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forall x: An Introduction to Formal Logic

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Description: forall x is an open access introductory textbook in formal logic. It covers translation, proofs, and formal semantics for sentential and predicate logic. forall x was written by P.D. Magnus, an associate professor at the University at Albany, State University of New York. Magnus received his PhD from UC San Diego.

Author: P.D. Magnus

Original source: www.fecundity.com

Adoption (faculty): Contact us if you are using this textbook in your course

Adaptations: Support for adapting an open textbook

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Creative Commons License
forall x: An Introduction to Formal Logic by P.D. Magnus is licensed under a Creative Commons Attribution 4.0 International License, except where otherwise noted.


Review this book

Reviews for 'forall x: An Introduction to Formal Logic'

Number of reviews: 2
Average Rating: 4.15 out of 5

1. Reviewed by: Dr. Milan Frankl
  • Institution: University Canada West
  • Title/Position: Professor
  • Overall Rating: 3.7 out of 5
  • Date:
  • License: Creative Commons License

Q: The text covers all areas and ideas of the subject appropriately and provides an effective index and/or glossary

The textbook covers most of the material one would need to absorb in an introductory logic course.

Some topics, like the Fitch proof system, are missing [not necessarily demeaning the textbook content – but very popular in the Logic community].

The textbook would benefit from online software tools like Logicalc [a JavaScript library that brings logical spreadsheet functionality to tables on HTML pages], which could apply to both face-to-face and online delivery methods.

See: http://logic.stanford.edu/logicalc/pages/tables.html

Comprehensiveness Rating: 4 out of 5

Q: Content is accurate, error-free and unbiased

Most of the definitions are appropriate.
Formality is acceptable at this introductory level.
Practice exercises are adequate.

I would suggest more solutions and more details in the solutions – instead of simply stating the answer. From time to time (maybe for every third exercise) provide a detailed solution process.

I haven’t found errors.

Content Accuracy Rating: 4 out of 5

Q: Content is up-to-date, but not in a way that will quickly make the text obsolete within a short period of time. The text is written and/or arranged in such a way that necessary updates will be relatively easy and straightforward to implement

No problem with longevity here. All the information has been (and will remain) relevant for quite some time.

Relevance Rating: 4 out of 5

Q: The text is written in lucid, accessible prose, and provides adequate context for any jargon/technical terminology used

The writing style is simple and accessible. Passive voice is prevalent unfortunately.

Use of technical jargon is a requirement – however, it is not overwhelming for this reader.

Note: I have extensive experience having written books on propositional calculus myself.

Clarity Rating: 4 out of 5

Q: The text is internally consistent in terms of terminology and framework

Indeed, the text’s consistency is acceptable. It may lack the rigour expected for a purely mathematical logic audience. In this context, terminology usage is adequate.

For example, I would have preferred the use of truth symbols in chapter 3 (on truth tables) rather than the letters T & F. Symbols offer a higher level of abstraction.

This is introduced in chapter 5 on formal semantics.

Consistency Rating: 4 out of 5

Q: The text is easily and readily divisible into smaller reading sections that can be assigned at different points within the course (i.e., enormous blocks of text without subheadings should be avoided). The text should not be overly self-referential, and should be easily reorganized and realigned with various subunits of a course without presenting much disruption to the reader.

The text contains a reasonable number of exercises.

Very few exercises are solved in a detailed and stepped way – easy to follow. This is one weakness of this textbook.

Lack of formal rigour is present in most cases, stemming from limited detail in most solution processes.

Pertinent references are included in the appendices.

Modularity Rating: 3 out of 5

Q: The topics in the text are presented in a logical, clear fashion

The theory is presented in short segments without referring the reader to outside sources.

Organization Rating: 4 out of 5

Q: The text is free of significant interface issues, including navigation problems, distortion of images/charts, and any other display features that may distract or confuse the reader

The relation between the table of content and the text is consistent allowing for easy navigation between the topics.

This includes direct access to relevant content for those who would like to jump to specific topics.

Interface Rating: 4 out of 5

Q: The text contains no grammatical errors

The text contains no obvious grammar or style errors.
Punctuations are correct and consistent.
Passive voice is prevalent, unfortunately.

Grammar Rating: 3 out of 5

Q: The text is not culturally insensitive or offensive in any way. It should make use of examples that are inclusive of a variety of races, ethnicities, and backgrounds

Cultural relevance might not apply here – unless the audience is not English speaking.

Ideally, a textbook on formal logic should be “culturally irrelevant” – i.e. language independent.

References to U.S. locations (Mount Rainier) or British TV shows (Monty Python), might not mean very much for a foreign online student.

Cultural Relevance Rating: 3 out of 5

Q: Are there any other comments you would like to make about this book, for example, its appropriateness in a Canadian context or specific updates you think need to be made?

It might be advisable to include some Canadian content when using examples (why not BC instead of Washington?) and to use a more “British” style rather than a U.S. one.

However, in my experience, Canadian students are used to U.S. writing styles (sic).

My concern is more for foreign student (India, China) who might be interested in taking online courses from B.C. institutions. In this case, a more Canadian content might be appropriate.

I would still recommend this textbook for an introductory course on logic for an advanced high-school class, college or first-year university level.

2. Reviewed by: Leslie Burkholder
  • Institution: University of British Columbia
  • Title/Position: Senior lecturer
  • Overall Rating: 4.6 out of 5
  • Date:
  • License: Creative Commons License

Q: The text covers all areas and ideas of the subject appropriately and provides an effective index and/or glossary

Pretty much.
There isn't a standard set of topics for an introductory symbolic logic course -- for example, one specified by a professional organization. But there is a fairly common set of topics. It includes
(1) Presenting the grammar (syntax) of a (first order) artificial symbolic logic language and the meanings of the symbols in the language. Sometimes this is just done informally and sometimes very formally or both.
(2) Techniques for translating from a natural language like English into formulas in the artificial symbolic logic language
(3) Discussion of various logical concepts or properties -- for example: validity, consistency, independence, logical truth and falsehood and contingency.
(4) Presentation of a semantic method for determining the presence or absence of these logical properties for sets of formulas in the artificial symbolic logic language and so the original natural language they might have been translated from. Examples are truth-tables, semantic tableau.
(5) Presentation of a proof method for determining the presence or absence of these logical properties for sets of formulas in the artificial symbolic logic language and so the original natural language they might have been translated from.

Comprehensiveness Rating: 4 out of 5

Q: Content is accurate, error-free and unbiased

Yes for sure.
This text covers all of these topics with one exception. The presentation of the semantic method considers only certain parts of the artificial symbolic logic language and not all of its parts or symbols. It leaves out quantified formulas.
One minor quibble from the beginning. The textbook says that the topic of symbolic logic is the concept or property of validity. But that isn't quite right or perhaps not the best way of saying things. There are many other topics or concepts symbolic logic concerns. See (3) on the previous page.

Content Accuracy Rating: 4 out of 5

Q: Content is up-to-date, but not in a way that will quickly make the text obsolete within a short period of time. The text is written and/or arranged in such a way that necessary updates will be relatively easy and straightforward to implement

Yes, I think this is true.

Relevance Rating: 5 out of 5

Q: The text is written in lucid, accessible prose, and provides adequate context for any jargon/technical terminology used

Yes this is true.
The Open Textbooks project might like to consider translating the textbook into other languages than English. Many students at BC colleges and universities do not have English as a first language. This might help promote the adoption of the texts across BC colleges and universities.
Of course this applies not just to this text but every other one that BC Open Textbooks is reviewing.

Clarity Rating: 5 out of 5

Q: The text is internally consistent in terms of terminology and framework

Yup

Consistency Rating: 5 out of 5

Q: The text is easily and readily divisible into smaller reading sections that can be assigned at different points within the course (i.e., enormous blocks of text without subheadings should be avoided). The text should not be overly self-referential, and should be easily reorganized and realigned with various subunits of a course without presenting much disruption to the reader.

The particular chapters could be ordered differently without disruption. But it would be hard to break up and reorder parts of the chapters.

Modularity Rating: 4 out of 5

Q: The topics in the text are presented in a logical, clear fashion

Yes.
The text does the topics listed on the first page of the review in a bit of a different order than many other textbooks. The common way in commercially available textbooks is to deal with all of (1)-(5) for a part of the symbolic language (the truth-functional part) and then come back and deal with all of (1)-(5) for the other part of the symbolic language (the quantificational part). The text goes through all of (1)-(5) for both parts or aspects together.
Which order is best is a question of what results in better learning. There is some evidence that mixing things up -- ie the standard way of doing things -- is better. But the evidence is from a quite different topic area, learning to identify painters.

Organization Rating: 5 out of 5

Q: The text is free of significant interface issues, including navigation problems, distortion of images/charts, and any other display features that may distract or confuse the reader

For sure yes

Interface Rating: 5 out of 5

Q: The text contains no grammatical errors

Not that I spotted

Grammar Rating: 5 out of 5

Q: The text is not culturally insensitive or offensive in any way. It should make use of examples that are inclusive of a variety of races, ethnicities, and backgrounds

Not offensive in any way. Examples and exercises are American.

Cultural Relevance Rating: 4 out of 5

Q: Are there any other comments you would like to make about this book, for example, its appropriateness in a Canadian context or specific updates you think need to be made?

Exercises and examples are American. Non-American although not necessarily Canadian ones would be good.
The Open Textbooks project might like to consider translating the textbook into other languages than English. Many students at BC colleges and universities do not have English as a first language. This might help promote the adoption of the texts across BC colleges and universities.
Of course this applies not just to this text but every other one that BC Open Textbooks is reviewing.