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Books > Philosophy > Topics in philosophy > Logic
Language and Philosophical Problems investigates problems about
mind, meaning and mathematics rooted in preconceptions of language.
It deals in particular with problems which are connected with our
tendency to be misled by certain prevailing views and
preconceptions about language. Philosophical claims made by
theorists of meaning are scrutinized and shown to be connected with
common views about the nature of certain mathematical notions and
methods. Drawing in particular on Wittgenstein's ideas, Sren
Stenlund demonstrates a strategy for tracing out and resolving
conceptual and philosophical problems. By a critical examination of
examples from different areas of philosophy, he shows that many
problems arise through the transgression of the limits of the use
of technical concepts and formal methods. Many prima facie
different kinds of problems are shown to have common roots, and
should thus be dealt and resolved together. Such an approach is
usually prevented by the influence of traditional philosophical
terminology and classification. The results of this investigation
make it clear that the received ways of subdividing the subject
matter of philosophy often conceal the roots of the problem.
Paradoxes of the Infinite presents one of the most insightful, yet
strangely unacknowledged, mathematical treatises of the 19th
century: Dr Bernard Bolzano's Paradoxien. This volume contains an
adept translation of the work itself by Donald A. Steele S.J., and
in addition an historical introduction, which includes a brief
biography as well as an evaluation of Bolzano the mathematician,
logician and physicist.
This is an important collection of new essays on various topics relating to realism and its rivals in metaphysics, logic, metaethics, and epistemology. The contributors include some of the leading authors in these fields and in several cases their essays constitute definitive statements of their views. Although not primarily historical this volume includes discussion of philosophers from the Middle Ages to the present day, from Aquinas to Wittgenstein. No one seriously interested in questions about realism can afford to be without this collection.
In this challenging and provocative analysis, Dale Jacquette argues
that contemporary philosophy labours under a number of historically
inherited delusions about the nature of logic and the philosophical
significance of certain formal properties of specific types of
logical constructions. Exposing some of the key misconceptions
about formal symbolic logic and its relation to thought, language
and the world, Jacquette clears the ground of some very
well-entrenched philosophical doctrines about the nature of logic,
including some of the most fundamental seldom-questioned parts of
elementary propositional and predicate-quantificational logic.
Having presented difficulties for conventional ways of thinking
about truth functionality, the metaphysics of reference and
predication, the role of a concept of truth in a theory of meaning,
among others, Jacquette proceeds to reshape the network of ideas
about traditional logic that philosophy has acquired along with
modern logic itself. In so doing Jacquette is able to offer a new
perspective on a number of existing problems in logic and
philosophy of logic.
Making Your Mind Matter is a practical guide to effective thinking
in college and in everyday life. Critical thinking guru Vincent
Ryan Ruggiero explains how and why the mind has been neglected in
American education, then teaches readers how to take charge of
their own mental development. Ruggiero presents a simple but
powerful model the WISE model (Wonder, Investigate, Speculate,
Evaluate). This model illustrates how to overcome obstacles to
thinking, resist manipulation, test ideas, analyze arguments, form
judgments, analyze ethical issues, and discuss ideas courteously
and effectively. This book is a brief, comprehensive,
authoritative, and accessible introduction to critical thinking,
perfect for all students and others interested in increasing the
power of their minds.
You've Got to Be Kidding!: How Jokes Can Help You Think is a
thoughtful and accessible analysis of the ways in which jokes
illustrate how we think critically, and how the thinking process
goes awry in everyday human situations Uses jokes to illustrate the
various mistakes or fallacies that are typically identified and
discussed in courses on critical reasoning Provides an effective
way to learn critical thinking skills since jokes often describe
real-life situations where it really matters whether a person
thinks well or not Demonstrates how philosophy is actually very
practical and clearly related to real- life human experiences
Explains how developing good reasoning habits can make a real
difference in all aspects of one's life
Truth Through Proof defends an anti-platonist philosophy of
mathematics derived from game formalism. Classic formalists claimed
implausibly that mathematical utterances are truth-valueless moves
in a game. Alan Weir aims to develop a more satisfactory successor
to game formalism utilising a widely accepted, broadly neo-Fregean
framework, in which the proposition expressed by an utterance is a
function of both sense and background circumstance. This framework
allows for sentences whose truth-conditions are not
representational, which are made true or false by conditions
residing in the circumstances of utterances but not transparently
in the sense.
Applications to projectivism and fiction pave the way for the claim
that mathematical utterances are made true or false by the
existence of concrete proofs or refutations, though these
truth-making conditions form no part of their sense or
informational content.
The position is compared with rivals, an account of the
applicability of mathematics developed, and a new account of the
nature of idealisation proffered in which it is argued that the
finitistic limitations Godel placed on proofs are without rational
justification. Finally a non-classical logical system is provided
in which excluded middle fails, yet enough logical power remains to
recapture the results of standard mathematics.
In 1942 G.E. Moore first wrote about the curious sort of 'nonsense'
exhibited by the statement 'it is raining but I do not believe it'.
What Moore discovered was a species of blindspots: consistent
propositions that cannot be rationally accepted by certain
individuals even though they might be true. In this book, Professor
Sorenson aims to provide a unified solution to a large family of
philosophical puzzles and paradoxes through a study of blindspots .
He devotes special attention to revealing their role in 'slippery
slope' reasoning.
Originally published in 1966 On the Syllogism and Other Logical
Writings assembles for the first time the five celebrated memoirs
of Augustus De Morgan on the syllogism. These are collected
together with the more condensed accounts of his researches given
in his Syllabus of a Proposed System of Logic an article on Logic
contributed to the English Cyclopaedia. De Morgan was among the
most distinguished of nineteenth century British mathematicians but
is chiefly remembered today as one of the founders of modern
mathematical logic. His writings on this subject have been little
read, however since apart from his Formal Logic, they lie buried
for the most part in inaccessible periodicals. De Morgan's own
later amendments are inserted in the text and the editorial
introduction gives a summary of the whole and traces in some detail
the course of the once-famous feud with Sir William Hamilton of
Edinburgh.
This reissue, first published in 1971, provides a brief historical
account of the Theory of Logical Types; and describes the problems
that gave rise to it, its various different formulations (Simple
and Ramified), the difficulties connected with each, and the
criticisms that have been directed against it. Professor Copi seeks
to make the subject accessible to the non-specialist and yet
provide a sufficiently rigorous exposition for the serious student
to see exactly what the theory is and how it works.
"Everything one might want for a course on [Frege and Russell] is
included, along with a seventy-five-page introduction that
carefully lays out the contributions of each essay." -- Bernard
Linsky, University of Alberta
"The old logic put thought in fetters, while the new logic gives it
wings." For the past century, philosophers working in the tradition
of Bertrand Russell - who promised to revolutionise philosophy by
introducing the 'new logic' of Frege and Peano - have employed
predicate logic as their formal language of choice. In this book,
Dr David Corfield presents a comparable revolution with a newly
emerging logic - modal homotopy type theory. Homotopy type theory
has recently been developed as a new foundational language for
mathematics, with a strong philosophical pedigree. Modal Homotopy
Type Theory: The Prospect of a New Logic for Philosophy offers an
introduction to this new language and its modal extension,
illustrated through innovative applications of the calculus to
language, metaphysics, and mathematics. The chapters build up to
the full language in stages, right up to the application of modal
homotopy type theory to current geometry. From a discussion of the
distinction between objects and events, the intrinsic treatment of
structure, the conception of modality as a form of general
variation to the representation of constructions in modern
geometry, we see how varied the applications of this powerful new
language can be.
This unique introduction fully engages and clearly explains
pragmatism, an approach to knowledge and philosophy that rejects
outmoded conceptions of objectivity while avoiding relativism and
subjectivism. It follows pragmatism's focus on the process of
inquiry rather than on abstract justifications meant to appease the
skeptic. According to pragmatists, getting to know the world is a
creative human enterprise, wherein we fashion our concepts in terms
of how they affect us practically, including in future inquiry.
This book fully illuminates that enterprise and the resulting
radical rethinking of basic philosophical conceptions like truth,
reality, and reason. Author Cornelis de Waal helps the reader
recognize, understand, and assess classical and current pragmatist
contributions-from Charles S. Peirce to Cornel West-evaluate
existing views from a pragmatist angle, formulate pragmatist
critiques, and develop a pragmatist viewpoint on a specific issue.
The book discusses: Classical pragmatists, including Peirce, James,
Dewey, and Addams; Contemporary figures, including Rorty, Putnam,
Haack, and West; Connections with other twentieth-century
approaches, including phenomenology, critical theory, and logical
positivism; Peirce's pragmatic maxim and its relation to James's
Will to Believe; Applications to philosophy of law, feminism, and
issues of race and racism.
First published in 1952, professor's Strawson's highly influential
Introduction to Logical Theory provides a detailed examination of
the relationship between the behaviour of words in common language
and the behaviour of symbols in a logical system. He seeks to
explain both the exact nature of the discipline known as Formal
Logic, and also to reveal something of the intricate logical
structure of ordinary unformalised discourse.
In 1945 Alonzo Church issued a pair of referee reports in which he
anonymously conveyed to Frederic Fitch a surprising proof showing
that wherever there is (empirical) ignorance there is also
logically unknowable truth. Fitch published this and a
generalization of the result in 1963. Ever since, philosophers have
been attempting to understand the significance and address the
counter-intuitiveness of this, the so-called paradox of
knowability.
This collection assembles Church's referee reports, Fitch's 1963
paper, and nineteen new papers on the knowability paradox. The
contributors include logicians and philosophers from three
continents, many of whom have already made important contributions
to the discussion of the problem. The volume contains a general
introduction to the paradox and the background literature, and is
divided into seven sections that roughly mark the central points of
debate. The sections include the history of the paradox, Michael
Dummett's constructivism, issues of paraconsistency, developments
of modal and temporal logics, Cartesian restricted theories of
truth, modal and mathematical fictionalism, and reconsiderations
about how, and whether, we ought to construe an anti-realist theory
of truth.
This multidisciplinary event was attended by 1,850 people from 61
countries brought together professionals from a broad spectrum of
disciplines, ranging from engineering and the sciences to the arts,
politics, economics and social sciences. Contributors included
Manfred Max-Eduardo Galeano, Robert Chambers and Orlando Fals
Borda.
This book aims to develop certain aspects of Gottlob Frege's theory
of meaning, especially those relevant to intentional logic. It
offers a new interpretation of the nature of senses, and attempts
to devise a logical calculus for the theory of sense and reference
that captures as closely as possible the views of the historical
Frege.
The Collected Works of John Stuart Mill took thirty years to
complete and is acknowledged as the definitive edition of J.S. Mill
and as one of the finest works editions ever completed. Mill's
contributions to philosophy, economics, and history, and in the
roles of scholar, politician and journalist can hardly be
overstated and this edition remains the only reliable version of
the full range of Mill's writings. Each volume contains extensive
notes, a new introduction and an index. Many of the volumes have
been unavailable for some time, but the Works are now again
available, both as a complete set and as individual volumes.
Computability and Logic has become a classic because of its
accessibility to students without a mathematical background and
because it covers not simply the staple topics of an intermediate
logic course, such as Godel's incompleteness theorems, but also a
large number of optional topics, from Turing's theory of
computability to Ramsey's theorem. This 2007 fifth edition has been
thoroughly revised by John Burgess. Including a selection of
exercises, adjusted for this edition, at the end of each chapter,
it offers a simpler treatment of the representability of recursive
functions, a traditional stumbling block for students on the way to
the Godel incompleteness theorems. This updated edition is also
accompanied by a website as well as an instructor's manual.
First Published in 1964, Studies in Metaphilosophy presents and
develop the hypothesis about the nature of metaphysical theories.
Each study is a fresh attempt to improve our understanding of what
a philosophical theory is and what its supporting arguments come
to. Author argues that philosophical theories are nothing more
substantial than linguistic chimeras and has the important function
of pointing up the need for the examination of the whole subject.
The volume discusses important themes like concept analysis,
systematic doubt, the method of deduction from fact, logical
necessitation, the nature of philosophical analysis, the nature of
value, the metaphysical concept of space, Moore and philosophical
analysis, the hidden structure of philosophical theories, and the
relevance of psychoanalysis to philosophy. This volume will be an
essential source for scholars and researchers of philosophy, logic,
and metaphysics.
In this book, Livingston develops the political implications of
formal results obtained over the course of the twentieth century in
set theory, metalogic, and computational theory. He argues that the
results achieved by thinkers such as Cantor, Russell, Godel,
Turing, and Cohen, even when they suggest inherent paradoxes and
limitations to the structuring capacities of language or symbolic
thought, have far-reaching implications for understanding the
nature of political communities and their development and
transformation. Alain Badiou's analysis of logical-mathematical
structures forms the backbone of his comprehensive and provocative
theory of ontology, politics, and the possibilities of radical
change. Through interpretive readings of Badiou's work as well as
the texts of Giorgio Agamben, Jacques Lacan, Jacques Derrida,
Gilles Deleuze, and Ludwig Wittgenstein, Livingston develops a
formally based taxonomy of critical positions on the nature and
structure of political communities. These readings, along with
readings of Parmenides and Plato, show how the formal results can
transfigure two interrelated and ancient problems of the One and
the Many: the problem of the relationship of a Form or Idea to the
many of its participants, and the problem of the relationship of a
social whole to its many constituents.
The New Rhetoric is founded on the idea that since "argumentation
aims at securing the adherence of those to whom it is addressed, it
is, in its entirety, relative to the audience to be influenced,"
says Chaim Perelman and L. Olbrechts-Tyteca, and they rely, in
particular, for their theory of argumentation on the twin concepts
of universal and particular audiences: while every argument is
directed to a specific individual or group, the orator decides what
information and what approaches will achieve the greatest adherence
according to an ideal audience. This ideal, Perelman explains, can
be embodied, for example, "in God, in all reasonable and competent
men, in the man deliberating or in an elite." Like particular
audiences, then, the universal audience is never fixed or absolute
but depends on the orator, the content and goals of the argument,
and the particular audience to whom the argument is addressed.
These considerations determine what information constitutes "facts"
and "reasonableness" and thus help to determine the universal
audience that, in turn, shapes the orator's approach. The adherence
of an audience is also determined by the orator's use of values, a
further key concept of the New Rhetoric. Perelman's treatment of
value and his view of epideictic rhetoric sets his approach apart
from that of the ancients and of Aristotle in particular.
Aristotle's division of rhetoric into three genres-forensic,
deliberative, and epideictic-is largely motivated by the judgments
required for each: forensic or legal arguments require verdicts on
past action, deliberative or political rhetoric seeks judgment on
future action, and epideictic or ceremonial rhetoric concerns
values associated with praise or blame and seeks no specific
decisions. For Aristotle, the epideictic genre was of limited
importance in the civic realm since it did not concern facts or
policies. Perelman, in contrast, believes not only that epideictic
rhetoric warrants more attention, but that the values normally
limited to that genre are in fact central to all argumentation.
"Epideictic oratory," Perelman argues, "has significant and
important argumentation for strengthening the disposition toward
action by increasing adherence to the values it lauds." These
values are central to the persuasiveness of arguments in all
rhetorical genres since the orator always attempts to "establish a
sense of communion centered around particular values recognized by
the audience."
Over fifteen years have passed since Cora Diamond and James Conant
turned Wittgenstein scholarship upside down with the program of
"resolute" reading, and ten years since this reading was
crystallized in the major collection The New Wittgenstein. This
approach remains at the center of the debate about Wittgenstein and
his philosophy, and this book draws together the latest thinking of
the world's leading Tractatarian scholars and promising newcomers.
Showcasing one piece alternately from each "camp", Beyond the
Tractatus Wars pairs newly commissioned pieces addressing differing
views on how to understand early Wittgenstein, providing for the
first time an arena in which the debate between "strong"
resolutists, "mild" resolutists and "elucidatory" readers of the
book can really take place. The collection includes famous
"samizdat" essays by Warren Goldfarb and Roger White that are
finally seeing the light of day.
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