There are quantum solutions for computational problems that make use of interference at some stage in the algorithm. These stages can be mapped into the physical setting of a single particle travelling through a many-armed interferometer. There has been recent foundational interest in theories beyond quantum theory. Here, we present a generalized formulation of computation in the context of a many-armed interferometer, and explore how theories can differ from quantum theory and still perform distributed calculations in this set-up. We shall (...) see that quaternionic quantum theory proves a suitable candidate, whereas box-world does not. We also find that a classical hidden variable model first presented by Spekkens : 32100, 2007) can also be used for this type of computation due to the epistemic restriction placed on the hidden variable. (shrink)

Energy is a crucial concept within classical and quantum physics. An essential tool to quantify energy is the Hamiltonian. Here, we consider how to define a Hamiltonian in general probabilistic theories—a framework in which quantum theory is a special case. We list desiderata which the definition should meet. For 3-dimensional systems, we provide a fully-defined recipe which satisfies these desiderata. We discuss the higher dimensional case where some freedom of choice is left remaining. We apply the definition to example toy (...) theories, and discuss how the quantum notion of time evolution as a phase between energy eigenstates generalises to other theories. (shrink)

Due to the significant and often careless human impact on the natural environment, there are serious problems facing the people of today and of future generations. To date, ethical, aesthetic, religious, and economic arguments for the conservation and protection of the natural environment have made relatively little headway. Another approach, one capable of garnering attention and motivating action, would be welcome. There is another approach, one that I will call a rights approach. Speaking generally, this approach is an attempt to (...) address environmental issues via the language and theory of legal and moral rights. Ultimately, it is our duties to our fellow humans that explain why we have duties regarding the natural environment. There are three main contenders among theories that can be called rights approaches to environmental issues. The first identifies the (alleged) human right to a healthful environment as the source of our obligations to conserve and protect nature. The second approach has it that our duties to nature arise from the rights of the constituents of nature themselves, its flora and fauna. The third approach to addressing environmental problems via rights is, I argue, the best path to environmental conservation and protection. This approach—which grounds duties toward nature on the human right to health—has the benefits of being a straightforward, uncontroversial, and simple approach to issues and problems that desperately need to be resolved. (shrink)

The topic of "Neurotheology" has garnered increasing attention in the academic, religious, scientific, and popular worlds. However, there have been no attempts at exploring more specifically how Jewish religious thought and experience may intersect with neurotheology. The Rabbi's Brain engages this groundbreaking area. Topics included relate to a neurotheological approach to the foundational beliefs that arise from the Torah and associated scriptures, Jewish learning, an exploration of the different elements of Judaism (i.e. Reform, Conservative, and Orthodox), an exploration of specifically (...) Jewish practices (i.e. Davening, Sabbath, Kosher), and a review of Jewish mysticism. (shrink)

It is commonly held that agents can be blameworthy only for acts that are morally wrong. But the claim, when combined with a plausible assumption about wrongness, leads to an implausible view about blameworthiness. The claim should be rejected. Agents can be blameworthy for acts that are not morally wrong. We will take up the claim in terms of three initially appealing, but jointly inconsistent propositions. The significance of noting the inconsistency is motivated by a consideration of a number of (...) theorists who have held, or at least flirted with, all three propositions. The best way to resolve the inconsistency is to reject the claim that blameworthiness requires wrongness. There are good reasons to conclude that a different relation between blameworthiness and wrongness can garner more intuitive support than the alternatives. (shrink)

Excerpt from A Guide to World-HistoryThe object of this book may best be indicated by explain ing briefly how the volume came to be written. As with the majority of people the author's acquaintance with history began at school. But, unlike the majority, he there contracted a taste for the subject which continued when his studies were no longer of a compulsory character. Naturally he was at first concerned with the more heroic and romantic aspects of the subject to be (...) found in our numerous drum-and-trumpet narratives. Gradually, however, he came to think that history might really have the scientific value so often attributed to it in the literature of the subject. Rightly interpreted could not history throw light on the present and into the avenues of the future The idea haunted him constantly, and he began reading up not only the most dry-as-dust chronicles, but also every book he could procure relating to the science or philosophy of history, as it is often called. After many years of almost unremitting study he believed he had garnered quite profitable ideas on general principles. But he still found himself baffled on such points as these.About the PublisherForgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.comThis book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works. (shrink)

The topic of "Neurotheology" has garnered increasing attention in the academic, religious, scientific, and popular worlds. However, there have been no attempts at exploring more specifically how Jewish religious thought and experience may intersect with neurotheology. The Rabbi's Brain engages this groundbreaking area. Topics included relate to a neurotheological approach to the foundational beliefs that arise from the Torah and associated scriptures, Jewish learning, an exploration of the different elements of Judaism (i.e. Reform, Conservative, and Orthodox), an exploration of specifically (...) Jewish practices (i.e. Davening, Sabbath, Kosher), and a review of Jewish mysticism. (shrink)

In the present paper the issue of using violence in protests to garner political gain is considered against the background of the Occupy movement and the varied responses to it. Although some may now feel, and certainly many did while the movement was at its peak, that the Occupy protestors should alter their tactics and embrace violence as an efficacious means to sought ends, it is argued here that such a move would be counterproductive and delegitimizing. Moral and psychological (...) impacts on the non-demonstrating public that protestors’ tactics can have are weighed against traditional arguments in favor of using violence. Sources of political legitimacy are also examined, and it is put forward that changes achieved by nonviolence are more likely to be accepted by society at large. Finally, contemporary thinkers and scholars of the left are encouraged to fill the roles open to them that have emerged with Occupy and related movements. (shrink)

Alasdair MacIntyre’s critique of managerial capitalism is well known, with some arguing that MacIntyrean thought is antithetical to contemporary capitalist business. Nevertheless, substantial efforts have been taken to demonstrate how different business activities constitute MacIntyrean practices, which points to an incoherence at the heart of MacIntyrean business ethics scholarship. This article proposes a way of bridging these perspectives, suggesting a reimagined MacIntyrean approach to business that is thoroughly ‘practice-led.’ A detailed comparison of accounting and management shows that while neither are (...) practices in ‘good order,’ they differ in significant ways: where management does not meet the criteria for a MacIntyrean practice, accounting is a ‘distorted’ practice. This leads to a categorisation of practice-led business activity, whereby the traditional tasks of management are subsumed, shared or subordinated to practices and practitioners. Insights on how this can be implemented are drawn from the ‘communities of practice’ literature and a consideration of professions. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Deification through the Cross:Reflections from an Implied Ideal WorshiperAndrew J. SummersonKhaled Anatolios's most recent book, Deification through the Cross,1 develops a definition of salvation out of his experience of the Byzantine liturgy. This experience of worship offers an immersion in what he calls "doxological contrition." By this, Anatolios means that Christ saves us by offering us the ability to participate in the mutual glorification of the persons of the (...) Holy Trinity by vicariously repenting for our sins. For Anatolios, this objective content is subjectively appropriated in Byzantine Christian worship. To explore this theme, Anatolios develops a working account of "doxological contrition" through a synthetic discussion of the Lenten Triodion and Pentecostarion, books of liturgical hymnography that govern the Byzantine worship from Lent to Pentecost. Anatolios derives his approach from the adaption of reader response theory, which aims to expose the effect a text should have on the "implied ideal reader." As such, his account speaks from the perspective of the "implied ideal worshiper"—presumably a theologically educated congregant who can seize these themes that evaporate into the ether as quickly as incense swung throughout the church during the services.Let me say from the outset, I heartily recommend Anatolios's book. It is both an ambitious work and a rewarding read. Ambitious because Anatolios's approach makes otherwise fragmented theological disciplines—liturgical [End Page 1089] studies, Scripture, historical theology, and systematics—fruitful dialogue partners in his exposition of a working account of the Christian experience of salvation. Rewarding because the reader can explore in depth the touchstones of the Christian tradition through Anatolios's deep retrieval of a more coherent soteriology. Deification of the Cross demonstrates the perennial value of historical theology to correctly account for the "half-forgotten, half misunderstood" details of the Christian tradition in the face of caricatures that at best misrepresent and at worst present an idolatrous, counterfeit Christianity.Eastern Christian Liturgy and RevelationPerhaps I am not Anatolios's ideal audience; I may be too close to the source material and lack objectivity. That aside, the bulk of my reflections on this book comes from the perspective of an "implied ideal worshiper." I do share some of Anatolios starting points. Like Anatolios, I am a convert, scholar, and Eastern Catholic priest. Furthermore, I also share the discontent with which Anatolios begins his book, though perhaps for different reasons. He bemoans a loss of the experience of salvation. My own vocation as priest and scholar comes out of a frustrated wonder. As a college student, I set out to learn about this Church and its Tradition. I learned about the Sunday experience I was supposed be having. It was in university when I read for the first time John Paul II's 1995 apostolic letter Orientale Lumen, written to acquaint the wider Catholic Church with the riches of the Christian East. John Paul II dedicated much reflection to the "genius of Eastern liturgy," emphasizing its power to envelop all our human senses into the fullness of the mystery of God. It is worth quoting in full:Within this framework, liturgical prayer in the East shows a great aptitude for involving the human person in his or her totality: the mystery is sung in the loftiness of its content, but also in the warmth of the sentiments it awakens in the heart of redeemed humanity. In the sacred act, even bodiliness is summoned to praise, and beauty, which in the East is one of the best loved names expressing the divine harmony and the model of humanity transfigured, appears everywhere: in the shape of the church, in the sounds, in the colors, in the lights, in the scents. The lengthy duration of the celebrations, the repeated invocations, everything expresses gradual identification with the mystery celebrated with one's whole person. Thus the prayer of the Church already becomes participation in the heavenly liturgy, an anticipation of the final beatitude.(§11) [End Page 1090]The experience of this liturgy has been quite potent throughout history. It led to the baptism of the entire kingdom of Rus' in 988 AD. As the story goes, its ruler, Vladimir the Great, sent emissaries to find a... (shrink)

Social learning has been shown to be an evolutionarily adaptive strategy, but it can be implemented via many different cognitive mechanisms. The adaptive advantage of social learning depends crucially on the ability of each learner to obtain relevant and accurate information from informants. The source of informants’ knowledge is a particularly important cue for evaluating advice from multiple informants; if the informants share the source of their information or have obtained their information from each other, then their testimony is statistically (...) dependent and may be less reliable than testimony from informants who do not share information. In this study, we use a Bayesian model to determine how rational learners should incorporate the effects of shared information when learning from other people, conducting three experiments that examine whether human learners behave similarly. We find that people are sensitive to a number of different patterns of dependency, supporting the use of a sophisticated strategy for social learning that goes beyond copying the majority, and broadening the situations in which social learning is likely to be an adaptive strategy. (shrink)

Detailed studies of people who have experienced the Capgras delusion (the delusion that certain other people, usually close relatives, have been replaced by impostors) have led to advances in constructing an account which can deal with the basic symptomatology, testing alternative possibilities, generating and testing non‐trivial predictions, and broadening the scope of the basic account to encompass other delusions. This paper outlines these developments. It uses them to explore implications for understanding the formation and maintenance of beliefs, and to discuss (...) basic principles of what has come to be known as cognitive neuropsychiatry. (shrink)

Central to Spinoza’s ethical theory is a model of human nature: the model of the free man. In this paper I argue that the idea of the free man is an inadequate idea when this is understood as the idea of a perfectly free finite thing. But when properly understood--that is, when the idea of the free man is understood as the idea of the perfection of our nature and power--the idea of the free man is a way of conceiving (...) God and is, as such, an adequate idea. (shrink)

An array of new cases of lies is presented in support of the idea that lying does not require an intention to be deceptive. The crucial feature of these cases is that the agents who lie have some sort of motivation to lie alternative to an intention to be deceptive. Such alternative motivation comes in multiple varieties, such that we should think that the possibility of lying without an intention to be deceptive is common.

The scientific knowledge needed to engage with policy issues like climate change, vaccination, and stem cell research often conflicts with our intuitive theories of the world. How resilient are our intuitive theories in the face of contradictory scientific knowledge? Here, we present evidence that intuitive theories in 10 domains of knowledge—astronomy, evolution, fractions, genetics, germs, matter, mechanics, physiology, thermodynamics, and waves—persist more than four decades beyond the acquisition of a mutually exclusive scientific theory. Participants were asked to verify two types (...) of scientific statements as quickly as possible: those that are consistent with intuition and those that involve the same conceptual relations but are inconsistent with intuition. Older adults were as accurate as younger adults at verifying both types of statements, but the lag in response times between intuition-consistent and intuition-inconsistent statements was significantly larger for older adults than for younger adults. This lag persisted even among professional scientists. Overall, these results suggest that the scientific literacy needed to engage with topics of global importance may be constrained by patterns of reasoning that emerge in childhood but persist long thereafter. (shrink)

According to a widely accepted reading of the "Ethics," Spinoza subscribes to a desire-satisfaction theory of value. A desire-satisfaction theory says that what has value is the satisfaction of one’s desires and whatever leads to the satisfaction of one’s desires. In this paper I argue that this standard reading is incorrect, and I show that in Spinoza’s view the foundation of what is truly valuable is the perfection of a person’s essence, not the satisfaction of a person’s desires.

Distributivism holds that private property should be widely distributed among as many as possible and that such a distribution best serves the common good. This paper applies a distributist approach rooted in subsidiarity to the contemporary issue of the unaffordability of single-family homes and the impact of investors buying up more single-family homes, increasing their own wealth at the expense of typical home buyers. Here, we will first consider multiple factors in the housing “crisis,” then highlight the impact of investors (...) on the market. Second, we will consider a critique and analysis of the situation from a distributist perspective, rooted in principles of private property, solidarity, dignity, and subsidiarity (particularly turning to G.K. Chesterton's view on the importance of home). Due consideration is given to some objections to such a distributist critique, with response. Finally, several examples of proposals and implemented practices are provided to discourage this growing trend concerning the concentration of ownership of housing by investors and to better enable homeownership by families. (shrink)

Evidence has accumulated that rod activation under mesopic and scotopic light levels alters visual perception and performance. Here we review the most recent developments in the measurement of rod and cone contributions to mesopic color perception and temporal processing, with a focus on data measured using the four-primary photostimulator method that independently controls rod and cone excitations. We discuss the findings in the context of rod inputs to the three primary retinogeniculate pathways to understand rod contributions to mesopic vision. Additionally, (...) we present evidence that hue perception is possible under scotopic, pure rod-mediated conditions that involves cortical mechanisms. (shrink)

Andrew Sayer undertakes a fundamental critique of social science's difficulties in acknowledging that people's relation to the world is one of concern. As sentient beings, capable of flourishing and suffering, and particularly vulnerable to how others treat us, our view of the world is substantially evaluative. Yet modernist ways of thinking encourage the common but extraordinary belief that values are beyond reason, and merely subjective or matters of convention, with little or nothing to do with the kind of beings (...) people are, the quality of their social relations, their material circumstances or well-being. The author shows how social theory and philosophy need to change to reflect the complexity of everyday ethical concerns and the importance people attach to dignity. He argues for a robustly critical social science that explains and evaluates social life from the standpoint of human flourishing. (shrink)

Until recently, discussion of virtues in the philosophy of mathematics has been fleeting and fragmentary at best. But in the last few years this has begun to change. As virtue theory has grown ever more influential, not just in ethics where virtues may seem most at home, but particularly in epistemology and the philosophy of science, some philosophers have sought to push virtues out into unexpected areas, including mathematics and its philosophy. But there are some mathematicians already there, ready to (...) meet them, who have explicitly invoked virtues in discussing what is necessary for a mathematician to succeed. In both ethics and epistemology, virtue theory tends to emphasize character virtues, the acquired excellences of people. But people are not the only sort of thing whose excellences may be identified as virtues. Theoretical virtues have attracted attention in the philosophy of science as components of an account of theory choice. Within the philosophy of mathematics, and mathematics itself, attention to virtues has emerged from a variety of disparate sources. Theoretical virtues have been put forward both to analyse the practice of proof and to justify axioms; intellectual virtues have found multiple applications in the epistemology of mathematics; and ethical virtues have been offered as a basis for understanding the social utility of mathematical practice. Indeed, some authors have advocated virtue epistemology as the correct epistemology for mathematics (and perhaps even as the basis for progress in the metaphysics of mathematics). This topical collection brings together several of the researchers who have begun to study mathematical practices from a virtue perspective with the intention of consolidating and encouraging this trend. (shrink)

In Part 4 of his "Ethics," Spinoza puts forward and defends what might appear to be the controversial Hobbesean thesis that the desire to prolong one’s life is the basis of virtue (i.e., E4p22). Indeed there is a tradition of commentators offering an egoistic, Hobbesean interpretation of Spinoza’s ethical theory. In this paper, however, I argue that we should not understand Spinozistic self-preservation in the commonsense, empiricist sense of prolonging our lives. Instead I argue that, for Spinoza, self-preservation is a (...) matter of perfection-preservation and perfection-enhancement, which does not essentially involve extending the duration of an individual’s existence. (shrink)

A list of resources for virtue theories of argumentation. Last updated October 31st, 2023.

What should a virtue theory of argumentation say about fallacious reasoning? If good arguments are virtuous, then fallacies are vicious. Yet fallacies cannot just be identified with vices, since vices are dispositional properties of agents whereas fallacies are types of argument. Rather, if the normativity of good argumentation is explicable in terms of virtues, we should expect the wrongness of bad argumentation to be explicable in terms of vices. This approach is defended through analysis of several fallacies, with particular emphasis (...) on the ad misericordiam. (shrink)

The social sciences, and particularly economics, play an important role in business. This article reviews the account of the interdisciplinary conversation between Catholic Social Teaching and the social sciences (especially economics) over the last century, and describes Benedict XVI’s development of this account in Caritas in Veritate . Over time the popes recognized that the technical approach of economics was a barrier to fruitful collaboration between economics and Catholic Social Teaching, both because the economic approach is reductionist, and because modern (...) social science is skeptical of comprehensive accounts of human nature. Through an appeal to charity in truth, one can deduce from Caritas in Veritate that economists, along with business and management theorists, need to take seriously the project of reflecting on and promoting true human goods in society. To love the person one must reflect on what is truly good for the person; to discover the true good of the person, one must love the person. (shrink)

Why we get the world wrong -- Intuitive theories of the physical world -- Matter : what is the world made of? How do those components interact? -- Energy : what makes something hot? What makes something loud? -- Gravity : what makes something heavy? What makes something fall? -- Motion : what makes objects move? What paths do moving objects take? -- Cosmos : what is the shape of our world? What is its place in the cosmos? -- Earth (...) : why do continents drift? Why do climates change? -- Intuitive theories of the biological world -- Life : what makes us alive? What causes us to die? -- Growth : why do we grow bigger? Why do we grow older? -- Inheritance : why do we resemble our parents? Where did we get our traits? -- Illness : what makes us ill? How does illness spread? -- Adaptation : why are there so many lifeforms? How do they change over time? -- Ancestry : where do species come from? How are they related? -- How to get the world right. (shrink)

Deep disagreements are characteristically resistant to rational resolution. This paper explores the contribution a virtue theoretic approach to argumentation can make towards settling the practical matter of what to do when confronted with apparent deep disagreement, with particular attention to the virtue of courage.

Recent literature on epistemic innocence develops the idea that a defective cognitive process may nevertheless merit special consideration insofar as it confers an epistemic benefit that would not otherwise be available. For example, confabulation may be epistemically innocent when it makes a subject more likely to form future true beliefs or helps her maintain a coherent self-concept. I consider the role of confabulation in typical cases of interpersonal gaslighting, and argue that confabulation will not be epistemically innocent in such cases (...) even if it does preserve a coherent self-concept or belief-set for the subject. Analyzing the role of confabulation in gaslighting illustrates its role in on-going interpersonal relationships, and augments already growing evidence that confabulation may be quite widespread. The role of confabulation in gaslighting shows that whether confabulation confers epistemic benefits will depend greatly on the interpersonal context in which it is deployed, while whether a coherent self-concept is epistemically beneficial will depend to a great extent on the content of that self-concept. This shows that the notion of an epistemically harmful or beneficial feature of a cognitive process can and should be further clarified, and that doing so has both theoretical and practical advantages in understanding epistemic innocence itself. (shrink)

The influence that philosophy of science has had on scientific practice is as controversial as it is undeniable, especially in the case of biology. The dynamic between philosophy and biology as disciplines has developed along two different lines that can be characterized as 'paternal', on the one hand, and more 'fraternal', on the other. The role Popperian principles of demarcation and falsifiability have played in both the systematics community as well as the ongoing evolution-creation debates illustrate these contrasting forms of (...) interdisciplinary engagement, underscoring the influence philosophy of science in shaping our contemporary understanding of biology in the North American context. However, a strict disciplinary distinction between philosophy and science may itself be a false dichotomy that risks hampering future development of the biological sciences. By actively engaging with philosophical considerations as an integral part of their scientific practice, nineteenth-century biologists offer an interesting counterpoint to current trends of overspecialization and provide a model of scientists who avoided extremes of antagonism with, or subservience to, philosophy. (shrink)

Few automated legal reasoning systems have been developed in domains of law in which a judicial decision maker has extensive discretion in the exercise of his or her powers. Discretionary domains challenge existing artificial intelligence paradigms because models of judicial reasoning are difficult, if not impossible to specify. We argue that judicial discretion adds to the characterisation of law as open textured in a way which has not been addressed by artificial intelligence and law researchers in depth. We demonstrate that (...) systems for reasoning with this form of open texture can be built by integrating rule sets with neural networks trained with data collected from standard past cases. The obstacles to this approach include difficulties in generating explanations once conclusions have been inferred, difficulties associated with the collection of sufficient data from past cases and difficulties associated with integrating two vastly different paradigms. A knowledge representation scheme based on the structure of arguments proposed by Toulmin has been used to overcome these obstacles. The system, known as Split Up, predicts judicial decisions in property proceedings within family law in Australia. Predictions from the system have been compared to those from a group of lawyers with favourable results. (shrink)

The traditional view of evidence in mathematics is that evidence is just proof and proof is just derivation. There are good reasons for thinking that this view should be rejected: it misrepresents both historical and current mathematical practice. Nonetheless, evidence, proof, and derivation are closely intertwined. This paper seeks to tease these concepts apart. It emphasizes the role of argumentation as a context shared by evidence, proofs, and derivations. The utility of argumentation theory, in general, and argumentation schemes, in particular, (...) as a methodology for the study of mathematical practice is thereby demonstrated. Argumentation schemes represent an almost untapped resource for mathematics education. Notably, they provide a consistent treatment of rigorous and non-rigorous argumentation, thereby working to exhibit the continuity of reasoning in mathematics with reasoning in other areas. Moreover, since argumentation schemes are a comparatively mature methodology, there is a substantial body of existing work to draw upon, including some increasingly sophisticated software tools. Such tools have significant potential for the analysis and evaluation of mathematical argumentation. The first four sections of the paper address the relationships of evidence to proof, proof to derivation, argument to proof, and argument to evidence, respectively. The final section directly addresses some of the educational implications of an argumentation scheme account of mathematical reasoning. (shrink)

I intend to bring recent work applying virtue theory to the study of argument to bear on a much older problem, that of disagreements that resist rational resolution, sometimes termed "deep disagreements". Just as some virtue epistemologists have lately shifted focus onto epistemic vices, I shall argue that a renewed focus on the vices of argument can help to illuminate deep disagreements. In particular, I address the role of arrogance, both as a factor in the diagnosis of deep disagreements and (...) as an obstacle to their mutually acceptable resolution. Arrogant arguers are likely to make any disagreements to which they are party seem deeper than they really are and arrogance impedes the strategies that we might adopt to resolve deep disagreements. As a case in point, since arrogant or otherwise vicious arguers cannot be trusted not to exploit such strategies for untoward ends, any policy for deep disagreement amelioration must require particularly close attention to the vices of argument, lest they be exploited by the unscrupulous. (shrink)

In their account of theory change in logic, Aberdein and Read distinguish 'glorious' from 'inglorious' revolutions--only the former preserves all 'the key components of a theory' [1]. A widespread view, expressed in these terms, is that empirical science characteristically exhibits inglorious revolutions but that revolutions in mathematics are at most glorious [2]. Here are three possible responses: 0. Accept that empirical science and mathematics are methodologically discontinuous; 1. Argue that mathematics can exhibit inglorious revolutions; 2. Deny that inglorious revolutions are (...) characteristic of science. Where Aberdein and Read take option 1, option 2 is preferred by Mizrahi [3]. This paper seeks to resolve this disagreement through consideration of some putative mathematical revolutions. [1] Andrew Aberdein and Stephen Read, The philosophy of alternative logics, The Development of Modern Logic (Leila Haaparanta, ed.), Oxford University Press, Oxford, 2009, pp. 613-723. [2] Donald Gillies (ed.), Revolutions in Mathematics, Oxford University Press, Oxford, 1992. [3] Moti Mizrahi, Kuhn's incommensurability thesis: What's the argument?, Social Epistemology 29 (2015), no. 4, 361-378. (shrink)