The Semantic Foundations of Logic Volume 1: Propositional Logics

Epstein, Richard L.; Carnielli, Walter; D’Ottaviano, Ítala M. Loffredo; Krajewski, Stanisław; Maddux, Roger D.

doi:10.1007/978-94-009-0525-2

Cited by 74 publications

(29 citation statements)

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“…e.g. Davidson 1967, Epstein 1990. To the former sort of a validity Brun (2004, 37) refers as informal formal validity and to the latter as informal material validity, which we subsequently abbreviate by formal i-validity and material i-validity, respectively.…”

Section: Brun's Criteria Of Adequate Formalizationmentioning

confidence: 99%

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The Problem of Validity Proofs

Baumgärtner

Lampert

2010

Grazer Philos Stud

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In philosophical contexts, logical formalisms are often resorted to as a means to render the validity and invalidity of informal arguments formally transparent. Since Oliver (1967) and Massey (1975), however, it has been recognized in the literature that identifying valid arguments is easier than identifying invalid ones. Still, any viable theory of adequate logical formalization should at least reliably identify valid arguments. This paper argues that accounts of logical formalization as developed by Blau (1977) and Brun (2004) do not meet that benchmark. The paper ends by suggesting different strategies to remedy the problem.

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Section: Brun's Criteria Of Adequate Formalizationmentioning

confidence: 99%

“…Blau (1977), Epstein (1990Epstein ( , 1994, Sainsbury (1993), or recently and most thoroughly Brun (2004). 1 As Brun's theory is by far the most detailed elaboration of approach (B), we base our upcoming discussion of the problems of identifying valid and invalid arguments on Brun's framework.…”

Section: Introductionmentioning

confidence: 99%

The Problem of Validity Proofs

Baumgärtner

Lampert

2010

Grazer Philos Stud

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“…15 This restriction to the first-order syntax is explicitly advanced as a possible formalization strategy by representatives of the traditional picture as Epstein (1990), p. 24, or Brun (2004 If it is presumed that an argument is formalized correctly only if all its component statements are formalized correctly, this trivialization problem merely affects arguments involving one single premise (cf. Brun (2004), p. 240 et sqq., for a detailed discussion of the trivialization problem).…”

Section: Against Reflective Equilibriummentioning

confidence: 99%

“…5 Instead, we assume the starting point of logical formalization to consist in interpretations of natural language texts and focus on the literature concerned with criteria of adequate formalization that serve to justify or evaluate formalization attempts. There exists only a handful of studies, including Blau (1977), Epstein (1990Epstein ( , 1994, Sainsbury (1991), or recently and most thoroughly Brun (2004), that explicitly focuss on the design of formalization criteria. To this second, criteria-driven thread in the formalization literature Brun (2004), p. 269, refers as the traditional project of formalization.…”

Section: Introductionmentioning

confidence: 99%

Adequate formalization

Baumgärtner

Lampert

2007

Synthese

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Abstract. This article identifies problems with regard to providing criteria that regulate the matching of logical formulae and natural language. We then take on to solve these problems by defining a necessary and sufficient criterion of adequate formalization. On the basis of this criterion we argue that logic should not be seen as an ars iudicandi capable of evaluating the validity or invalidity of informal arguments, but as an ars explicandi that renders transparent the formal structure of informal reasoning.

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“…Indeed, a book by Epstein (1994) poses several such questions. Automation has quickly settled some of Epstein's open questions.…”

Section: Significant Successesmentioning

confidence: 99%

The Automation of Sound Reasoning and Successful Proof Finding

Wos¹,

Fitelson²

2006

A Companion to Philosophical Logic

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The consideration of careful reasoning can be traced to Aristotle and earlier authors. The possibility of rigorous rules for drawing conclusions can certainly be traced to the Middle Ages when types of syllogism were studied. Shortly after the introduction of computers, the audacious scientist naturally envisioned the automation of sound reasoning -reasoning in which conclusions that are drawn follow logically and inevitably from the given hypotheses. Did the idea spring from the intent to emulate Sherlock Holmes and Mr. Spock (of Star Trek) in fiction and Hilbert and Tarski and other great minds in nonfiction? Each of them applied logical reasoning to answer questions, solve problems, and find proofs. But can such logical reasoning be fully automated? Can a single computer program be designed to offer sufficient power in the cited contexts? Indeed, while the use of computers was quickly accepted for numerical calculations and data processing, intense skepticism persisted -even in the early 1960s -regarding the ability of computers to apply effective reasoning. The following simple (but perhaps deceptive) example provides a taste of the type of argument that might have been used to support this skepticism.If one is given a puzzle concerning who holds which jobs, is told that the job of nurse is held by a male, and is asked about the possible jobs for Roberta, one quickly concludes that she is not the nurse. How could a computer program rapidly draw this correct conclusion? After all, the computer would not know that Roberta is (implicitly) female, and, of greater usefulness, it would not know that being a female implies that one is not a male. In fact, even a person often does not realize that the latter fact is used in drawing the correct conclusion for this puzzle. Since the answering of deep questions and the solving of hard problems require far more lengthy paths of reasoning, where do things stand today regarding the automation of drawing conclusions that are sound and relevant, and what is the contemporary view concerning this effort?In answer to the latter question, still debated with vigor and fascination is the value of automation both in the context of inference rule application for drawing conclusions and in the context of useful proof finding, whether the area be mathematics, logic, circuit design, program verification, or puzzle solving. This essay may settle the issue

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The Semantic Foundations of Logic Volume 1: Propositional Logics

Cited by 74 publications

References 0 publications

The Problem of Validity Proofs

The Problem of Validity Proofs

Adequate formalization

The Automation of Sound Reasoning and Successful Proof Finding

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