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

On Truth Review

On Truth
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On Truth ReviewI write this review because there are criticisms that are irrelevant concerning the lack of creativity involved in the writing of this book. One criticism is that it is not thorough. It is not the be-all and end-all. It is a quick, accessible, interesting, insightful read though.
As an undergraduate I double-majored in German & Philosophy. Now I am about to complete my M.A. in German Studies and pursue philosophy as a hobby. I am a pragmatist.
As a pragmatist, the book is also particularly scintillating to me. I am a pragmatist as a direct consequence of William James's Pragmatism, my favourite work of philosophy. I am also reading James's The Meaning of Truth from time to time.
Frankfurt raises a fascinating problem in this work: the problem of a beneficial lie. He also cites 2 works by Montaigne ("Of Liars") and Kant ("On a Supposed Right to Lie from Altruistic Motives"), which I now feel compelled to read if I can obtain thru interlibrary loan.
Frankfurt argues that yes, some things are relative, but reminds me of the importance of getting it right. As I was schooled by a professor steeped in postmodernism, I have to find myself keeping postmodern tendences in thinking in check. Yes, engineers and architects and doctors do not have time for discussing some non-beneficial abstract notion of relativism, nor are they paid to do so. If this was all they focused on, they would not excel in their professions, and would not be successful.
I found this work insightful and personally helpful. More importantly, I found it culturally responsible and with a strong sense of social conscience so absent amongst philosophers that seem more and more ethically bankrupt. The most relevant questions are the most important. The question of truth is one that is relevant to us all. Thus, it is one of the most important.
This is a good starting place and I feel may change peoples lives who have a tendency to lie. I have considered buying it as a gift for some friends of mine, so well did I like this book.On Truth Overview

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Isabelle/HOL: A Proof Assistant for Higher-Order Logic (Lecture Notes in Computer Science) Review

Isabelle/HOL: A Proof Assistant for Higher-Order Logic (Lecture Notes in Computer Science)
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Isabelle/HOL: A Proof Assistant for Higher-Order Logic (Lecture Notes in Computer Science) ReviewIsabelle is fantastic, and this is an excellent tutorial.
With Isabelle, all the mystery of math and proof goes away
and everything becomes concrete... just like programming.
The only improvement that I'd like to see is that the
tutorial be rewritten using the Isar proof language.Isabelle/HOL: A Proof Assistant for Higher-Order Logic (Lecture Notes in Computer Science) Overview

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Philosophies of Mathematics Review

Philosophies of Mathematics
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Philosophies of Mathematics ReviewThis is a splendid book, teeming with virtues. But along with its many merits there is one drawback, which I'll mention later. First, the good stuff. Philosophies of Mathematics is primarily a textbook, designed to introduce logicism, intuitionism, and Hilbert's formalism to beginners at a moderately high level. It does this exceptionally well. The expositions are crisp and clear from start to finish. The authors say their book is accessible to anyone with a bit of elementary logic. Well, maybe. Those familiar with mathematics texts know the expressions `self-contained, but assumes a level of mathematical maturity.' I suspect that something like that goes for this book; philosophy undergraduates with no mathematics might be overwhelmed. But for the slightly more advanced reader (with, say, basic logic and one or two university mathematics courses), this book is the perfect introduction to the topics it covers.
What does it cover? The classic period in the philosophy of mathematics, namely, Logicism, Intuitionism, and Hilbert's formalism, here called Finitism. This, of course, is not particularly unusual. What is novel, and what makes the book such a valuable introduction, are three meaty, technical chapters on set theory, intuitionistic mathematics, and Gödel's theorem. Thus, after a standard discussion of the logicism of Frege and Russell showing how set theory develops out of logic, there is a very nice (though somewhat compact) presentation of basic set theory. The standard axioms of ZF are given, all the basic operations are defined, then it is shown how the real numbers (in the form of Cauchy sequences) can be derived. The discussion includes Cantor's theorem and the hierarchy of infinite numbers. This is done in forty-odd pages. There is enough material and in enough detail for a reader to get a feel for the plausibility of a reduction of all of mathematics to set theory. And if set theory can be reduced to logic, then one can get a feel for the scope of the classical logicist programme. I say `classical' because the authors do not take up the current "neo-logicist" programme, except to mention its existence.
The chapter on Intuitionism is devoted to Brouwer but also much influenced by Dummett. There is no mention of Bishop. The discussion even of Brouwer is perhaps a bit thin when it comes to what motivates him philosophically. But even the most ambitious would-be expositors find Brouwer's talk of the perception of time daunting. The emphasis is on provability and they draw the consequences for logic in considerable detail. Following this chapter is another devoted to constructive mathematics wherein George and Velleman prove a number of intuitionistic versions of classical theorems. This is extremely welcome, since most philosophical discussions merely wave their hands when it comes to the mathematical details.
The finitism chapter gives a standard account of Hilbert's formalism. The aims and achievements are outlined and so are the Gödel results that brought Hilbert's programme to a crashing halt. The incompleteness results are then given a chapter of their own. The exposition of Gödel is particularly good, and particularly thorough for a book on the philosophy of mathematics. The necessary technicalities are all here. Detailed proofs are given most of the time, and skipped in favour of a discussion of plausibility only when the technicalities require a great effort for a small payoff in understanding.
There is no other philosophy of mathematics book with extensive exercises. Philosophy of mathematics is a technical subject in itself and it relies on extensive knowledge of other technicalities. The exercises in this book will help to bring students up to speed.
I said there is one drawback. The book deals with the "classical" period in the philosophy of mathematics. There is not a word about current issues. There is no mention of naturalism (Maddy, Kitcher), or structuralism (Hellman, Resnik, Shapiro), or fictionalism (Field); there is no discussion of "experimental" mathematics, of the role of computers, of visualization, or of the interaction of mathematics and the sciences. Excellent though Philosophies of Mathematics is, one cannot get a proper sense from reading it of the field as it exists today. The authors are aware of this and in the preface express the view that `...contemporary work is best evaluated against a backdrop of understanding that encompasses these three great historical attempts to tame the phenomenon of mathematics.' There is no quarrelling with this. It's an excellent introduction to and guide through a golden age in the philosophy of mathematics.Philosophies of Mathematics Overview

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From Logic to Logic Programming (Foundations of Computing) Review

From Logic to Logic Programming (Foundations of Computing)
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From Logic to Logic Programming (Foundations of Computing) ReviewThis book is an excellent introduction to logic as it is applied to logic programming. It begins with a set of mathematical preliminaries, mathematical induction, trees, multisets, ordinals and cardinals. This is a ten-page refresher that most readers will be able to skip. Chapter two covers propositional logic, but this is not a standard overview of the subject. Advanced theorems such as the Soundness and Completeness theorems are stated and succinctly proven.
First-order logic is the topic of chapter three, and the coverage is thorough with it being aimed directly at the topic of chapter four, which is program-definability. In any complex programming project, one of the most difficult problems to resolve is how the data is to be represented in the computer. Chapter four explains how domains such as the natural numbers, binary notation and lists can be represented using the Herbrand Universe model.
The final three chapters cover linear resolution, infinite derivations, computability and negation. Mathematical proofs can be based on either verification of a positive or affirmation of a negative. Linear resolution can only deduce positive information from programs, infinite derivations and negation can be used to affirm a negative, indirectly deducing the opposite positive. Exercises are included at the end of each chapter, but no solutions are given.
This book is the best place to begin if you want to understand the mathematical foundations of logic programming. However, at least one course in mathematical logic is a precondition to that understanding.
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unSpun: Finding Facts in a World of Disinformation Review

unSpun: Finding Facts in a World of Disinformation
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unSpun: Finding Facts in a World of Disinformation ReviewAt least I think it's a great book, but now I'm not so sure. The authors, Brooks Jackson, and Kathleen Hall Jamieson have done such an outstanding job of showing me why I bought the electric scissors I didn't need and how I was focusing so much on watching the healthy people on the television doing Tai Chi in the park, I completely overlooked the possible side effects of the drug the commercial was pedaling. Now that I've listened and found out that it may lead to complete loss of body hair, tailbone growth, swelling of the lips and tongue, excessive weight gain, webbed feet, tooth loss, emesis and leprosy, I've stopped taking the drug.
Starting out with the first snake oil salesman making outrageous claims, to political advertisements by republicans and democrats, by Bush and Kerry, we learn that virtually none of them can be trusted because they appeal to our biases, our perception, our experiences, and cynicism with words that are open to interpretation such as clinically tested, larger, better, more people trust or use..., on average, and other caveats that deserve closer scrutiny. (I've also added to the list: "Read with an open mind," and "Only for those who can be objective").
If that isn't bad enough, the authors show us how our personal experiences and eyewitness accounts can be manipulated by others and by our own biases. For example, when subjects were shown two lines of differing lengths, they often reported that the shorter one was longer, once they learned that everyone else (supposedly) had selected the shorter line. An even better one is the neighboring review: One, who has made his conservative feelings clear, felt that there was more "left favoring" bias to this book. A commenter said that he felt there was more "right-favoring" bias. This is a classic recommendation for the book.
The most fascinating thing I took from this short paperback is that people will cling to their beliefs more tenaciously in the face of overwhelming evidence that reveals their position is incorrect or invalid, that people will short-circuit their own brains and readily accept as fact that which conforms to their own beliefs, and that we must learn to question bias, sources, evidence, and our cynicism before parting with our money or accepting information as knowledge or fact.
So, I can guarantee that you will be 100% satisfied as were the people in my survey who read this book compared with another. Two out of three found this not only a better read, but reported that it killed the germs that cause bad breath, took inches off their waistline, and removed wrinkles. So, what are you waiting for? Get started today. Start reading. After all, you have everything to lose!
Guaranteed! Or, my name isn't Axel Schnookenhoffer!
unSpun: Finding Facts in a World of Disinformation Overview

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Meaning Of Meaning Review

Meaning Of Meaning
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Meaning Of Meaning ReviewI first encountered reference to this book when reading about the semantic web. The key innovation was the "semiotic triangle" where we are encouraged to think of things, thoughts and symbols in separate and distinct domains. I now use the "semantic triangle" (a more approachable name) in many of my semantic web training classes. The key concept to get across to students is that when computers need to communicate, there are many limitations when using symbols alone, which can have many different meaning within different contexts. For example the word "run" has over 50 different meanings according to WordNet. A more robust way to exchange information between computers is to associate data elements with concepts. This books was one of the first books to build these models of communication.Meaning Of Meaning Overview

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A Rulebook for Arguments Review

A Rulebook for Arguments
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A Rulebook for Arguments ReviewA college applicant allegedly wrote the following one-word essay to describe himself: "Concise." While I was tempted to coopt that entire essay as a review for this book, ultimately I decided to be more verbose: first, some general remarks about the relevance of this book, then a summary of its content.
I often lament that the mythical "average person" does not appreciate what counts as evidence, nor distinguish between prejudice and rational conclusion. This is particularly evident in the realm of politics, where inflammatory rhetoric is the rule and rational argument the exception. If this tiny book (or its equivalent) were required reading for every high school senior, or college freshman, I wager there would be a wholesale shift in the texture and value of day-to-day discourse. No longer would we hear "Don't vote for that crook!", but the more sober, albeit prolix, application of modus tollens, "Public office requires honesty. Jones is dishonest. Therefore, Jones should not be elected to public office."
Of course, "Don't vote for that crook!" will never be abandoned for the simple reason that it is good tight prose. Yet, wouldn't it be grand if it were crystal clear to everyone that it is simply shorthand for the more prolix version? I claim that it would, for then we would be apt to challenge such a remark with "What evidence do you have that Jones is dishonest?", rather than "Would you rather I vote for that child molester, Smith?" The latter invites further character assassination of Jones, if not impeachment of his entire lineage. Perhaps I'm just a stuffy academic, but I can't help thinking that the introduction of a bit of cool logic into every-day discourse would lower our collective blood pressure and maybe, just maybe, allow us to occasionally see beyond our prejudices.
This wonderful little book lists 44 specific suggestions, or "rules", for injecting much-needed logic into argumentative discourse. In the author's words, each rule is "illustrated and explained soundly but above all briefly"; Hence, to Weston the book is a "rulebook" not a textbook. Weston continues "In this book, 'to give an argument' means to offer a set of reasons or evidence in support of a conclusion." This is in contrast to the variety accompanied by loud invective and broken china.
Throughout the book, Weston offers advice that we would all do well to remember. For example, he reminds us that one can neither craft nor analyze an argument by merely consulting our prejudices, and that "it is your reasons, not your language, that must persuade." With regard to language, Weston asserts that prejudicial or loaded language "preaches only to the converted, but careful presentation of the facts can itself convert." Moreover, "It is not a mistake to have strong views. The mistake is to have nothing else." Well put.
Weston also injects some broadly applicable principles of critical thinking (although he does not label them as such). For instance, in contemplating possible solutions, explanations, or causes, he urges us to continually look for more options, rather than immediately narrowing them. In so doing, we can state our case more fairly, and possibly head off objections more effectively. But perhaps the most important admonition is this: "If you can't imagine how anyone could hold the view you are attacking, you just don't understand it yet." Imagine a world in which all disputants took this to heart!
Beginning with short arguments consisting of a sentence or two, Weston builds to a chapter on crafting effective long arguments. As usual, Weston anticipates common blunders and warns us, for example, to first "find out what each side considers the strongest arguments for its position." He then prepares us for the inevitable process of rewriting and reorganizing our arguments as we accumulate evidence and analyze positions on all sides. He coolly advises us to adopt a different strategy, or even a different conclusion, should we discover that our initial inclinations are not adequately supported by the available evidence. While this may seem obvious, it would be wonderful if everyone actually did this.
Weston provides some concrete advice on writing, such as developing one idea per paragraph, getting to the point quickly, and stating the conclusion clearly and directly. According to Weston, you ought not "fence more land than you can plow. One argument well-developed is better than three only sketched." To do otherwise would be like "preferring ten very leaky buckets to one well-sealed one." Finally, Weston urges us to preemptively raise possible counter-arguments and to develop them in sufficient detail that our readers will fully appreciate the position we are disarming.
The book includes a short but helpful chapter on fallacies, focusing primarily on the two "great fallacies" of generalizing from incomplete information and overlooking alternative explanations. One angle that I found illuminating is that several classic fallacies are in fact species of "overlooking alternatives", such as "affirming the consequent", "denying the antecedent", and "false dilemma". Several fallacies were discussed in this chapter that I have not encountered elsewhere, at least not by these names: specifically, the fallacies of "persuasive definition", "poisoning the well", "provincialism", and "weasel words". All are tersely but amply illustrated. Weston concludes with a brief chapter on definitions, of which there are several varieties: stipulative, operational, essential, and genus-and-differentia. I found these distinctions to be equally illuminating. As Richard Feynman said, "To name a thing is not the same as to know a thing", yet it is often a step in the right direction.
In summary, I found this book to be an excellent guide to crafting effective arguments. Although I have studied formal logic fairly extensively, and even informal logic to a lesser degree, this book left me with many new ideas, and made familiar old ideas suddenly more cogent and relevant. And, it's concise.A Rulebook for Arguments Overview

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On Bullshit Review

On Bullshit
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On Bullshit ReviewI got this book after seeing Prof. Frankfurt on the Daily Show with John Stewart. Having a bachelors degree in philosophy I was intrigued. Here are some of my observations:
1) This book is not traditionally funny. If you are looking for a joke book get one, this is a work of philosophy and as such has a degree of intellectual humor. Some of the observations and comments are funny but overall this is not a joke book, rather it is designed with a specific philosophical purpose... (he's an "ivy league" Philosophy Professor and published by Princeton)
2) Very short but to the point. I read the whole book in less than an hour. That being said there is a lot of content which deserves meaningful reflection... its one of those books that you will probably end up going "ahhh haaa" at least at one point.
3) Inexpensive. Its under ten bucks... some may say that its pricey for such a small book but if you enjoy it, whose to say what the intrinsic value will be to you down the road.
4) Warning... this is not the most complex or even dense piece of philosophy. Certainly its not like reading Hegel or another "headache philosopher" but this is a work of philosphy. As long as you know that going into this there should be no problems. A friend of mine read this book thinking it would be comical and fun, almost expecting jokes and punch-lines... he was disappointed.
The last thing I will say is that I really enjoyed the book and I can imagine many people really reading this book a couple of times and really liking it. I am already recommending it to some of my friends and lawschool professors... If you do decide to buy this book... ENJOY!On Bullshit Overview

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Introductory Logic: Student (4th edition) Review

Introductory Logic: Student (4th edition)
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Introductory Logic: Student (4th edition) ReviewThis workbook is designed to teach logic, and to do it from an unapologetically Christian slant. Chocked full of easy-to-understand lessons, each section ends with one (and sometimes two) exercises. This book is well designed, and should be considered by anyone interested in teaching his or her children formal logic.
My one and only complaint against this book is that the exercises do not include an answer page. But, I found the exercises easy enough that I could do my own correcting. So, I must say that I found this to be a great book and an excellent tool. I highly recommend it.Introductory Logic: Student (4th edition) Overview

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Introduction to Objectivist Epistemology: Expanded Second Edition Review

Introduction to Objectivist Epistemology: Expanded Second Edition
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Introduction to Objectivist Epistemology: Expanded Second Edition ReviewThis book is precisely what the title states. It is an "introduction" and as such is the gateway to Rand's theory of knowledge by way of her theory of concepts. Human knowledge is conceptual knowledge and Rand validates the objectivity of concepts by explaining, from the ground up, the method by which they are formed in the mind. The points she makes which seem misguided and arbitrary are cleared up in subsequent re-readings as long as the reader keeps in mind that once she defines a term, she does not deviate from its meaning. For most of us who are generally unsure about specific definitions of terms and rely on our feelings to give meaning to the words we read, discipline is required. For those who start with an axe to grind based on their disagreements with Rand's political philosophy, deliberate mis-interpretations of terms generally abound (as can be seen in most of the on-line reviews.) One such example is the damning of Rand over her claim to have solved the problem of "universals". In this context, this problem refers to the issue of the relationship between concepts and their perceptual referents; the HISTORICAL problem of universals. It is unfortunately too common to find those who are willing to drop this necessary context and argue against the Objectivist claim based on various meanings of the term universal, few of which are relevant to the issue at hand.
It is amusing to read disagreements of the Objectivist theory of concepts which are addressed and cleared up in the appendix. The appendix of the second edition of I to OE really is amazing. It is simply transcripts of round table discussions of professors who had read the original text presenting their questions and objections on finer points of epistemology. Rand was, apparently, at her intellectual pinnacle at this point, and any potentially hazy points are clarified beyond question.
The criticism that this is not presented in as scholarly a way as an epistemological monograph should be has its merits. The preface clearly states that main work is a reprint of a series of articles in which Rand presented her theory of concept formation. I certainly would have preferred a more scholastic presentation and a deeper exploration of the background of certain ideas, but this was Rand's style. She did not "write down" to her readers and her writing requires objective truth seekers to do their own research. I have, on multiple occasions, encountered the criticism that a reader was left wondering what Bertrand Russell was attempting to "perpetrate" in his theory of numbers. After encountering this passage I went to a philosophy text and read a passage describing Russell's theory of numbers as an attempt to create a purely logical language which would allow one to understand numbers without relating them to their perceptual referents. Since Rand demonstrates that concepts are valid within the context of the totality of human consciousness, and that abstractions must be derived primarily from their perceptual referents (numbers, specifically, are covered) which form their fundamental context, the dismissal of Russell stands.
For those who are familiar with Rand only from Atlas Shrugged and The Fountainhead, this is a fascinating opportunity to understand the underlying support of a novelist's reasoning process, rarely made this explicit.Introduction to Objectivist Epistemology: Expanded Second Edition Overview

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Aristotle: Posterior Analytics. Topica. (Loeb Classical Library No. 391) (v. 2) Review

Aristotle: Posterior Analytics. Topica. (Loeb Classical Library No. 391) (v. 2)
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Aristotle: Posterior Analytics. Topica. (Loeb Classical Library No. 391) (v. 2) ReviewA great translation of one of the most important works in the history of philosophy. All titles in the Loeb Classical Library are highly recomended for their accuracy and for their technical quality. Definitely a must have.Aristotle: Posterior Analytics. Topica. (Loeb Classical Library No. 391) (v. 2) Overview

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