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Books > Humanities > Philosophy > Topics in philosophy > Logic
Forms of Truth and the Unity of Knowledge addresses a philosophical
subject-the nature of truth and knowledge-but treats it in a way
that draws on insights beyond the usual confines of modern
philosophy. This ambitious collection includes contributions from
established scholars in philosophy, theology, mathematics,
chemistry, biology, psychology, literary criticism, history, and
architecture. It represents an attempt to integrate the insights of
these disciplines and to help them probe their own basic
presuppositions and methods. The essays in Forms of Truth and the
Unity of Knowledge are collected into five parts, the first dealing
with division of knowledge into multiple disciplines in Western
intellectual history; the second with the foundational disciplines
of epistemology, logic, and mathematics; the third with explanation
in the natural sciences; the fourth with truth and understanding in
disciplines of the humanities; and the fifth with art and theology.
Contributors: Vittorio Hoesle, Keith Lehrer, Robert Hanna, Laurent
Lafforgue, Thomas Nowak, Francisco J. Ayala, Zygmunt Pizlo, Osborne
Wiggins, Allan Gibbard, Carsten Dutt, Aviezer Tucker, Nicola Di
Cosmo, Michael Lykoudis, and Celia Deane-Drummond.
Kit Fine has since the 1970s been one of the leading contributors
to work at the intersection of logic and metaphysics. This is his
eagerly-awaited first book in the area. It draws together a series
of essays, three of them previously unpublished, on possibility,
necessity, and tense. These puzzling aspects of the way the world
is have been the focus of considerable philosophical attention in
recent decades. Fine gives here the definitive exposition and
defence of certain positions for which he is well known: the
intelligibility of modality de re; the primitiveness of the modal;
and the primacy of the actual over the possible. But the book also
argues for several positions that are not so familiar: the
existence of distinctive forms of natural and normative necessity,
not reducible to any form of metaphysical necessity; the need to
make a distinction between the worldly and the unworldly, analogous
to the distinction between the tensed and the tenseless; and the
viability of a non-standard form of realism about tense, which
recognizes the tensed character of reality without conceding that
there is any privileged standpoint from which it is to be viewed.
Modality and Tense covers a wide range of topics from many
different areas: the possible-worlds analysis of counterfactuals;
the compatibility of special relativity with presentism; the
implications of ethical naturalism; and the nature of
first-personal experience. A helpful introduction orients the
reader and offers a way into some of the most original work in
contemporary philosophy.
This contributed volume explores the ways logical skills have been
perceived over the course of history. The authors approach the
topic from the lenses of philosophy, anthropology, sociology, and
history to examine two opposing perceptions of logic: the first as
an innate human ability and the second as a skill that can be
learned and mastered. Chapters focus on the social and political
dynamics of the use of logic throughout history, utilizing case
studies and critical analyses. Specific topics covered include: the
rise of logical skills problems concerning medieval notions of
idiocy and rationality decolonizing natural logic natural logic and
the course of time Logical Skills: Social-Historical Perspectives
will appeal to undergraduate and graduate students, as well as
researchers in the fields of history, sociology, philosophy, and
logic. Psychology and colonial studies scholars will also find this
volume to be of particular interest.
A comprehensive philosophical introduction to set theory. Anyone
wishing to work on the logical foundations of mathematics must
understand set theory, which lies at its heart. Potter offers a
thorough account of cardinal and ordinal arithmetic, and the
various axiom candidates. He discusses in detail the project of
set-theoretic reduction, which aims to interpret the rest of
mathematics in terms of set theory. The key question here is how to
deal with the paradoxes that bedevil set theory. Potter offers a
strikingly simple version of the most widely accepted response to
the paradoxes, which classifies sets by means of a hierarchy of
levels. What makes the book unique is that it interweaves a careful
presentation of the technical material with a penetrating
philosophical critique. Potter does not merely expound the theory
dogmatically but at every stage discusses in detail the reasons
that can be offered for believing it to be true.
This book is dedicated to the life and work of the mathematician
Joachim Lambek (1922-2014). The editors gather together noted
experts to discuss the state of the art of various of Lambek's
works in logic, category theory, and linguistics and to celebrate
his contributions to those areas over the course of his
multifaceted career. After early work in combinatorics and
elementary number theory, Lambek became a distinguished algebraist
(notably in ring theory). In the 1960s, he began to work in
category theory, categorical algebra, logic, proof theory, and
foundations of computability. In a parallel development, beginning
in the late 1950s and for the rest of his career, Lambek also
worked extensively in mathematical linguistics and computational
approaches to natural languages. He and his collaborators perfected
production and type grammars for numerous natural languages. Lambek
grammars form an early noncommutative precursor to Girard's linear
logic. In a surprising development (2000), he introduced a novel
and deeper algebraic framework (which he called pregroup grammars)
for analyzing natural language, along with algebraic, higher
category, and proof-theoretic semantics. This book is of interest
to mathematicians, logicians, linguists, and computer scientists.
This book presents reflections on the relationship between
narratives and argumentative discourse. It focuses on their
functional and structural similarities or dissimilarities, and
offers diverse perspectives and conceptual tools for analyzing the
narratives' potential power for justification, explanation and
persuasion. Divided into two sections, the first Part, under the
title "Narratives as Sources of Knowledge and Argument", includes
five chapters addressing rather general, theoretical and
characteristically philosophical issues related to the
argumentative analysis and understanding of narratives. We may
perceive here how scholars in Argumentation Theory have recently
approached certain topics that have a close connection with
mainstream discussions in epistemology and the cognitive sciences
about the justificatory potential of narratives. The second Part,
entitled "Argumentative Narratives in Context", brings us six more
chapters that concentrate on either particular functions played by
argumentatively-oriented narratives or particular practices that
may benefit from the use of special kinds of narratives. Here the
focus is either on the detailed analysis of contextualized examples
of narratives with argumentative qualities or on the careful
understanding of the particular demands of certain well-defined
situated activities, as diverse as scientific theorizing or war
policing, that may be satisfied by certain uses of narrative
discourse.
F. H. Bradley was the greatest of the British Idealists, but for
much of this century his views have been neglected, primarily as a
result of the severe criticism to which they were subjected by
Russell and Moore. In recent years, however, there has been a
resurgence of interest in and a widespread reappraisal of his work.
W. J. Mander offers a general introduction to Bradley's metaphysics
and its logical foundations, and shows that much of his philosophy
has been seriously misunderstood. Dr Mander argues that any
adequate treatment of Bradley's thought must take full account of
his unique dual inheritance from the traditions of British
empiricism and Hegelian rationalism. The scholarship of recent
years is assessed, and new interpretations are offered of Bradley's
views about truth, predication, and relations, and of his arguments
for idealism. This book is a clear and helpful guide for those new
to this difficult but fascinating thinker, and at the same time an
original and stimulating contribution to the re-evaluation of his
work.
Critical thinking is becoming increasingly prominent as an academic
discipline taught and examined in schools and universities, as well
as a crucial skill for everyday life. To be a successful critical
thinker it is vital to understand how the different concepts and
terms are defined and used. The terminology often presents a
stumbling block for the beginner, since much of it is used
imprecisely in everyday language. This definitive A to Z guide
provides precise definitions for over 130 terms and concepts used
in critical thinking. Each entry presents a short definition
followed by a more detailed explanation and authoritative
clarification. Armed with the tools and knowledge provided in these
pages, the reader will be able to distinguish an assertion from an
argument, a flaw from a fallacy, a correlation from a cause and a
fact from an opinion. The book is an invaluable resource for
teachers and students of critical thinking, providing all the tools
necessary to effectively analyse, evaluate, question and reason for
yourself.
Alfred Tarski was one of the two giants of the twentieth-century
development of logic, along with Kurt Goedel. The four volumes of
this collection contain all of Tarski's papers and abstracts
published during his lifetime, as well as a comprehensive
bibliography. Here will be found many of the works, spanning the
period 1921 through 1979, which are the bedrock of contemporary
areas of logic, whether in mathematics or philosophy. These areas
include the theory of truth in formalized languages, decision
methods and undecidable theories, foundations of geometry, set
theory, and model theory, algebraic logic, and universal algebra.
'David Pole, in his The Later Philosophy of Wittgenstein, makes an
admirable attempt to clarify the central points of Wittgenstein's
philosophy in a straightforward manner. He approaches it from the
outside with sympathy and good sense. And since he combines a clear
head with a fluent style of writing - a combination that is rare
among the initiated - his book will prove an excellent introduction
for those who need a succinct account of Wittgenstein's later
philosophy without any mystical overtones.' - The Economist 'There
is now a real need for a commentary on what must in frankness be
admitted to be an exceedingly difficult corpus of philosophy. Mr
Pole's little book is a response to that need; if small in bulk, it
is rich in ideas... and all students of Wittgenstein will turn to
it with gratitude.' - Sunday Times
This book offers a comprehensive critical survey of issues of
historical interpretation and evaluation in Bertrand Russell's 1918
logical atomism lectures and logical atomism itself. These lectures
record the culmination of Russell's thought in response to
discussions with Wittgenstein on the nature of judgement and
philosophy of logic and with Moore and other philosophical realists
about epistemology and ontological atomism, and to Whitehead and
Russell's novel extension of revolutionary nineteenth-century work
in mathematics and logic. Russell's logical atomism lectures have
had a lasting impact on analytic philosophy and on Russell's
contemporaries including Carnap, Ramsey, Stebbing, and
Wittgenstein. Comprised of 14 original essays, this book will
demonstrate how the direct and indirect influence of these lectures
thus runs deep and wide.
Current edition description Written by two of the leading experts
in critical thinking, this book focuses on an integrated, universal
concept of critical thinking that is both substantive and
applicable to any and every situation in which human thinking is
necessary. It provides readerse with the basic intellectual tools
needed for life-long learning, helping them understand the mind and
how its three functions - thinking, feeling, motivation - influence
and are influenced by one another. This book fosters the
development of fair-minded critical thinking. Features the
intellectual standards: clarity, precision, accuracy, logicalness,
significance, depth, breadth, and fairness; The importance of good
questioning; and intellectual tools to read for deep and lasting
comprehension, and to write in ways that show clarity of
reasonability of thought. For all that want to improve their
critical thinking skills to apply to their job or life. The text
features: Think for Yourself activities - throughout each chapter.
(Ex. pp 29, 127). ~Help students take ownership of basic concepts
as they learn them. Practical and learnable format. ~Simplifies
complex ideas to make learning easier for students. Focus on
thinking across the disciplines. (Ex. pp 119-120). ~Helps students
to think within the various disciplines, rather than memorizing
facts. Students are taught to learn to think like an historian,
like a scientist, like a psychologist, etc. Critical thinking focus
- When students internalize intellectual standards - such as
clarity, precision, accuracy, logicalness, significance, depth,
breadth, and fairness - they use them on a daily basis to upgrade
their thinking, and to assess the thinking of others. (Ex. 12,
152). ~Gives students intellectual standards they can use in every
dimension of their thinking. Features intellectual tools to read
for deep and lasting comprehension, and to write in ways that show
clarity of reasonability of thought. (Ex. 133). ~Teaches students
to read closely and write substantively. Good questions are the key
to good thinking - Thinkers who know how to ask relevant questions
in context are better able to think their way through complex
issues. (Ex. pp 83, 87, 93). ~Teaches students to ask the questions
the best thinkers ask. Website - www.criticalthinking.org. ~Links
students to the world's largest and most prestigious critical
thinking website and provides forums for student and faculty
discussions. International approach - with translations into
German, French, Spanish, Japanese, Chinese, Russian, and Malay.
~Provides students with the opportunity to read portions of the
text in their native language. "This book is well-written, lucid
and contains abundant examples and applications that not only
enliven the subject matter but present relevant contexts for
building understanding and advanced critical thinking. In addition,
it is faithful to the complexity and work required to improve one's
thinking. It does not soft-pedal the challenge but actually throws
down the gauntlet to the worthy Reader to pick it up." --Stephen J.
Knopp, Ph.D., Ohio University "This concise version is a more
comprehensive and robust textbook. Many Critical Thinking books
cover thinking from a narrow angle, but Paul and Elder offer a
model of critical thinking that can be applied not only to academic
disciplines but also to life in general." --Connie Wolfe, Surry
Community College
In three comprehensive volumes, Logic of the Future presents a full
panorama of Charles S. Peirce's important late writings. Among the
most influential American thinkers, Peirce took his existential
graphs to be his greatest contribution to human thought. The
manuscripts from 1895-1913, most of which are published here for
the first time, testify the richness and open-endedness of his
theory of logic and its applications. They also invite us to
reconsider our ordinary conceptions of reasoning as well as the
conventional stories told about the evolution of modern logic. This
second volume collects Peirce's writings on existential graphs
related to his Lowell Lectures of 1903, the annus mirabilis of his
that became decisive in the development of the mature theory of the
graphical method of logic.
Approaching Infinity addresses seventeen paradoxes of the infinite,
most of which have no generally accepted solutions. The book
addresses these paradoxes using a new theory of infinity, which
entails that an infinite series is uncompletable when it requires
something to possess an infinite intensive magnitude. Along the
way, the author addresses the nature of numbers, sets, geometric
points, and related matters. The book addresses the need for a
theory of infinity, and reviews both old and new theories of
infinity. It discussing the purposes of studying infinity and the
troubles with traditional approaches to the problem, and concludes
by offering a solution to some existing paradoxes.
The volume is published on the occasion of the birth centennial of
Eugenio Coseriu (1921-2002). It is the first collective volume to
appear in English in which various scholars present a variety of
perspectives on Coseriu's scholarly work and discuss its continuing
relevance for the language sciences. Coseriu's international
reputation has suffered from his commitment to publish in languages
such as Spanish, German, French, Italian, Romanian and Portuguese,
to the detriment of English. As a consequence, his work is less
well-known outside Romance and German linguistics. The volume aims
to raise the general awareness of Coseriu's work among linguists
around the world, in accordance with Coseriu's own adage that it
takes a constructive mindset (acknowledging "accomplishments and
limitations") to do justice to all scholarly work in the
humanities. The articles are organized into three major thematic
clusters: 1) philosophy of language, 2) history of the language
sciences and 3) theory and practice of "Integral Linguistics". The
volume is essential reading for anyone working in these fields and
for those seeking to gain deeper understanding of Coseriu's goal to
develop a unitary approach to language which takes as its point of
departure the "activity of speaking".
This book discusses how scientific and other types of cognition
make use of models, abduction, and explanatory reasoning in order
to produce important or creative changes in theories and concepts.
It includes revised contributions presented during the
international conference on Model-Based Reasoning (MBR'015), held
on June 25-27 in Sestri Levante, Italy. The book is divided into
three main parts, the first of which focuses on models, reasoning
and representation. It highlights key theoretical concepts from an
applied perspective, addressing issues concerning information
visualization, experimental methods and design. The second part
goes a step further, examining abduction, problem solving and
reasoning. The respective contributions analyze different types of
reasoning, discussing various concepts of inference and creativity
and their relationship with experimental data. In turn, the third
part reports on a number of historical, epistemological and
technological issues. By analyzing possible contradictions in
modern research and describing representative case studies in
experimental research, this part aims at fostering new discussions
and stimulating new ideas. All in all, the book provides
researchers and graduate students in the field of applied
philosophy, epistemology, cognitive science and artificial
intelligence alike with an authoritative snapshot of current
theories and applications of model-based reasoning.
Alain Badiou's Being and Event continues to impact philosophical
investigations into the question of Being. By exploring the central
role set theory plays in this influential work, Burhanuddin Baki
presents the first extended study of Badiou's use of mathematics in
Being and Event. Adopting a clear, straightforward approach, Baki
gathers together and explains the technical details of the relevant
high-level mathematics in Being and Event. He examines Badiou's
philosophical framework in close detail, showing exactly how it is
'conditioned' by the technical mathematics. Clarifying the relevant
details of Badiou's mathematics, Baki looks at the four core topics
Badiou employs from set theory: the formal axiomatic system of ZFC;
cardinal and ordinal numbers; Kurt Goedel's concept of
constructability; and Cohen's technique of forcing. Baki then
rebuilds Badiou's philosophical meditations in relation to their
conditioning by the mathematics, paying particular attention to
Cohen's forcing, which informs Badiou's analysis of the event.
Providing valuable insights into Badiou's philosophy of
mathematics, Badiou's Being and Event and the Mathematics of Set
Theory offers an excellent commentary and a new reading of Badiou's
most complex and important work.
A proof is a successful demonstration that a conclusion necessarily
follows by logical reasoning from axioms which are considered
evident for the given context and agreed upon by the community. It
is this concept that sets mathematics apart from other disciplines
and distinguishes it as the prototype of a deductive science.
Proofs thus are utterly relevant for research, teaching and
communication in mathematics and of particular interest for the
philosophy of mathematics. In computer science, moreover, proofs
have proved to be a rich source for already certified algorithms.
This book provides the reader with a collection of articles
covering relevant current research topics circled around the
concept 'proof'. It tries to give due consideration to the depth
and breadth of the subject by discussing its philosophical and
methodological aspects, addressing foundational issues induced by
Hilbert's Programme and the benefits of the arising formal notions
of proof, without neglecting reasoning in natural language proofs
and applications in computer science such as program extraction.
Saul Kripke's Naming and Necessity was one of the most influential
philosophical works of the twentieth century. In this collection of
essays leading specialists explore issues arising from this and
other works of Kripke's.
This new digital edition of The Trial and Death of Socrates:
Euthyphro, Apology, Crito and Phaedo presents Benjamin Jowett's
classic translations, as revised by Enhanced Media Publishing. A
number of new or expanded annotations are also included.
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