde, dass sie unter dem gleichen Problem wie Hegel, Husserl und Heidegger leiden (oder dass sie sich nur in gewissem Maße von Drogen- und accumbensSexsüchtigen unterscheiden, indem sie durch Stimulation ihrer Frontalkortik durch die Lieferung von Dopamin (und über 100 anderen Chemikalien) über das ventrale Tegmentum und den Kern motiviertwerden, aber es ist klar. Während die Phänomenologen nur viel Zeit verschwendeten, verschwenden sie die Erde und die Zukunft ihres Nachkommen. (shrink)

Angell's logic of analytic containment AC has been shown to be characterized by a 9-valued matrix NC by Ferguson, and by a 16-valued matrix by Fine. We show that the former is the image of a surjective homomorphism from the latter, i.e., an epimorphic image. The epimorphism was found with the help of MUltlog, which also provides a tableau calculus for NC extended by quantifiers that generalize conjunction and disjunction.

Purpose: This thematic literature review explores the critical role of competent writing skills in law enforcement, examining its impact on career progression, agency reputation, and legal proceedings. The purpose is to synthesize existing literature to identify research gaps and suggest directions for future studies. Methods: Google Scholar, ERIC, and the Jerry Falwell Library searches were conducted to capture a broad range of studies involving police report writing, its impact on officers, law enforcement agencies, and the criminal justice system, and writing (...) improvement strategies. Although not required for this review, the work followed PRISMA-ScR guidelines. Results: The initial search yielded numerous qualitative and quantitative studies. This review categorizes the findings into themes of the importance of writing proficiency, the influence of organizational culture, training and education, and technological integration, highlighting the variability and scope of the existing literature. Conclusions: The review shows the need for well-structured research to substantiate the factors contributing to effective law enforcement report writing. It recommends areas for in-depth exploration in future systematic reviews or primary studies, especially longitudinal studies on the effects of targeted training programs, organizational culture shifts, and technological integration on writing proficiency. Application in Law Enforcement: For trainers and instructors, integrating comprehensive report writing programs into training for law enforcement officers can enhance professional skills and accountability. Effective report writing improves documentation accuracy, supports legal proceedings, and enhances career progression. Incorporating targeted report writing training can holistically enhance the performance and professionalism of law enforcement officers. (shrink)

David Hilbert's finitistic standpoint is a conception of elementary number theory designed to answer the intuitionist doubts regarding the security and certainty of mathematics. Hilbert was unfortunately not exact in delineating what that viewpoint was, and Hilbert himself changed his usage of the term through the 1920s and 30s. The purpose of this paper is to outline what the main problems are in understanding Hilbert and Bernays on this issue, based on some publications by them which have so far received (...) little attention, and on a number of philosophical reconstructions of the viewpoint (in particular, by Hand, Kitcher, and Tait). (shrink)

This paper discusses the relation between Crispin Wright’s alethic pluralism and my global expressivism. I argue that on many topics Wright’s own view counts as expressivism in my sense, but that truth itself is a striking exception. Unlike me, Wright never seems to countenance an expressivist account of truth, though the materials needed are available to him in his approaches to other topics.

In The Boundary Stones of Thought, Rumfitt defends classical logic against challenges from intuitionistic mathematics and vagueness, using a semantics of pre-topologies on possibilities, and a topological semantics on predicates, respectively. These semantics are suggestive but the characterizations of negation face difficulties that may undermine their usefulness in Rumfitt’s project.

One goal of this paper is to argue that autobiographical memories are extended and distributed across embodied brains and environmental resources. This is important because such distributed memories play a constitutive role in our narrative identity. So, some of the building blocks of our narrative identity are not brain-bound but extended and distributed. Recognising the distributed nature of memory and narrative identity, invites us to find treatments and strategies focusing on the environment in which dementia patients are situated. A second (...) goal of this paper is to suggest various of such strategies, including lifelogging technologies such as SenseCams, life story books, multimedia biographies, memory boxes, ambient intelligence systems, and virtual reality applications. Such technologies allow dementia patients to remember their personal past in a way that wouldn’t be possible by merely relying on their biological memory, in that way aiding in preserving their narrative identity and positively contributing to their sense of well-being. (shrink)

Does artificial intelligence (AI) pose existential risks to humanity? Some critics feel this question is getting too much attention, and want to push it aside in favour of conversations about the immediate risks of AI. These critics now include the journal Nature, where a recent editorial urges us to 'stop talking about tomorrow's AI doomsday when AI poses risks today.' We argue that this is a serious failure of judgement, on Nature's part. In science, as in everyday life, we expect (...) influential actors to consider the consequences of error. As the world's leading scientific journal, Nature is certainly an influential actor, especially so in the absence of robust global regulation of AI. Yet it has manifestly failed to consider the cost of error in this case. (shrink)

This is an unpublished piece from July 1998. It discusses the use of semantic notions such as reference in the Canberra Plan, the question whether this use creates a problematic circularity if the Canberra Plan is applied to the semantic notions themselves, and the relation of this question to Putnam’s model-theoretic argument. I used some of the ideas in later papers such as (Price 2004, 2009) and (Menzies & Price, 2009), but the bulk of discussion of the relation (...) of my concern to Putnam’s argument (and to responses to Putnam by others) never made it into print. (shrink)

This piece was written circa 1982–83, drawing in part on material from my PhD thesis (The Problem of the Single Case, Cambridge, 1981). In the thesis I proposed what would now be called an expressivist account of judgements of the form ‘It is probable that p’. One chapter, on which this paper builds, tried to defend the view against the Frege-Geach argument. This piece earned a revise and resubmit from Philosophical Review, but was never resubmitted. Parts of it made their (...) way into my ‘Semantic Minimalism and the Frege Point’, in Tsohatzidis, S.L.(ed.), Foundations of Speech Act Theory: Philosophical and Linguistic Perspectives, Routledge, 1994, pp. 132–55 (reprinted in Naturalism without Mirrors, Oxford, 2011, ch. 3) – though that paper favours a different approach to the Frege-Geach argument, leaning more heavily on semantic minimalism. I’m putting this piece online to facilitate self-citation. (shrink)

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)

Methods available for the axiomatization of arbitrary finite-valued logics can be applied to obtain sound and complete intelim rules for all truth-functional connectives of classical logic including the Sheffer stroke and Peirce’s arrow. The restriction to a single conclusion in standard systems of natural deduction requires the introduction of additional rules to make the resulting systems complete; these rules are nevertheless still simple and correspond straightforwardly to the classical absurdity rule. Omitting these rules results in systems for intuitionistic versions of (...) the connectives in question. (shrink)