Cauman, Leigh S.. First Order Logic: An Introduction
1998, Walter de Gruyter & Co.
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Added by: Berta Grimau, Contributed by: Matt ClemensPublisher's Note: This teaching book is designed to help its readers to reason systematically, reliably, and to some extent self-consciously, in the course of their ordinary pursuits-primarily in inquiry and in decision making. The principles and techniques recommended are explained and justified - not just stated; the aim is to teach orderly thinking, not the manipulation of symbols. The structure of material follows that of Quine's Methods of Logic, and may be used as an introduction to that work, with sections on truth-functional logic, predicate logic, relational logic, and identity and description. Exercises are based on problems designed by authors including Quine, John Cooley, Richard Jeffrey, and Lewis Carroll.Comment: This book is adequate for a first course on formal logic. Moreover, its table of contents follows that of Quine's "Methods of Logic", thus it can serve as an introduction or as a reference text for the study of the latter.
Silva, Francisca. First-Order Aboutness Theory
2025, Erkenntnis.
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Added by: Viviane FairbankAbstract:
We seem to have a good grasp of how the subject matters of truth-functional composites depends on their components: it’s simply fusion (Hawke in Australas J Philos 96:697–723, 2018, Fine in Philos Studies 177:129–171, 2020, Plebani and Spolaore in Philos Q 71:605–622, 2021, Plebani and Spolaore in Philos Stud 181:247–265, 2021, Berto in Topics of Thought, Oxford University Press, Oxford, 2022). But what relation should the subject matter of subsentential components bear to the subject matter of the sentences they feature in, and what to say about the quantified sentences of first-order predicate logic? Given how well we seem to understand sentential subject matter in the context of propositional logic, I propose a reduction of the subject matter of subsentential components and of quantified sentences to the subject matter of quantifier-free sentences. I argue that the view squares with the Fregean intuitions that gave rise to the construction of first-order logic as we know it today, motivating its adequacy as a theory of subject matter for first-order languages. I then show that this first-order aboutness theory has predictive and explanatory power, leading us to accept a modified version of Yablo’s (Aboutness, Princeton University Press, Princeton, 2014) principle of immanent closure, as well as a new conception of arbitrary objects/reference. Finally, I propose some potential developments and restrictions.Comment: This paper is a useful example of the kind of work being done in contemporary aboutness theory and its associated formal tools, and hence might be referenced in any intermediate/advanced course on such topics.
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