Logic: A God-Centered Approach to the Foundation of Western Thought

by Vern S. Poythress

Overview

For the well-rounded Christian looking to improve their critical thinking skills, here is an accessible introduction to the study of logic (parts 1 & 2) as well as an in-depth treatment of the discipline (parts 3 & 4) from a professor with 6 academic degrees and over 30 years experience teaching. Questions for further reflection are included at the end of each chapter as well as helpful diagrams and charts that are appropriate for use in high school, home school, college, and graduate-level classrooms. Overall, Vern Poythress has undertaken a radical recasting of the study of logic in this revolutionary work from a Christian worldview.

Product Details

ISBN-13:	9781433532320
Publisher:	Crossway
Publication date:	02/28/2013
Sold by:	Barnes & Noble
Format:	eBook
Pages:	736
File size:	5 MB

About the Author

Vern S. Poythress (PhD, Harvard University; ThD, University of Stellenbosch) is Distinguished Professor of New Testament, Biblical Interpretation, and Systematic Theology at Westminster Theological Seminary in Philadelphia, Pennsylvania, where he has taught for four decades. In addition to earning six academic degrees, he is the author of numerous books and articles on biblical interpretation, language, and science.

Vern S. Poythress (PhD, Harvard University; ThD, University of Stellenbosch) is Distinguished Professor of New Testament, Biblical Interpretation, and Systematic Theology at Westminster Theological Seminary in Philadelphia, Pennsylvania, where he has taught for four decades. In addition to earning six academic degrees, he is the author of numerous books and articles on biblical interpretation, language, and science.

Read an Excerpt

CHAPTER 1

Logic in Tension

In the original Star Trek TV series, the characters Spock and Leonard McCoy are opposites. Spock is logical; McCoy is passionate. Spock is cold; McCoy is hot. The contrast raises lots of questions. How does logic fit in with our humanity? Is logic opposite to emotion? What should we be like as human beings — logical or emotional or both?

Logic and Humanity

The Star Trek series gained popularity not only because it had entertaining plots but also because it laid out in narrative form some of the big questions about man and his relation to the cosmos. Who are we? What is the meaning of life? What is the cosmic purpose of humanity? Why do logic and emotion struggle within us?

Viewers' reactions to Spock reveal different attitudes toward logic. To some people, Spock's logic is an ideal. To others, he may be either admirable or pitiable, but he lacks something. The creators of the show make their own comment by revealing that, while McCoy is human, Spock is the offspring from a Vulcan father and a human mother. He is only half human. A deeper look at Spock reveals further complexity: though Spock endeavors to follow logic, he sometimes struggles with inner emotions because of his human side. Does this fictional portrayal hint that logic is not enough?

What about us? How do we relate to logic? Does it appeal to us? Or do we feel that by itself it is too "cold"?

Some people are more logical, some more emotional. Some people think that we have problems because we are not logical enough. Others think that we are much too logical. In their view, devotion to logic creates difficulties, and we ought to move beyond logic to something else — to nature or mysticism or art. Science, in the minds of some, is driven by logic and by a tightly defined, cold rationality. Human beings in their full personality are driven by warmth: they have desires and emotions and imagination, which are aptly expressed in the arts, in leisure, in entertainment, and in the humanities. Science, according to this view, is at odds with the humanities and with what is most precious to us.

So what is logic? Is it important? How do we understand its relation to emotion, intuition, and other aspects of human life? How do we use it? Does it have limits?

Christian Logic?

I believe that common conceptions about logic do not provide healthy answers to these questions. We need a new approach to the subject — we need a distinctively Christian approach.

Is there such a thing as a Christian view of logic? We would not be surprised to find a distinctively Christian approach to theology or ethics, because the Bible has much to say about God and ethics. But could there be a distinctively Christian approach to logic? Many people would say no. They would say that logic is what it is, irrespective of religious belief. I think that the reality is more complicated. There is a Christian view of logic. But it will take some time to see why.1 Readers may, if they wish, treat this book as a general introduction to logic. Our discussion does not assume any previous acquaintance with the subject. We try to make the ideas accessible by including simple explanations with each new concept. But the discussion also has pertinence for experts, because we do not take a conventional approach. We develop a distinctively Christian approach. Human thinking about logic needs redeeming. As a result, it will take us some time to come to the point of discussing details that typically become the focus of logic textbooks.

For Further Reflection

1. What makes the difference between Spock and McCoy so fascinating?

2. What different reactions are there to Spock as a character, and what do they say about people's views about logic?

3. When people think about an ideal for humanity, what role do they assign to logic?

4. How might human beings deal with the apparent tension between logic and emotion? What implications are there for the nature of our humanity?

5. Why might some people think that a distinctively Christian approach to logic makes no sense?

CHAPTER 2

Why Study Logic?

Why should we bother to study logic? Spock exemplifies one part of its importance. On the one hand, Spock's rational analysis gives the Star Trek crew valuable advice. On the other hand, we struggle with an apparent conflict between logic and emotion, or even between logic and humanness. We need a remedy.

We can find other reasons for studying logic. Some people find logic intrinsically interesting. For them, it is fun. Others study it for practical purposes. They hope that studying logic can help them sharpen their ability to reason carefully. Practice in logic can help us detect logical errors in reasoning, which have been called logical fallacies.

The Influence of Logic

Logic is important for another, historical reason. Logic has had a profound influence on the whole history of Western thought. In the Western world, the formal study of logic began largely with the Greek philosopher Aristotle — though Aristotle built to some extent on his philosophical predecessors, Socrates and Plato.1 Plato and Aristotle hoped to find deep truths about the nature of the world by careful reasoning. Aristotle's study of logic tried to codify the most basic forms of reasoning. This codification could then serve as a solid foundation for philosophical investigations trying to answer the big questions about the nature of reality and the meaning of life.

Western philosophy ever since Aristotle's time has followed in the steps of Plato and Aristotle. Philosophers have reasoned. They have used logic. Up until the nineteenth century, with few exceptions, they built on the foundation of Aristotle's logic. The nineteenth and twentieth centuries have seen further, more technical developments in logic, which have gone well beyond what Aristotle achieved. But for the most part these developments have enhanced rather than overthrown the classical logic developed by Aristotle. (For more detailed discussion of logic and philosophy, see part IV.F, especially appendix F2. For some alternatives to classical logic, see chapters 63 and 64.)

Logic and philosophy have had a broad influence on intellectual culture in the West. Philosophy has directly influenced intellectual life, because it has seemed to many people to offer the most profound and far-reaching kind of knowledge. Science has taken a leading role in more recent times, but for centuries reasoning in intellectual centers was influenced and guided by ideas from philosophy.

In addition, logic has had indirect influence. People engage in reasoning in every area of serious study, not just in philosophy. In almost every sphere, universities today rely on reasoning — in natural sciences, medicine, historical studies, law, economics, political science, language study, literary analysis, mathematics. Academic work aspires to conduct its reasoning rigorously. And logic is a model for rigor. Reasoning in universities today still has underneath it the foundation for logic that Aristotle laid.

Though Aristotle's logic functions as a foundation for Western thought, we should not exaggerate its role. In both the past and the present, much influential reasoning takes the form of informal reasoning and does not explicitly invoke Aristotelian logic or any kind of formally organized logic. Appropriately, logicians themselves distinguish between the formal logic that Aristotle developed and the informal logic involved in more ordinary instances of reasoning. Yet rigorous formal logic offers an ideal that can still influence what people expect and how people evaluate informal reasoning. Logic has an influence far wider than its core.

Logic has also influenced perceptions about the contrast between rationality on the one hand and emotion, desire, and imagination on the other. The historical movement called the Enlightenment championed reason. But soon people became restless. They sensed that reason was not enough. Reason gave us only half of humanity — or less. The Enlightenment stimulated a reaction, the Romantic movement, which depreciated reason and championed the imaginative, the spontaneous, the natural, and the pre-rational aspects of humanity. Like the opposition between sciences and humanities, the opposition between the Enlightenment and the Romantic movement expresses the contrast between logic and emotion, or between Spock and McCoy. Thus, the contrast between Spock and McCoy has analogues that play out in culture and history.

At the foundation of this cultural opposition lies logic. It feeds into the Enlightenment's conception of reason, and it shapes the Romantic opposition to the Enlightenment as well, because the opposition defines itself in reaction to reason.

This foundation for Western thought in logic needs to be redone. And that means that the whole of Western thought has to be redone. It is a most serious issue.

Arguments

What do we mean by logic? One textbook on logic defines it as "the analysis and appraisal of arguments." When we hear the word argument, we may picture a situation where two people are having a dispute with each other — perhaps a bitter, heated dispute. They are fighting verbally, each person vigorously defending his own view. But the word argument can be used not only to describe quarrels but to describe any reasoning in support of a conclusion.

Arguments of this kind may crop up in friendly settings. An advertisement for a car may present arguments to persuade you to buy one. The advertisement tells you that its car gives you good gas mileage. It is durable. It has special computerized features to play your favorite songs. It has a luxurious interior. It looks cool. And so on. These are informal arguments in favor of buying the car.

We meet arguments not only when someone else is trying to lay out the desirable features of a product, but when we are quietly trying to decide something for ourselves. For example, Irene may be "arguing with herself" about which college to attend. College A is closer to home. College B has lower tuition. College A is reputed to have a better program in economics. College B has a beautiful rural campus. College A is right in the middle of exciting city life. College B has a larger student body. Irene formulates arguments in her own mind in favor of each of the options. Arguments are useful not only for small purchases, but also for major decisions like choosing a college or deciding what kind of job to pursue.

We also meet arguments in academic settings. A university class may lay out reasoning to reach conclusions in chemistry or in the history of World War I. When a class considers disputed ideas, the class members may study arguments both for and against the ideas. Underneath the particular arguments lies a foundation in logic, which analyzes general principles of argument.

Arguments can help to lead us to a wise conclusion. But they can also lead us astray. For example, a student says, "Either you get an A in the course or you show that you are an idiot." But might there be a third alternative? The presentation of two extreme alternatives as if they were the only alternatives is called the fallacy of bifurcation. There are other forms of fallacy as well. A fallacy is a kind of argument that may sound plausible but that uses tricks rather than solid reasoning. Logic includes the study of various kinds of fallacies. People hope that by studying fallacies they may more easily detect them in the future.

Arguments in the Bible

Arguments occur in the Bible. We should not be surprised, because the Bible describes human life in all its ups and downs. For example, a major argument takes place in 2 Samuel 17:1–14. Absalom, the son of David, has just mounted a rebellion against the kingship of his father David. He has forced David out of Jerusalem, the capital city. But as long as David is alive, Absalom's own position in power remains in jeopardy. Absalom asks for advice from Ahithophel, who has a reputation for giving shrewd counsel (2 Sam. 16:23). Absalom also consults Hushai, who gives opposite advice. Ahithophel says Absalom should attack David right away with a small force of select troops (17:1). Hushai advises Absalom to wait in order to assemble a large army. Both Ahithophel and Hushai give supporting reasons in favor of their stratagems.

Absalom and his supporters think that Hushai's advice is better. Hushai's arguments are convincing; but they lead to disaster. Absalom is killed in the battle that eventually takes place (2 Sam. 18:15). Clearly an argument can be a major turning point in a person's life, and even in the life of a whole kingdom — in this case, the kingdom of Israel.

The arguments from Ahithophel and Hushai are even more striking because the reader of 2 Samuel receives some information that Absalom and Ahithophel did not know. Hushai is pretending to serve Absalom, but secretly he is loyal to David. In fact, David has earlier told Hushai to go to Absalom and to try to interfere by dissuading Absalom from following Ahithophel's advice (2 Sam. 15:34). Hushai appears to Absalom to give his advice sincerely, and the arguments that he offers are plausible and attractive. But the reader can infer that Hushai does not believe in these arguments himself. He is acting out a role. Hushai's arguments therefore have two layers: what he intends Absalom to understand and what he himself understands and intends. In fact, the arguments have a third layer, because God the Lord is active behind the scenes: "For the LORD had ordained to defeat the good counsel of Ahithophel, so that the LORD might bring harm upon Absalom" (17:14).

Arguments can be used to deceive and manipulate. But they can also become part of wise counsel. At one point David has decided to order his men to attack Nabal and kill him. Abigail, Nabal's wife, comes out and dissuades him with her arguments (1 Sam. 25:23–31). David is persuaded, and blesses Abigail for having kept him back from sin (v. 33). The story has a further happy ending because after Nabal dies — by God's act rather than David's — David and Abigail marry (v. 42). Abigail's arguments have steered David toward righteous action and away from sin.

We meet still further arguments within the Bible, including arguments that address all-important religious decisions. The serpent in Genesis 3 gives arguments to try to induce Adam and Eve to sin. Elijah in 1 Kings 18 gives arguments (and a demonstration) to try to turn the people of Israel away from worshiping Baal and toward worshiping the Lord, the true God of Israel. Since Elijah presents himself as a prophet of God, his arguments claim to be not merely human but also divine. Elijah claims that God is presenting the arguments to Israel through him.

The New Testament indicates that God continues to speak, and it includes arguments to call people to come to Christ for salvation. The apostle Peter presents arguments in his sermon in Acts 2:14–36. Since Peter is an apostle, commissioned by Christ, these arguments also present themselves as divine arguments. The apostle Paul presents arguments in his sermons here and there in Acts. Acts 13:16–41; 14:15–17; and 17:22–31 give examples. In addition, some of the summaries of Paul's preaching mention argument and reasoning:

And Paul went in, as was his custom, and on three Sabbath days he reasoned with them from the Scriptures, explaining and proving that it was necessary for the Christ to suffer and to rise from the dead, and saying, "This Jesus, whom I proclaim to you, is the Christ." (Acts 17:3)

So he [Paul] reasoned in the synagogue with the Jews and the devout persons, and in the marketplace every day with those who happened to be there. (Acts 17:17)

And he [Paul] reasoned in the synagogue every Sabbath, and tried to persuade Jews and Greeks. (Acts 18:4)

And he [Paul] entered the synagogue and for three months spoke boldly, reasoning and persuading them about the kingdom of God. (Acts 19:8)

We also hear of arguments within the church when controversies arose:

And after Paul and Barnabas had no small dissension and debate with them, Paul and Barnabas and some of the others were appointed to go up to Jerusalem to the apostles and the elders about this question. (Acts 15:2)

The apostles and the elders were gathered together to consider this matter. And after there had been much debate, Peter stood up ... (Acts 15:6–7)

In 1 Corinthians 15 Paul presents an extended argument to try to correct wavering in the Corinthian church over the question of whether there will be a future resurrection of the body.

The Bible contains many other types of communication in addition to arguments. It has songs, historical reports, prophecies, and so on. But we can use the idea of argument and persuasion as a perspective on everything the Bible does. In a looser sense, we can say that the whole of the Bible functions as an argument to induce us to change ourselves, our beliefs, and our behavior.

(Continues…)

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Excerpted from "Logic"
by .
Copyright © 2013 Vern Sheridan Poythress.
Excerpted by permission of Good News Publishers.
All rights reserved. No part of this excerpt may be reproduced or reprinted without permission in writing from the publisher.
Excerpts are provided by Dial-A-Book Inc. solely for the personal use of visitors to this web site.

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Table of Contents

Tables and Illustrations,
Symbols Used in Parts II–IV,
Preface,
Part I: Elementary Logic,
Part I.A: Introducing Logic and Argument,
1 Logic in Tension,
2 Why Study Logic?,
3 What Do We Trust?,
4 Formal Logic,
5 Inductive Logic,
6 The Importance of Formal Logic,
Part I.B: God in Logic,
7 Logic Revealing God,
8 Logic as Personal,
9 Logic within Language,
10 Suppressing the Truth,
11 Logic and the Trinity,
12 The Absoluteness of God,
13 Logic and Necessity,
14 Transcendence and Immanence,
15 Reflections on the Mediation of Human Knowledge of Logic,
16 Fallacies and God,
Part I.C: The Problem of Classification,
17 Analogy,
18 Unity and Diversity,
19 Stability of Meaning,
20 Form and Meaning,
21 Context for Meaning,
22 Persons and Logic,
23 Logic and Religious Antithesis,
24 Theistic Proofs,
25 Rethinking Western Thought,
Part I.D: Aristotelian Syllogisms,
26 Theistic Foundations for a Syllogism,
27 Venn Diagrams,
28 Syllogisms of the First Figure,
29 Checking Validity by Venn Diagrams,
Part II: Aspects of Propositional Logic,
Part II. A: Truth in Logic,
30 Truth in Logic: Truth Functions,
31 Divine Origin of Logical Functions,
32 Complex Expressions,
Part II. B: Perspectives on Truth in Logic,
33 Venn Diagrams for Truth Functions,
34 Other Representations of Logical Truth and Falsehood,
35 Boolean Algebra,
36 Truth-functional Equivalence,
37 Harmony in Truth,
38 Perspectives on Truth Functions,
Part II. C: Propositional Logic,
39 Introducing Propositional Logic,
40 Axioms of Propositional Logic,
41 Alternative Axioms,
42 Dispensing with Axioms,
43 Perspectives on Propositional Logic,
44 Soundness and Completeness of Propositional Logic,
45 Imitations of Transcendence,
Part III: Enriching Logic,
Part III. A: Predicate Logic,
46 Introducing Predicate Logic,
47 Theistic Foundations for Predicates,
Part III. B: Quantification,
48 Quantification,
49 The Theistic Foundation for Quantification,
50 Axioms and Deductions for Quantification,
51 Soundness of Quantification,
Part III. C: Including Equality and Functions,
52 Equality,
53 Functions,
Part III. D: Introducing Formal Systems,
54 Troubles in Mathematics,
55 Axiomatizing Mathematics,
56 Studying Proofs,
57 Theistic Foundations for Proof Theory,
58 A Computational Perspective,
59 Theistic Foundations of Computation,
60 Models,
61 Theistic Foundations for Models,
Part III. E: Special Logics and More Enriched Logics,
62 Higher-order Quantification,
63 Multivalued Logic,
64 Intuitionistic Logic,
65 Modal Logic,
66 Theistic Foundations for Modal Logic,
67 Models for Modal Logic,
68 Conclusion,
Part IV: Supplements,
Part IV. A: Supplements to Elementary Logic,
A1 Antinomies with Sets: The Set of All Sets and Russell's Paradox,
A2 Deriving Syllogisms of the First Figure,
A3 Syllogisms of the Second Figure,
A4 Syllogisms of the Third and Fourth Figures,
Part IV.B: Supplementary Proofs for Propositional Logic,
B1 Some Proofs for Boolean Algebra,
B2 Deriving Whitehead and Russell's Axioms,
B3 Practice in Proofs,
B4 The Rule of Replacement,
B5 Reasoning toward the Completeness of Propositional Logic,
Part IV.C: Proofs for Quantification,
C1 Deductions of Rules for Quantification,
C2 Natural Deduction of Syllogisms,
Part IV. D: Proofs for Formal Systems,
D1 Introducing GÃdel's First Incompleteness Theorem,
D2 Simple Proofs within a Formal System,
D3 Deriving Natural Deduction and the Associative Axiom,
D4 Helping Lemmas,
Part IV. E: Other Proofs,
E1 The Halting Problem for Computer Programs,
E2 Diagonalization,
Part IV. F: Philosophy and Logic,
F1 Kantian Subjectivism,
F2 The Role of Logic in Philosophy,
F3 A View of Modern Logic,
F4 Modal Ontological Argument,
F5 Reforming Ontology and Logic,
Bibliography,