In this paper, I assume, perhaps controversially, that translation into a language of formal logic is not the method by which mathematicians assess mathematical reasoning. Instead, I argue that the actual practice of analyzing, evaluating and critiquing mathematical reasoning resembles, and perhaps equates with, the practice of informal logic or argumentation theory. It doesn’t matter whether the reasoning is a full-fledged mathematical proof or merely some non-deductive mathematical justification: in either case, the methodology of assessment overlaps to a large extent (...) with argument assessment in non-mathematical contexts. I demonstrate this claim by considering the assessment of axiomatic or deductive proofs, probabilistic evidence, computer-aided proofs, and the acceptance of axioms. I also consider Jody Azzouni’s ‘derivation indicator’ view of proofs because it places derivations—which may be thought to invoke formal logic—at the center of mathematical justificatory practice. However, when the notion of ‘derivation’ at work in Azzouni’s view is clarified, it is seen to accord with, rather than to count against, the informal logical view I support. Finally, I pose several open questions for the development of a theory of mathematical argument. (shrink)

I argue that a basic similarity analysis of analogical reasoning handles many apparent cases of visual analogy. I consider how the visual and verbal elements interact in analogical cases. Finally, I offer two analyses of visual elements. One analysis is evidential. The visual elements are evidence for their ver-bal counterparts. One is non-evidential: the visual elements link to verbal elements without providing evi-dence for those elements. The result is to make more room for the logical analysis of visual argumentation.

Written by experts in the field, this volume presents a comprehensive investigation into the relationship between argumentation theory and the philosophy of mathematical practice. Argumentation theory studies reasoning and argument, and especially those aspects not addressed, or not addressed well, by formal deduction. The philosophy of mathematical practice diverges from mainstream philosophy of mathematics in the emphasis it places on what the majority of working mathematicians actually do, rather than on mathematical foundations. -/- The book begins by first challenging the (...) assumption that there is no role for informal logic in mathematics. Next, it details the usefulness of argumentation theory in the understanding of mathematical practice, offering an impressively diverse set of examples, covering the history of mathematics, mathematics education and, perhaps surprisingly, formal proof verification. From there, the book demonstrates that mathematics also offers a valuable testbed for argumentation theory. Coverage concludes by defending attention to mathematical argumentation as the basis for new perspectives on the philosophy of mathematics. ​. (shrink)

Post-war argumentation theorists have tended to regard argumentation as one thing and mathematical proof as another. Perelman (1958, 1969), for example, defined the word ‘argumentation’ stipulatively as a contrast term to ‘demonstration’: whereas mathematical reasoning as theorized by modern formal logic, he writes, is a matter of deducing theorems from axioms in accordance with stipulated rules of transformation, argumentation aims at gaining the adherence of minds (Perelman 1969, pp. 1–2). Toulmin (1958) contrasted his “jurisprudential model” of argument, according to which (...) the validity of an argument is a matter of its following proper procedure, with a “geometrical model” according to which validity is a matter of its having a proper shape comparable to the shape of a triangle (Toulmin 1958, p. 95). Johnson (2000, pp. 231–232) argues explicitly that a mathematical proof is not an argument.In the collection under review, Andrew Aberdein and Ian Dove have assembled a number of recent. (shrink)

In “Image, Evidence, Argument,” Ian Dove defends an intriguing ‘middle ground’ between those who argue that there are “visual arguments” and skeptics who argue that there are not. I discuss one of Dove’s key examples, proposing a different analysis of it, arguing that there are problems with the “verbal repackaging” of the argument he suggests.

An exploration of the possible place and purpose of a postmodernizing planning, in the pursuit of ecological wisdom - defined, in Ken Wilber's terms, as how to get people to agree on how to live in accord with nature. Placemaking - conceived as a form of applied Integral Ecology - is hypothesized as an appropriate planning response, driven by a more explicit "spirit-friendly" outlook, with an associated critique of contemporary conventional notions of growth and sustainability. Place and placemaking are viewed (...) as furnishing the rich relief of an ecologically wise planning. (shrink)

Death from cancer is usually due to metastasis. Fortunately, most cells that escape from a primary tumor fail to form metastases. Identifying reasons for this failure will help development of anti‐metastatic therapies. Intravital videomicroscopy (IVVM) can be used to observe cancer cells injected into live animals. Co‐injected microspheres can be used to assess cell survival. These techniques have been used to show that circulating tumor cells generally arrest in the microcirculation and may extravasate with high efficiency. While many tumor cells (...) may survive in a secondary site, only a small subset form micrometastases and only a subset of these micrometastases persist to form vascularized macrometastases. Furthermore, solitary tumor cells may remain dormant for long periods of time in secondary sites. These findings suggest that metastatic growth and angiogenesis are prime targets for anti‐metastatic therapy. BioEssays 24:885–893, 2002. © 2002 Wiley Periodicals, Inc. (shrink)

Smith was devoted in his attentions to Hume as he lay dying, but, ever the man of prudence, gave his best friend some pain through unwillingness to see through the press the Dialogues concerning Natural Religion. In the event, Smith was violently abused by Christians for describing Hume in a published letter as approaching as near to the idea of a ‘perfectly wise and virtuous man’ as human weakness permits. Smith would have been in further trouble if his 1778 Machiavellian (...) advice about a solution to the American problem had been published, for it advocated returning Canada to the French, and Florida to the Spaniards, to ensure that independent Americans would become allies of Britain. (shrink)

I explore how empathetic visual argument may be the mode best suited for eliciting appropriate force to the reasons given by arguers who face systematic identity prejudices. In the verbal mode, this force is often skewed through epistemic injustice (Fricker 2007), argumentative injustice (Bondy 2010), and discursive injustice (Kukla 2010). Highlighting their reliance on the Aristotelian sense of enthymeme, I show how visual arguments are highly context specific. Using Ian Dove’s Visual Scheming (2016) and the theory of the Retort (...) collective (2004) via case study, I demonstrate how the visual mode can leave the appropriate force in the arguer’s control. (shrink)

Popper claims that error indicates what to avoid and there is no recipe for how to proceed. Most rationalist philosophers ignore his arguments and still try to justify their views instead of trying to improve upon them by criticizing them and conjecturing alternatives. In public discourse barren forms of justification are widespread. More and better critical institutions are required, and these require political compromise on shared aims.

This case study article draws upon experiences of a doctoral student and supervisor to reflect on the way in which we construct ethical narratives around our research. We seek to draw attention to the manner in which strict adherence to ERB guidelines can be problematic and risks causing more harm than it seeks to mitigate. We aim to show that we as researchers should focus on the potential harm caused to particularly vulnerable participants and draw attention to the need to (...) refocus conceptions of ethics away from a narrow, bureaucratic framework and towards moral concerns so as to avoid causing undue harm. (shrink)

There are more ways than one for philosophy of education to go to the dogs. Thinking of ourselves as (or assuming ourselves to be) living human beings, we do no.

THE SCHOLARLY LITERATURE on Aquinas' De aeternitate mundi is considerable; the controversy which has spawned it seems to have involved two major points of dispute. First there is the problem of dating the work; while some commentators believe it to have been written at an earlier stage in Aquinas' career--in the 1250s--the majority view is that it is a much later work, written in the early 1270s. Second, there is the problem of the continuity of doctrine between this work and (...) the other texts Aquinas has left us on the issue of the world's temporal duration. Does he propose the same position in all, or does De aeternitate mundi represent a departure? These two points of dispute come together when scholars discuss the historical context of this work. Thomas Bukowski sees it as an early defence of an unchanging position against the attacks of Bonaventure; Ignatius Brady sees it as a late defence of an unchanging position against the attacks of John Pecham. John Wippel, by contrast, takes it as a late departure from a previous view, and James Weisheipl, concurring with Wippel, attributes this change to Aquinas' study of Aristotle's Physics in the period before his second Paris regency. (shrink)

Health economists claim to use market economics combined with the microeconomic concepts of opportunity cost and the margin to advise on priority setting. However, they are advising on setting priorities through a macro-economic analysis using the costs of the supplier, thus prioritising the producer and not the consumer as the dynamic of economic activity. For health economists any contention within priority setting is due to lack of data not their confusion over fundamental concepts.

Barbados is a center of international genetic research premised on race. Drawing on ethnographic fieldwork following Johns Hopkins studies carried out in Barbados, this article explores this travel for research. This biomedical science relies on a conflicting significance of Barbados: as a site of suffering, due to the disparities of disease, and, conversely, a site of ease, playing on desires and pleasures of escaping too much asceticism in biomedicine. For the American researchers, Barbados becomes a locus of desire to ethically (...) address the African diaspora without the quandaries of accusations and recriminations experienced in carrying out such work in urban America. The concept of cathartic science is used to describe an endeavor that creates a controlled space to know and act on some perceived sufferer without risk of being complicit in the suffering. These medical migrations of researchers to Barbados are paralleled by Bajan families participating in the American studies as a kind of proxy medical migration to the US, bitterly reflecting on the care available to them at home. This article explores the motives of this mutual travel, as a biomedicalized Barbados becomes a spectral figure for patients and researchers fraught with race, injustice, and desire. The article extends the concept of cathartic science from genomics of race to medical anthropology to foreground the desires and anxieties of any science of suffering. (shrink)