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Added by: Fenner Stanley TanswellAbstract:
Over a period of more than 30 years, more than 100 mathematicians worked on a project to classify mathematical objects known as finite simple groups. The Classification, when officially declared completed in 1981, ranged between 300 and 500 articles and ran somewhere between 5,000 and 10,000 journal pages. Mathematicians have hailed the project as one of the greatest mathematical achievements of the 20th century, and it surpasses, both in scale and scope, any other mathematical proof of the 20th century. The history of the Classification points to the importance of face-to-face interaction and close teaching relationships in the production and transformation of theoretical knowledge. The techniques and methods that governed much of the work in finite simple group theory circulated via personal, often informal, communication, rather than in published proofs. Consequently, the printed proofs that would constitute the Classification Theorem functioned as a sort of shorthand for and formalization of proofs that had already been established during personal interactions among mathematicians. The proof of the Classification was at once both a material artifact and a crystallization of one community’s shared practices, values, histories, and expertise. However, beginning in the 1980s, the original proof of the Classification faced the threat of ‘uninvention’. The papers that constituted it could still be found scattered throughout the mathematical literature, but no one other than the dwindling community of group theorists would know how to find them or how to piece them together. Faced with this problem, finite group theorists resolved to produce a ‘second-generation proof’ to streamline and centralize the Classification. This project highlights that the proof and the community of finite simple groups theorists who produced it were co-constitutive–one formed and reformed by the other.Sznajder, Marta. Janina Hosiasson-Lindenbaum on Analogical Reasoning: New Sources2022, Erkenntnis 89(4): 1349–1365.-
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Added by: Viviane FairbankAbstract:
Janina Hosiasson-Lindenbaum is a known figure in philosophy of probability of the 1930s. A previously unpublished manuscript fills in the blanks in the full picture of her work on inductive reasoning by analogy, until now only accessible through a single publication. In this paper, I present Hosiasson’s work on analogical reasoning, bringing together her early publications that were never translated from Polish, and the recently discovered unpublished work. I then show how her late work relates to Rudolf Carnap’s approach to “analogy by similarity” developed in the 1960s. Hosiasson turns out to be a predecessor of the line of research that models analogical influence as inductive relevance. A translation of Hosiasson’s manuscript concludes the paper.
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Sznajder, Marta. Inductive Logic as Explication: The Evolution of Carnap’s Notion of Logical Probability2018, The Monist 101(4): 417–440.-
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Added by: Viviane FairbankAbstract:
According to a popular interpretation, Carnap’s interpretation of probability had evolved from a logical towards a subjective conception. However Carnap himself insisted that his basic philosophical view of probability was always the same. I address this apparent clash between Carnap's self-identification and the subsequent interpretations of his work. Following its original intentions, I reconstruct inductive logic as an explication. The emerging picture is of a versatile linguistic framework, whose main function is not the discovery of objective logical relations in the object language, but the stipulation of conceptual possibilities. Within this representation, I map out the changes that the project went through. Seen from such an explication-based perspective, inductive logic becomes quite hard to categorize using the standard labels.
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Tao, Terence. What is good mathematics?2007, Bulletin of the American Mathematical Society, 44(4): 623-634.-
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Added by: Fenner Stanley TanswellAbstract:
Some personal thoughts and opinions on what “good quality mathematics” is and whether one should try to define this term rigorously. As a case study, the story of Szemer´edi’s theorem is presented.Comment (from this Blueprint): Tao is a mathematician who has written extensively about mathematics as a discipline. In this piece he considers what counts as “good mathematics”. The opening section that I’ve recommended has a long list of possible meanings of “good mathematics” and considers what this plurality means for mathematics. (The remainder details the history of Szemerédi’s theorem, and argues that good mathematics also involves contributing to a great story of mathematics. However, it gets a bit technical, so only look into it if you’re particularly interested in the details of the case.)
Taylor, Elanor. Explanation and The Right to Explanation2023, Journal of the American Philosophical Association 1:1-16-
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Added by: Deryn Mair ThomasAbstract:
In response to widespread use of automated decision-making technology, some have considered a right to explanation. In this paper I draw on insights from philosophical work on explanation to present a series of challenges to this idea, showing that the normative motivations for access to such explanations ask for something difficult, if not impossible, to extract from automated systems. I consider an alternative, outcomes-focused approach to the normative evaluation of automated decision-making, and recommend it as a way to pursue the goods originally associated with explainability.
Comment: This paper offers a clear overview of the literature on the right to explanation and counters the mainstream view that, in the context of automated decision-making technology, that we hold such a right. It would therefore offer a useful introduction to ideas about explanability in relation to the ethics of AI and automated technologies, and could be used in a reading group context as well as in upper undergraduate and graduate level courses.
ter Meulen, Alice. Logic and Natural Language2001, In Lou Goble (ed.), The Blackwell Guide to Philosophical Logic. Blackwell-
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Added by: Franci MangravitiAbstract:
Logicians have always found inspiration for new research in the ordinary language that is used on a daily basis and acquired naturally in childhood. Whereas the logical issues in the foundations of mathematics motivated the development of mathematical logic with its emphasis on notions of proof, validity, axiomatization, decidability, consistency, and completeness, the logical analysis of natural language motivated the development of philosophical logic with its emphasis on semantic notions of presupposition, entailment, modality, conditionals, and intensionality. The relation between research programs in both mathematical and philosophical logic and natural language syntax and semantics as branches of theoretical linguistics has increased in importance throughout the last fifty years. This chapter reviews the development of one particularly interesting and lively area of interaction between formal logic and linguistics—the semantics of natural language. Research in this emergent field has proved fruitful for the development of empirically, cognitively adequate models of reasoning with partial information, sharing or exchanging information, dynamic interpretation in context, belief revision and other cognitive processes.
Comment: Can be helpful in an introductory course to philosophy of language or in an introductory course to logic, to emphasize the connection with linguistics. There are basically no formal prerequisites.
Thalos, Mariam. A modest proposal for interpreting structural explanations1998, British Journal for the Philosophy of Science 49(2): 279-295.-
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Added by: Nick Novelli
Abstract: Social sciences face a well-known problem, which is an instance of a general problem faced as well by psychological and biological sciences: the problem of establishing their legitimate existence alongside physics. This, as will become clear, is a problem in metaphysics. I will show how a new account of structural explanations, put forward by Frank Jackson and Philip Pettit, which is designed to solve this metaphysical problem with social sciences in mind, fails to treat the problem in any importantly new way. Then I will propose a more modest approach, and show how it does not deserve the criticism directed at a prototype by Jackson and PettitComment: An interesting argument for the value of structual explanations in sociology. Useful in the context of a discussion of reductionism or of the proper classification of social sciences as real science.
Thalos, Mariam. Explanation is a genus: An essay on the varieties of scientific explanation2002, Synthese 130(3): 317-354.-
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Added by: Nick Novelli
Abstract: I shall endeavor to show that every physical theory since Newton explainswithout drawing attention to causes-that, in other words, physical theories as physical theories aspire to explain under an ideal quite distinctfrom that of causal explanation. If I am right, then even if sometimes theexplanations achieved by a physical theory are not in violation ofthe standard of causal explanation, this is purely an accident. For physicaltheories, as I will show, do not, as such, aim at accommodating the goals oraspirations of causal explanation. This will serve as the founding insightfor a new theory of explanation, which will itself serve as the cornerstoneof a new theory of scientific method.Comment: A striking argument that science does not employ causal explanations. Since this is a commonly-held assumption, this would be interesting to present in the context of scientific methodology, or in an exploration of causation as part of a challenge to whether the idea of causation is actually useful or necessary. Provides good historical context to support its claims. Best taught at an advanced or graduate level.
Thalos, Mariam. Nonreductive physics2006, Synthese 149(1): 133-178.-
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Added by: Nick Novelli
Abstract: This paper documents a wide range of nonreductive scientific treatments of phenomena in the domain of physics. These treatments strongly resist characterization as explanations of macrobehavior exclusively in terms of behavior of microconstituents. For they are treatments in which macroquantities are cast in the role of genuine and irreducible degrees of freedom.Comment: A good argument against reduction, grounded in scientific practice. Would be useful in a philosophy of science or a metaphysics context to explore and challenge the idea of reduction. Does a good job of explaining some fairly technical concepts as clearly as possible, but still best suited to graduate or upper-level undergraduate teaching.
Uckelman, Sara L.. A Quantified Temporal Logic for Ampliation and Restriction2013, Vivarium 51(1-4): 485-510.-
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Added by: Berta Grimau, Contributed by: Sara L. Uckelman
Abstract: Temporal logic as a modern discipline is separate from classical logic; it is seen as an addition or expansion of the more basic propositional and predicate logics. This approach is in contrast with logic in the Middle Ages, which was primarily intended as a tool for the analysis of natural language. Because all natural language sentences have tensed verbs, medieval logic is inherently a temporal logic. This fact is most clearly exemplified in medieval theories of supposition. As a case study, we look at the supposition theory of Lambert of Lagny (Auxerre), extracting from it a temporal logic and providing a formalization of that logic.Comment: This article employs modal-temporal logic with Kripke semantics to formalize a particular supposition theory (Lambert of Lagny’s). Thus, it includes an original proposal. Moreover, it provides both an introduction to medieval supposition theory and an introduction to Kripke semantics. So, it could be used as a means to work on either of those topics. It does not involve many technicalities, but a bit of familiarity with modal logic is recommended.
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Steingart, Alma. A Group Theory of Group Theory: Collaborative Mathematics and the ‘Uninvention’ of a 1000-page Proof
2012, Social Studies of Science, 42(2): 185-213.
Comment (from this Blueprint): Steingart is a sociologist who charts the history and sociology of the development of the extremely large and highly collaborative Classification Theorem. She shows that the proof involved a community deciding on shared values, standards of reliability, expertise, and ways of communicating. For example, the community became tolerant of so-called “local errors” so long as these did not put the main result at risk. Furthermore, Steingart discusses how the proof’s text is distributed across a wide number of places and requires expertise to navigate, leaving the proof in danger of uninvention if the experts retire from mathematics.