Irvine, Andrew D. 1996. "Philosophy of Logic." In Routledge History of Philosophy. Volume Ix: Philosophy of Science, Logic and
Mathematics in the Twentieth Century, edited by Kearney, Richard, 9-49. New York: Routledge.
Putnam, Hilary. 1971. Philosophy of Logic. New York: Harper & Row.
Quine, Willard van Orman. 1970. Philosophy of Logic. Harvard: Harvard University Press.
Fisher, Jennifer. 2008. On the Philosophy of Logic. Belmont: Thomson Wadsworth.
Haack, Susan. 1978. Philosophy of Logics. Cambridge: Cambridge University Press.
Contents: Preface XI, Notation and abbreviations XV; 1. 'Philosophy of logics' 1; 2. Validity 11; 3. Sentence connectives 28; 4. Quantifiers
39; 5. Singular terms; 56; 6. Sentences, statements, propositions 74; 7. Theories of truth 86; 8. Paradoxes 135; 9. Logic and logics152; 10. Modal logic 170;
11. Many-valued logic 204; 12. Some metaphysical and epistemological questions about logic 221; Glossary 243; Advice on reading 253, Bibliography 255; Index
"My concern, in this book, is with the philosophy, rather than the history, of logic. But my strategy has been devised with an eye to the
history of the interplay of formal and philosophical issues which I have just sketched. I begin with a consideration of some problems raised by the standard
logical apparatus - the interpretation of sentence connectives, sentence letters, quantifiers, variables, individual constants, the concepts of validity,
truth, logical truth; I turn, from chapter 9 onwards, to a consideration of the way some of these problems motivate formal innovations, 'extended' and
'deviant' logics, and to the ways in which these new formalisms lead, in turn, to a reevaluation of the philosophical issues; and I conclude, in the final
chapter, with some questions - and rather fewer answers - about the metaphysical and epistemological status of logic, the relations between formal and natural
languages, and the relevance of logic to reasoning.
And two recurring themes of the book also reflect this historical perspective. What seem to me to be the vital philosophical issues in logic
are focussed by consideration (i) of the plurality of logical systems and (ii) of the ways in which formal calculi bear on the assessment of informal argument.
More specifically, I shall be urging that, in view of the existence of alternative logics, prudence demands a reasonably radical stance on the question of the
epistemological status of logic, and that the interpretation of formal results is a delicate task in which judicious attention to the purposes of formalisation
is highly desirable.
I have tried to produce a book which will be useful as an introduction to the philosophical problems which logic raises, which will be
intelligible to students with a grasp of elementary formal logic and some acquaintance with philosophical issues, but no previous knowledge of the philosophy
of logic. But I haven't offered simple answers, or even simple questions; for the interesting issues in philosophy of logic are complex and difficult. I have
tried instead to begin at the beginning, to explain technicalities, and to illustrate highly general problems with specific case studies. To this end I have
supplied, for those new to the subject, a glossary of possibly unfamiliar terms used in the text, and some advice on finding one's way about the literature;
while, for those anxious to go further, I have included a generous (but I hope not intimidating) Bibliography." (from the Preface).
Grayling, Anthony. 1997. An Introduction to Philosophical Logic. Oxford: Blackwell.
Third revised edition (First edition 1982; second edition 1990).
Contents: Preface V, 1. Philosophical logic, the philosophy of logic, philosophy and logic 1; 2. The proposition 12; 3. Necessity,
analiticity, and the a priori 33; 4. Existence, presuppositions and descriptions 88; 5. Truth: the pragmatic, coherence and correspondence theories 122; 6.
Truth: semantics, deflation, indefinability and evaluation 147; 7. Meaning, reference, verification and use 188; 8. Truth, meaning, realism and anti-realism
234; 9. Realism, anti-realism, idealism, relativism 285; Bibliography 324; Index 336.
"The topics to be discussed are: the proposition, analyticity, necessity, existence, identity, truth, meaning and reference. These, at least,
are the topics mentioned in chapter headings. In fact the list is more extensive, for in the course of these chapters there are also discussions of possible
worlds, realisms of related sorts, anti-realism, and other questions. It is not possible to give an overview of philosophical logic without ranging widely in
this way, but it will be clear that because each topic invites, and indeed commands, whole volumes to itself, the discussions I give do not pretend to be more
than prefaces to the detailed treatments found in the original literature.
These topics are collected under the unifying label 'philosophical logic' for three principal reasons. It marks their interrelatedness, for a
good understanding of any of them requires an understanding of the others. It marks their central importance in all serious philosophical discussion. And it
reflects the influence of developments in logic since the late nineteenth century, which have afforded an access of power in dealing with many philosophical
problems afresh, not only because we have become technically better equipped for the task, but also because developments in logical machinery have promoted and
facilitated a certain methodological style which has proved extraordinarily fruitful in philosophy. That methodological style is analysis.
The invention of symbolic calculi would not have impelled philosophical developments by itself had it not been for the fact, quickly spotted
by Frege and Russell, that they immediately prompt a range of philosophical questions, centrally among them questions about the nature of meaning and truth -
which is in short to say, language; and language vitally interests philosophers because it provides our route to a philosophical understanding of thought and
the world. The greatest single impetus to current preoccupations with philosophical logic comes indeed from interest in language, to understand which we need
progress in this area. (pp. 1-2).
Hausman, Alan, Kahane, Howard, and Tidman, Paul. 2009. Logic and Philosophy. A Modern Introduction. Boston: Wadsworth.
Eleventh edition (First edition 1969).
Engel, Pascal. 1992. The Norm of Truth. An Introduction to the Philosophy of Logic. Toronto: Toronto University Press.
Contents: Acknowledgements VIII; List of logical symbols XII; Introduction 1;
Part 1. Elementary structures 13
1. Propositions 15; 2. The meaning of propositional connectives 35; 3. Subject and predicate 56; 4. Varieties of quantification 68;
Part 2. Truth and meaning 93
5. Theories of truth 95; 6. Truth, meaning and realism 118;
Part 3. Limits of extensionality 143
7. Modalities, possibles and essences 145; 8. Reference and propositional attitudes 161; 9. Identity 183; 10. Vagueness 199;
Part 4. The domain of logic 217
11. The province of logic 219; 12. Logical necessity 254; 13. Logic and rationality 291; Conclusion 321; Notes 324; Bibliography 356;
Glossary-Index 371; Name Index 379.
"This book is an introduction to the philosophy of logic. But 'philosophy of logic' is an umbrella term which covers a variety of different
questions and styles of enquiry. I do not think that there is a single, well established, conception of the subject, and the one offered in this book does not
pretend to represent them all. Although I shall not attempt to give a precise definition, it will be useful to indicate where my own treatment and choice of
topics differs from other approaches.
By 'logic' I shall mean, in the usual sense, the theory of inferences that are valid in virtue of their form. It is in general admitted that
this definition applies only to deductive logic, and that the theory of inductive inferences does not belong to 'formal logic' in the
ordinary sense. (...)
Our present use of the term 'philosophical logic' is mostly post-Fregean and post-Russellian. Frege called 'logic' not only his own formal
system, but also his reflections about the nature of his formalism and about meaning and truth in general. Although Frege himself does not use the term
'philosophical logic', it is clear that these reflections are close to our contemporary understanding of that term. His insistence on the fact that 'logic' in
the wide sense is concerned with language in general and should be kept separate from both psychology and the theory of knowledge justifies Dummett's claim
that Frege's inquiries belong also to the philosophy of language and that this discipline holds for him the position of a primary philosophy. Russell proposed
explicitly the term philosophical logic for a general enquiry into the nature of 'logical forms'. By this he did not mean only a study of the structure of
logical languages, but also of the logical structures of natural languages, which would have both epistemological and ontological consequences.'
Our present conceptions of philosophical logic bear strongly their Fregean and Russellian heritages. Philosophical logic is taken to be
continuous with the philosophy of language, and to use logic as a tool for the analysis of thought. But there are two main versions of what philosophical logic
is, which differ in the respective weight or authority that is granted to logical analysis. One of them assigns precise limits to this authority, and can be
called informal philosophical logic, whereas the other aims at contorting and extending this authority, and can be called formal philosophical
logic." (from the Introduction).
Wolfram, Sybil. 1989. Philosophical Logic. An Introduction. London: Routledge.
Contents: Preface XIII; 1. Introduction 1. 2. Reference and truth 26; 3. Necessary truth and the analytic-synthetic distinction 80; 4.
Aspects of truth 129; 5. Negation 162; 6. Existence and identity 191; 7. Aspects of meaning 229; Appendix: Examination questions 252; Bibliography of works
referred to 263; Glossary 270; Index 278.
"Logic may be said to be the study of correct and incorrect reasoning. This includes the study of what makes arguments consistent or
inconsistent, valid or invalid, sound or unsound (on these terms see 1.2.1). It has two branches, known as formal (or symbolic) logic and
One of the branches of logic, formal logic, codifies arguments and supplies tests of consistency and validity, starting from axioms,
that is, from definitions and rules for assessing the consistency and validity of arguments.' At the present time there are two main systems of formal logic,
usually known as the propositional calculus and the predicate calculus. The propositional calculus concerns relations of what it terms
'propositions' to each other. The predicate calculus codifies inferences which may be drawn on account of certain features of the content of
The other branch of logic, philosophical logic, which is my concern here, is very much more difficult to delimit and define. It can
be said to study arguments, meaning, truth. Its subject matter is closely related to that of formal logic but its objects are different. Rather than setting
out to codify valid arguments and to supply axioms and notations allowing the assessment of increasingly complex arguments, it examines the bricks and mortar
from which such systems are built. Although it aims, among other things, to illuminate or sometimes question the formalization of arguments into systems with
axioms which have been effected, it is not restricted to a study of arguments which formal logic has codified." (pp. 1-2).
Lambert, Karel, and Fraasen, Bas C.van. 1972. Derivation and Counterexample. An Introduction to Philosophical Logic. Encino:
"Since there are already many elementary logic texts in existence, and since logic is taught today at many levels, we shall explain, first,
the specific purposes to which we think this text is suited, and second, how this text differs from other similar texts.
In many philosophy departments today a distinction is drawn between the following topics in undergraduate logic teaching:
(a) general introduction,
(b) techniques of deductive logic,
(d) philosophical uses of logic.
In addition there are texts and courses devoted to advanced work in mathematical logic for students wishing to specialize.
We conceive the present text to be usable in the teaching of (b)-(d), to students who either have had a general introduction to logic or who
are allowed (and this is frequent enough) to begin symbolic logic without such an introduction. Topics that we would normally expect to have been covered on
the introductory level include the nature of arguments and validity, the use/mention distinction, the nature of definition, and perhaps the use of Venn
diagrams and truth-tables. A good example of a book designed especially for this general introductory level is Wesley Salmon's Logic (Prentice-Hall,
After the introductory level, the instructor generally has a choice (or the student is offered a choice) whether to emphasize the
philosophical side or the mathematical side of logic. Here our text is designed specifically for those whose interest is in philosophical aspects and uses of
With this aim in mind, we have introduced a number of innovations into the exposition, but at the same time have made sure that the
standard body of elementary symbolic logic is covered.
Our main innovations, however, are in the third part, which covers the logic of singular terms. Here we extend the language of classical
logic by admitting singular terms, and extend our rules so as to license inferences involving such terms. The resulting extensions of classical logic are
called free logic and free description theory. We take care to discuss explicitly the philosophical basis of such notions as possible worlds,
domains of discourse, existence, reference and description, utilized in the first three parts, and to compare our approach with historical precedents. This is
done, to some extent, as these notions are introduced, and also to some extent in Parts Four and Five.
Although there are today many good treatments of metalogic available, they are generally aimed at more advanced levels of instruction. We
have aimed to make our presentation of metalogic more elementary than is usual. First of all, as soon as the student is able to use deductive techniques, he is
also in a position to prove the admissibility of further deductive rules. By placing such admissibility proofs in Parts One and Two, a certain amount of proof
theory is taught along with the deductive techniques. Part Four is devoted to semantics, that is, to a scrutiny of the adequacy of the logical system developed
in the first three parts. Since the book is aimed specifically at the philosophy student, we treat only the finite cases; we believe that in this way the
student will be able to master the main theoretical concepts and methods without the use of sophisticated mathematical techniques. It must be noted that here
the previous parallel development of the tableau rules greatly simplifies the presentation.
In Part Five, we discuss the philosophical basis of the logic of existence and description theory, with special reference to the question of
extensionality. In addition, we discuss the philosophical uses of free logic in connection with set theory, intentional dosicourse, thought and perception,
modal concepts, and the concept of truth. The term "philosophical logic" is used increasingly to designated a specific discipline (indeed, the newly created
Journal of Philosophical Logic will be entirely devoted to it), and we hope that Part Five will provide a useful introduction to some of its main areas of
research." (from the Preface IX-XI).
Burgess, John P. 2009. Philosophical Logic. Princeton: Princeton University Press.
Read, Stephen. 1995. Thinking About Logic. An Introduction to the Philosophy of Logic. New York: Oxford University Press.
Contents: Introduction 1; 1. Truth, pure and simple: language and the world 5; 2. The power of logic: logical consequence 35; 3. To think but
of an If: theories of conditionals 64; 4. The incredulous stare: possible worlds 96; 5. Plato's beard: on what there is and what there isn't 121; 6. Well, I'll
be hanged! The semantic paradoxes 148; 7. Bald men forever: the sorites paradoxes 173; 8. Whose line is it anyway? The constructivist challenge 203; Select
Bibliography 241; Glossary 248; Index 253.
"This book is an introduction to the philosophy of logic. We often see an area of philosophy marked out as the philosophy of logic and
language; and there are indeed close connections between logical themes and themes in the analysis of language. But they are also quite distinct. In the
philosophy of language the focus is on meaning and reference, on what are known as the semantic connections between language and the world.
In contrast, the central topic of the philosophy of logic is inference, that is, logical consequence, or what follows correctly from what.
What conclusions may legitimately be inferred from what sets of premisses? One answer to this question makes play with the notion of truth-preservation: valid
arguments are those in which truth is preserved, where the truth of the premisses guarantees the truth of the conclusion. Since truth itself is arguably the
third member of a closely knit trio comprising meaning, reference, and truth, the connection with philosophy of language is immediately secured. (...)
It is with these issues of truth and correct inference that we are to engage in this book; and central to that engagement, we will find, is
paradox. Paradox is the philosophers' enchantment, their fetish. It fascinates them, as a light does a moth. But at the same time, it cannot be endured. Every
force available must be brought to bear to remove it. The philosopher is the shaman, whose task is to save us and rid us of the evil demon.
Paradox can arise in many places, but here we concentrate on two in particular, one set united by semantic issues, the other by a fuzziness
inherent in certain concepts. In both cases the puzzle arises because natural, simple, and what seem clearly reasonable assumptions lead one very quickly to
contradiction, confusion, and embarrassment. There is something awful and fascinating about their transparency, there is an enjoyment in surveying their
variety, the rich diversity of examples.
But their real philosophical value lies in the purging of the unfounded and uncritical assumptions which led to them. They demand resolution,
and in their resolution we learn more about the nature of truth, the nature of consequence, and the nature of reality, than any extended survey of basic
principles can give. Only when those seemingly innocent principles meet the challenge of paradox and come under a gaze tutored by realization of what will
follow, do we really see the troubles that lie latent within them.
We start, therefore, at the heart of philosophy of logic, with the concept of truth, examining those basic principles which seem compelling
in how language measures up to the world. But I eschew a simple catalogue of positions held by the great and the good. That could be very dull, and perhaps not
really instructive either. Rather, I try to weave a narrative, to show how natural conceptions arise, how they may be articulated, and how they can come
unstuck. I hope that the puzzles themselves will capture the readers' imaginations, and tempt them onwards to further, more detailed reading, as indicated in
the summary to each chapter. The idea is to paint a continuous picture of a network of ideas treated in their own right and in their own intimate
relationships, largely divorced from historical or technical detail." pp. 1-3 (from the Introduction).
Sainsbury, Mark. 2001. Logical Forms. An Introduction to Philosophical Logic. Oxford: Blackwell.
Second revised edition (First edition 1991).
Contents: Preface to the first edition VI; Preface to the second edition VII; Introduction 1; 1. Validity 5; 2. Truth functionality 54; 3.
Conditionals and probabilities 122; 4. Quantification 153; 5. Necessity 257; 6. The project of formalization 339; Glossary 392; List of symbols 403;
Bibliography 406; Index 419.
"This book is an introduction to philosophical logic. It is primarily intended for people who have some acquaintance with deductive methods
in elementary formal logic, but who have yet to study associated philosophical problems. However, I do not presuppose knowledge of deductive methods, so the
book could be used as a way of embarking on philosophical logic from scratch.
Russell coined the phrase 'philosophical logic' to describe a programme in philosophy: that of tackling philosophical problems by formalizing
problematic sentences in what appeared to Russell to be the language of logic: the formal language of Principia Mathematica. My use of the
term 'philosophical logic' is close to Russell's. Most of this book is devoted to discussions of problems of formalizing English in formal logical
I take validity to be the central concept in logic. In the first chapter I raise the question of why logicians study this property in
connection with artificial languages, which no one speaks, rather than in connection with some natural language like English. In chapters 2-5 I indicate some
of the possibilities and problems for formalizing English in three artificial logical languages: that of propositional logic (chapter 2), of first order
quantificational logic (chapter 4) and of modal logic (chapter 5). The final chapter takes up the purely philosophical discussion, and, using what has been
learned on the way, addresses such questions as whether there was any point in those efforts at formalizing, what can be meant by the logical form of
an English sentence, what is the domain of logic, and what is a logical constant.
In this approach, one inevitably encounters not only questions in the philosophy of logic, but also questions in the philosophy of language,
as when one considers how best to formalize English sentences containing empty names, or definite descriptions, or adverbs, or verbs of propositional
attitude." (pp. 1-2).
Englebretsen, George, and Sayward, Charles. 2011. Philosophical Logic. An Introduction to Advanced Topics. New York: Continuum.
Contents: List of Symbols X; 1. Introduction 1; 2. Sentential Logic 13; 3. Quantificational Logic 52; 4. Sententia Modal Logic 74; 5.
Quantification and Modality 93; 6. Set Theory 103; 7. Incompleteness 130; 8. An Introduction to Term Logic 139; 9. The Elements of a Modal term Logic 166;
References 176; Rules, Axioms, and Principles 177; Glossary 184; Index 195-198.
"Post-Fregean mathematical logic began with a concern for foundational issues in mathematics. However, by the 1930s philosophers had not only
contributed to the building and refinement of various formal systems, but they had also begun an exploitation of them for primarily philosophical ends. While
many schools of philosophy today eschew any kind of technical, logical work, an ability to use (or at least a familiarity with) the tools provided by formal
logic systems is still taken as essential by most of those who consider themselves analytic philosophers. Moreover, recent years have witnessed a growing
interest in formal logic among philosophers who stand on friendly terms with computer theory, cognitive psychology, game theory, linguistics, economics, law,
and so on. At the same time, techniques developed in formal logic continue to shed light on both traditional and contemporary issues in epistemology,
metaphysics, philosophy of mind, philosophy of science, philosophy of language, and so forth.
In what follows, students who have already learned something of classical mathematical logic are introduced to some other ways of doing
formal logic: classical logic rests on the concepts of truth and falsity, whereas constructivists logic accounts for inference in terms of defense and
refutation; classical logic usually makes use of a semantic theory based on models, whereas the alternative introduced here is based on the idea of truth sets;
classical logic tends to interpret quantification objectually, whereas this alternative allows for a substitutional interpretation of quantifiers. As well, a
radically different approach, fundamentally different from any version of mathematical logic, is also introduced. It is one that harkens back to the earliest
stages in the history of formal logic but is equipped with the resources demanded of any formal logic today." (pp. 1-2).