European Mathematical Society - cool, t. (consultancy & econometrics)
https://euro-math-soc.eu/publisher/cool-t-consultancy-econometrics
enA Logic of Exceptions
https://euro-math-soc.eu/review/logic-exceptions
<div class="field field-name-field-review-review field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"><p>As the title suggests this book discusses the subject of logic. It begins with the basic elements but it also introduces new elements such as a logic of exceptions. Hence the last part of the book requires a more advanced level. It also includes part of the exciting history of philosophy, mathematics and logic, that usually doesn’t appear in other logic texts.<br />
The examples are written in Mathematica which is a language or system for doing mathematics on the computer, but you can still read and understand this book even if you are not familiar with Mathematica and you decide not to run the programs. In any case the basics are supplied.<br />
The book is organised in three parts:<br />
Part I – The basic propositional operators are introduced.<br />
Part II – This part deals with the basic notions of inference: inferences, syllogisms, axiomatics and proof theory. It is first developed for propositional logic and then for predicate logic. For the first time, the existence of sentences that require some three-valued logic is discussed. (There are propositions that are either true or false (two-valued) and sentences that may be true, false or indeterminate.)<br />
It also includes a short history of the Liar paradox , which is the root of many other paradoxes and its different solution approaches such as the theory of types, proof theory and three-valued logic. It analyses the problems which arise in the first two approaches, so that the author defends that only three-valued logic allows for a consistent development.<br />
The historical review of the Liar shows how various cases propose the introduction of an exception as part of the proposed solution. Hence a logic of exceptions is developed.<br />
Part III - This part deals with three-valued logic. First of all, the author discusses the need to introduce a third value different to true or false. Once again the basic operators are considered and its definitions modified because of this third value.<br />
Finally three-valued logic is applied to the Liar paradox, which is now solved. Gödel’s theorems, and Brouwer’s intuitionism are revisited.</p>
</div></div></div></div><div class="field field-name-field-review-reviewer field-type-text field-label-inline clearfix"><div class="field-label">Reviewer: </div><div class="field-items"><div class="field-item even">Margarita Bradley</div></div></div><div class="field field-name-field-review-legacy-affiliation field-type-text field-label-inline clearfix"><div class="field-label">Affiliation: </div><div class="field-items"><div class="field-item even">Universidad Complutense de Madrid</div></div></div><div class="field field-name-field-review-desc field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"><p>This book begins introducing the basic notions of propositional and predicate logic, but in the last chapters new concepts are developed such as a logic of exceptions (there may be exceptions to the rules applied) and a three-valued logic.<br />
The author believes that three-valued logic is the way to solve the Liar paradox and other paradoxes related to it, including Gödel’s theorems.<br />
The examples are written in Mathematica.</p>
</div></div></div></div><span class="vocabulary field field-name-field-review-author field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Author: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/author/thomas-colignatus" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">thomas colignatus</a></li></ul></span><span class="vocabulary field field-name-field-review-publisher field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Publisher: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/publisher/cool-t-consultancy-econometrics" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">cool, t. (consultancy & econometrics)</a></li></ul></span><div class="field field-name-field-review-pub field-type-number-integer field-label-inline clearfix"><div class="field-label">Published: </div><div class="field-items"><div class="field-item even">2011</div></div></div><div class="field field-name-field-review-isbn field-type-text field-label-inline clearfix"><div class="field-label">ISBN: </div><div class="field-items"><div class="field-item even">978-90-804774-7-6</div></div></div><span class="vocabulary field field-name-field-review-msc field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc/03-mathematical-logic-and-foundations" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">03 Mathematical logic and foundations</a></li></ul></span>Tue, 24 Jan 2012 12:52:18 +0000Anonymous45436 at https://euro-math-soc.euhttps://euro-math-soc.eu/review/logic-exceptions#commentsConquest of the Plane
https://euro-math-soc.eu/review/conquest-plane
<div class="field field-name-field-review-review field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"><p>This book is a primer on Calculus and Analytic Geometry and not a text book, but it has a textbook format. It has different functions for different readers: students, teachers and professionals that apply mathematics. The first four parts have been written with the students in mind, while the fifth part explains the didactics to both teachers and students in didactics of mathematics.</p>
<p>It is claimed that the book can be studied with and without "The Economics Pack, Applications of Mathematica", but it is worthwhile mentioning that the book does not include exercises, this program provides the exercises required by the reader to confirm he has understood the matter correctly.</p>
<p>The contents of the book are the following:</p>
<p>(1) Arithmetic, Algebra and Geometry with coordinates: lines, circles and vectors.<br />
(2) Trigonometry, the Complex plane and Linear Algebra.<br />
(3) Calculus, developped fully from algebra.<br />
(4) Applications from physics, economics and statistics.<br />
(6) An extensive discussion of the didactics.</p>
<p>The reading must be aware that this book can produce disquieting feelings. Indeed, I felt myself uncomfortable, since I was reading very elementary mathematics I knew well, but the unusual notations and presentation created a barrier to my understanding. Moreover, according to the author style, he introduces surprisingly rather deep digressions explaining why he has chosen a concrete approach to introduce some notion. The reader must be very attentive at this point, since this kind of comments constitutes one of the most valuable characteristics of this book.</p>
<p>Once the reader becomes familiar with the notations and the author style, he/she will enjoy the book. I am convinced that this work will help the students to recognize what they should know but they ignore, and so it could be intended as a refresher course. It also helps those parents who try to help their kids with math and, mainly, the book provides new insights for the teacher both in didactics and mathematics itself.</p>
<p>Some words are needed to warn researchers in Physics, Economics or Biology that the mathematical background needed by theme exceeds enormously the contents of this book.</p>
</div></div></div></div><div class="field field-name-field-review-reviewer field-type-text field-label-inline clearfix"><div class="field-label">Reviewer: </div><div class="field-items"><div class="field-item even">Jose Manuel Gamboa</div></div></div><div class="field field-name-field-review-legacy-affiliation field-type-text field-label-inline clearfix"><div class="field-label">Affiliation: </div><div class="field-items"><div class="field-item even">UCM</div></div></div><div class="field field-name-field-review-desc field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"><p>This book is a primer on Calculus and Analytic Geometry and not a text book, but it has a textbook format. It has different functions for different readers: students, teachers and professionals that apply mathematics. The first four parts have been written with the students in mind, while the fifth part explains the didactics to both teachers and students in didactics of mathematics.</p>
<p>Contents:<br />
(1) Arithmetic, Algebra and Geometry with coordinates: lines, circles and vectors.<br />
(2) Trigonometry, the Complex plane and Linear Algebra.<br />
(3) Calculus, developped fully from algebra.<br />
(4) Applications from physics, economics and statistics.<br />
(6) An extensive discussion of the didactics.</p>
</div></div></div></div><span class="vocabulary field field-name-field-review-author field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Author: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/author/thomas-colignatus" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">thomas colignatus</a></li></ul></span><span class="vocabulary field field-name-field-review-publisher field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Publisher: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/publisher/cool-t-consultancy-econometrics" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">cool, t. (consultancy & econometrics)</a></li></ul></span><div class="field field-name-field-review-pub field-type-number-integer field-label-inline clearfix"><div class="field-label">Published: </div><div class="field-items"><div class="field-item even">2011</div></div></div><div class="field field-name-field-review-isbn field-type-text field-label-inline clearfix"><div class="field-label">ISBN: </div><div class="field-items"><div class="field-item even">978-90-804774-6-9</div></div></div><span class="vocabulary field field-name-field-review-msc field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc/97-mathematics-education" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">97 Mathematics education</a></li></ul></span><span class="vocabulary field field-name-field-review-msc-full field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc-full/97b50" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">97b50</a></li></ul></span>Fri, 14 Oct 2011 19:05:24 +0000Anonymous45425 at https://euro-math-soc.euhttps://euro-math-soc.eu/review/conquest-plane#comments