The Unity of Linguistic Meaning by John Collins (University of Oxford Press) The problem of the unity of the proposition is almost as old as philosophy itself, and was one of the central themes of early analytical philosophy, greatly exercising the minds of Frege, Russell, Wittgenstein, and Ramsey. The problem is how propositions or meanings can be simultaneously unities (single things) and complexes, made up of parts that are autonomous of the positions they happen to fill in any given proposition. The problem has been associated with numerous paradoxes and has motivated general theories of thought and meaning, but has eluded any consensual resolution; indeed, the problem is sometimes thought to be wholly erroneous, a result of atomistic assumptions we should reject. In short, the problem has been thought to be of merely historical interest. Collins argues that the problem is very real and poses a challenge to any theory of linguistic meaning. He seeks to resolve the problem by laying down some minimal desiderata on a solution and presenting a uniquely satisfying account. The first part of the book surveys and rejects extant 'solutions' and dismissals of the problem from (especially) Frege and Russell, and a host of more contemporary thinkers, including Davidson and Dummett. The book's second part offers a novel solution based upon the properties of a basic syntactic principle called 'Merge', which may be said to create objects inside objects, thus showing how unities can be both single things but also made up of proper parts. The solution is defended from both philosophical and linguistic perspectives. The overarching ambition of the book, therefore, is to strengthen the ties between current linguistics and contemporary philosophy of language in a way that is genuinely sensitive to the history of both fields.
Excerpt: The volume you are reading tackles the venerable philosophical problem of the unity of the proposition, albeit idiosyncratically by way of some of the most recent work in generative syntactic theory. Far from being a mere juxtaposition (think: Wittgenstein and Golf or Heidegger and Cats), I hope to show that syntactic theory sheds much needed light on the unity problem. At the very least, I hope that a reader initially liable to think the marriage of `unity' and syntactic theory barren or just gross will recognize the possibility of fecundity, even if not by way of my peculiar positioning of the parties. Hence, my title refers to linguistic meaning, not propositions.
The unity problem goes back at least to Plato, and I don't for a second think that I have resolved all of the problems that sail under the banner of `unity'. I do not, for example, spend too long on the unity of facts or states of affairs. My concern is for the unity problem as it arises for linguistic meaning. The problem here is to say how the individual items of a complex linguistic structure combine to form a meaningful whole, where the means of combination cannot be just another part of the whole (that way regress beckons), nor be wholly exiguous, for how the parts are combined matters to what the whole means. If my solution to this problem works for one's favoured view of facts, then well and good, but I do not consider an account of facts to be a desideratum on an account of linguistic unities.
The problem I shall consider, in some form or other, was at the heart of the work of Frege, Russell, and early Wittgenstein. After a period of quiet, the problem looms large once more, as witnessed by the number of recent monographs, wholly or partly, dedicated to the problem (including Davidson's last work) and a flurry of papers. Such current interest in the problem is perhaps due to the great increase in scholarly work on early analytical philosophy, and many people who write on the topic appear to see the problem as inseparable from that historical context. I certainly do not think that the unity problem is an issue only for the exegetes. It is, by my reckoning, a fundamental first-order problem that any account of language must resolve. To my mind, Frege et al. did not succeed in resolving the problem of unity as I conceive of it, notwithstanding their great insights. If I'm right, a pressing historical question is why the problem was neglected for so long, given that an adequate solution was missing. The answer, as far as I can see, is the presumption that some form of `top down' or 'judgement first' priority principle holds generally in semantics. So, the unities, as it were, are the given, not their constituents; the unity problem arises from a topsy-turvy conception of the foundations of semantics. This thought, I argue, is fundamentally wrong; in particular, it fails to take up the burden of explaining why we have the unities we have, as opposed to any others. This is not an undue insistence on an inappropriate
atomistic model. We explain the difference between interpretable and uninterpretable unities on the basis of their constituents that make a determinate contribution to their hosts in both cases. We do not explain the difference by saying `We wouldn't say that' or `We can't believe that' or `That can't be true'. All of those remarks might be truly uttered when one is faced with an uninterpretable string, but their veracity in turn is to be explained by the fact that the structure in question is the way it is. I suspect that the common view that language is an aspect of our communicative, conventional, intentional, normative wherewithal is responsible for the shunning of the explanatory burden. From my perspective, this common approach is unacceptable precisely because it fails to explain the relevant phenomena. Taking the need for explanation in this area to be a fundamental desideratum, I seek the solution to the unity problem in the resources provided by generative linguistics.
Merge is the basic operation in much current syntactic theory and it possesses just the features demanded by my independently formulated desiderata on an adequate account of `unity'. Merge, basically, puts items together in a way that creates structure. Although specifiable in purely formal terms, I understand Merge to combine lexical items that possess an inherent complexity. This solution, I hope, will be amenable to all. One needn't, for example, have any particular sympathy for minimalist syntax. Here, then, is a nice example of how thinking about current science in relation to age-old philosophical problems need not be reductive or crude; on the contrary, it may light the way to a philosophically satisfying resolution, or at least that is my contention.
My philosophical bottom line is that judgement (or the proposition judged) is not the given in matters linguistic; rather, we should view structured linguistic meaning as the product of a general mechanism—Merge, but call it what you like—that is specifiable independently of any judgements at all, and which targets intrinsically complex items. Only by taking such a course can we properly meet the explanatory burden of making sense of how linguistic unities are made up of elements.
Even if the more or less sympathetic reader can be brought around to recognize the relevance and potential significance of syntactic ideas to the unity problem, the problem remains of how to communicate the syntactic work to a philosophical audience. After all, no-one really wants to write a book that will only be properly understood by someone who has had one's own thoughts. I have endeavoured at all times to make the presentation clear and accessible for someone not versed in syntactic matters. Only Chapter 7 might be regarded as linguistics; happily, readers not interested in the fate of Merge from a linguistics perspective may skip it. Any interdisciplinary venture runs the risk of alienating some readers, but I do sincerely hope that any moments of obscurity on my part will encourage the reader to root out the source material rather than close the book.
The book is divided into seven chapters. The first chapter deals with a major preliminary issue about the relationship between thought and language. Whatever one's view of the relative priority of the notions, I argue that language has an inherent interest for the unity issue. So, I am not concerned with the unity of the proposition as a much as the unity of linguistic meaning. The burden of the first chapter is to show that even if one thinks there are propositions and that there is a live unity problem for them, the unity problem as it pertains to language remains undiminished. Chapter 2 sets out the unity problem as I shall understand it and offers three desiderata on a solution. The third chapter focuses on a common idea, beginning with Frege, that the unity problem might be resolved or dissolved by way of adopting a priority thesis according to which the sentence or judgement has explanatory priority over the word. Although very common, I think this idea is quite mistaken, for it fails to explain the difference between interpretable and uninterpretable structures. Being able to tell such structures apart is precisely what an account of unity should do. Such a desideratum has been missed, I think, because of the common philosophical preoccupation with psychologism and atomism. As I see it, regardless of the real and unreal evils of psychologism, we should still want much explained that the priority thesis casts in shadow. Chapter 4 runs through a gamut of solutions to the problem, fmishing off with an extended discussion of the various incarnations of Russell's multiple relation theory. In each case, I seek to show that my desiderata have not been fully met, and that each of the `solutions' has problems peculiar to it. The fifth chapter lays out a positive account of unity by way of Merge as intimated above. The basic idea here will be that Merge answers to our independent desiderata on the resolution of the unity problem. So, if you have bought the first four chapters, you should buy the fifth, even if it does appear philosophically peculiar. The sixth chapter is dedicated to clarifying and defending the account on offer against some likely philosophical objections.
Merge is a core idea of much recent syntactic theory, but the notion in itself is a very simple formal device, which can be grasped by anyone with a bit of logic or set theory under their belt. Merge, however, is not the entire answer. We also need to think of lexical items (words) as complexes with their inherent properties. The seventh and final chapter defends the basic concepts employed in my account of unity against some objections to them raised in contemporary syntactic theory. The average philosophical reader should be able to follow the first five chapters without much bothering about some of the linguistic detail. I hope, too, that most readers will be sufficiently up to speed by the final chapter that they will actually be interested to see how some of the ideas play out in linguistics. Furthermore, I think that it is a non-negotiable constraint on the proper use of syntactic theory in philosophy that the alien ideas are in fact presented and defended largely on their own terms. This shouldn't be controversial. If, say, Merge is just a confused idea from a linguistic perspective, then my argument fails; in particular, it is crucial for my argument that Merge is a primitively sound notion, a claim denied by some linguists. Showing that the notions I am using are linguistically kosher is not a philosophical project as such, but it is still essential to the kind of philosophical project with which I am engaged. The alternatives to becoming involved with linguistics are absurd or disreputable: to ignore linguistics when doing philosophy of language, to employ linguistic concepts without a proper understanding of them, or to oblige one's reader to take one's word for it. Frankly, the more philosophers of language learn linguistics the better things will be for both disciplines.
My initial plan for the volume included two lengthy opening chapters: one on naturalism in general; the other on language in particular. The chapters would have cast some light on my approach to the unity problem, but not so much to justify essentially having two books jostling for space between the covers of one. For the record, though, I take language—the actual phenomenon, not some or other concept of language—to be a uniquely human cognitive capacity that has been successfully studied by progressive scientific inquiry for a good few decades. We know a lot, but there is far more we do not know. I am also an individualist about language, which simply means that the language capacity is individuated by the relevant theories without reference to externalia. I am, in short, an individualist about language in much the same way that Burge (2010) is an anti-individualist about perception. Where such matters are relevant, I have sought to make my position clear (especially in Chapter 6). In truth, though, a fully convincing presentation of these issues would require another volume (watch this space); see Collins (2008, 2009b) and references therein for some thoughts on the matter.
I have no wish to bang anyone over the head with naturalism and I think that none of the arguments to follow depend upon naturalistic assumptions, although they certainly reflect a naturalistic orientation. I do not go in for thought experiments or intuition mongering; still less am I interested in experimental philosophy. I am interested in language—the actual complex phenomenon—not, primarily, what anyone thinks about it, whether by way of a survey or looking inward. I treat Russell, Frege et al. as also being interested in language. It is hardly controversial to point out that throughout most of the twentieth century the philosophy of language took in the rest of philosophy's washing. This has all too often resulted in conceptions of language predicated upon epistemological and metaphysical positions that do not at all reflect the facts of language (as late as the mid-90s, a hefty companion to the philosophy of language could be published, the vast majority of whose articles had scarcely anything to do with language). For example, one really doesn't need to conduct longitudinal studies on language acquisition to discover that children are not `trained' or `drilled' in language. The very idea would perhaps not occur to anyone who did not have an expensive education. More substantially, the philosophical disputes about realism vs. anti-realism have apparently contributed nothing to our understanding of language, even though much of the debate was supposed to bear on the facts of language acquisition. Similarly, en vogue two-dimensional semantics possesses, as far as I can see, no significance for inquiry into linguistic competence; indeed, the governing distinctions of the approach appear ideally suited to condemn it to irrelevance. There is also, of course, the endemic thought that an adequate semantics should deliver a correct or at least sensible ontology. I shall have something to say about this hypothesis, but only as it bears upon possible alternatives to my account of unity (see Chapter 6). The conclusion will be that the certainty the claim attracts is inversely propositional to the weight the arguments in its favour carry.
So, I am interested in language for its own sake, not to defeat the sceptic about other minds or to tell me anything about the status of excluded middle or to determine a sensible ontology or (heaven forefend) to tell me anything at all about zombies.
My principal complaint against all prior accounts of the unity problem is that certain explanatory demands are neglected; in particular, why there are any unities at all and how individual items determine the difference between the interpretability and non-interpretability of their host structures. Of course, for some thinkers, such demands are not recognized; others reject them. I do not think that these burdens can be ignored or evaded. The unique human capacity for language (unbounded discrete expression of uncaused content) is a phenomenon, as real as photosynthesis or gravity. That is our target, although, to be sure, we know so little yet that the constraints the phenomenon imposes are quite general. As things stand, I think of unity as a philosophical as much as an empirical problem; that is, a problem constrained by the facts, but also one that requires a certain reconceptualization of the phenomenon. Perhaps, as Austin would say, we shall `kick it upstairs' sometime soon. If so, that would be a philosophical success. In this spirit, the explanatory demands I insist be met are not bred from a confusion of `reason' with `cause', as if linguistic understanding must be rendered into some privileged naturalistic vocabulary—not a bit of it. What needs to be explained is how one structure is interpretable whereas another is not, due to differences of their parts. This demand does not strike me as ideological in the least; indeed, to neglect it is nigh-on to neglect the very phenomenon of linguistic understanding. Be that as it may, the problem has been neglected. To be sure, one person's bedrock is another person's problem. For my part, explanation is required where one can rationally continue to ask `Why?'. As far as we can presently tell, with a real phenomenon such as linguistic understanding, there is no end to the 'Why?'s. I take it to be uncontroversial that the tremendous depth of explanation achieved in the physical sciences is precisely due to an absence of the premature foreclosing of explanation. In physics, our spade perhaps does turn, not at intuition or the available data, but something more like mathematical rigidity (Einstein's term). Likewise, in philosophy our spade should turn only where we cannot go on, not where we can find some or other way not to go on. Thus it is with the unity problem. It is resolvable easily enough if we stop wondering why the unities are as they are and not some other way, but then we should want a reason to stop wondering why. In short, the burden of argument is on her who would have us stop wondering rather than upon us inquisitive souls. After all, philosophy is not a disease of the mind, waiting for a cure, any cure. As Strawson put it: `the best rebuttal of the view that there is no room for a certain question is to produce a satisfactory answer to that question'.
Although I have been reflecting on the `unity' question for many years, I have not published anything directly on the problem. My motivation properly to put fingers to keyboard came from a talk Jeff King gave at Birmingham in 2006 on material that made its way into his book The Nature and Structure of Content. Jeff's talk and book led to a paper of mine (2007). I began work on the present book, however, with Jeff's own
solution to the unity problem really at the back of my mind. Only after I had the basic idea down did I note the apparent similarity of our views, even though my earlier paper had criticized Jeff's position for its use of syntax to resolve the unity problem. I still think my initial criticism is sound. It did occur to me to include a version of the paper as a final chapter, but the book is long enough as it is, and people are free to read the paper independently; besides, the gist of my complaint is easily stated and is so in my sixth chapter.
Jeff, in line with most contemporary philosophers, begins with the unity problem as it struck Russell in 1903 (Principles of Mathematics). Of course, the problem, as mentioned, has a far greater vintage, being central to Plato, Kant, many others in-between, and Bradley, with whom Russell was in dispute circa 1903. It would be a worthy endeavour to elaborate this history. I have something to say about Kant in Chapter 5, but since my concern is with linguistic unity, Russell is a proper starting point, regardless of his own views about language at the time. I trust that my truncated history does not lend undue credence to what I have to say.
Central to my discussion of unity is that none of the great early analytical figures---Frege, Russell (whatever incarnation), and Wittgenstein—had an adequate solution to `unity' as I shall pose the problem. I am all too aware that the literature on these figures is vast and ever growing. I am sure to have at least failed to spot some reading that would save one of them from some immediate criticism. I should want to say that the great scholarly attention paid to the early analytical trio is an unalloyed good (well, the attention paid to Frege and Russell, in particular, the Wittgenstein fetishism is often risible). It strikes me, however, that many scholars have an unjustified confidence that the `unity' problem has been resolved. They appear to presume that the problem was a consequence of Russell's peculiar ontology of 1903, ourproblem now being how best to spell out Frege's avoidance of it or Wittgenstein's solution of it, or to present how Russell managed to avoid the problem after all. From a purely historical perspective, it is perfectly appropriate to narrow one's scope to the three greats (we should not forget Ramsey). Still, history is one thing, a solution to a first-order problem is another thing, and it is far from obvious, to say the least, that any of the principal characters had an adequate solution. I hope to establish this without anachronism or shoddy scholarship, although I readily acknowledge that my scholarly chops in this area are wanting. On my view, the unity problem is a quandary for any account of linguistic meaning. Frege, Russell, and Wittgenstein had great insights, which I would be the last to demean, but we should be inspired by them, not be their acolytes. The boundaries of the issue are for us to mark out.
Deductive Logic by Warren Goldfarb (Hackett Publishing Company) provides a straightforward, lively but rigorous, introduction to truth-functional and predicate logic, complete with lucid examples and incisive exercises, for which Warren Goldfarb is renowned.
This is one of the kindest, most avuncular logic books I have ever read on logic. Every page is evidence of the author's warmth toward his students and his dedication to conveying logic to them in a way that respects them as mature persons. His thorough mastery of the subject and its philosophy is another feature that distinguishes this book from the mountain of logic texts written by inexperienced assistant professors and by persons for whom logic is a mere sideline, not a professional specialty as it is with Goldfarb, an accomplished and respected logician who has been teaching this material for over twenty years. No logic book I know of conveys kind warmth toward the readers or deeply modest non-dogmatic competence in the field more than Goldfarb's DEDUCTIVE LOGIC. The usual scientistic hocus-pocus, formalistic pedantry and breezy dogmatism are nowhere to be found in this book. Its examples are chosen to appeal to the intelligent humanities student, not merely to the mathematical science or computer engineering student. They are carefully and tastefully crafted to avoid irrelevant linguistic complexities, both logical and sociological.
The author took over responsibility for Harvard's legendary
introductory logic course Philosophy 140 in 1979 when W. V. Quine retired. A
form of Quine's distinctive, if not idiosyncratic, philosophy and organization
of logic has been meticulously and creatively implemented. Accordingly, but
perhaps to the surprise of readers not familiar with the Quinean approach,
deduction in the sense of step-by-step inferring of conclusions implied by given
premises is substantially deferred until Section 33 of the books 44 Sections.
The 44 sections averaging six pages in length are unequally divided into four
Parts titled respectively: Truth-functional Logic, Monadic Quantification
Theory, Polyadic Quantification Theory, and Identity and Names. The material in
this book has been thoroughly classroom-tested. Most first-edition logic texts
are loaded with errors that are exasperating to students and instructors alike.
My reading has turned only one (non-exasperating) error: on pages 18, 69, and
289 the space in Augustus De Morgan's last name is omitted. Despite an honest
effort to detect further errors typographical and otherwise the reviewer, to his
amazement, has found none.
If a college instructor wants to present a Quinean form of modern first-order logic with identity and names but without functions in a competent, accurate and thoughtful way while avoiding patronizing spoon-feeding, this might be the best text. No other book I know comes close. On the other hand, if an instructor wants to convey the sometimes agonizing rough-and-tumble of contemporary or historical philosophy of logic, or the astounding struggles, dead-ends, missed opportunities, lapses in objectivity and embarrassing errors, even inconsistencies, involved in the historical development of currently accepted versions of the science painfully born in Ancient Athens, this book is not even a candidate. The words `Aristotle', `Boole', `contradiction', `epistemic', `ontic', `paradox', proof', `speech-act', `Tarski' and `tautology' do not occur in the index. There is no bibliography of readings in history and philosophy of logic and no list of current journals in the field. From the study of this excellent text, some students might infer that logic is a fascinating, rewarding and useful science that is virtually complete and uncontroversial. But they might also get the impression that it has no past and no future, that it will persist eternally in its present perfect form, and that it is an island of peaceful rationality. Logic may seem to lift the mind's eye toward the Platonic Form of Reason.
Excerpt: Logic is the study of principles of reasoning. It is concerned not with how people actually reason, but rather with how people ought to reason if they wish to ensure the truth of their results. That is, by "principles of logic" we mean those that yield correct reasoning. Moreover, the principles of logic are general: they do not govern reasoning in one specific subject matter or another, but with reasoning as it applies to any and all areas of study.
Reasoning is a matter of drawing conclusions, or inferring. Hence in logic we are often concerned with arguments, that is, inferences from premises to conclusions. An example familiar since antiquity is this:
All persons are mortal.
Socrates is a person.
Therefore, Socrates is mortal.
The first two statements are the premises; the third is the conclusion. (Of course, in everyday life, arguments are seldom laid out quite so neatly. That is a rhetorical matter, and not our concern here.) The argument is a deductive argument: the conclusion follows logically from the premises. This feature is often characterized in intuitive terms, in several different ways: if the premises are true then the conclusion must be true; it is impossible that the premises be true and the conclusion false; the truth of the premises assures the truth of the conclusion; to commit oneself to the truth of the premises is ipso facto to commit oneself to the truth of the conclusion. Much of this book is devoted to the project of assessing arguments which claim to be deductive, but to do this we also have to analyze what it means to say that a conclusion logically follows from premises. The task is to formulate a precise and rigorous definition to replace the intuitive characterizations.
Clearly, whether or not the conclusion of an argument logically follows from the premises is not simply a matter of the truth or falsity of the premises and conclusion. Rather, as we shall see in detail, the correctness of the argument depends on the form of the statements that make up the argument: the way those statements are constructed from smaller parts, some of which will occur multiply in those statements. Thus, we are led to investigate structural features of statements, in particular, how the truth or falsity of a statement depends on the parts from which it is constructed and the way they are put together. As W. V. Quine memorably put it, "Logic chases truth up the tree of grammar."
This book is divided into four parts. In the first, we treat truth functional logic, which concerns those structures signaled in ordinary language by "and", "or", "not", and "if ... then". The second takes up simple quantificational logic, which treats "all" and "some". The third extends quantificational logic to cover cases that result when nested structures of "all" and "some" are allowed, as in statements like "Everybody loves somebody sometime". Finally, Part IV discusses the logic of identity ("is equal to", "is the same as") and of complex names.
Each of parts IIII is divided into three chapters, representing three stages of our enterprise.
A) Analysis of Discourse. We seek to discern in ordinary statements their structural features, and to characterize those features. We aim at displaying their logical construction: how language is used to express logical forms. Now, ordinary language is extraordinarily variegated. To make the assessment of logical relations possible, we seek to paraphrase ordinary statements into a more uniform symbolic notation. Paraphrased statements display transparently how they are constructed from simpler parts.
B) Logical Assessment. Having put statements into a symbolic form, we can now investigate the formal relations of statements that yield deductive arguments. We show how to manipulate the forms, and we give procedures for ascertaining whether the conclusion of an argument does indeed follow logically from the premises.
C) Reflection. Here we reflect on`the logical concepts and the methods developed in the previous chapter, and we investigate their general properties. For example, we might seek general earmarks of any correct deductive argument or inquire about the adequacy and comprehensiveness of the techniques for logical assessment. In this stage, we reason about reasoning, thereby enacting Frege's dictum, "Reason's proper study is itself".
Exercises appear at the end of the volume, arranged by the part and chapter to which they pertain.
A Companion to Philosophical Logic by Dale Jacquette (Blackwell Companions to Philosophy: Blackwell) This collection of newly commissioned essays by international contributors offers a representative overview of the most important developments in contemporary philosophical logic. Written by experts from a variety of different logical and philosophical perspectives, the volume presents controversies in philosophical implications and applications of formal symbolic logic.
A Companion to Philosophical Logic is likely to become the standard reference to the introductory scope of philosophical logics. Its accessible articles allow a general reader to grasp the defining characteristics of much exciting work in logic. Highly recommended.
Each section features contributors currently active in research who explain the central ideas of their special field and take a philosophical stand on recent issues in the intersection of logic and analytic philosophy. Taken together the essays survey major trends and offer original insights to advance research and philosophical discussion. A Companion to Philosophical Logic provides a comprehensive state-of-the-art handbook for students and professional researchers in philosophical logic.
Contents: Preface. Acknowledgments. List of Contributors. Introduction: Logic, Philosophy, and Philosophical Logic: Dale Jacquette (Pennsylvania State University). Part I: Historical Development of Logic: 1. Ancient Greek Philosophical Logic: Robin Smith (Texas A&M University). 2. History of Logic: Medieval: B.G. Sundholm (Leiden University) and E.P. Bos (Leiden University). 3. The Rise of Modern Logic: Rolf George (University of Waterloo) and James Van Evra (University of Waterloo). Part II: Symbolic Logic and Ordinary Language: 4. Language, Logic,`and Form: Kent Bach (San Francisco State University). 5. Puzzles About Intensionality: Nathan Salmon (University of California, Santa Barbara). 6. Symbolic Logic and Natural Language: Emma Borg (University of Reading) and Ernest Lepore (Rutgers University). Part III: Philosophical Dimensions of Logical Paradoxes: 7. Logical Paradoxes: James Cargile (University of Virginia). 8. Semantical and Logical Paradox: Keith Simmons (University of North Carolina at Chapel Hill). 9. Philosophical Implications of Logical Paradoxes: Roy A. Sorensen (Dartmouth College). Part IV: Truth and Definite Description in Semantic Analysis: 10. Truth, the Liar, and Tarski's Semantics: Gila Sher (University of California, San Diego). 11. Truth, the Liar, and Tarskian Truth Definition: Greg Ray (University of Florida). 12. Descriptions and Logical Form: Gary Ostertag (New York University). 13. Russell's Theory of Definite Descriptions as a Paradigm for Philosophy: Gregory Landini (University of Iowa). Part V: Concepts of Logical Consequence: 14. Necessity, Meaning, and Rationality: The Notion of Logical Consequence: Stewart Shapiro (Ohio State University). 15. Varieties of Consequence : B.G. Sundholm (Leiden University). 16. Modality of Deductively Valid Inference : Dale Jacquette (Pennsylvania State University). Part VI Logic, Existence, and Ontology: 17. Quantifiers, Being and Canonical Notation: Paul Gochet (University of Lige). 18. From Logic to Ontology: Some Problems of Predication, Negation and Possibility: Herbert Hochberg (University of Texas). 19. Putting Language First: The "Liberation" of Logic from Ontology: Ermanno Bencivenga (University of California, Irvine). Part VII: Metatheory and the Scope and Limits of Logic: 20. Metatheory: Alasdair Urquhart (University of Toronto). 21. Metatheory of Logics and the Characterization Problem: Jan Wolenski (Jagiellonian University). 22. Logic in Finite Structures: Definability, Complexity, and Randomness: Scott Weinstein (University of Pennsylvania). Part VIII: Logical Foundations of Set Theory and Mathematics: 23. Logic and Ontology: Numbers and Sets: Jos Benardete (Syracuse University). 24. Logical Foundations of Set Theory and Mathematics: Mary Tiles (University of Hawaii). 25. Property-Theoretic Foundations of Mathematics: Michael Jubien (University of California, Davis). Part IX: Modal Logics and Semantics: 26. Modal Logic: Johan van Benthem (University of Amsterdam). 27. First Order Alethic Modal Logic: Melvin Fitting (City University of New York). 28. Proofs and Expressiveness in Alethic Modal Logic: Maarten de Rijke (University of Amsterdam) and Heinrich Wansing (Dresden University of Technology). 29. Alethic Modal Logics and Semantics: Gerhard Schurz (University of Erfurt). 30. Epistemic Logic: Nicholas Rescher (University of Pittsburgh). 31. Deontic, Epistemic, and Temporal Modal Logics: Risto Hilpinen (University of Miami). Part X: Intuitionistic, Free, and Many-Valued Logics: 32. Intuitionism: Dirk van Dalen (University of Utrecht) and Mark van Atten (University of Utrecht). 33. Many-Valued, Free, and Intuitionistic Logics: Richard Grandy (Rice University). 34. Many-Valued Logic: Grzegorz Malinowski (University of Lodz). Part XI: Inductive, Fuzzy, and Quantum Probability Logics: 35. Inductive Logic : Stephen Glaister (University of Washington). 36. Heterodox Probability Theory: Peter Forrest (University of New England). 37. Why Fuzzy Logic?: Petr Hjek (Academy of Sciences of the Czech Republic). Part XII: Relevance and Paraconsistent Logics: 38. Relevance Logic: Edwin Mares (Victoria University of Wellington). 39. Paraconsistency: Bryson Brown (University of Lethbridge). 40. Logicians Setting Together Contradictories: A Perspective on Relevance, Paraconsistency, and Dialetheism: Graham Priest (University of Melbourne). Part XIII: Logic, Machine Theory, and Cognitive Science: 41. The Logical and the Physical: Andrew W. Hodges (Wadham College, Oxford University). 42. Modern Logic and its Role in the Study of Knowledge: Peter A. Flach (University of Bristol). 43. Actions and Normative Positions: A Modal-Logical Approach : Robert Demolombe (Toulouse Center) and Andrew J.I. Jones (University of Oslo). Part XIV: Mechanization of Logical Inference and Proof Discovery: 44. The Automation of Sound Reasoning and Successful Proof Finding: Larry Wos (Argonne National Laboratory) and Branden Fitelson (Yale University). 45. A Computational Logic for Applicative Common LISP: J. Strother Moore (University of Texas) and Matt Kaufmann (Advanced Micro Devices, Inc). 46. Sampling Labelled Deductive Systems: D.M. Gabbay (King's College). Resources for Further Study. Index.
Philosophy of Logic: An Anthology by Dale Jacquette (Blackwell Philosophy Anthologies: Blackwell) The essays in this anthology include some of the most important recent scholarship in philosophy of logic. I have deliberately avoided republishing papers that are readily available in other anthologies, or that are more closely related to philosophy of language or philosophy of mathematics, regardless of their influence in contemporary work in logic. My intention has been to make this volume a more unique distinctive resource that will complement rather than duplicate other selections of readings currently available. Although some of the papers are more technical than others, all are intended for and can be read with good understanding by beginning students in philosophy who have completed a first course in symbolic logic.
My choice of papers has been guided by a sense of major issues in philosophy of logic that have shaped recent discussion and contributed to ongoing research programs in theoretical and applied philosophical logic. To this end, I have organized the papers thematically rather than chronologically, to give the best overview of philosophical issues connected with logical analysis and the development of formal systems of symbolic logic. The papers range from general topics in classical logic to specialized investigations of the concept of meaning and truth, the interpretation of quantifiers in predicate logic, the theory of valid inference and logical entailment, and problems of alethic modality, intensionality, and propositional attitude. These are undoubtedly among the central problems of philosophical logic reflecting some of the most intriguing new directions in the field, but they by no means exhaust the possibilities.Additional writings related to the philosophy of logic can be found in my Blackwell collection Philosophy of Mathematics: An Anthology. Newly commissioned papers on additional topics, concerning the metatheory of logic, logical and semantic paradoxes, nonstandard logics of many different sorts, fuzzy logic, relevance logics, paraconsistent logics, free logics, monotonic versus nonmonotic systems, applied logics in mathematics, science, probability theory, formal semantics, linguistic modeling, computer and cognitive applications, ethics, epistemology, and time, are collected in my Blackwell Companion to Philosophical Logic. The present book will serve its purpose if it helps provide readers at all levels with the necessary background and a sufficient sense of interest in its subject to continue philosophical inquiry and pursue advanced study of the methods, uses and longstanding problems in the philosophy of logic.
Understanding Symbolic Logic by Virginia Klenk (Prentice Hall) This book is intended as a comprehensive introduction to symbolic logic. It presupposes no prior acquaintance with either logic or mathematics, and it includes all the standard topics through relational predicate logic with identity. The book was written in the conviction that any student can master symbolic logic, and it is designed to give the student as much help as possible in attaining that mastery.
The main part of the book is divided into twenty units, each of which has an introduction and a statement of study objectives so that the student has an overview of what is to come and knows exactly what is required in order to master the unit. The explanatory material for each unit is divided into several subsections, each of which has a specific function and covers one relatively small, clearly defined topic. The clear separation of topics and the division into easily comprehended small "bites" allow the student to master the material step by step without being overwhelmed by an indigestible mass of information.
One‑variable predicate logic is developed, in detail, independently of relational predicate logic, and identity is presented in two separate units. The semantics of predicate logic is also developed in a separate unit, as is the semantics for sentential logic. In addition to the basic material, there are several "extra credit" units, which provide a glimpse into alternative methods of logic and more advanced topics.
I have tried to give as detailed explanations as possible, both for specific techniques, such as drawing up truth tables or constructing proofs, and for the rationale behind these techniques. It seems to me as important for a student to understand why things are done in a certain way as to learn the techniques themselves, and in this book I have tried to supply the whys" as well as the hows."
The book does, however, supply the hows" in abundance. Aside from the detailed explanations, there are numerous examples worked out in the text: various types of truth tables, a great many detailed, step‑by‑step symbolizations, and over fifty fully worked out proofs. In addition, there are copious exercises, with answers to fully half of these provided at the back of the book. Stars indicate problems for which answers are given.
Because of the detailed explanations, the extensive coverage, and the clear division of topics, the book is extremely flexible. It can be used in either freshman courses or upper‑division courses and is suitable for quarter, semester, or even two-quarter courses. In one quarter, for instance, one might cover just Units 1 through 14; in a semester course, Units 1 through 15,17, and 18; and in a two‑quarter course one might cover the entire book, including the supplementary units. Because of the step‑by‑step approach and the numerous examples and exercises, the book can also be used in self‑paced classes. Suggestions on how to structure such a course are included in the Instructor's Manual.A new edition has given me the opportunity to make numerous changes that should clarify and streamline the presentation. In addition to updating examples and exercises, I have provided new or expanded explanations for many topics that students might find puzzling and have made scores of relatively minor changes that significantly clarify the material. The most substantial changes are in sections covering logical form and the distinction between form and substitution instance.
Logic, Form, and Grammar by Peter Long (International Library of Philosophy: Routledge) contains Peter Long's important essay, Logic, Form and Grammar, which resolves many difficulties for the logical form of an argument where the reasoning is hypothetical. Also included are two essays on classical problems in philosophical logic, relating to logical form and formal relations. The notion of logical form and its application are at the heart of some of the classical problems in philosophical logic and are the focus of Peter Longs investigations in the three essays that comprise this volume.
Peter Long first examines the notion of logical form as it applies to arguments involving hypothetical statements. In particular, he considers what logicians take to be paradigms of 'formally valid' arguments, such as 'If today is Wednesday then tomorrow is Thursday; today is Wednesday: therefore tomorrow is Thursday'. Long points to an important problem with such arguments. Whilst they are valid under the form If p then q; p: therefore q, this form is not a logical form. But in that case how can logic claim to be the science of formal inference? Long resolves this difficulty by drawing a fundamental distinction within the notion of the form under which an argument is valid. With this distinction it becomes possible for the first time to determine the status of any formally valid argument involving hypotheticals.The remainder of the book takes up the notion of logical form as it applies to such simple propositions as `This sheet is white' and `London is north of Paris'. When we speak of, say, the first as giving expression to the relation of a thing's having a property, what is in question is a formal relation and we call it such because the relation is expressed through this proposition having the form. Peter Long shows that the confusion of such formal relations with relations proper is common in philosophy and is at the root of the theory that properties and relations are universals, and is responsible for the assimilation of facts to complexes.
THE IS-OUGHT PROBLEM: An Investigation in Philosophical Logic by Gerhard Schurz ($120.00, hardcover, Kluwer Academic Pubishers; ISBN: 0792344103) Can OUGHT be derived from IS? This book presents a systematic investigation of this time-honored philosophical problem by means of modern alethicdeontic predicate logic. Two comprehensive introductory chapters into the philosophical and logical foundations make the text understandable also for nonlogicians, ethicists, social scientists and students of philosophy. New in this study are two leitmotifs: relevance and metalogical generality. It turns out that is-ought inferences indeed exist, but they are all irrelevant in a precise logical sense. New proof techniques allow to establish this result for very broad classes of logics.
This book investigates a traditional problem of philosophy by means of modern logic. It is addressed to logicians as well as to philosophers or scientists, in particular to ethicists.
The book is a study in philosophical logic. This means that it approaches the is-ought problem mainly from the side of modern logic, but it has not only a logical but also a genuine philosophical ambition, and so it contains several purely philosophical considerations. These are condensed in first on the philosophical background of the is-ought problem, later on ethical applications of the logical results, concluding on the philosophical investigation of is-ought bridge principles, and in several interlude paragraphs of the book.
A profound philosophical investigation of the question of analytical or strongly intersubjective is-ought bridge principles supplements the logical study. The final results imply incisive limitations for the justifiability of ethics as opposed to empirical science.
The most far-reaching logical results of the study are situated as "theorems"; further results, which are neither lemmas nor corollaries, are called "propositions".Examples of is-ought-inferences violating Humes thesis are reflected in "facts" The proofs of theorems about logical foundations which do not directly touch the is-ought problem are collected in a separate Appendix.
In the famous passage of his Treatise, David Hume put forward a basic argument against the argumentative praxis of ethicists of his time. He stated that from what is (or is not), nothing about what ought to be (or ought not to be) can logically be concluded. This is Humes is-ought thesis. Consequently, the is-ought problem is the question whether, and under which conditions, this thesis is true. Let us repeat the frequently quoted passage from Hume once more:
"In every system of morality, which I have hitherto met with, I have always remarkd, that the author proceeds for some time in the ordinary way of reasoning, and establishes the being of a God, or makes observations concerning human affairs; when of a sudden I am surprizd to find, that instead of the usual copulations of propositions, is, and is not, I meet with no proposition that is not connected with an ought, or an ought not. This change is imperceptible; but is, however, of the last consequence. For as this ought, or ought not, expresses some new relation or affirmation, tis necessary that it shoud be observd and explaind; and at the same time that a reason should be given, for what seems altogether inconceivable, how this new relation can be a deduction from others, which are entirely different from it. But as authors do not commonly use this precaution, I shall presume to recommend it to the readers; and am persuaded, that this small attention woud subvert all the vulgar systems of morality..."
The notion of "ought", that is, of an ethical obligation or norm, respectively, is obviously related to the notion of an ethical value. All ethical systems assume some analytically true connection between these two notions to the effect that, roughly speaking, what is ethically good (in itself as well as in its consequences) ought to be done, and vice versa. So the is-ought problem has an obvious twin brother in the question whether ethical value statements can be logically inferred from fact statements. To clarify the terminology, we call a statement about what is i.e. a statement about the facts, may they be singular or general, accidental or necessary a descriptive statement; a statement about what ought to be a normative statement, a statement about what is valuable a valuative statement, and finally a statement which is either normative or valuative an ethical statement. Although we will focus in the following on the is-ought problem, it is clear that all our results simultaneously apply to Hume problem in its more general formulation, namely, whether any ethical statements can logically be inferred from descriptive statements.
In our interpretation of the quoted passage from Hume, we have understood "deduction" in the sense of logically valid inference. This is the standard interpretation of Humes thesis. If we speak in the following of Humes is-ought thesis (or of the is-ought problem) simpliciter we always understand it in this standard sense: as the thesis, that n ethical statement can be logically inferred from any descriptive statement. However, the is-ought problem may also be understood in the extended sense, as the question whether ethical statements may be inferred from descriptive statements in a broader sense of inference which includes also some "nonlogical" kinds of inference (whatever that may be). Indeed, some authors like MacIntyre think that Hume understands "deduction" in this broader sense of "inference" .It is clear that the philosophically extended is-ought thesis entails the standard is-ought thesis, but not vice versa. At a certain stage of our investigation, the standard is-ought problem will automatically turn into the extended is-ought problem.
Humes argument has lost nothing of its importance in present time, and probably will never do so. For on the ground of our moral attitudes there is a thicket of intuitions about what is good and what is bad, intuitions which stem from what we have learned throughout our childhood and which usually enter our moral reasoning in an unreflective way. We are easily led to allow certain deep but nevertheless basically subjective intuitions to turn a seemingly factual claim into a normative or valuative assertion, without our taking notice of it. Often, this lack of reflection on their own valuations leads people to a dogmatic attitude, because they mistakenly think of their own moral position as based on "facts" and thus as being unrefutable, and so they reject contradicting positions as obviously irrational. This leads, then, to debates about moral affairs which are driven by blind engagement and fanatism, instead of mutual understanding and rational discourse.
An example is the vehement debate about abortion in present day. The crucial point of this debate is the question which factual property of the unborn child is sufficient for attributing to it the same unrestricted right to live as we attribute it to born persons at least in our western civilization. For the one party in this debate, which often appeals to the importance of our moral conscience and instinct, it is obvious that this at this moment a human being has been created and life begins. Going to the other extreme, there factual property is the fertilization are philosophers like Peter Singer or Norbert Hoerster who have argued that this factual property is the beginning of the personality of the baby, which includes elementary self-interests as well as an elementary awareness of them. From the latter position it unavoidably follows that not only embryos but even very young babies, which have not developed these marks of personality, do not have the unrestricted right to live which older children or adults have. This consequence is shocking to the former party, which more than once has called the mentioned philosophers inhuman. Vice versa, several of these philosophers have a conspicuous tendency to call the former party irrational and incapable of moral argument. But if Humes thesis is true, then there is just no point in trying to prove that one of the mentioned positions is objectively true and thus to refute the other because it is not possible to derive the right to live from one of the mentioned empirical facts. There are different possible views on the matter of abortion, as there exist different ethical world views. Of course, this does not mean that there is no possibility of rational argument. But it means that, if Humes thesis is true, then all what rational argument can do and this is important enough! is to give a clear exposition of the possible views and their ethical premises; but it cannot lead to the one truth among the possible positions. The decision of abortion must be, in the end, a collective social decision based on some form of democratic consensus, but not a matter of refuting or eliminating one or more of the possible moral attitudes. If the parties in the debate would be more aware about this point, much of the hate and demagogy could be avoided.
To summarize: in order to increase tolerance, mutual understanding and, thus, the rationality in our moral discourse, one must constantly be aware of the difficulty, if not impossibility, of justifying moral values as in natural science, by an appeal to the empirical facts, and in connection with that, one must constantly be aware of the multitude of different but equally possible moral attitudes. This is, in my view, the reason why the importance of the is-ought problem will never disappear.
So far we have spoken about the practical importance of the is-ought problem. Clearly, a logical-theoretical study of it, like this study is one, is a quite different thing. Its concepts and results will be necessarily abstract and seemingly distant from practical moral reasoning. But if one goes through them, one will see that in the end they can be applied in various ways to practical moral reasoning...
Nature cannot tell us which ethical concept is the right one: we have to decide. Intersubjective agreement in ethics is not given by a common nature which exists independently from us. In Peirces words, it is not the intersubjective result of the empirical research community. It is basically the result of a common culture which enables mutual understanding and a common life practice. But cultures are historically rather divergent. To strive for or against cultural homogeneity is itself an ethical question. However, questions like these are certainly beyond the purpose of this investigation, which was to show that ethical theories cannot be intersubjectively justified like theories of science.
Referees comments: "...the most complete and in-depth work written on the logical treatment of Humes Law. It has the rare quality of being an authentic work of philosophical logic, in the sense that it uses logical techniques even highly sophisticated and new ones to address a specific theme of philosophical reflection, without restricting itself to pure formal research..."
1. PHILOSOPHICAL BACKGROUND AND PROGRAM OF THE STUDY
1.1 The Is-Ought Problem and its Significance
1.2 Choice of an Adequate Logical Framework
1.3 Distinction between Descriptive and Normative among the Primitive Symbols
1.4 Difficulties in the Explication of Humes Thesis: Priors Paradox
1.5 In which Logics Shall Humes Thesis Be Investigated?
Reflections on the Concept of "Logic"
1.5.1 "Logic" in the Mathematical and Philosophical Sense: Reflections on the Logic Analytic Synthetic Distinction
1.5.2 Varieties of Modal Logics and their Philosophical Importance
1.6 Logics without Bridge Principles: Program and Survey of Results
1.7 The Question of Bridge Principles
1.7.1 On the Relation between the Logical and the Semantic Is Ought Problem
1.7.2 The Open Question Argument and Its Limitations
1.8 The Is-Ought Problem in the Philosophically Extended Sense
1.9 A Short Summary of the Plan of the Book
2. THE LOGICAL BACKGROUND: A.D. I LOGICS
2.2 The Formalization of Natural Language in :e
2.4 Representation and Axiomatization
2.4.1 The Minimal a.d. I logic Kadj
2.4.2 Normal Extensions of Kado
2.4.3 Uniform Substitution for Predicates
2.4.4 Normal Extensions of Kadj
2.4.5 Deductibility and Consequence
2.5 Correctness and Completeness
2.6 Validity Preserving Operations on Models and Frames
11.10 Consequences for the Scientific Justifiability of Ethical Theories
12. ARE SYNTHETIC BRIDGE PRINCIPLES SCIENTIFICALLY JUSTIFIABLE?
12.1 Ethical Concepts as Theoretical Concepts: Holistic Justification Procedures
12.2 On the Limits of the Justifiability of Synthetic Bridge Principles A Comparison Between Physics and Ethics
A. I Interchange of substitution for predicates and for individual variables
A.2 Transitivity of predicate substitutions
A.3 Uniform substitution for predicates in Kadl
A.4 Skeletons of Kadl axiom schemata
A.5 Preservation of frame-validity under cosubstitution
A.6 Advancing V, a and d-rule
A.7 Model-completeness for a.d.1 logics
A.8 Singleton frames for a.d.1logics which are not propositionally representable
A.9 Canonical a.0 logics with incomplete I-counterparts
A.10 Canonicity transfer from a.0 to a. I logics
A. 11 Canonicity transfer from monornodal to combined bimodal I logics
A. 12 Halld-6 n-completeness and the Bolzanocriterion
A. 13 Correspondence and canonicity for (NI5)
A.14 Domains of I.l.models
A.15 Characterization of a.d.l Logics
A.16 Characterization of a.d.(G) 2 logics
A. 17 Admissibility of (VGR)
TABLE OF DEFINITIONS, LEMMATA, PROPOSITIONS, THEOREMS, COROLLARIES, FACTS, FIGURES AND PROBLEMS
EFFECTIVE LOGIC COMPUTATION by Klaus Truemper (hardcover, 560 pages, John Wiley & Sons; ISBN: 0471238864) covers the emerging area of logic computation the use of advanced mathematical methods to solve complex problems in logic. This logic system is useful for the construction of expert systems, such as automated handwriting analysis, traffic control systems, and data mining. A serious book for those interested in algorithms to solve satisfiability and minimum satisfiability problems. While mostly dealing with the theory behind Truempers practical algorithms, the book also provides discussions of applications to major problem classes. The topic of this book is essentially the starting point for solving these problems, that is ways in which a complex problem may be broken down into a number of smaller ones. Required reference for all students of logic interested in practical applications in engineering and computation.