In this paper I address the question of whether the incompleteness theorems imply that “the mind cannot be mechanized,” where this is understood in the specific sense that “the mathematical outputs of the idealized human mind do not coincide with the mathematical outputs of any idealized finite machine.” Gödel argued that his incompleteness theorems implied a weaker, disjunctive conclusion to the effect that either “the mind cannot be mechanized” or “mathematical truth outstrips the idealized human mind.” Others, most notably, Lucas (...) and Penrose, have claimed more—they have claimed that the incompleteness theorems actually imply the first disjunct. I will show that by sharpening the fundamental concepts involved and articulating the background assumptions governing them, one can prove Gödel’s disjunction, one can show that the arguments of Lucas and Penrose fail, and one can see what likely led proponents of the first disjunct astray. (shrink)

The paper begins with an examination of Gödel's views on absolute undecidability and related topics in set theory. These views are sharpened and assessed in light of recent developments. It is argued that a convincing case can be made for axioms that settle many of the questions undecided by the standard axioms and that in a precise sense the program for large cardinals is a complete success “below” CH. It is also argued that there are reasonable scenarios for settling CH (...) and that there is not currently a convincing case to the effect that a given statement is absolutely undecidable. (shrink)

The HOD Dichotomy Theorem states that if there is an extendible cardinal, δ, then either HOD is “close” to V or HOD is “far” from V. The question is whether the future will lead to the first or the second side of the dichotomy. Is HOD “close” to V, or “far” from V? There is a program aimed at establishing the first alternative—the “close” side of the HOD Dichotomy. This is the program of inner model theory. In recent years the (...) third author has provided evidence that there is an ultimate inner model—Ultimate-L—and he has isolated a natural conjecture associated with the model—the Ultimate-L Conjecture. This conjecture implies that that the first alternative holds—HOD is “close” to V. This is the future in which pattern prevails. In this paper we introduce a very different program, one aimed at establishing the second alternative—the “far” side of the HOD Dichotomy. This is the program of large cardinals beyond choice. Kunen famously showed that if AC holds then there cannot be a Reinhardt cardinal. It has remained open whether Reinhardt cardinals are consistent in ZF alone. It turns out that there is an entire hierarchy of choiceless large cardinals of which Reinhardt cardinals are only the beginning, and, surprisingly, this hierarchy appears to be highly ordered and amenable to systematic investigation, as we shall show in this paper. The point is that if these choiceless large cardinals are consistent then the Ultimate-L Conjecture must fail. This is the future where chaos prevails. (shrink)

Gödel argued that his incompleteness theorems imply that either “the mind cannot be mechanized” or “there are absolutely undecidable sentences.” In the precursor to this paper I examined the early arguments for the first disjunct. In the present paper I examine the most sophisticated argument for the first disjunct, namely, Penrose’s new argument. It turns out that Penrose’s argument requires a type-free notion of truth and a type-free notion of absolute provability. I show that there is a natural such system, (...) DTK. I prove a series of results which show that Gödel’s disjunction is provable in the system, Penrose’s argument is invalid in the system, there can be no proof or refutation of either disjunct in the system, the independence results are robust in that they persist when one strengthens the principles governing absolute provability, and there are reasons to believe that the situation will not improve under any plausible alteration of the underlying theory of truth. (shrink)

Gödel initiated the program of finding and justifying axioms that effect a significant reduction in incompleteness and he drew a fundamental distinction between intrinsic and extrinsic justifications. Reflection principles are the most promising candidates for new axioms that are intrinsically justified. Taking as our starting point Tait’s work on general reflection principles, we prove a series of limitative results concerning this approach. These results collectively show that general reflection principles are either weak ) or inconsistent. The philosophical significance of these (...) results is discussed. (shrink)

In this paper we investigate strong logics of first and second order that have certain absoluteness properties. We begin with an investigation of first order logic and the strong logics ω-logic and β-logic, isolating two facets of absoluteness, namely, generic invariance and faithfulness. It turns out that absoluteness is relative in the sense that stronger background assumptions secure greater degrees of absoluteness. Our aim is to investigate the hierarchies of strong logics of first and second order that are generically invariant (...) and faithful against the backdrop of the strongest large cardinal hypotheses. We show that there is a close correspondence between the two hierarchies and we characterize the strongest logic in each hierarchy. On the first-order side, this leads to a new presentation of Woodin's Ω-logic. On the second-order side, we compare the strongest logic with full second-order logic and argue that the comparison lends support to Quine's claim that second-order logic is really set theory in sheep's clothing. (shrink)

The independence results in set theory invite the search for new and justified axioms. In Chapter 1 I set the stage by examining three approaches to justifying the axioms of standard set theory and argue that the approach via reflection principles is the most successful. In Chapter 2 I analyse the limitations of ZF and use this analysis to set up a mathematically precise minimal hurdle which any set of new axioms must overcome if it is to effect a significant (...) reduction in incompleteness. In Chapter 3 I examine the standard method of justifying new axioms---reflection principles---and prove a result which shows that no reflection principle can overcome the minimal hurdle and yield a significant reduction in incompleteness. In Chapter 4 I introduce a new approach to justifying new axioms---extension principles---and show that such principles can overcome the minimal hurdle and much more, in particular, such principles imply PD and that the theory of second-order arithmetic cannot be altered by set size forcing. I show that in a sense these principles are inevitable. In Chapter 5 I close with a brief discussion of meta-mathematical justifications stemming from the work of Woodin. These touch on the continuum hypothesis and other questions which are beyond the reach of standard large cardinals. (shrink)

In 1985 the second author showed that if there is a proper class of measurable Woodin cardinals and $V^{B1} $ and $V^{B2} $ are generic extensions of V satisfying CH then $V^{B1} $ and $V^{B2} $ agree on all $\Sigma _1^2 $ -statements. In terms of the strong logic Ω-logic this can be reformulated by saying that under the above large cardinal assumption ZFC + CH is Ω-complete for $\Sigma _1^2 $ Moreover. CH is the unique $\Sigma _1^2 $ -statement (...) with this feature in the sense that any other $\Sigma _1^2 $ -statement with this feature is Ω-equivalent to CH over ZFC. It is natural to look for other strengthenings of ZFC that have an even greater degree of Ω-completeness. For example, one can ask for recursively enumerable axioms A such that relative to large cardinal axioms ZFC + A is Ω-complete for all of third-order arithmetic. Going further, for each specifiable segment $V_\lambda $ of the universe of sets (for example, one might take $V_\lambda $ to be the least level that satisfies there is a proper class of huge cardinals), one can ask for recursively enumerable axioms A such that relative to large cardinal axioms ZFC + A is Ω-complete for the theory of $V_\lambda $ . If such theories exist, extend one another, and are unique in the sense that any other such theory B with the same level of Ω-completeness as A is actually Ω-equivalent to A over ZFC, then this would show that there is a unique Ω-complete picture of the successive fragments of the universe of sets and it would make for a very strong case for axioms complementing large cardinal axioms. In this paper we show that uniqueness must fail. In particular, we show that if there is one such theory that Ω-implies CH then there is another that Ω-implies¬CH. (shrink)

In this paper I examine Feferman’s reasons for maintaining that while the statements of first-order number theory are “completely clear'” and “completely definite,”' many of the statements of analysis and set theory are “inherently vague'” and “indefinite.”' I critique his four central arguments and argue that in the end the entire case rests on the brute intuition that the concept of subsets of natural numbers—along with the richer concepts of set theory—is not “clear enough to secure definiteness.” My response to (...) this final, remaining point will be that the concept of “being clear enough to secure definiteness” is about as clear a case of an inherently vague and indefinite concept as one might find, and as such it can bear little weight in making a case against the definiteness of analysis and set theory. (shrink)

This volume contains the proceedings of the Logic at Harvard conference in honor of W. Hugh Woodin's 60th birthday, held March 27–29, 2015, at Harvard University. It presents a collection of papers related to the work of Woodin, who has been one of the leading figures in set theory since the early 1980s. The topics cover many of the areas central to Woodin's work, including large cardinals, determinacy, descriptive set theory and the continuum problem, as well as connections between set (...) theory and Banach spaces, recursion theory, and philosophy, each reflecting a period of Woodin's career. Other topics covered are forcing axioms, inner model theory, the partition calculus, and the theory of ultrafilters. This volume should make a suitable introduction to Woodin's work and the concerns which motivate it. The papers should be of interest to graduate students and researchers in both mathematics and philosophy of mathematics, particularly in set theory, foundations and related areas. (shrink)

This reissue of his collection of early essays, Logico-Linguistic Papers, is published with a brand new introduction by Professor Strawson but, apart from minor ...

A historical investigation of the exclusion of Africa and Asia from modern histories of philosophy.

A complete system of classical Aristotelian logic intended for honors high school and college.

In a thoughtful reassessment of the meaning of life and death, a noted philosopher offers a new definition for life that contrasts a world dependent on biological maintenance with one controlled by state-of-the-art medical technology. Tour.

Ohne Rücksicht auf disziplinäre Schranken bringt dieses Buch verschiedene nicht-reduktionistische Lerntheorien miteinander ins Gespräch. In einem offenen Diskurs, der die Konzepte zueinander in Beziehung setzt, werden die unterschiedlichen Perspektiven kritisch abgewogen und hinsichtlich ihrer Stärken und Schwächen diskutiert.

Delo se loteva vprašanja aktualnosti pojma subjekta v filozofiji in politiki skozi analizo tistih avtorjev, ki so ga domnevno najbolj radikalno pokopali: pokaže, da vznik radikalno novega in problematika subjekta zavzema osrednje mesto v Deleuzovi filozofiji, kakor tudi v Lyotardovi pozni misli posvečeni praznini, v Foucaultovi obravnavi biopolitike in biooblasti, v delu Negrija in Hardta o Imperiju, ter nazadnje v Badioujevi predelavi temeljnih filozofskih kategorij biti, resnice in subjekta, na osnovi katerih je dandanes znova možna renesansa filozofije. Ta ima po (...) Badiouju štiri razsežnosti, ki se v delu Vznik subjekta nenehno prepletajo: »V osnovi želja filozofije implicira razsežnost upora: ni filozofije brez nezadovoljstva mišljenja v njegovem soočenju s svetom, kakršen je. Pa vendar želja filozofije vključuje tudi logiko: to je, prepričanje v moč argumenta in uma.«. (shrink)

Not only the direct physical experiences of deployment can severely harm soldiers’ mental health. Witnessing violations of their moral principles by the enemy, or by their fellow soldiers and superiors, can also have a devastating impact. It can cause soldiers’ moral disorientation, increasing feelings of shame, guilt, or hate, and the need for general answers on questions of right and wrong. Various attempts have been made to keep soldiers mentally sane. One is to provide convincing causes for their deployment, which (...) risks an “end justifies the means” way of thinking. The good cause can provide a moral justification for horrible atrocities. Another method, introduced in the USA, Canada, and Australia, aims to strengthen military personnel’s resistance by promoting and maintaining a happy, optimistic state of mind through the use of positive psychology. Alongside making soldiers “morally fit” for all kinds of situations, the focus could also be on moral recovery and forgiveness. Such a care-based military ethics approach, aimed at mutual understanding and interdependence, could help soldiers handle the emotional impact of moral conflicts. This demands that military units reflect on their organizational culture and rethink oaths and codes of conduct that focus mainly on efficiency and readiness, as well as the soldierly self-image with its seemingly still deeply rooted warrior ethos. Today, resilience and positive psychology in the military is apparently mainly geared to assuring its soldiers’ readiness. An appropriate set of virtues and understanding of virtue ethics that are less centered on self-perfection and autonomy could point to a different form of character-building and lead to a better understanding of others. (shrink)

The relationship of part to whole is one of the most fundamental there is; this is the first and only full-length study of this concept. This book shows that mereology, the formal theory of part and whole, is essential to ontology. Peter Simons surveys and criticizes previous theories, especially the standard extensional view, and proposes a more adequate account which encompasses both temporal and modal considerations in detail. 'Parts could easily be the standard book on mereology for the next (...) twenty or thirty years.' Timothy Williamson, Grazer Philosophische Studien. (shrink)

This chapter provides an introduction to higher-order metaphysics as well as to the contributions to this volume. We discuss five topics, corresponding to the five parts of this volume, and summarize the contributions to each part. First, we motivate the usefulness of higher-order quantification in metaphysics using a number of examples, and discuss the question of how such quantifiers should be interpreted. We provide a brief introduction to the most common forms of higher-order logics used in metaphysics, and indicate a (...) number of questions which can be raised in such systems using logical vocabulary alone. Using a further example, we return to applications of higher-order logics in metaphysics. We also mention key developments in the history of higher-order logic as it pertains to metaphysics. Finally, we mention certain arguments which have been raised against the use of higher-order logic, and some ways of responding to them. (shrink)

Confirmation bias is one of the most widely discussed epistemically problematic cognitions, challenging reliable belief formation and the correction of inaccurate views. Given its problematic nature, it remains unclear why the bias evolved and is still with us today. To offer an explanation, several philosophers and scientists have argued that the bias is in fact adaptive. I critically discuss three recent proposals of this kind before developing a novel alternative, what I call the ‘reality-matching account’. According to the account, confirmation (...) bias evolved because it helps us influence people and social structures so that they come to match our beliefs about them. This can result in significant developmental and epistemic benefits for us and other people, ensuring that over time we don’t become epistemically disconnected from social reality but can navigate it more easily. While that might not be the only evolved function of confirmation bias, it is an important one that has so far been neglected in the theorizing on the bias. (shrink)

In this lucid and penetrating book, Peter A. Schouls considers Locke's major writings in terms of the closely related ideas of freedom, progress, mastery, reason, and education.

In recent years, it has been argued more than once that situations determine our conduct to a much greater extent than our character does. This argument rests on the findings of social psychologists such as Stanley Milgram, who have popularized the idea that we can all be brought to harm innocent others. An increasing number of philosophers and ethicists make use of such findings, and some of them have argued that this so-called situationist challenge fatally undermines virtue ethics. As virtue (...) ethics is currently the most popular underpinning for ethics education in the military, it is important to know to what extent the claim situationists make is correct. Fortunately, a closer look indicates that an interactionist perspective, with our character and the situation interplaying, is more accurate than the situationist perspective. (shrink)

In this short but meaty book, Peter Unger questions the objective answers that have been given to central problems in philosophy. As Unger hypothesizes, many of these problems are unanswerable, including the problems of knowledge and scepticism, the problems of free will, and problems of causation and explanation. In each case, he argues, we arrive at one answer only relative to an assumption about the meaning of key terms, terms like "know" and like "cause," even while we arrive at (...) an opposite answer relative to quite different assumptions, but equally arbitrary assumptions, about what the key terms mean. (shrink)

Members of the field of philosophy have, just as other people, political convictions or, as psychologists call them, ideologies. How are different ideologies distributed and perceived in the field? Using the familiar distinction between the political left and right, we surveyed an international sample of 794 subjects in philosophy. We found that survey participants clearly leaned left (75%), while right-leaning individuals (14%) and moderates (11%) were underrepresented. Moreover, and strikingly, across the political spectrum, from very left-leaning individuals and moderates to (...) very right-leaning individuals, participants reported experiencing ideological hostility in the field, occasionally even from those from their own side of the political spectrum. Finally, while about half of the subjects believed that discrimination against left- or right-leaning individuals in the field is not justified, a significant minority displayed an explicit willingness to discriminate against colleagues with the opposite ideology. Our findings are both surprising and important, because a commitment to tolerance and equality is widespread in philosophy, and there is reason to think that ideological similarity, hostility, and discrimination undermine reliable belief formation in many areas of the discipline. (shrink)

Narrative thinking -- Narrative thinking about one's past -- Grief : a case study -- Narrative thinking about one's future -- Self-forgiveness : a case study -- The narrative sense of self -- Narrative, truth, life, and fiction.

Introduction Max Horkheimer was born on February in Stuttgart. By the time he died, on 7 July in Nuremberg, he had played a decisive role in launching and ...

While Hermann Levin Goldschmidt didn’t read Yiddish anarchists, there seems to have been a convergent evolution in their thinking. Goldschmidt’s looking up to Jewish lore as a source of liberating creativity is commonly encountered in Yiddish anarchist texts. His view of action as a constant response to internal and external challenges in the struggle for an open future is developed by Isaac Nachman Steinberg on the basis of nineteenth-century vitalism. Goldschmidt’s theory of anarchist individualism as willed self-limiting solidarity has a (...) compelling parallel in Hillel Solotaroff’s view of history. His use of impressionism and photography to eternalize the immediacy of human actuality is akin to Rudolf Rocker’s championing of decadent literature. In both cases, the goal of anarchism is not a dictatorship of the former downtrodden, but a continuous and contradictory evolution of freedom in ever-changing contexts. (shrink)

The norm of assertion, to be in force, is a social norm. What is the content of our social norm of assertion? Various linguistic arguments purport to show that to assert is to represent oneself as knowing. But to represent oneself as knowing does not entail that assertion is governed by a knowledge norm. At best these linguistic arguments provide indirect support for a knowledge norm. Furthermore, there are alternative, non-normative explanations for the linguistic data (as in recent work from (...) Van Elswyk). Direct arguments would rely on normative judgments about the permissibility or impermissibility of assertions with and without the speaker knowing the content asserted. John Turri's work experimental results purport to show that our norm of assertion is factive, and probably knowledge. But as a number of recent experimentalists (Kneer, Reuter and Broessel, Marsili and Wiegmann) have shown, Turri's results rely on the problemmatic use of 'should' as in 'Maria should assert that she owns a 1990 watch.' Correcting for this, these experimentalists provide strong evidence that our norm of assertion is not factive. The standard reply to evidence like this from the assertion of unlucky falsehoods is the excuse maneuver. But Marsili and Wiegmann, following Turri's protocol for testing for excuse validation, show that participants who judge that assertions unlucky falsehoods are permissible are not guilty of excuse validation. Given our current understanding of the experimental evidence, knowledge is not our norm of assertion. (shrink)

Metz holds that we can use African communal ethics to constitute global economic practices such as appropriation, production, distribution and consumption in such a way that promotes harmonious relations. In this article, I will show that Metz’s reformist approach to constituting the global economic practices is problematic as it fails to deal with the fundamental problem that pertains to a racialised world order that is structurally configured by coloniality of being. I will show that reformist approaches such as Metz’s use (...) of African communal ethics to constitute global economic practices in a way that promotes harmonious relations are undesirable attempts that are opposed and curtailed by a structural racialised logic/ontology of the world that governs and supervises the evolution of the world economic structures and practices in a way which undermines harmonious relations and in a way which causes economic marginalisation and impoverishment of historically disadvantaged indigenous Africans. (shrink)

Poellner here offers a comprehensive interpretation of Nietzsche's later ideas on epistemology and metaphysics, drawing extensively not only on his published works but also his voluminous notebooks, largely unpublished in English. He examines Nietzsche's various distinct lines of thought on the traditionally central areas of philosophy and shows in what specific sense Nietzsche, as he himself claimed, might be said to have moved beyond these questions. He pays considerable attention throughout both to the historical context of Nietzsche's writings and to (...) subsequent developments in philosophy--English-language as well as Continental. (shrink)

Why do we engage in folk psychology, that is, why do we think about and ascribe propositional attitudes such as beliefs, desires, intentions etc. to people? On the standard view, folk psychology is primarily for mindreading, for detecting mental states and explaining and/or predicting people’s behaviour in terms of them. In contrast, McGeer (1996, 2007, 2015), and Zawidzki (2008, 2013) maintain that folk psychology is not primarily for mindreading but for mindshaping, that is, for moulding people’s behavior and minds (e.g., (...) via the imposition of social norms) so that coordination becomes easier. Mindreading is derived from and only as effective as it is because of mindshaping, not vice versa. I critically assess McGeer’s, and Zawidzki’s proposal and contend that three common motivations for the mindshaping view do not provide sufficient support for their particular version of it. I argue furthermore that their proposal underestimates the role that epistemic processing plays for mindshaping. And I provide reasons for favouring an alternative according to which, in social cognition involving ascriptions of propositional attitudes, neither mindshaping nor mindreading is primary but both are complementary in that effective mindshaping depends as much on mindreading as effective mindreading depends on mindshaping. (shrink)

Philosophy of music has flourished in the last thirty years, with great advances made in the understanding of the nature of music and its aesthetics. Peter Kivy has been at the center of this flourishing, and now offers his personal introduction to philosophy of music, a clear and lively explanation of how he sees the most important and interesting philosophical issues relating to music. Anyone interested in music will find this a stimulating introduction to some fascinating questions and ideas.

What is the biological function of perception? I hold perception, especially visual perception in humans, has the biological function of accurately representing the environment. Tyler Burge argues this cannot be so in Origins of Objectivity (Oxford, 2010), for accuracy is a semantical relationship and not, as such, a practical matter. Burge also provides a supporting example. I rebut the argument and the example. Accuracy is sometimes also a practical matter if accuracy partly explains how perception contributes to survival and reproduction.

Martine Nida-Rümelin (1996) argues that color science indicates behaviorally undetectable spectrum inversion is possible and raises this possibility as an objection to functionalist accounts of visual states of color. I show that her argument does not rest solely on color science, but also on a philosophically controversial assumption, namely, that visual states of color supervene on physiological states. However, this assumption, on the part of philosophers or vision scientists, has the effect of simply ruling out certain versions of functionalism. While (...) Nida-Rümelin is quite right to search for empirical tests for claims about the nature of visual states, philosophical issues remain pivotal in determining the correctness of these claims. (shrink)

Abstractabstract:Karl Marx’s acerbic observation in the opening lines of The Eighteenth Brumaire that “all facts and personages of great importance in world history occur the first time as tragedy, the second as farce” may be profitably applied to a reconsideration of literary farce sui generis, a genre represented in this article by a long-neglected work of utopian fiction, Archibald Marshall’s Upsidonia (1915). Although Upsidonia’s current disregard is arguably undeserved, the article’s chief interest is not to reclaim the novel on aesthetic (...) grounds but to illuminate the mechanics of what Marx would call its “serious buffoonery.” In its persistent reversal of capitalist principles and relations, Upsidonia naturally invites readers to revisit Marx, whose mordant gambit may serve as a key to Marshall’s own farcical plot and praxis, rooted in return and repetition, the essential maneuvers of farce itself. (shrink)

This introduction by leading scholar Peter Trawny is the first to tackle the Black Notebooks, whose recent publication revealed the extent of Heidegger's anti-Semitism. Trawny directly confronts the most problematic aspects of Heidegger's thought, also fully surveying his work, from early writings to his magnum opus, Being and Time.

This volume suggests a novel treatment of context in the analysis of everyday interaction. On a theoretical level, it advocates a switch of focus from 'context' as a preestablished, monolithic category which constringes co-participants' verbal and nonverbal behaviour, to an active notion of 'contextualization': in order to make oneself understood, participants have to establish and maintain those shared contextual frames which in turn are relevant to the local interpretation of their verbal and nonverbal activities. On an empirical level, the volume (...) contains exemplary analyses that show how participants employ 'contextualization cues' of prosodic (rhythm, intonation, tempo, etc.) or nonverbal (gaze, gesture, etc.) nature in order to 'achieve context'.The volume is also an appraisal of the theory of contextualization developed by John Gumperz. In their contributions, researchers from various schools of research, such as conversation analysis, micro-ethnography, phonetics/phonology and metapragmatics, relate their work to this theory. (shrink)