Bringing elementary logic out of the academic darkness into the light of day, Paul Tomassi makes logic fully accessible for anyone attempting to come to grips with the complexities of this challenging subject. Including student-friendly exercises, illustrations, summaries and a glossary of terms, _Logic_ introduces and explains: * The Theory of Validity * The Language of Propositional Logic * Proof-Theory for Propositional Logic * Formal Semantics for Propositional Logic including the Truth-Tree Method * The Language of Quantificational Logic including the (...) Theory of Descriptions. _Logic _is an ideal textbook for any logic student: perfect for revision, staying on top of coursework or for anyone wanting to learn about the subject. Related downloadable software for Macs and PCs is available for this title at www.logic.routledge.com. (shrink)

"One of the most careful and intensive among the introductory texts that can be used with a wide range of students. It builds remarkably sophisticated technical skills, a good sense of the nature of a formal system, and a solid and extensive background for more advanced work in logic.... The emphasis throughout is on natural deduction derivations, and the text's deductive systems are its greatest strength. Lemmon's unusual procedure of presenting derivations before truth tables is very effective." --Sarah Stebbins, The (...) Journal of Symbolic Logic. (shrink)

This volume examines the notion of an analytic proof as a natural deduction, suggesting that the proof's value may be understood as its normal form--a concept with significant implications to proof-theoretic semantics.

Truths are determined not by what we believe, but by the way the world is. Or so realists about truth believe. Philosophers call such theories correspondence theories of truth. Truthmaking theory, which now has many adherents among contemporary philosophers, is the most recent development of a realist theory of truth, and in this book D. M. Armstrong offers the first full-length study of this theory. He examines its applications to different sorts of truth, including contingent truths, modal truths, truths about (...) the past and the future, and mathematical truths. In a clear, even-handed and non-technical discussion he makes a compelling case for truthmaking and its importance in philosophy. His book marks a significant contribution to the debate and will be of interest to a wide range of readers working in analytical philosophy. (shrink)

Challenging the myth that mathematical objects can be defined into existence, Bigelow here employs Armstrong's metaphysical materialism to cast new light on mathematics. He identifies natural, real, and imaginary numbers and sets with specified physical properties and relations and, by so doing, draws mathematics back from its sterile, abstract exile into the midst of the physical world.

Peter Milne has tried to refure Truthmaker Maximalism. the thesis that every truth has a truthmaker, by producing a simple and direct counterexample to it, the sentence M: This sentence has no truthmaker. I argue that, contrary to what Milne argues, on Truthmaker Maximalism M is equivalent to the Liar, which gives the truthmaker maximalist a way to defend his position from Milne's counterexample: to argue that M expresses no proposition.

Reponse to Peter Milne (2005)'s argument agaist maximalism about truthmaking.

I argue that sounds are best conceived not as pressure waves that travel through a medium, nor as physical properties of the objects ordinarily thought to be the sources of sounds, but rather as events of a certain kind. Sounds are particular events in which a surrounding medium is disturbed or set into wavelike motion by the activities of a body or interacting bodies. This Event View of sounds provides for a uni- ?ed perceptual account of several pervasive sound phenomena, (...) including transmission through barriers, constructive and destructive interference, and echoes. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Journal of the History of Philosophy 38.1 (2000) 27-40 [Access article in PDF] Sensible Qualities: The Case of Sound Robert Pasnau University of Colorado 1. Background The Aristotelian tradition distinguishes the familiar five external senses from the less familiar internal senses. Aristotle himself did not in fact use this terminology of 'external' and 'internal,' but the division became common in the work of Arab and Hebrew philosophers, and in (...) the Latin West the distinction is taken for granted.1 I am going to put to one side the obscurities involved in the various internal senses of phantasia, imagination, memory, etc.; I will instead focus on the external senses. These five external senses—sight, hearing, smell, taste, touch—have their familiar counterparts in the external world: color, sound, odor, flavor, and the various tangible qualities. (The tangible qualities, unfortunately, resist being reduced to a single genus, and are typically listed as hot and cold, wet and dry, etc., where this etc. stands in for the complete list that one might or might not be able to give.2 ) These sensibilia (I will simply speak of sensibles) were known as the proper or special objects of the external senses.In addition to these proper objects, the senses were taken to have five common objects—size, shape, number, motion, rest—and also an unlimited variety of incidental objects, the per accidens sensibles—Coriscus, one's enemy, a horse race, etc. These per accidens sensibles are in a way the most interesting and important sense objects of all. They are interesting, first, inasmuch as one of the hardest and most interesting problems about perception is the problem of seeing as, which seems to be precisely the phenomenon at issue [End Page 27] here. They are important, also, inasmuch as genuine perception, as we now think of it, almost always involves the perception of something sensible per accidens. Our everyday sensory experiences revolve around the experience of seeing objects of certain kinds. We can of course step back and decide that what we are really seeing is colors and shapes. But that is not how we ordinarily see things.Despite their interest and importance, I want to put aside these per accidens sensibles, and focus instead on the common and proper sensibles, both of which Aristotle described as sensible per se (kath' hauta). In his classic statement on the objects of sensation, at De anima II 6, 418a7-25, Aristotle suggests that the grounds for distinguishing the per se from the per accidens are that the former sensibles are capable in their own right of making an impression on the senses. Color itself affects the external senses, and so does size. Coriscus, however, considered as Coriscus, does no such thing. He affects the senses only inasmuch as he is colored, perfumed, etc.3 To focus on the per se sensibles, then, is to focus on those things in the world that are suited to make impressions on the external senses.Why are some such sensibles proper, whereas others are common? The well-known rule of thumb here, reflected in how we refer to these sensibles, is that each proper sensible can be perceived by only one of the external senses. The common sensibles are those per se sensibles that fail this test. (Note that, of the common sensibles, only number, movement and rest are truly common to all five of the senses; shape and size are perceptible only by touch and sight.4 ) It is not clear, however, that this is the appropriate criterion for distinguishing the proper from the common sensibles. Albert the Great, for instance, argues that a proper sensible must meet three tests: (1) It is sensed by only one sense; (2) this sense is not capable of error with respect to it; and (3) the organ of this sense is naturally suited to be affected by it alone.5 The last of these tests is problematic, however, for at least two reasons. First, it is problematic for touch, given that the tangible qualities resist being reduced to a single genus. Second, more seriously... (shrink)

Solves Vann McGee's counterexample to Modus Ponens within classical logic by disclosing the suppressed premises and bringing them /within/ the argument.

... ISBN0199215928 ... -/- Abstract: Vision dominates philosophical thinking about perception, and theorizing about experience in cognitive science traditionally has focused on a visual model. This book presents a systematic treatment of sounds and auditory experience. It demonstrates how thinking about audition and appreciating the relationships among multiple sense modalities enriches our understanding of perception. It articulates the central questions that comprise the philosophy of sound, and proposes a novel theory of sounds and their perception. Against the widely accepted philosophical (...) view that sounds are among the secondary or sensible qualities, and against the scientific view that sounds are waves that propagate through a medium such as air or water, the book argues that sounds are events in which objects or interacting bodies disturb a surrounding medium. This does not imply that sounds propagate through a medium, such as air or water. Rather, sounds are events that take place in one's environment at or near their sources. This account captures the way in which sounds essentially are creatures of time and situates sounds in the world. Sounds are not ethereal, mysterious entities. It also provides a powerful account of echoes, interference, reverberation, Doppler effects, and perceptual constancies that surpasses the explanatory richness of alternative theories. Investigating sounds and audition demonstrates that considering other sense modalities teaches what we could not otherwise learn from thinking exclusively about the visual. This book concludes by arguing that a surprising class of cross-modal perceptual illusions demonstrates that the perceptual modalities cannot be completely understood in isolation, and that a visuocentric model for theorizing about perception — according to which perceptual modalities are discrete modes of experience and autonomous domains of philosophical and scientific inquiry — ought to be abandoned. -/- . (shrink)

Echo experiences are illusory experiences of ordinary primary sounds. Just as there is no new object that we see at the surface of a mirror, there is no new sound that we hear at a reflecting surface. The sound that we hear as an echo just is the original primary sound, though its perception involves illusions of place, time, and qualities. The case of echoes need not force us to adopt a conception according to which sounds are persisting object-like particulars (...) that travel through space. (shrink)

Curry's paradox, sometimes described as a general version of the better known Russell's paradox, has intrigued logicians for some time. This paper examines the paradox in a natural deduction setting and critically examines some proposed restrictions to the logic by Fitch and Prawitz. We then offer a tentative counterexample to a conjecture by Tennant proposing a criterion for what is to count as a genuine paradox.

It is known that a number of inference principles can be used to trivialise the axioms of naïve comprehension - the axioms underlying the naïve theory of sets. In this paper we systematise and extend these known results, to provide a number of general classes of axioms responsible for trivialising naïve comprehension.

We discuss the distinction between the sensory modalities; the metaphysics of sounds; and the structure of sound space. We defend a physicalist conception of sounds, without accepting the identification of sounds with sound-waves in the medium. Sounds, we hold, are events in resonating objects. We evaluate the two main accounts of orientation in perceptual space: relationism and absolutism. We then address Strawson's problem of whether the logical space of sounds could be spatial in the full sense of the term. In (...) the Appendix, we discuss the logic of perceptual auditory reports, and show their compatibility with our theory of sounds. (shrink)

Vision has dominated philosophical thinking about perceptual experience and the nature of its objects. Color has long been the focus of debates about the metaphysics of sensible qualities, and philosophers have struggled to articulate the conditions on the visual experience of mind-independent objects. With few notable exceptions, "visuocentrism" has shaped our understanding of the nature and functions of perception, and of our conception of its objects. The predominant line of thought from the early modern era to the present is that, (...) in the philosophically interesting respects, as things are with vision, so they are with hearing, touch, olfaction, and the rest. A closely related line of thought has been particularly strong in the case of the secondary qualities. (shrink)

Truth and Ontology concludes that some truths do not depend on being in any substantive way at all.

First paragraph: Truthmaker theory maintains that for every truth there is something, some thing, some entity, that makes it true. Balking at the prospect that logical truths are made true by any particular thing, a consequence that may in fact be hard to avoid (see Restall 1996, Read 2000), this principle of truthmaking is sometimes restricted to (logically) contingent truths. I aim to show that even in its restricted form, the principle is provably false.

This book introduces an important group of logics that have come to be known under the umbrella term 'susbstructural'. Substructural logics have independently led to significant developments in philosophy, computing and linguistics. _An Introduction to Substrucural Logics_ is the first book to systematically survey the new results and the significant impact that this class of logics has had on a wide range of fields.The following topics are covered: * Proof Theory * Propositional Structures * Frames * Decidability * Coda Both (...) students and professors of philosophy, computing, linguistics, and mathematics will find this to be an important addition to their reading. (shrink)