Preface

Nothing contributes more certainly to individual and collective human flourishing than reasoning well within the context of mutual, authentic love. This project focuses on the former, reasoning dimension. The latter and more important dimension is left to you.

For most of recorded history, scholarly formation—deliberate training in human intellectual excellence—was a rarity enjoyed by a privileged few. Such education emphasized reasoning (philosophy), reading, writing, speaking, history, mathematics, arts, cosmology and science, and similar humane fundamentals. Today, a formal education leading to basic, functional literacy is no longer rare, but the happy norm enjoyed by most. Some of the basic areas of study have developed dramatically, and new ones have been added, but some have also atrophied. A critical one that has almost entirely disappeared is direct training in reasoning.

Only about one in twenty contemporary students receive direct training in basic logic, critical thinking, or similar, and most of those courses teach a truncated, sterilized version of Aristotelian logic that has seen little or no substantive development since the late Middle Ages. A much smaller percentage of people, probably less than 1%, might be exposed to contemporary, symbolic logic in college—usually some version of Propositional, Predicate, Relational, or First Order logic. A microscopic percentage of students might go on to learn modal or alethic logic in graduate or postgraduate study. Most of these college-level courses present logic as something deeply abstract, mathematical, and generally impractical.

The lack of training to distinguish true claims from false, combined with the ability to produce audio, images, and videos that are practically indistinguishable from reality, leaves the average person and society as a whole in a new and profoundly vulnerable position. The same technology that has brought us unprecedented comforts, affluence, recreation, and luxuries is becoming an instrument of mass deception, manipulation, and control. The ability to discern truth despite what is right before our “lying eyes” might never have been more important than it is right now, nor less common.

This project aims to provide a practical introduction to the basic reasoning skills that used to be taught to and expected of every educated person. The goal is to help equip the learner with principles and practices that can help us more reliably discern truth. The system is called Philalethic Logic (pronounced “fil-uh-leh-thik”), and this volume presents it in a simplified, practical form. PL has some overlap with common logic systems, but there are four important distinctives:

1. Philalethic Logic is grounded in how human cognition actually functions and in the ideal intentions of our ideas and language.

2. Philalethic Logic has a simplified symbolic system and syntax (though it can be converted to First Order and other systems if needed).

3. Philalethic Logic implements compound operators like disjunction and implication in their full relational-humane sense (and modal consequences). This increases system complexity, but resolves the nagging problems and confusion in common truth-functional logic systems.

4. Philalethic Logic relies exclusively on truth-tree decomposition techniques for validation processes (though natural deduction would still work just fine).

Learning logic is not merely a matter of gaining information, but of learning, developing, and practicing a complex skill. To that end, the reader is encouraged to proceed at a moderate pace and to do the exercises throughout. It may be beneficial to go through the book with a friend or family member.

The text is constantly under review for improvement. Suggestions and corrections are invited and welcome.

A Note for the Teacher

Most students who can understand and apply algebra will be able to handle Philalethic Logic as presented in this volume, but it takes time to learn and be able to reliably apply the principles. The materials from this text and various supplements can be extended over a complete, 36-week academic year—ideal for many home schools and private academies (the later chapters are complex enough that it could even be stretched to two years, especially if the supplemental materials are used). It can also be condensed to 18, 12, or even 8-week terms as found in many colleges. See the Teacher & Parent Supplement for guides on how to distribute the chapters over different time-spans. The Supplement also contains detailed answer keys to the questions in this text.

A separate Student Workbook is also available, and a corresponding answer key for teachers and parents.

Though teachers and parents are welcome to independently use these resources to lead or supplement their own logic courses, we have both pre-recorded and live presentations available for all materials through our web site. The author, Seth Murray, is also available for private and small group tutoring. See https://www.philalethiclogic.com for more information.

Man judges rightly that by his intellect he surpasses the material universe, for he shares in the light of the divine mind. By relentlessly employing his talents through the ages he has indeed made progress in the practical sciences and in technology and the liberal arts. In our times he has won superlative victories, especially in his probing of the material world and in subjecting it to himself. Still he has always searched for more penetrating truths, and finds them. For his intelligence is not confined to observable data alone, but can with genuine certitude attain to reality itself as knowable, though in consequence of sin that certitude is partly obscured and weakened.

The intellectual nature of the human person is perfected by wisdom and needs to be, for wisdom gently attracts the mind of man to a quest and a love for what is true and good. Steeped in wisdom, man passes through visible realities to those which are unseen. Our era needs such wisdom more than bygone ages if the discoveries made by man are to be further humanized. For the future of the world stands in peril unless wiser men are forthcoming.

—Gaudium et Spes §15

The fear of the Lord is the beginning of wisdom.

—Proverbs 9:10 (Douay-Rheims)