Showing papers in "History and Philosophy of Logic in 2015"
TL;DR: In this paper, attempts are made to reconstruct networks of scholars and ideas prevalent in the 1950s, and to identify a specific group of actors interested in theorizing about computations in computers and attracted to the idea of language as a frame in which to understand computation.
Abstract: In the popular imagination, the relevance of Turing's theoretical ideas to people producing actual machines was significant and appreciated by everybody involved in computing from the moment he published his 1936 paper ‘On Computable Numbers’. Careful historians are aware that this popular conception is deeply misleading. We know from previous work by Campbell-Kelly, Aspray, Akera, Olley, Priestley, Daylight, Mounier-Kuhn, Haigh, and others that several computing pioneers, including Aiken, Eckert, Mauchly, and Zuse, did not depend on (let alone were they aware of) Turing's 1936 universal-machine concept. Furthermore, it is not clear whether any substance in von Neumann's celebrated 1945 ‘First Draft Report on the EDVAC’ is influenced in any identifiable way by Turing's work. This raises the questions: (i) When does Turing enter the field? (ii) Why did the Association for Computing Machinery (ACM) honor Turing by associating his name to ACM's most prestigious award, the Turing Award? Previous authors have ...
40 citations
TL;DR: This paper provided a historical exposition of John Buridan's theory of divided modal propositions and developed a semantic interpretation of the theory which pays particular attention to the ampliation of modal terms.
Abstract: In this paper, we provide a historical exposition of John Buridan's theory of divided modal propositions. We then develop a semantic interpretation of Buridan's theory which pays particular attention to Buridan's ampliation of modal terms. We show that these semantics correctly capture his syllogistic reasoning.
27 citations
TL;DR: The first critical edition of Peter of Spain's Tractatus appeared in a critical edition by L.M. de Rijk (1972) as discussed by the authors, which is a handbook on logic; it is now estimated that it dates from the second quarter of the thirteenth century.
Abstract: Peter of Spain's Tractatus, which appeared in a first critical edition by L.M. de Rijk (1972), is a handbook on logic; it is now estimated that it dates from the second quarter of the thirteenth ce...
17 citations
TL;DR: This paper cast doubt upon the view that Albert was dependent upon Thomas Manlevelt's logico-philosophical views, and counter argues that it is in fact ManLevelt who knows and cites Albert's views in his recently edited Porphyrian Questions, rather than vice versa.
Abstract: The essay casts doubt upon the view that Albert was criticizing or was dependent upon Thomas Manlevelt's logico-philosophical views, and counter argues that it is in fact Manlevelt who knows and cites Albert's views in his recently edited Porphyrian Questions, rather than vice versa. The argument for this conclusion proceeds in two stages. First, it is argued that the brief comment Albert makes about ‘conjunct descent’ (descensus copulatim) in treating the definition of merely confused supposition his Perutilis Logica does not conclusively show that Albert is criticizing the logico-philosophical view of Thomas Manlevelt, as the notion of ‘conjunct descent’ is already present in the work of Heytesbury. Hence, Albert may have been referring to him, since the unique contribution of Thomas Manlevelt to the definition of merely confused personal supposition appears completely unknown to Albert. Second, it is argued that the views in the Porphyrian Questions on the nature of the continuum, quantity, and disposi...
15 citations
TL;DR: Fetzer and like-minded thinkers as mentioned in this paper claim that program verification is not even a theoretical possibility, and offer a certain argument for this far-reaching claim, which is demonstrably self-refuting.
Abstract: Fetzer famously claims that program verification is not even a theoretical possibility, and offers a certain argument for this far-reaching claim. Unfortunately for Fetzer, and like-minded thinkers, this position-argument pair, while based on a seminal insight that program verification, despite its Platonic proof-theoretic airs, is plagued by the inevitable unreliability of messy, real-world causation, is demonstrably self-refuting. As I soon show, Fetzer (and indeed anyone else who provides an argument- or proof-based attack on program verification) is like the person who claims: ‘My sole claim is that every claim expressed by an English sentence and starting with the phrase “My sole claim” is false’. Or, more accurately, such thinkers are like the person who claims that modus tollens is invalid, and supports this claim by giving an argument that itself employs this rule of inference.
12 citations
TL;DR: In this article, a contextual analysis of Frege's Grundlagen, section 64, is presented, with the context of a widespread debate in Germany on "directions" as a central notion in the theory of parallels.
Abstract: I offer in this paper a contextual analysis of Frege's Grundlagen, section 64. It is surprising that with so much ink spilled on that section, the sources of Frege's discussion of definitions by abstraction have remained elusive. I hope to have filled this gap by providing textual evidence coming from, among other sources, Grassmann, Schlomilch, and the tradition of textbooks in geometry for secondary schools (including a textbook Frege had used when teaching in a Privatschule in Jena in 1882–1884). In addition, I put Frege's considerations in the context of a widespread debate in Germany on ‘directions’ as a central notion in the theory of parallels.
11 citations
TL;DR: The evaluation of arguments was not the sole concern of logicians in ancient India as mentioned in this paper, but the interaction between logic and ontology was also an interesting example of the interaction as mentioned in this paper.
Abstract: The evaluation of arguments was not the sole concern of logicians in ancient India. Early Nyāya and the later Navya-Nyāya provide an interesting example of the interaction between logic and ontology. In their attempt to develop a kind of property-location logic (Navya-)Naiyāyikas had to consider what kind of restrictions they should impose on the residence relation between a property and its locus (which might again be a property). Can we admit circular residence relations or infinitely descending chains of properties, each depending on its successor as its locus? Early Naiyāyikas and to some extent also Navya-Naiyāyikas regard these phenomena as a kind of absurdity and they want to rule them out. Their intuitions about properties are close to well-founded systems of set theory, whereas the author of the Navya-Nyāya work Upādhidarpaṇa is a proponent of a non-well-founded property concept. Despite certain similarities with sets properties are still regarded as intensional objects in Navya-Nyāya. In the pre...
9 citations
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TL;DR: In this article, the authors outline the intellectual biography of the Berlin Group and the Society for Empirical/Scientific Philosophy in Berlin, including the work of Dubislav, who applied the method of axiomatic to produce original work in logic and formalist philosophy of mathematics.
Abstract: This paper outlines the intellectual biography of Walter Dubislav. Besides being a leading member of the Berlin Group headed by Hans Reichenbach, Dubislav played a defining role as well in the Society for Empirical/Scientific Philosophy in Berlin. A student of David Hilbert, Dubislav applied the method of axiomatic to produce original work in logic and formalist philosophy of mathematics. He also introduced the elements of a formalist philosophy of science and addressed more general problems concerning the substantiation of human knowledge. What set Dubislav apart from the other logical empiricists was his expertise in the history of logic and exact philosophy which enabled him to elucidate and advance the thinking in both disciplines. In the realm of logic proper, Dubislav is best known for his pioneering work in theory of definitions. What is more, he did original work on the so called ‘quasi truth-tables’ which aided Reichenbach in developing his logic of probability. Dubislav also elaborated an influe...
8 citations
TL;DR: In this article, the authors characterize the existential import equivalence of predicate Q(x) and show that existential import is quite abundant and no less so than import-free predicates.
Abstract: Contrary to common misconceptions, today's logic is not devoid of existential import: the universalized conditional ∀ x [S(x)→ P(x)] implies its corresponding existentialized conjunction ∃ x [S(x) & P(x)], not in all cases, but in some. We characterize the proexamples by proving the Existential-Import Equivalence: The antecedent S(x) of the universalized conditional alone determines whether the universalized conditional has existential import, i.e. whether it implies its corresponding existentialized conjunction.A predicate is an open formula having only x free. An existential-import predicate Q(x) is one whose existentialization, ∃ x Q(x), is logically true; otherwise, Q(x) is existential-import-free or simply import-free.How abundant or widespread is existential import? How abundant or widespread are existential-import predicates in themselves or in comparison to import-free predicates? We show that existential-import predicates are quite abundant, and no less so than import-free predicates. Existential...
7 citations
TL;DR: In this paper, a detailed analysis and a comparison of their contributions to the philosophy of logic have been carried out, and the results of their analysis are presented for the first time.
Abstract: Friedrich Nietzsche and Luitzen Egbertus Jan Brouwer had strong personalities and freely expressed unconventional opinions. In particular, they dared to challenge the traditional view that considered Aristotelian logic as being absolute and intrinsic to man. Although they formed this opinion in different ways and in different contexts (Nietzsche was born in Saxony and lived in the second half of the nineteenth century, beginning his career as a classical philologist before turning to philosophy; Brouwer was a Dutch mathematician who lived from 1881 to 1966), they both based it on a view of life that considered it as a struggle for power in which logic was a weapon. Therefore, it is interesting to carry out an in-depth analysis on the origins, the core of their opinions concerning logic and the consequences. As a matter of fact, a detailed analysis and a comparison of their contributions to the philosophy of logic have not yet been carried out. In this paper, I intend to present the results of my research ...
7 citations
TL;DR: In this paper, it has been argued that this solution is ad hoc since it would only apply to self-referencing sentences and weakens Buridan's theory of truth, making his logic without truth a "logic without truth".
Abstract: Jean Buridan has offered a solution to the Liar Paradox, i.e. to the problem of assigning a truth-value to the sentence ‘What I am saying is false’. It has been argued that either (1) this solution is ad hoc since it would only apply to self-referencing sentences [Read, S. 2002. ‘The Liar Paradox from John Buridan back to Thomas Bradwardine’, Vivarium, 40 (2), 189–218] or else (2) it weakens his theory of truth, making his ‘a logic without truth’ [Klima, G. 2008. ‘Logic without truth: Buridan on the Liar’, in S. Rahman, T. Tulenheimo and E. Genot, Unity, Truth and the Liar: The Modern Relevance of Medieval Solutions to the Liar Paradox, Berlin: Springer, 87–112 (Chapter 5); Dutilh Novaes, C. 2011. ‘Lessons on truth from mediaeval solutions to the Liar Paradox’, The Philosophical Quarterly, 61 (242), 58–78]. Against (1), I will argue that Buridan's solution by means of truth by supposition does not involve new principles. Self-referential sentences force us to handle supposition more carefully, which does ...
TL;DR: This paper introduces how logic is connected to computer science and gives an overview of some of the main sources and is intended as an introduction to a journal special issue on the history and philosophy of logic in computer science.
Abstract: This paper introduces how logic is connected to computer science and gives an overview of some of the main sources. It is intended as an introduction a to a journal special issue on the history and philosophy of logic in computer science.
TL;DR: In this paper, the authors investigate the modalites de l'integration of the logique formelle dans l'idee husserlienne de la logique pure in the Prole.
Abstract: Au terme des Prolegomenes (1900), Husserl formule son idee de la logique pure en la structurant sur deux niveaux: l'un, superieur, de la logique formelle fonde transcendantalement et d'un point de vue epistemologique par l'autre, inferieur, d'une morphologie des categories. Seul le second de ces deux niveaux est traite dans les Recherches logiques (1901), tandis que les travaux theoriques en logique formelle menes par Husserl a la meme epoque en paraissent plutot independants. Cet article est consacre a ces travaux tels que recueillis dans les appendices VI-X du volume 12 des Husserliana (1970a). Mettant en evidence la theorie de la signification qui les sous-tend par le biais d'une analyse de la question dite de l'extension des systemes d'axiomes et de sa resolution au moyen d'une notion de completude, son objectif est d'expliciter les modalites de l'integration de la logique formelle dans l'idee husserlienne de la logique pure au tournant du xx siecle.When formulating his idea of pure logic in the Prole...
TL;DR: Aristotle's explanation of what is said "of every" and "of none" has been interpreted either as involving individuals (of which something is said 'of every' or 'of none'), or as regarding exclusively universal terms as discussed by the authors.
Abstract: Aristotle's explanation of what is said ‘of every’ and ‘of none’ has been interpreted either as involving individuals (of which something is said ‘of every’, or of which something is said ‘of none’), or as regarding exclusively universal terms. I claim that Alexander of Aphrodisias endorsed this latter interpretation of the dictum de omni et de nullo. This interpretation affects our understanding of Alexander's syllogistic: as a matter of fact, Alexander maintained that the dictum de omni et de nullo is one of the core principles of syllogistic.
TL;DR: The Hilbert-Bernays theorem as discussed by the authors states that for any satisfiable first-order quantificational schema S, one can write out linguistic expressions that are guaranteed to yield a true sentence of elementary arithmetic when they are substituted for the predicate letters in S. The theorem implies that if L is a consistent, fully interpreted language rich enough to express elementary arithmetic, then a schema S is valid if and only if every sentence of L that can be obtained by substituting predicates of L for predicate letter in S is true.
Abstract: The Hilbert–Bernays Theorem establishes that for any satisfiable first-order quantificational schema S, one can write out linguistic expressions that are guaranteed to yield a true sentence of elementary arithmetic when they are substituted for the predicate letters in S The theorem implies that if L is a consistent, fully interpreted language rich enough to express elementary arithmetic, then a schema S is valid if and only if every sentence of L that can be obtained by substituting predicates of L for predicate letters in S is true The theorem therefore licenses us to define validity substitutionally in languages rich enough to express arithmetic The heart of the theorem is an arithmetization of Godel's completeness proof for first-order predicate logic Hilbert and Bernays were the first to prove that there is such an arithmetization Kleene established a strengthened version of it, and Kreisel, Mostowski, and Putnam refined Kleene's result Despite the later refinements, Kleene's presentation of th
TL;DR: In this paper, the authors argue that, in the Prior Analytics, higher and above the well-known reduction through impossibility of figures, Aristotle is resorting to a general procedure of demonstrating through impossibility in various contexts, i.e. to demonstrate that it is impossible for things to be otherwise than stated.
Abstract: I argue that, in the Prior Analytics, higher and above the well-known ‘reduction through impossibility’ of figures, Aristotle is resorting to a general procedure of demonstrating through impossibility in various contexts. This is shown from the analysis of the role of adunaton in conversions of premises and other demonstrations where modal or truth-value consistency is indirectly shown to be valid through impossibility. Following the meaning of impossible as ‘non-existent’, the system is also completed by rejecting any invalid combinations of terms in deductions or conversions. The notion of impossibility reaches the core of Aristotle's system in the Prior Analytics. On the one hand, the use of adunaton shows that he is following one of the two requisites for demonstrative science formulated in the Posterior Analytics, i.e. to demonstrate that it is impossible for things to be otherwise than stated. On the other hand, that demonstrations through impossibility are rooted in the notion of contradiction supp...
TL;DR: This paper argued that dialectical determinate negation involves a view of negation as a contradictory forming operator, and can therefore count as formal negation in every respect, but they did not distinguish between different accounts of the relationship between negation, contradiction and content.
Abstract: Some authors have claimed that Hegel's ‘determinate negation’ should be distinguished from ‘logical’ or ‘formal’ negation, that is, from a view of negation as a contradictory forming operator. In contrast, I argue that dialectical determinate negation involves a view of negation as a contradictory forming operator, and can therefore count as formal negation in every respect. However, as it is clear in contemporary glutty semantics of negation, one may distinguish between different accounts of the relationship between negation, contradiction and content. I suggest that, differently from classical negation, and as glutty negation, dialectical negation has partial content.
TL;DR: In the early 2000s, Greg Frost-Arnold and Paulo Mancosu each independently discovered Rudolf Carnap's shorthand notes of conversations that Carnap had with Alfred Tarski and W. V. Quine.
Abstract: In the early 2000s, Greg Frost-Arnold and Paulo Mancosu each independently discovered Rudolf Carnap's shorthand notes of conversations that Carnap had with Alfred Tarski and W. V. Quine during the ...
TL;DR: According to the editors, Alfred Tarski: Early work in Poland - Geometry and Teaching has three main goals (p. x) as mentioned in this paper : 1) to publish translations so that all of the work will be accessi...
Abstract: According to the editors, Alfred Tarski: Early work in Poland – Geometry and Teaching has three main goals (p. x). First, to publish translations so that all of Alfred Tarski's work will be accessi...
TL;DR: This exploration spans the development of this notion from its origins in recursion theory to the forms it takes in the context of the more recent event-based analyses of sequential and concurrent computations, touching upon the relations of continuity with non-determinism.
Abstract: Continuity is perhaps the most familiar characterization of the finitary character of the operations performed in computation. We sketch the historical and conceptual development of this notion by interpreting it as a unifying theme across three main varieties of semantical theories of programming: denotational, axiomatic and event-based. Our exploration spans the development of this notion from its origins in recursion theory to the forms it takes in the context of the more recent event-based analyses of sequential and concurrent computations, touching upon the relations of continuity with non-determinism.
TL;DR: This paper studies one popular example often used in proposals to turn software engineering and programming into more systematic disciplines, the computation of a list of primes, to discuss some salient features of the proposed programming paradigms.
Abstract: In response to the so-called ‘software crisis’ of the late 1960s, many approaches were proposed to turn (parts of) software engineering and programming into more systematic disciplines, to turn an art into a science. This paper studies one popular example often used in these proposals, the computation of a list of primes, to discuss some salient features of the proposed programming paradigms. It also looks at the actual implementation in the early 1970s of the prime program on a time-sharing system (MULTICS) and on a complex scientific computer (ILLIAC IV). Confronting theory with practice uncovers what the programming paradigms fail to grasp: the interaction with the user and the interaction with the machine.
TL;DR: The second volume of Charles Parsons' selected papers as mentioned in this paper, dedicated to Solomon Feferman, Wilfred Sieg, and William Tait, collects eleven mainly historical essays and reviews on philosophy and philosop...
Abstract: The second volume of Charles Parsons’ selected papers, dedicated to Solomon Feferman, Wilfred Sieg, and William Tait, collects eleven mainly historical essays and reviews on philosophy and philosop...
TL;DR: In this article, the authors present a review of the history of formal logic, where it has often been coupled by constructive proposals advocating either replacement or supplementing with other forms of logic.
Abstract: Criticism of formal logic is a familiar topic from the history of philosophy, where it has often been coupled by constructive proposals advocating either replacement or supplementation. The essays ...
TL;DR: This work gives several historical examples and illustrates the changing pattern of mutual accommodation between human practices and computer technology, and argues for a more explicitly dialectical and critical approach to the history and philosophy of programming.
Abstract: We start with a example of assembler programming, and show how even at this low level the structure of the programming language does not directly mirror the structure of the hardware, but that it is also decisively influenced by the human practices surrounding computer use, and that assembly language gives a view of the hardware which is accommodated to human interests and capabilities. We give several historical examples and illustrate the changing pattern of mutual accommodation between human practices and computer technology, and argue for a more explicitly dialectical and critical approach to the history and philosophy of programming.
TL;DR: There has been no coherent and commonly accepted standard for Frege's logico-philosophical terminology, and several researchers in the last decade as mentioned in this paper have proposed their own standard for translating Frege.
Abstract: There is nothing straightforward about translating Frege. Up to now there has been no coherent and commonly accepted standard for his logico-philosophical terminology, and several researchers in th...