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Bimbo, Katalin. Proof Theory: Sequent Calculi and Related Formalisms
2015, CRC Press, Boca Raton, FL
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Added by: Berta Grimau
Publisher's Note: Although sequent calculi constitute an important category of proof systems, they are not as well known as axiomatic and natural deduction systems. Addressing this deficiency, Proof Theory: Sequent Calculi and Related Formalisms presents a comprehensive treatment of sequent calculi, including a wide range of variations. It focuses on sequent calculi for various non-classical logics, from intuitionistic logic to relevance logic, linear logic, and modal logic. In the first chapters, the author emphasizes classical logic and a variety of different sequent calculi for classical and intuitionistic logics. She then presents other non-classical logics and meta-logical results, including decidability results obtained specifically using sequent calculus formalizations of logics.

Comment: This book can be used in a variety of advanced undergraduate and postgraduate courses. Chapters 1, 2, 3 and 8 may be useful in an advanced undergraduate or beginning graduate course, where an emphasis is placed on classical logic and on a range of different proof calculi (mainly for classical logic). Chapters 4, 5 and 6 deal almost exclusively with non-classical logics. Chapters 7 and 9 are rich in meta-logical results, including results that have been obtained specifically using sequent calculus formalizations of various logics. These last five chapters might be used in a graduate course that embraces classical and nonclassical logics together with their meta-theory. To facilitate the use of the book as a text in a course, the text is peppered with exercises. In general, the starring indicates an increase in difficulty, however, sometimes an exercise is starred simply because it goes beyond the scope of the book or it is very lengthy. Solutions to selected exercises may be found on the web at the URL www.ualberta.ca/˜bimbo/ProofTheoryBook.

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Blanchette, Patricia. Frege and Hilbert on Consistency
1996, Journal of Philosophy 93 (7):317
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Added by: Clotilde Torregrossa, Contributed by: Alex Yates
Abstract: Gottlob Frege's work in logic and the foundations of mathemat- ics centers on claims of logical entailment; most important among these is the claim that arithmetical truths are entailed by purely logical principles. Occupying a less central but nonetheless important role in Frege's work are claims about failures of entailment. Here, the clearest examples are his theses that the truths of geometry are not entailed by the truths of logic or of arithmetic, and that some of them are not entailed by each other. As he, and we, would put it: the truths of Eluclidean geometry are independent of the truths of logic, and some of them are independent of one another.' Frege's talk of independence and related notions sounds familiar to a modern ear: a proposition is independent of a collection of propositions just in case it is not a consequence of that collection, and a proposition or collection of propositions is consistent just in case no contradiction is a consequence of it. But some of Frege's views and procedures are decidedly tinmodern. Despite developing an extremely sophisticated apparattus for demonstrating that one claim is a consequience of others, Frege offers not a single demon- stration that one claim is not a conseqtuence of others. Thus, in par- tictular, he gives no proofs of independence or of consistency. This is no accident. Despite his firm commitment to the independence and consistency claims just mentioned, Frege holds that independence and consistency cannot systematically be demonstrated.2 Frege's view here is particularly striking in light of the fact that his contemporaries had a fruitful and systematic method for proving consistency and independence, a method which was well known to him. One of the clearest applications of this method in Frege's day came in David Hilbert's 1899 Foundations of Geometry,3 in which he es- tablishes via essentially our own modern method the consistency and independence of various axioms and axiom systems for Euclidean geometry. Frege's reaction to Hilbert's work was that it was simply a failure: that its central methods were incapable of demonstrating consistency and independence, and that its usefulness in the founda- tions of mathematics was highly questionable.4 Regarding the general usefulness of the method, it is clear that Frege was wrong; the last one hundred years of work in logic and mathemat- ics gives ample evidence of the fruitfulness of those techniques which grow directly from the Hilbert-style approach. The standard view today is that Frege was also wrong in his claim that Hilbert's methods fail to demonstrate consistency and independence. The view would seem to be that Frege largely missed Hilbert's point, and that a better under- standing of Hilbert's techniques would have revealed to Frege their success. Despite Frege's historic role as the founder of the methods we now use to demonstrate positive consequence-results, he simply failed, on this account, to understand the ways in which Hilbert's methods could be used to demonstrate negative consequence-results. The purpose of this paper is to question this account of the Frege- Hilbert disagreement. By 1899, Frege had a well-developed view of log- ical consequence, consistency, and independence, a view which was central to his foundational work in arithmetic and to the epistemologi- cal significance of that work. Given this understanding of the logical relations, I shall argue, Hilbert's demonstrations do fail. Successful as they were in demonstrating significant metatheoretic results, Hilbert's proofs do not establish the consistency and independence, in Frege's sense, of geometrical axioms. This point is important, I think, both for an understanding of the basis of Frege's epistemological claims about mathematics, and for an understanding of just how different Frege's conception of logic is from the modern model-theoretic conception that has grown out of the Hilbert-style approach to consistency.

Comment: Good for a historically-based course on philosophy of logic or mathematics.

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Blanchette, Patricia. Frege’s Conception of Logic
2012, New York: Oxford University Press.
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Added by: Clotilde Torregrossa, Contributed by: Alex Yates
Publisher's Note: In Frege's Conception of Logic Patricia A. Blanchette explores the relationship between Gottlob Frege's understanding of conceptual analysis and his understanding of logic. She argues that the fruitfulness of Frege's conception of logic, and the illuminating differences between that conception and those more modern views that have largely supplanted it, are best understood against the backdrop of a clear account of the role of conceptual analysis in logical investigation. The first part of the book locates the role of conceptual analysis in Frege's logicist project. Blanchette argues that despite a number of difficulties, Frege's use of analysis in the service of logicism is a powerful and coherent tool. As a result of coming to grips with his use of that tool, we can see that there is, despite appearances, no conflict between Frege's intention to demonstrate the grounds of ordinary arithmetic and the fact that the numerals of his derived sentences fail to co-refer with ordinary numerals. In the second part of the book, Blanchette explores the resulting conception of logic itself, and some of the straightforward ways in which Frege's conception differs from its now-familiar descendants. In particular, Blanchette argues that consistency, as Frege understands it, differs significantly from the kind of consistency demonstrable via the construction of models. To appreciate this difference is to appreciate the extent to which Frege was right in his debate with Hilbert over consistency- and independence-proofs in geometry. For similar reasons, modern results such as the completeness of formal systems and the categoricity of theories do not have for Frege the same importance they are commonly taken to have by his post-Tarskian descendants. These differences, together with the coherence of Frege's position, provide reason for caution with respect to the appeal to formal systems and their properties in the treatment of fundamental logical properties and relations.

Comment: This book would be a suitable resource for independent study, or for a historically oriented course on philosophy of logic, of math, or on early analytic philosophy, especially one which looks at philosophical approaches to axiomatic systems.

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Blanchette, Patricia. Logical Consequence
2001, In Lou Goble (Ed). Blackwell Guide to Philosophical Logic. Wiley-Blackwell: 115-135.
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Added by: Berta Grimau, Contributed by: Patricia Blanchette
Abstract: Description: This article is a short overview of philosophical and formal issues in the treatment and analysis of logical consequence. The purpose of the paper is to provide a brief introduction to the central issues surrounding two questions: (1) that of the nature of logical consequence and (2) that of the extension of logical consequence. It puts special emphasis in the role played by formal systems in the investigation of logical consequence.

Comment: This article can be used as background or overview reading in a course on the notion of logical consequence. It could also be used in a general course on philosophy of logic having a section on this topic. It makes very little use of technical notation, even though familiarity with first-order logic is required. It closes with a useful list of suggested further readings.

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Blanchette, Patricia. Models and Modality
2000, Synthese 124(1): 45-72.
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Added by: Berta Grimau, Contributed by: Patricia Blanchette
Abstract: This paper examines the connection between model-theoretic truth and necessary truth. It is argued that though the model-theoretic truths of some standard languages are demonstrably "necessary" (in a precise sense), the widespread view of model-theoretic truth as providing a general guarantee of necessity is mistaken. Several arguments to the contrary are criticized.

Comment: This text would be best used as secondary reading in an intermediate or an advanced philosophy of logic course. For example, it can be used as a secondary reading in a section on the connection between model-theoretic truth and necessary truth.

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Blyden, Edward Wilmot. Christianity, Islam, and the Negro Race
1887, Black Classic Press
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, Contributed by: Quentin Pharr
Publisher’s Note: A native of St. Thomas, West Indies, Edward Wilmot Blyden (1832-1912) lived most of his life on the African continent. He was an accomplished educator, linguist, writer, and world traveler, who strongly defended the unique character of Africa and its people. Christianity, Islam and the Negro Race is an essential collection of his writings on race, culture, and the African personality.

Comment: This collection of essays is seminal in the intellectual foundations of Pan-Africanism, African Islamism, African Anti-colonialism, the Back-to-Africa Movement, and the educational revival in Liberia/West Africa. The essays are great for courses on African thought, or African anti-colonialism/postcolonialism. They would also be excellent companion texts for reading Marcus Garvey or Kwame Nkrumah, or vice versa.

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Bobzien, Susanne. Ancient Logic
2016, The Stanford Encyclopedia of Philosophy
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Added by: Berta Grimau, Contributed by: Giada Fratantonio
Summary: A comprehensive introduction to ancient (western) logic from the 5th century BCE to the 6th century CE, with an emphasis on topics which may be of interest to contemporary logicians. Topics include pre-Aristotelian logic, Aristotelian logic, Peripatetic logic, Stoic Logic and a note on Epicureans and their views on logic.

Comment: This paper would be ideal as an introductory overview for a course on ancient logic. Alternatively, it could serve as an overview for a module on ancient logic within a more general course on the history of logic. No prior knowledge of logic is required; formalisms are for the most part avoided in the paper. Note that this is a SEP entry, so it's completely accessible to students.

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Bobzien, Susanne. Stoic Syllogistic
1996, Oxford Studies in Ancient Philosophy 14: 133-92.
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Added by: Berta Grimau, Contributed by: Giada Fratantonio
Abstract: For the Stoics, a syllogism is a formally valid argument; the primary function of their syllogistic is to establish such formal validity. Stoic syllogistic is a system of formal logic that relies on two types of argumental rules: (i) 5 rules (the accounts of the indemonstrables) which determine whether any given argument is an indemonstrable argument, i.e. an elementary syllogism the validity of which is not in need of further demonstration; (ii) one unary and three binary argumental rules which establish the formal validity of non-indemonstrable arguments by analysing them in one or more steps into one or more indemonstrable arguments (cut type rules and antilogism). The function of these rules is to reduce given non-indemonstrable arguments to indemonstrable syllogisms. Moreover, the Stoic method of deduction differs from standard modern ones in that the direction is reversed (similar to tableau methods). The Stoic system may hence be called an argumental reductive system of deduction. In this paper, a reconstruction of this system of logic is presented, and similarities to relevance logic are pointed out.

Comment: This paper can be used as specialised/further reading for an advanced undergrad or postgraduate course on ancient logic or as a primary reading in an advanced undergrad or postgraduate course on Stoic logic. Alternatively, given that the text argues that there are important parallels between Stoic logic and Relevance logic, it could be used in a course on Relevance logic as well. It requires prior knowledge of logic (in particular, proof theory).

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Boden, Margaret A.. Intentionality and physical systems
1970, Philosophy of Science 32 (June):200-214.
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Added by: Clotilde Torregrossa, Contributed by: Simon Fokt
Abstract: Intentionality is characteristic of many psychological phenomena. It is commonly held by philosophers that intentionality cannot be ascribed to purely physical systems. This view does not merely deny that psychological language can be reduced to physiological language. It also claims that the appropriateness of some psychological explanation excludes the possibility of any underlying physiological or causal account adequate to explain intentional behavior. This is a thesis which I do not accept. I shall argue that physical systems of a specific sort will show the characteristic features of intentionality. Psychological subjects are, under an alternative description, purely physical systems of a certain sort. The intentional description and the physical description are logically distinct, and are not intertranslatable. Nevertheless, the features of intentionality may be explained by a purely causal account, in the sense that they may be shown to be totally dependent upon physical processes.

Comment:

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Bokulich, Alisa. Distinguishing Explanatory from Nonexplanatory Fictions
2012, Philosophy of Science 79(5): 725-737.
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Added by: Jamie Collin
Abstract: There is a growing recognition that fictions have a number of legitimate functions in science, even when it comes to scientific explanation. However, the question then arises, what distinguishes an explanatory fiction from a nonexplanatory one? Here I examine two cases - one in which there is a consensus in the scientific community that the fiction is explanatory and another in which the fiction is not explanatory. I shall show how my account of "model explanations" is able to explain this asymmetry, and argue that realism - of a more subtle form - does have a role in distinguishing explanatory from nonexplanatory fictions.

Comment: This would be useful in a course on the philosophy of science or the philosophy of fiction. It is particularly useful for teaching, as it is cutting edge in the philosophy of science but not particularly technical.

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Bokulich, Alisa. How scientific models can explain
2009, Synthese 180(1): 33-45.
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Added by: Laura Jimenez
Abstract: Scientific models invariably involve some degree of idealization, abstraction, or fictionalization of their target system. Nonetheless, I argue that there are circumstances under which such false models can offer genuine scientific explanations. After reviewing three different proposals in the literature for how models can explain, I shall introduce a more general account of what I call model explanations, which specify the conditions under which models can be counted as explanatory. I shall illustrate this new framework by applying it to the case of Bohr's model of the atom, and conclude by drawing some distinctions between phenomenological models, explanatory models, and fictional models.

Comment: Interesting paper about scientific modelling. It is easy to read and could serve as an introduction to the topic. The paper explores three approaches to Model Explanations: mechanist model explanations, covering-law model explanations, and causal model explanations. The explanatory function in models is illustrated with the example of Bohr's atom. This article is recommended for undergraduate students.

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Bortolotti, Lisa, Daniela Cutas. Reproductive and Parental Autonomy: An Argument for Compulsory Education
2009, Reproductive Biomedicine Online, 19 (Ethics Supplement): 5-14.
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Added by: Rochelle DuFord
Abstract: In this paper we argue that society should make available reliable information about parenting to everybody from an early age. The reason why parental education is important (when offered in a comprehensive and systematic way) is that it can help young people understand better the responsibilities associated with reproduction, and the skills required for parenting. This would allow them to make more informed life-choices about reproduction and parenting, and exercise their autonomy with respect to these choices. We do not believe that parental education would constitute a limitation of individual freedom. Rather, the acquisition of relevant information about reproduction and parenting and the acquisition of self-knowledge with respect to reproductive and parenting choices can help give shape to individual life plans. We make a case for compulsory parental education on the basis of the need to respect and enhance individual reproductive and parental autonomy within a culture that presents contradictory attitudes towards reproduction and where decisions about whether to become a parent are subject to significant pressure and scrutiny.

Comment: This text provides a clear overview of debates about reproductive autonomy and compulsory education. It also contains responses to well known criticisms of compulsory parental education. It would be best used in a course dealing with issues of parenthood and procreation, reproduction, or autonomy in a medical context.

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Bowell, Tracy, Gary Kemp. Critical Thinking: A Concise Guide
2014, Routledge; 4 edition.
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Added by: Berta Grimau
Publisher's note: We are frequently confronted with arguments. Arguments are attempts to persuade us - to influence our beliefs and actions - by giving us reasons to believe this or that. Critical Thinking: A Concise Guide will equip students with the concepts and techniques used in the identification, analysis and assessment of arguments. Through precise and accessible discussion, this book provides the tools to become a successful critical thinker, one who can act and believe in accordance with good reasons, and who can articulate and make explicit those reasons. Key topics discussed include:
  • Core concepts in argumentation.
  • How language can serve to obscure or conceal the real content of arguments; how to distinguish argumentation from rhetoric.
  • How to avoid common confusions surrounding words such as 'truth', 'knowledge' and 'opinion'.
  • How to identify and evaluate the most common types of argument.
  • How to distinguish good reasoning from bad in terms of deductive validly and induction.

Comment: Appropriate for complete beginners to logic and philosophy. Adequate for an introduction to critical thinking. It doesn't presuppose any previous knowledge of logic. Moreover, there is an interactive website for the book which provides resources for both instructors and students including new examples and case studies, flashcards, sample questions, practice questions and answers, student activities and a test bank of questions for use in the classroom.

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Brading, Katherine, Elena Castellani. Symmetry and Symmetry Breaking
2013, The Standford Encyclopedia of Philosophy
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Added by: Laura Jimenez
Introduction: Symmetry considerations dominate modern fundamental physics, both in quantum theory and in relativity. Philosophers are now beginning to devote increasing attention to such issues as the significance of gauge symmetry, quantum particle identity in the light of permutation symmetry, how to make sense of parity violation, the role of symmetry breaking, the empirical status of symmetry principles, and so forth. These issues relate directly to traditional problems in the philosophy of science, including the status of the laws of nature, the relationships between mathematics, physical theory, and the world, and the extent to which mathematics suggests new physics. This entry begins with a brief description of the historical roots and emergence of the concept of symmetry that is at work in modern science. It then turns to the application of this concept to physics, distinguishing between two different uses of symmetry: symmetry principles versus symmetry arguments. It mentions the different varieties of physical symmetries, outlining the ways in which they were introduced into physics. Then, stepping back from the details of the various symmetries, it makes some remarks of a general nature concerning the status and significance of symmetries in physics.

Comment: This article offers a good introduction to the topic of symmetries. The entry begins with a brief description of the historical roots and emergence of the concept of symmetry that could serve as a reading for undergraduates. It then turns to the application of this concept to physics and merges the discussion with issues in relativity and quantum mechanics. This second part of the article is thus more suitable to postgraduate courses in philosophy of science, specially, philosophy of physics. It could serve as a secondary reading for those researching the laws of nature.

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Briggs, Rachael. Distorted Reflection
2009, Philosophical Review 118(1): 59-85.
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Added by: Berta Grimau, Contributed by: Antony Eagle
Abstract: Diachronic Dutch book arguments seem to support both conditionalization and Bas van Fraassen's Reflection principle. But the Reflection principle is vulnerable to numerous counterexamples. This essay addresses two questions: first, under what circumstances should an agent obey Reflection, and second, should the counterexamples to Reflection make us doubt the Dutch book for conditionalization? In response to the first question, this essay formulates a new 'Qualified Reflection' principle, which states that an agent should obey Reflection only if he or she is certain that he or she will conditionalize on veridical evidence in the future. Qualified Reflection follows from the probability calculus together with a few idealizing assumptions. The essay then formulates a 'Distorted Reflection' principle that approximates Reflection even in cases where the agent is not quite certain that he or she will conditionalize on veridical evidence. In response to the second question, the essay argues that contrary to a common misconception, not all Dutch books dramatize incoherence - some dramatize a less blameworthy sort of epistemic frailty that the essay calls 'self-doubt'. The distinction between Dutch books that dramatize incoherence and those that dramatize self-doubt cross-cuts the distinction between synchronic and diachronic Dutch books. The essay explains why the Dutch book for conditionalization reveals true incoherence, whereas the Dutch book for Reflection reveals only self-doubt.

Comment: Appropriate for a graduate level philosophy of probability or formal philosophy seminar. It's a useful adjunct to other readings on the reflection principle which has been recently much discussed.

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