Logic Done Well: Introduction

In his fascinating book, The Screwtape Letters, C.S. Lewis imagines a series of letters written by one demon, Screwtape, to his demon nephew, Wormwood. As you can expect, the content of these fictional letters reflected the demonic characteristics of the fictional author, as the author described God as "the Enemy," not even invoking His holy name. In the preface to that book, Lewis notes that he had originally intended to write a book from the perspective of angels, but he felt he would be unable to convincingly convey the absolute purity and holiness of heaven, that place where God and all that is good resides. For Lewis, the demonic was more relatable, closer to home.

Lewis's difficulty with conveying the eternally Good reflects a broader difficulty in human experience and discourse; it is far easier to say what something isn't, rather than what something is. What is a chair? Does a chair, by nature, have four legs? Do all chairs have backs or wheels? We can't easily describe what a chair is by nature, but we can confidently say what it isn't. It isn't a table (though a chair can be used as if it were a table). It isn't a computer. Humans have often found that they can circumscribe a being's nature by contrasting it with unlike things. God is not finite (i.e., God is infinite). God is not a liar. God is not physical. In theology, this way of circumscribing God's nature through negative claims is called "apophatic" theology.

In a way, we've done this with the series, "Logic Gone Wrong." We've circumscribed the right use of logic by contrasting it from examples of using it wrongly. We've circumscribed some intellectual virtues by contrasting them from intellectual vices. As you might expect, then, it's more difficult to describe right uses of logic than wrong uses of logic. Examples are not as numerous as they are with fallacies. Indeed, this is to be expected. As I've been writing about fallacies, real-world examples are all too easy to find. Often, the question of applicability is more difficult to answer in using logic well. When you learn the precise difference between modus ponens and modus tollens, it is fair to ask how you'll ever use any of this. And indeed, for each of these widely accepted forms of right argumentation, you will find some contrarian logician (an already contrarian bunch) who will deny its universal validity.

So, it's more difficult to positively ascribe than it is to negatively detract. This insight alone could be the topic of discussion for another post, but it is proper to begin with this idea as we consider the right use of logic, how to do it well. There is a deep irony about the difficulty of positive ascription: it is the goal not only of inquiry but of life itself! Ancient Greek philosophers noticed this 2,500 years ago. Plato described philosophical inquiry as the process that brings the inquirer closer to the heavenly realm of the Forms. Aristotle sees the whole of life as the process of living in such a way that one's character is conformed to the "good life," a life of flourishing.

Scripture teaches this as well, though its conception of attaining to the good, true, and beautiful is both divine and personal. We are to imitate Christ (Ephesians 5:1-2). Jesus commands us to be perfect as His Father is perfect (Matthew 5:48). The great irony of these commands is that we can hardly conceive of God, let alone be like Him! We desire with the whole of ourselves to attain to that which is good, true, and beautiful, but it is precisely when we desire this that we are confronted with our limitations as human beings. To positively ascribe is necessary for our flourishing, but it is also one of the hardest things for us to do.

How does this relate to logic? Logic, when applied to argumentation, concerns itself entirely with the structure or form of arguments. It cares only for whether the conclusion of an argument follows from its premises, not whether those premises are true. But logic is likewise indispensable from the search for truth. If we know that a claim is true, logic leads us from what we know to what we don't, as long as there is a valid connection between the claim we know and the claim we don't know. Logic is about finding those connections. When we find a valid connection, we stand to gain tremendously in gaining knowledge. But it is a difficult process, as any philosopher would tell you.

The narrow-mindedness of logic leads to some humorous examples of valid arguments. Consider, for instance, these two arguments:

1. Either Severus Snape is King of France, or Dumbledore is alive and well.

2. Severus Snape is not King of France.

3. Therefore, Dumbledore is alive and well.

To the great and continual disappointment of all Harry Potter fans, J.K. Rowling's characters don't exist. The argument is not likely to convince anyone of anything, but it is valid. The conclusion is guaranteed by the truth of the premises. Here is another example:

1. If the universe has a beginning, then the universe has a transcendent cause.

2. The universe has a beginning.

3. Therefore, the universe has a transcendent cause.

This is one of the most famous current arguments for God's existence. One of the strengths of this argument is that it proceeds from a premise on which the vast majority of people agree, that is, that the universe has a beginning at the Big Bang. To many, the beginning of the universe is so well-established scientifically that they would claim even to know that the universe began to exist. This argument supplies a further premise in the form of a conditional: if the universe began to exist, then the universe has a transcendent cause. The reason for believing this premise is another well-established metaphysical principle: everything that begins to exist must have a cause. Again, many people, once given that metaphysical principle, would say that they know it to be true. Thus, the power of this argument is that it proceeds from what people generally know to what they may not know or believe: that the universe has a transcendent cause. Some extra reflection will lead us to the realization that this transcendent cause is God (see the post on this argument if you're interested).

Thus, while valid argumentation can be used to make silly arguments, it can yield profound results. The benefit of validity is that it clarifies what needs to be shown for the conclusion to be proven. The argument for God's existence above is valid. This is certain. So, if the argument fails, it must fail because one or both of the premises is false. The atheist, then, in order to undermine this argument, must show that one or both of the premises is false.

Throughout this series, we will consider forms of valid argumentation. As we discuss these forms of valid argumentation, we will discover something strange and mysterious about valid arguments. They are such that we can affirm their validity without testing every argument of that form for its validity. They are such that their parts can be boiled down in order to isolate in a more pure way the form of the argument. Thus, we will learn that this valid argument form:

1. p -> q

2. p

3. q...

is much like an equation of the following form:

y = mx+b

With the valid argument form, as with the equation, the proper values can be substituted for the variables in order to yield a valid result. This is why we can make valid silly arguments like the one above.

As in mathematics, that we can do this with our discourse - make valid arguments by putting them in the correct forms - is a bit of a mystery. Why is discourse such that its structure can yield novel discoveries is a well-ordered and predictable way? As Christians, once we've come to understand the intricate and elegant structure of our discourse and its connections with language, we understand more of what it means when John refers to the Son of God as Logos, or reason, in the first chapter of his Gospel. God is a God of order and reason, and this explains why we discover order in our discourse. Thus, studying logic is a means of intellectual worship. It is also the reason why thinking well honors the Lord.

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