Formal Logic

Formal Logic: A Philosophical Approach

Paul Hoyningen-Huene
Translated by Alex Levine
Copyright Date: 2004
Pages: 272
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  • Book Info
    Formal Logic
    Book Description:

    Many texts on logic are written with a mathematical emphasis, and focus primarily on the development of a formal apparatus and associated techniques. In other, more philosophical texts, the topic is often presented as an indulgent collection of musings on issues for which technical solutions have long since been devised.

    What has been missing until now is an attempt to unite the motives underlying both approaches. Paul Hoyningen-Huene'sFormal Logicseeks to find a balance between the necessity of formal considerations and the importance of full reflection and explanation about the seemingly arbitrary steps that occasionally confound even the most serious student of logic. Alex Levine's artful translation conveys both the content and style of the German edition. Filled with examples, exercises, and a straightforward look at some of the most common problems in teaching the subject, this work is eminently suitable for the classroom.

    eISBN: 978-0-8229-7259-4
    Subjects: Philosophy

Table of Contents

  1. Front Matter
    (pp. i-iv)
  2. Table of Contents
    (pp. v-vi)
  3. Translatorʹs Preface
    (pp. vii-viii)
    Alex Levine
  4. Preface
    (pp. ix-xiv)
    Paul Hoyningen-Huene
  5. 1 Introduction
    (pp. 1-25)

    This chapter introduces the subject of formal logic. Toward this end it seems natural to begin with a definition, one that explains what formal logic is. This is the normal practice in teaching a whole range of specialized fields, but in philosophy a definition is usually a false start, at least it is if we take the definition seriously and plan to stick to it. A definition determines how the thing being defined is to be understood. In philosophy, however, we must first come to some preliminary understanding of the thing (in some broad sense of the word ‘thing’), an...

  6. 2 Statement Logic
    (pp. 26-123)

    Statement logic, to which we now turn, is sometimes also called “sentential logic” or “propositional logic.” The rationale behind the first of these alternative names is clear enough, since statements are a kind of sentence. As for the second, the meanings of statements are, for various reasons, sometimes stipulated to be independent of the statements themselves, in which case it is said that a statement expresses a proposition and that such propositions, rather than statements, should properly be understood as the bearers of logical form (see I.4.1.4.e). In any case, we recall that we turned our attention to statement logic...

  7. 3 Predicate Logic
    (pp. 124-180)

    We ought to begin by asking what remains, if anything, for an introduction to logic to accomplish now that our discussion of statement logic has been concluded. After all, the problems originally formulated in the introduction to this volume have been addressed, and the most important metalogical concepts explained, especially the notion of valid inference. But a motive for taking formal logic further appears immediately when we recall our very first example from section I.1:

    Example 3.1.All logicians are human.

    All humans need sleep.

    Therefore, All logicians need sleep.

    In our introductory chapter, this prototype valid inference served as...

  8. 4 The Mathematical Approach to Statement Logic
    (pp. 181-208)

    In the present chapter, we will take a second stab at statement logic, going right back to the drawing board. We will have to forget everything we have learned about statement logic so far, at least to the extent of not allowing ourselves to make use of any prior knowledge injustifyingthe claims we are about to make. Our prior knowledge of statement logic will, however, play an important role inmotivatingour investigation. This role is best understood as follows. In our earlier treatment of statement logic, we learned to understand the reasoning behind our definitions of particular...

  9. Appendix 1. An Additional Proof
    (pp. 209-211)
  10. Appendix 2. Solutions to Exercises
    (pp. 212-252)
    Christopher von Bülow and Alex Levine
  11. Appendix 3. Suggestions for Further Reading
    (pp. 253-254)