2025,
-
Expand entry
-
Publisher’s Note:
Mathematical logic has grown from an exotic branch of mathematics into an indispensable tool in computer science as well as other parts of mathematics. This concise book presents the subject of mathematical logic in a lively and approachable fashion although logic can be a formidably abstruse topic, even for mathematicians. This second edition of What is Mathematical Logic?, originally published 50 years ago, deals with important ideas in modern mathematical logic, without the detialed mathematical work required of those with a professional interest in logic. The ideas are set forth simply and clearly in a pleasant style and, despite the book's relative brevity, all the basic material is covered in these pages. Three new chapters have been added, coevering automatic theorem proving, logic beyond traditional first order logic, and other logics including intuitionistic, free, and modal logics. Students of computer science and mathematical logic will find it a stimulating introduction and valuable supplement for courses, including current further reading suggestions in this lively area at the intersection of mathematics, philosophy, and computer science.Comment: This book is an accessible overview of mathematical logic. The text can be used in an introductory logic course as supplementary reading.
Barcan Marcus, Ruth. Modalities: Philosophical Essays
1995, Oxford University Press.
-
Expand entry
-
Added by: Viviane FairbankAbstract:
This book is a collection of papers by Ruth Barcan Marcus, covering much ground in the development of her thought, and spanning from 1961 to 1990. Many of the papers deal with logical, semantic, metaphysical, and epistemological issues in intensional logic, and in particular, modalities. Some important themes that run through these papers are extensionality, the necessity of identity, the directly referential conception of proper names as “tags,” essentialism, substitutional quantification, and possibilia and possible worlds. What emerges from them is a robust defense of quantified modal logic in the light of a host of objections, particularly from Quine. Modalities also includes two papers on belief, which have consequences for epistemic logic and more widely for theories of rationality; two papers on ethical issues, which have consequences for deontic logic and practical reasoning; and finally, two papers on historical figures, Spinoza and Russell, dealing with the ontological proof of God's existence, and the nature of particularity, identity, and individuation, respectively.Comment: As Barcan Marcus surveys many of the central issues in (the epistemology and metaphysics of) modality and (quantified) modal logic, many of the papers in this collection could be included in survey courses on these topics.
Barrow-Green, June. Historical Context of the Gender Gap in Mathematics
2019, in World Women in Mathematics 2018: Proceedings of the First World Meeting for Women in Mathematics, Carolina Araujo et al. (eds.). Springer, Cham.
-
Expand entry
-
Added by: Fenner Stanley TanswellAbstract:
This chapter is based on the talk that I gave in August 2018 at the ICM in Rio de Janeiro at the panel on The Gender Gap in Mathematical and Natural Sciences from a Historical Perspective. It provides some examples of the challenges and prejudices faced by women mathematicians during last two hundred and fifty years. I make no claim for completeness but hope that the examples will help to shed light on some of the problems many women mathematicians still face today.Comment (from this Blueprint): Barrow-Green is a historian of mathematics. In this paper she documents some of the challenges that women faced in mathematics over the last 250 years, discussing many famous women mathematicians and the prejudices and injustices they faced.
Basso, Alessandra, Lisciandra, Chiara, Marchionni, Caterina. Hypothetical models in social science: their features and uses
2017, Springer Handbook of Model-Based Science. Magnani, L. & Bertolotti, T. (eds.). Springer, 413-433
-
Expand entry
-
Added by: Björn Freter, Contributed by: Johanna ThomaAbstract: The chapter addresses the philosophical issues raised by the use of hypothetical modeling in the social sciences. Hypothetical modeling involves the construction and analysis of simple hypothetical systems to represent complex social phenomena for the purpose of understanding those social phenomena. To highlight its main features hypothetical modeling is compared both to laboratory experimentation and to computer simulation. In analogy with laboratory experiments, hypothetical models can be conceived of as scientific representations that attempt to isolate, theoretically, the working of causal mechanisms or capacities from disturbing factors. However, unlike experiments, hypothetical models need to deal with the epistemic uncertainty due to the inevitable presence of unrealistic assumptions introduced for purposes of analytical tractability. Computer simulations have been claimed to be able to overcome some of the strictures of analytical tractability. Still they differ from hypothetical models in how they derive conclusions and in the kind of understanding they provide. The inevitable presence of unrealistic assumptions makes the legitimacy of the use of hypothetical modeling to learn about the world a particularly pressing problem in the social sciences. A review of the contemporary philosophical debate shows that there is still little agreement on what social scientific models are and what they are for. This suggests that there might not be a single answer to the question of what is the epistemic value of hypothetical models in the social sciences.Comment: This is a very useful and accessible overview of hypothetical modelling in the social sciences, and the philosophical debates it has given rise to.
Beebee, Helen. Necessary Connections and the Problem of Induction
2011, Noûs 45(3): 504-527.
-
Expand entry
-
Added by: Laura JimenezSummary: In this paper Beebee argues that the problem of induction, which she describes as a genuine sceptical problem, is the same for Humeans than for Necessitarians. Neither scientific essentialists nor Armstrong can solve the problem of induction by appealing to IBE (Inference to the Best Explanation), for both arguments take an illicit inductive step.Comment: This paper describes in a comprehensible way Armstrong's and the Humean approaches to the problem of induction. Ideal for postgraduate philosophy of science courses, although it could be a further reading for undergraduate courses as well.
Bell, Macalester. Against Simple Removal: A Defence of Defacement as a Response to Racist Monuments
2021, Journal of Applied Philosophy, 39(5): 778-792
-
Expand entry
-
Added by: Ten-Herng LaiAbstract:
In recent years, protesters around the world have been calling for the removal of commemorations honouring those who are, by contemporary standards, generally regarded as seriously morally compromised by their racism. According to one line of thought, leaving racist memorials in place is profoundly disrespectful, and doing so tacitly condones, and perhaps even celebrates, the racism of those honoured and memorialized. The best response is to remove the monuments altogether. In this article, I first argue against a prominent offense-based account of the wrong of simply leaving memorials in place, unaltered, before offering my own account of this wrong. In at least some cases, these memorials wrong insofar as they express and exemplify a morally objectionable attitude of race-based contempt. I go on to argue that the best way of answering this disrespect is through a process of expressively “dehonouring” the subject. Removal of these commemorations is ultimately misguided, in many cases, because removal, by itself, cannot adequately dishonour, and simple removal does not fully answer the ways in which these memorials wrong. I defend a more nuanced approach to answering the wrong posed by these monuments, and I argue that public expressions of contempt through defacement have an ineliminable role to play in an apt dishonouring process.Comment (from this Blueprint): Two things should be noted in this paper. First, many have discussed the importance of stopping or blocking the harm of objectionable commemorations. This paper goes a step further and discusses the importance of “answering” the wrong done by these monuments. Second, the paper engages with a “negative” emotion, namely, contempt, that is present at both racist monuments and the effort to confront them. It allows us to see the legitimate role this negative emotion may play in the struggle for equality: contempt can be apt towards inapt contempt expressed through racist monuments. It also nicely spells out the potential practical implications of taking this negative emotion seriously.
Bergmann, Merrie. An Introduction to Many-Valued and Fuzzy Logic: Semantics, Algebras, and Derivation Systems
2008, Cambridge University Press.
-
Expand entry
-
Added by: Berta GrimauPublisher's note: This volume is an accessible introduction to the subject of many-valued and fuzzy logic suitable for use in relevant advanced undergraduate and graduate courses. The text opens with a discussion of the philosophical issues that give rise to fuzzy logic - problems arising from vague language - and returns to those issues as logical systems are presented. For historical and pedagogical reasons, three valued logical systems are presented as useful intermediate systems for studying the principles and theory behind fuzzy logic. The major fuzzy logical systems - Lukasiewicz, Godel, and product logics - are then presented as generalizations of three-valued systems that successfully address the problems of vagueness. Semantic and axiomatic systems for three-valued and fuzzy logics are examined along with an introduction to the algebras characteristic of those systems. A clear presentation of technical concepts, this book includes exercises throughout the text that pose straightforward problems, ask students to continue proofs begun in the text, and engage them in the comparison of logical systems.Comment: This book is ideal for an intermediate-level course on many-valued and/or fuzzy logic. Although it includes a presentation of propositional and first-order logic, it is intended for students who are familiar with classical logic. However, no previous knowledge of many-valued or fuzzy logic is required. It can also be used as a secondary reading for a general course on non-classical logics. In the words of the author: 'The truth-valued semantic chapters are independent of the algebraic and axiomatic ones, so that either of the latter may be skipped. Except for Section 13.3 of Chapter 13, the axiomatic chapters are also independent of the algebraic ones, and an instructor who chooses to skip the algebraic material can simply ignore the latter part of 13.3. Finally, Lukasiewicz fuzzy logic is presented independently of Gödel and product fuzzy logics, thus allowing an instructor to focus solely on the former. There are exercises throughout the text. Some pose straightforward problems for the student to solve, but many exercises also ask students to continue proofs begun in the text, to prove results analogous to those in the text, and to compare the various logical systems that are presented.' This book is ideal for an intermediate-level course on many-valued and/or fuzzy logic. Although it includes a presentation of propositional and first-order logic, it is intended for students who are familiar with classical logic. However, no previous knowledge of many-valued or fuzzy logic is required. It can also be used as a secondary reading for a general course on non-classical logics. In the words of the author: 'The truth-valued semantic chapters are independent of the algebraic and axiomatic ones, so that either of the latter may be skipped. Except for Section 13.3 of Chapter 13, the axiomatic chapters are also independent of the algebraic ones, and an instructor who chooses to skip the algebraic material can simply ignore the latter part of 13.3. Finally, Lukasiewicz fuzzy logic is presented independently of Gödel and product fuzzy logics, thus allowing an instructor to focus solely on the former. There are exercises throughout the text. Some pose straightforward problems for the student to solve, but many exercises also ask students to continue proofs begun in the text, to prove results analogous to those in the text, and to compare the various logical systems that are presented.'
2003, Mcgraw-Hill.
-
Expand entry
-
Added by: Berta GrimauSummary: This book is an introductory textbook on mathematical logic. It covers Propositional Logic and Predicate Logic. For each of these formalisms it presents its syntax and formal semantics as well as a tableaux-style method of consistency-checking and a natural deduction-style deductive calculus. Moreover, it discusses the metatheory of both logics.Comment: This book would be ideal for an introductory course on symbolic logic. It presupposes no previous training in logic, and because it covers sentential logic through the metatheory of first-order predicate logic, it is suitable for both introductory and intermediate courses in symbolic logic. The instructor who does not want to emphasize metatheory can simply omit Chapters 6 and 11. The chapters on truth-trees and the chapters on derivations are independent, so it is possible to cover truth-trees but not derivations and vice versa. However, the chapters on truth-trees do depend on the chapters presenting semantics; that is, Chapter 4 depends on Chapter 3 and Chapter 9 depends on Chapter 8. In contrast, the derivation chapters can be covered without first covering semantics. The Logic Book includes large exercise sets for all chapters. Answers to unstarred exercises appear in the Student Solutions Manual, available at www.mhhe.com/bergmann6e, while answers to starred exercises appear in the Instructor's Manual, which can be obtained by following the instructions on the same web page.
Berninger, Anja. Commemorating Public Figures–In Favour of a Fictionalist Position
2020, Journal of Applied Philosophy
-
Expand entry
-
Added by: Ten-Herng LaiAbstract:
In this article, I discuss the commemoration of public figures such as Nelson Mandela and Yitzhak Rabin. In many cases, our commemoration of such figures is based on the admiration we feel for them. However, closer inspection reveals that most (if not all) of those we currently honour do not qualify as fitting objects of admiration. Yet, we may still have the strong intuition that we ought to continue commemorating them in this way. I highlight two problems that arise here: the problem that the expressed admiration does not seem appropriate with respect to the object and the problem that continued commemorative practices lead to rationality issues. In response to these issues, I suggest taking a fictionalist position with respect to commemoration. This crucially involves sharply distinguishing between commemorative and other discourses, as well as understanding the objects of our commemorative practices as fictional objects.Comment (from this Blueprint): This is a persuasive article arguing for a somewhat counter-intutive conclusion. The fictionalist approach, that what we honour is not the historical figure, but some idealised version of them, seems to capture what we actually do in the real world, even if we think we are not doing this. Do compare the position on eliminativism with Frowe's paper.
Besson, Corine. Logical knowledge and ordinary reasoning
2012, Philosophical Studies 158 (1):59-82.
-
Expand entry
-
Added by: Berta GrimauAbstract: This paper argues that the prominent accounts of logical knowledge have the consequence that they conflict with ordinary reasoning. On these accounts knowing a logical principle, for instance, is having a disposition to infer according to it. These accounts in particular conflict with so-called 'reasoned change in view', where someone does not infer according to a logical principle but revise their views instead. The paper also outlines a propositional account of logical knowledge which does not conflict with ordinary reasoning.Comment: This paper proposes a certain characterisation of what it is to have knowledge of logical principles which makes it compatible with the way in which we reason ordinarily. It can be seen as an alternative to Harman's view in 'Change in View' according to which ordinary people do not at all 'employ' a deductive logic in reasoning. Thus this paper could be used in a course on the role of logic in reasoning, following the reading of Harman's work. More generally, this reading is suitable for any advanced undergraduate course or postgraduate course on the topic of rationality.
Can’t find it?
Contribute the texts you think should be here and we’ll add them soon!