Showing posts with label logic. Show all posts
Showing posts with label logic. Show all posts

Proof and Other Dilemmas: Mathematics and Philosophy (Spectrum) Review

Proof and Other Dilemmas: Mathematics and Philosophy (Spectrum)
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Proof and Other Dilemmas: Mathematics and Philosophy (Spectrum) ReviewThe following is quoted from a review by John Corcoran to appear in Mathematical Reviews.
This volume is in the Mathematical Association of America's Spectrum Series, which is intended to "appeal to a broad range of readers, including students and teachers of mathematics, mathematical amateurs, and researchers". Its sixteen chapters are individual essays each written by a different author. The authors are said to be "leading mathematicians, mathematics educators, and philosophers of mathematics". It also includes a 20-page introduction by one of the editors. The seventeen essays are intended to be "a sampler of current topics in philosophy of mathematics"; the essays by philosophers are said to "provide a much gentler introduction to what philosophers have been discussing over the last 30 years than will be found in a typical book". This should not be taken to mean that these essays give a summary or overview of the last 30 years of philosophy of mathematics. The book also includes a glossary of the "more common philosophical terms (such as epistemology, ontology, etc.)". The content of the book fully justifies the subtitle "Mathematics and Philosophy"; but nothing seems to explain the implication in the main title "Proof and other Dilemmas" that proof is a dilemma, nor is there anything to indicate which "other dilemmas" are intended.
Unfortunately, there are no indexes. There is no easy way to see how the terms in the glossary are actually used in the book or to compare different authors on the same issue or topic. For example, an index would reveal that the realist philosophy of mathematics called "platonism" is widely accepted--both as "the default position among philosophers" (pages xv and 179) and as the view "still dominant among working mathematicians" (page 40); but an index would also reveal that platonism is widely rejected--by leading mathematicians Paul Cohen and Saunders Mac Lane, and also by "most of the famous mathematicians who have expressed themselves on the question" (page 140). An index would greatly improve the usefulness of the book: it would prevent many misleading impressions.
The glossary is neither well-written nor accurate: for example, existential import is confused with ontological commitment, token is confused with occurrence, entailment is confused with implication, and there is no hint of awareness of the multiple meanings that have been attached to the word `implication' and its cognates--to mention a small selection from the 30 entries. Any reader new to philosophy of mathematics is advised to ignore the glossary and to rely instead on one of the several excellent philosophy dictionaries made by philosophers. One favorite is the 1999 Cambridge Dictionary of Philosophy.
The first three essays concern the focus in the title of the book: proof, as in "demonstrative proof" as opposed to "proof theory". All three are subjectivist in that they emphasize subjective belief or "conviction" while ignoring objective cognition--the idea that a proof proves a proposition to be true: a proof produces knowledge in the strict sense, not just persuasion. Moreover, there is no reference to the traditional "truth-and-consequence" conception of proof: that a proposition is proved to be true by showing that it is a logical consequence of known truths, i. e. by deducing the conclusion from established premises--leaving no room for pictures, constructions, diagrams, analogue or digital devices, or anything other than deductive reasoning once the premises have been taken.
Overall the book is not easy to read or easy to use. There are however some generally excellent articles--those by Michael Detlefsen, Stewart Shapiro, and Julian Cole stand out--but even these are heavy going, even for someone familiar with previous writings by the same author. Moreover, in almost every essay there are scattered passages containing informative scholarship, useful insights, and interesting and provocative points.
Proof and Other Dilemmas: Mathematics and Philosophy (Spectrum) OverviewDuring the first 75 years of the twentieth century almost all work in the philosophy of mathematics concerned foundational questions. In the last quarter of the century, philosophers of mathematics began to return to basic questions concerning the philosophy of mathematics such as, what is the nature of mathematical knowledge and of mathematical objects, and how is mathematics related to science? Two new schools of philosophy of mathematics, social constructivism and structuralism, were added to the four traditional views (formalism, intuitionalism, logicism, and platonism). The advent of the computer led to proofs and the development of mathematics assisted by computer, and to questions of the role of the computer in mathematics. This book of 16 essays, all written specifically for this volume, is the first to explore this range of new developments in a language accessible to mathematicians. Approximately half the essays were written by mathematicians, and consider questions that philosophers are not yet discussing. The other half, written by philsophers of mathematics, summarize the discussion in that community during the last 35 years. In each case, a connection is made to issues relevant to the teach of mathematics.

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Ontological Engineering: with examples from the areas of Knowledge Management, e-Commerce and the Semantic Web. First Edition (Advanced Information and Knowledge Processing) Review

Ontological Engineering: with examples from the areas of Knowledge Management, e-Commerce and the Semantic Web. First Edition (Advanced Information and Knowledge Processing)
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Ontological Engineering: with examples from the areas of Knowledge Management, e-Commerce and the Semantic Web. First Edition (Advanced Information and Knowledge Processing) ReviewThe word `ontology' is usually associated with philosophical speculation on the reality of things, and if one checks the literature on philosophy one will find a diverse number of opinions on this reality. Engineers and scientists typically view philosophical musings on any topic as being impractical, and indulging oneself in these musings will cause one to lose sight of the topic or problem at hand. Rather than simplify the problem and make it understandable, philosophy tends in most cases to complicate it by endless debate on definitions and the use of sophisticated rhetoric that seems to have no bearing on the problem at hand. The conceptual spaces generated by these debates can become gigantic and therefore unwieldy, thus making the problem appear more complex than it actually is.
In the information age however, ontology has become a word that has taken on enormous practical significance. Business and scientific research are both areas that have increasingly relied on information technology not only to organize information but also to analyze data and make accurate predictions. In addition, financial constraints have forced many businesses to automate most of their internal processes, and this automation has brought about its own unique challenges. This push to automation usually involves being able to differentiate one thing from another, or one collection of data from another, or one concept from another. Thus one needs to think about questions of ontology, and this (very practical) need has brought about the rise of the field of `ontological engineering', which is the topic of this book.
The authors have given a good general overview of the different approaches to the creation of ontologies. There are many of them, some of which seem "natural", while others seem more esoteric. The reader though will obtain an objective discussion of the ontologies that the authors chose to include in the book. Discussions of the ones that are not included can readily be found on the Internet.
Given the plethora of ontologies that have been invented, it would be of interest to the ontological engineer to find common ground between them. The re-use of a particular ontology may be stymied by the different ontological commitments it is adhering to or it's actual content. In order to use it, it must therefore be "re-engineered". The authors discuss this prospect in the book, and define `ontological re-engineering' as the process where a conceptual model of an implemented ontology is transformed into one that is more suitable. The code in which the ontology is written is first reverse engineered, and then the conceptual model is reorganized into the new one. The new conceptual model is then implemented.
Also discussed in the book, and of enormous practical interest, is the automation of the ontology building process. Called `ontology learning' by the authors, they discuss a few of the ways in which this could take place. One of these methods concerns ontology learning using a `corpus of texts', and involves being able to distinguish between the `linguistic' and `conceptual' levels. Knowledge at the linguistic level is described in linguistic terms, while at the conceptual level in terms of concepts and the relations between them. Ontology learning is thus dependent on how the linguistic structures are exemplified in the conceptual level. Relations at the conceptual level for example could be extracted from sequences of words in the text that conform to a certain pattern. Another method comes from data mining and involves the use of association rules to find relations between concepts. The authors discuss two well-known methods for ontology learning from texts. Both of these methods are interesting in that they can apparently learn in contexts or environments that are not domain-specific. Being able to learn over different domains is very important from the standpoint of the artificial intelligence community and these methods are a step in that direction. The processes of `alignment', `merging', and `cooperative construction' of ontologies that are discussed in the book are also of great interest in artificial intelligence, since they too will be of assistance in the attempt to design a machine that can reason over multiple domains.
The ontologies that are actually built are of course not unique. This results in a kind of semantic or cognitive relativism between the environments that might be built on different ontologies, even in the same domain. Merging and alignment both address this relativism, along with other techniques that are discussed in the book. The selection of the actual language that is used to create an ontology is also somewhat arbitrary. The authors devote a fair amount of space in the book to the different languages that have been used to build ontologies. Through an elementary example, they discuss eleven different languages, namely KIF, Ontolingua, LOOM, OCML, Flogic, SHOE, XOL, RDF(S), OIL, DAML+OIL, and OWL. The choice of a language is dictated by what one is seeking in terms of `expressiveness' and what kind of reasoning patterns are to be deployed when using the ontology. The authors point to a tradeoff between the expressive power of the language and the reasoning patterns that are attached to the language. The expressiveness of a language is directly proportional to the complexity of the reasoning patterns that are used.
Ontological engineering as it presently exists is still carried out by a human engineer. To create an ontology every time from scratch would be tedious, and so it is no surprise that tools were invented to make ontology creation more straightforward. Some of these tools are discussed in the book, such as KAON, OilEd, Ontolingua, OntoSaurus, Protege-2000, WebODE, and WebOnto, along with assessments as to their utility. The discussion is helpful for newcomers to ontological engineering who need guidance as to what direction to take. The automation of ontology building would of course be a major advance. To accomplish this however would require that the machine be able to simultaneously and recursively construct the knowledge base and reason over it effectively. This is a formidable challenge indeed.Ontological Engineering: with examples from the areas of Knowledge Management, e-Commerce and the Semantic Web. First Edition (Advanced Information and Knowledge Processing) OverviewOntologies provide a common vocabulary of an area and define, with different levels of formality, the meaning of the terms and the relationships between them. Ontological engineering refers to the set of activities concerning the ontology development process, the ontology life cycle, the methods and methodologies for building ontologies, and the tool suites and languages that support them. During the last decade, increasing attention has been focused on ontologies. Ontologies are now widely used in knowledge engineering, artificial intelligence and computer science; in applications related to areas such as knowledge management, natural language processing, e-commerce, intelligent information integration, bio-informatics, education; and in new emerging fields like the semantic web. The book presents the major issues of ontological engineering and describes the most outstanding ontologies currently available. It covers the practical aspects of selecting and applying methodologies, languages, and tools for building ontologies. "Ontological Engineering" will be of great value to students and researchers, and to developers who want to integrate ontologies in their information systems.

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On The Origin of the Human Mind. Three Theories: Uniqueness of the Human Mind, Evolution of the Human Mind, and The Neurological Basis of Conscious Experience Review

On The Origin of the Human Mind. Three Theories: Uniqueness of the Human Mind, Evolution of the Human Mind, and The Neurological Basis of Conscious Experience
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On The Origin of the Human Mind. Three Theories: Uniqueness of the Human Mind, Evolution of the Human Mind, and The Neurological Basis of Conscious Experience ReviewDespite the title of the book "On the Origin of the Human Mind" is not a complete presentation of evolutionary origin of the human brain and cognitive capacity. If it is what you are looking for, you better read David Bjorklund's book "The Origin of Mind" that is the best introduction to the subject to my knowledge. Dr. Vyshedskiy's book is subtitled " Three theories: Uniqueness of the Human Mind, Evolution of the Human Mind, and The Neurological Basis of Conscious Experience". For a book of 168 pages it is a very ambitious program. In fact the book should be better seen as a collection of three essays loosely linked by a common theme: "mental synthesis".
Dr. Vyshedskiy starts from the question "What makes us human?" If we look at apes we find that they share with us many characteristics that many people think specifically human such as self awareness, displaying emotion, smiling, reading other apes' minds, using complex social codified behaviours, using tools and transmitting a limited acquired culture to their offspring. He also credits apes, and also bees, birds, whales, and dolphins, with a limited language, something very questionable (it depends on the definition of language that one uses). He also think that abstract thinking, defined as "the process of generalization by reducing the information content of a concept or an observable phenomenon" is not specific to the human mind because "Vervet monkeys of East Africa have concept of leopard, snakes eagle and baboon"(pp. 16-7) (Here we might have a confusion between concept and representation). If language and abstract thinking do not make the difference, what will do it? Dr. Vyshedshiy's answer is "mental synthesis", something that Dr. Vyshedskiy thinks is a new theory but which has a number of things in common with other theories on the origin of language and rationality. Dr. Vyshedskiy defines mental synthesis as "the process of synthesizing a new, never-before-seen image from two or more mental images" (p. 22). Although animals are able to communicate, a chimp, for example, "cannot describe to another chimp a never-before-seen object because chimps cannot synthesize a new, never-before-seen image in their mind" (p.27). Without mental synthesis human language could never have arisen, and for that reason Dr. Vyshedskiy call human language "synthesizing language" (p. 28). The difference between non synthesizing languages and synthesizing language is that the former cannot create a new image in the listener's mind (p. 31). Animal can only learn to manipulate symbols or learn a limited number of word but they cannot use that capacity to solve problem or to plan actions. It is mental synthesis that allows us to analyse problems and to visually plan the action to be taken in our mind (p. 20). Here comes a very interesting development. Chimps can create and use tools, but the way they do it is fundamentally different from humans. For example a chimp can use a stick to fish termite. He needs to break a twig from a tree, remove the leaves and sharpen it with is teeth to shape it as a spear. The way he learns the process is by observing other apes doing it and learning the process by trial and error. It might take a chimp several months or even several years to master the whole process. The reason is that the chimp does not have a mental template of the tool. The way he learns is by remembering the actions that bring the reward through automated movements. "This long time frame of technique acquisition is similar to that is needed by humans to learn to play tennis, ski, ice-skate, play a musical instrument..." (p. 36). But when the chimps look at the stick they see only the stick. They do not see a tool and they do not have a concept of tool or even a concept of a stick for fishing termites. Here comes Dr. Vyshedskiy's theory of language: language is based on "mental synthesis" which must have evolved a long time before language appeared. Language allows human to plan their actions and to share the plan with other humans. In order to do that humans use "mental frames" which are "synthesized in the minds of the listeners" as "identical copies of the frames in the mind of the speaker. Thus the complex human language evolved to serve the purposes of synthesizing new images in the mind of the listeners" (p. 40). However pure mental synthesis is the absence of language remain possible (p. 42) and occur in different part of the brain.
In the second part of the book, Dr. Vyshedskiy tries to define when and how mental synthesis has appeared during human evolution. The origin of mental synthesis must be found in the development of the hominid's visual system. Because hominids could not compete in terms of strength and speed, when they started walking in the African savannah they had to develop a system of early recognition of predators. That new system was not based on recognition of the whole image like other animals, but on visual analysis consisting in decomposing a template of the predators in different components such as tail, ears, body, paws, etc., (pp. 75-6). Human became capable of assembling and dissembling mental image and that capacity is became the basis of mental analysis by generalizing of the mental process to other cognitive areas (p. 92). It also provides an interesting explanation of dreams and hallucinations (p. 153). In modern human, "visual analysis is primary a function of the left hemisphere and recognition of a whole object via amodal completion is primary a function of the right hemisphere" (pp. 76-7). "Improvement of the visual system in general and visual analysis in particular enable Homo habilis to manufacture the first stone choppers" because homo habilis had acquired " a mental template of a chopper"(p. 79-80). Homo habilis did not improve Oldowan tools for nearly a million year; Homo erectus erectus did not improve Acheulean tools for nearly two million years. The stasis in tool manufacturing can only be explained "by the limitation of the brain structure" (p. 80) (In my view it can also be explained by the absence of mirror neurons not yet developed). It is the refinement of the visual system that "drove the evolution of hominids" (p. 81). "Around 2.4 million years ago, the visual analysis system acquired elements of voluntary analysis" (p. 92) and 2 million years ago "the visual and prefrontal cortices developed significantly in Homo ergaster and Homo erectus" allowing "voluntarily dissecting the visual percept into fine details" (p.132). Development of the speech apparatus came later and was a consequence of a better visual system. "As hominids were able to separate more and more elements from the visual image, they needed more and more words to describe these elements" (p. 82). However it is only Homo sapiens that became fully able to synthesize mental image and to develop synthesizing language.
Part three of the book is more technical and tries to identify how mental image are formed at the neuronal level. It implies the solving by evolution of many technical problems such as neuronal synchronization (pp. 115-21) and the specialization of different areas in the prefrontal cortex (pp. 121-30). As those problems are covered by standard neuroscience literature I will not go into the details. Suffice is to say that the different part of a mental image are stored in different part of the brain and must be reassembled when the brain want to recall a memory (p. 107). This fact allows the synthezation of "never-before-seen image" by combining different components of different images. "The final step of the evolution of Homo was the acquisition of mental synthesis. About 100,000 years ago, the prefrontal cortex of Homo sapiens developed the capacity to synchronize several neuronal ensembles in one frame of consciousness" (p. 133).
I gave only three stars to the book for several reasons. (a) Mental synthesis is not a fully developed theory and more "work in process". The theory appears to be more an intuition that something solidly demonstrated. The author often gives the impression to be in hurry with no time for details. Facts that presented as "new" are sometimes known for decades. Scientific methodology is often weak. (b) The three part of the book are not integrated leading to overlap and repetition. (c) Dr. Vyshedskiy is obviously well versed in biology and neurosciences but does not seem to have any knowledge of development psychology, cognitive psychology and more important theories of the origin of language and rationality (evolutionary linguistic and psycholinguistic). (d) The book often lack in precise references for the facts and research quoted and therefore is difficult to use and to quote in an academic context. Despite all these flaws, in only 168 pages Dr. Vyshedskiy has achieved a very illuminating synthesis of a large array of scientific facts and produced a coherent theory of great interest. The theory might not be as new or as original as the author thinks, but there is an interesting convergence with other researches showing that the author might be close to truth. Whereas most theories in evolutionary linguistic put the emphasis on neuronal requirements for language, Dr. Vyshedskiy shows that the evolution of pre-linguistic cognitive capacity are as much vital as the evolution of linguistic capacity for understanding how modern human intellectual capability evolved. A more detailed and focussed book would be welcomed. I can only wish that Dr. Vyshedskiy, who apparently has accepted a management position in a R&R company, will return soon to academic life.
On The Origin of the Human Mind. Three Theories: Uniqueness of the Human Mind, Evolution of the Human Mind, and The Neurological Basis of Conscious Experience Overview
Some of the most time-honored questions in philosophy, psychology, and neurosciencecenter on the uniqueness of the human mind. How do we think? What makes us sodifferent from all the other animals on planet Earth? What was the process thatcreated the human mind? Is this process unique or can it be repeated on otherplanets? The book "On the Origin of the Human Mind" attemptsto provide an answer to these questions. It is organized into three chapters:

Chapter I "Uniqueness of the Human Mind" introducesthe reader to recent research into animal behavior, communication, culture andlearning, as well as controlled animal intelligence experiments and offers anew hypothesis of what makes the human mind unique.

Chapter II "Evolution of the Human Mind" combines latestgenetics research and archeological discoveries to help readers understand hominidevolution. The author discusses the forces that influenced the development ofthe hominid intelligence and offers a step-by-step theory that links improvementin visual information processing to speech development and to the types of stonetools manufactured by the hominids.

Chapter III "The Neurological Basis of Conscious Experience"takes the reader on an exciting journey into the neurobiology of the human mind.The author introduces the reader to the structure and function of the brainand then presents recent insights into brain organization derived from cognitivepsychology, brain imaging, animal experiments, and the studies of patients withdiseases of the brain. The book concludes with a unifying theory of the mindand a discussion of the evolution of the human brain and the uniqueness of thehuman mind from the neurological perspective.

Audience The book speaks best to readers who want to approach the mind from a scientificperspective. The book is written in easy-to-read engaging style. No previousknowledge in psychology, paleoanthropology, or neuroscience is necessary.

Hardcover edition The book is illustrated and printed in full-color.


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Philosophical Investigations Review

Philosophical Investigations
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Philosophical Investigations ReviewEven though Wittgenstein's German is nothing like Kant's, providing a good translation of his work is a challenge given all that one must bring into consideration. Anscombe's original translation had its merits, but it also had a number of frustrating flaws.
One of the many problems with Anscombe's translation of PI is her translation of both "hinweisende Erklärung" and "hinweisende Definition" as "ostensive definition," where the former is more literally read as "ostensive explanation" and the latter as "ostensive definition." See, e.g., §§27 and 28 of an earlier edition. And as one can see from Wittgenstein's discussion, there are times when he uses "hinweisende Erklärung" to mean "ostensive explanation" as opposed to actually ostensively defining a word, e.g., §31. And sometimes he uses them together almost interchangeably, e.g., the last two lines of §28. One of the most glaring cases of Anscombe ignoring the distinction is in §6 where the German reads, "Dies will ich nicht `hinweisende Erklärung', oder `Definition', nennen...." and the English translation reads simply "I do not want to call this `ostensive definition'...."
One way this difference, and Anscombe's failure to track it, is important is that giving an explanation is a much more open ended activity than giving a definition in a somewhat similar way as the German word for "game," "das Spiel," is more open than the English word, since "das Spiel" can also mean the more open concept of play.
One small "problem" presented by the updated translation is that the changes make past expressions no longer so apt, e.g., talk of a "no stage-setting" interpretation of the failure of the private ostensive definition in §258, based on the remarks about stage-setting in §257, is now problematic, since the new translation does not make use of the expression "stage-setting." This is a small problem, however.
While I respect Hacker's work, I do not agree with how easily he attributes substantive views to Wittgenstein; so I worry about how Hacker's methodological assumptions about Wittgenstein influence his input on the revisions. Nevertheless, I do not have a similar worry about Schulte, and I know that both Hacker and Schulte took into consideration the suggestions of other Wittgenstein scholars when making the revisions.
It is too soon to tell now, but I am excited to see what kind of an effect this new edition has on Wittgenstein studies.Philosophical Investigations OverviewIncorporating significant editorial changes from earlier editions, the fourth edition of Ludwig Wittgenstein's Philosophical Investigations is the definitive en face German-English version of the most important work of 20th-century philosophy

The extensively revised English translation incorporates many hundreds of changes to Anscombe's original translation
Footnoted remarks in the earlier editions have now been relocated in the text
What was previously referred to as ‘Part 2' is now republished as Philosophy of Psychology – A Fragment, and all the remarks in it are numbered for ease of reference
New detailed editorial endnotes explain decisions of translators and identify references and allusions in Wittgenstein's original text
Now features new essays on the history of the Philosophical Investigations, and the problems of translating Wittgenstein's text



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