*Editor’s Note: As Christians, we ought to strive to be the best thinkers we can be. Why? It’s because thinking reasonably is one of the hallmarks of humanity as God intended us to be. Thinking well helps us avoid painful mistakes and seek wise solutions. Thinking well helps us wisely engage people who are far from God. The study of logic is one way we can improve our ability to think well. I recently caught up with Christian apologist and philosopher Winfried Corduan, PhD, whose many books explore how we can use our intellect well for glorifying God and helping seekers find him. In this conversation, we talk about one of Corduan’s academic interests, logic, and how studying logic can help thoughtful Christians.
Q. So, will studying logic automatically make you a better thinker?
It can help, but I do not believe that this is necessarily the case. Taking a course in ethics will not make you a more moral person, studying medicine will not make you healthier, and the pursuit of logic does not automatically turn you into a critical thinker. There is always a gap between knowing a theory and its application in your life.
Q. But studying logic is important?
Absolutely. Logic works because God created an orderly universe to which we are privileged to apply logical truths. Logic is not something invented by human beings. We discover the logical principles in our thoughts and interactions and then formulate rules and symbols to represent them.
Just as a natural scientist examines the data he has accumulated and finds regularity, the logician examines the coherence and consistency of the concepts that govern our thinking, and both can be sure that they are not forcing something chaotic into order because the order is already there, courtesy of our Creator.
“The order is already there, courtesy of our Creator.”
Q. Let’s talk about “syllogisms.” First of all, what’s an example of a syllogism?
Aristotle, who lived in the fourth century B.C., is credited with the deductive syllogism, and here’s an example:
All members are politicians.
All senators are members.
Therefore, all senators are politicians.
This type of syllogism is called a “categorical syllogism,” because it’s an argument built on categorical statements. Basically, you are asserting or denying something about a particular category of people or things.
Q. What makes a good syllogism as opposed to a bad one?
A couple terms that are important here are “sound” and “valid.” First, an argument is considered “sound” if both conditions are met:
- All of the premises are true, and
- The conclusion follows from the premises. (Put another way, if it is impossible for the premises to be true and the conclusion to be false.)
The second condition (i.e., that the conclusion follows logically from the premises) is what makes an argument “valid.”
So, here’s a syllogism in which the premises are true (#1) but the conclusion does not follow logically from the premises (#2).
All birds lay eggs.
All duck-billed platypuses lay eggs.
Therefore, all duck-billed platypuses are birds.
Even with both premises being true, the conclusion doesn’t logically follow. So, it’s not a “valid” argument. (And therefore, even though the premises are true, it’s also not a “sound” argument, since to be a sound argument, the argument needs to be valid and the premises need to be true.)
Q. What are some of the main types of syllogisms?
As I mentioned, some syllogisms form an argument using categorical statements (such as, “all horses are quadrupeds”), and these are called “categorical syllogisms.” Both of the syllogisms we’ve looked at so far are categorical syllogisms (the members/politicians/senators example and the birds/eggs/platypuses example).
Another type of syllogism is the “hypothetical syllogism.” These are if-then arguments. For example,
If it is a unicorn, then it is a magical creature.
It is a unicorn.
Therefore, it is a magical creature.
There are also “disjunctions” or “disjunctive syllogisms.” These are built on either-or statements. For example,
At 9 o’clock in the morning Smith was either at home or on a bus.
Smith wasn’t on a bus.
Therefore Smith was at home.
Each of these syllogisms has its own rules as to what makes them valid arguments. For example, the way to get a valid conclusion for a hypothetical syllogism is either to affirm the first part (i.e., the if part) or deny/negate the second part (i.e., the then part). If you want to get a valid conclusion in a disjunctive syllogism, you first need to deny/negate one of the options.
“Each of these syllogisms has its own rules as to what makes them valid arguments.”
Q. So, studying logic gives us rules for making valid arguments, for making sure the argument has the correct form. But how does the study of logic help us know whether we’re making true arguments (not just formally correct ones)?
This is where it’s helpful to make a distinction between “formal logic” and “informal logic.” Whereas formal logic deals with the correct form of an argument (i.e., whether it’s valid or not), informal logic helps us analyze the content of the argument. Informal logic does not mean “chaotic thinking.” In fact, informal logic has its own rules and principles.
For example, one rule is that you need to consider the nature of definitions. Even without having had any formal preparation for this way of thinking, you likely already know that a good definition of a word or phrase must give the reader a fairly good idea of the object being defined without using the expression you’re trying to define. To use the word you’re defining in the definition would be circular reasoning.
“To use the word you’re defining in the definition would be circular reasoning.”
Here are some more principles from the study of informal logic:
- You must make sure that your conclusion is not already stated in your premises. The conclusion must be contained implicitly within all of the premises added together, but it may not be directly stated, or you will commit the fallacy of reasoning in a circle. The key to diagnose this fallacy is to check whether your conclusion would still stand if you were to remove some of the premises; if so, you may be arguing in a circle; if not, your argument may still not be valid but would probably not be circular.
- You must remember that, just because two events occur one after the other, that does not mean that the first one caused the second.
- You must adhere strictly to the subject that your argument addresses rather than wander off into something irrelevant, such as judging the person who is making or criticizing an argument (ad hominem).
- You may not resort to rhetoric that specifically focuses entirely on an emotional response, such as pity (ad misericordiam).
- And surely your argument would be worthless if it were supported by the threat that someone’s rejection of the alleged conclusion would lead to punishment (ad baculum).
These are just a few principles of “informal” logic, and it is extremely worthwhile to master the insights that we gain there. If it is possible to become a better thinker by studying logic, surely this is the field on which to concentrate, at least at first.
Q. Could you give us some examples of how studying logic can help us in the area of Christian apologetics?
Sure. There are some arguments, for example, for God’s existence, that are made clearer when put in syllogistic form. Many Christian philosophers have used the “kalam cosmological argument,” which takes the following form as a categorical syllogism:
Everything that begins to exist has a cause.
The universe began to exist.
Therefore, the universe has a cause.
There’s a famous argument given against the existence of God by the ancient philosopher Epicurus, and it can be helpful, in thinking through the argument, to look at it in syllogistic form. When made fleshed out into a hypothetical, if-then syllogism, Epicurus’ argument goes like this:
If God is all-powerful, he could get rid of all evil.
If God is all-good, he would want to get rid of all evil.
Evil exists.
Therefore, an all-powerful, all-good, all-powerful God doesn’t exist.
“There are some arguments, for example, for God’s existence, that are made clearer when put in syllogistic form.”
In this case, the form of the syllogism is valid, but we can certainly challenge the truthfulness of the premises. For example, many Christian philosophers have challenged the first premise in this way: Is it true that an all-powerful God has the ability to get rid of all evil? Yes, but what about if he has—at the same time—given humans free will? They reason that, if God has given humans free will to choose good or evil, then it’s literally an impossibility for him at the same time to get rid of all evil. It’s one or the other, for even an all-powerful God cannot give us free will while at the same time refusing to give us free will. In this way, the first premise fails, and thus the argument as a whole fails.
Q. Sometimes skeptics will point to inconsistencies in the Bible as reasons we shouldn’t trust it. How might a study of logic help us with this issue?
I mentioned the “disjunctive” syllogism. This is the either-or syllogism, and in order to draw a valid conclusion, you have to be able to show that one of the options is false. With a disjunctive syllogism, you can’t draw a conclusion by showing that one of the options is true—because it’s always possible that both options could be true. Again, in order to draw a valid conclusion, you have to show that one of the options is false.
This is an important principle because frequently Bible critics point out alleged inconsistencies in the Bible on the basis that if one statement is true, then the other one must be false. A more careful understanding would show that there really is no inconsistency, and that both statements are plausibly true. Just two cases in point from the Gospel of John:
Did Jesus clear the temple at the beginning of his ministry (as reported in the other three Gospels) or toward the end (as John has it)? Logically, there is certainly no inconsistency here. In fact, since the area the merchants were occupying was intended to be the only place in the temple compound where Gentiles could worship God, it is quite likely that Jesus would show his displeasure with them on several visits to Jerusalem.
“A more careful understanding would show that there really is no inconsistency, and that both statements are plausibly true.”
Did Jesus die before (Gospel of John) or on the day of Passover (the Synoptic Gospels)? Surely, he could not have done both. However, the disjunctive question assumes a stable universal date for the Passover throughout Judea and Galilee. But we know that there were several calendars being used at the time, similar to the way Eastern Orthodox Christians celebrate Christmas and Easter on different days than Western Christians. The Eastern church still uses the calendar as constructed under Julius Caesar, aptly named the “Julian Calendar,” while Western countries have adopted the “Gregorian Calendar,” due to Pope Gregory XIII, who made it mandatory for the church in the sixteenth century.
Similarly, we know that the Jewish group called the Essenes always celebrated the Passover on a Wednesday. Regardless of the length of the year, the day of the vernal equinox was considered the first day of the year, beginning with the month of Nisan—which differed from the year and date as calculated by the Pharisees and Sadducees. There may even have been other calendars used by different groups. The Samaritans, who were planted in Judea by the Babylonians, adopted the Jewish religion, though with some serious differences; to this day, they celebrate Passover later than the mainline date.
The point is that dogmatism concerning the date of Passover is not possible, and, depending on the reckoning, Jesus may have died after the Essene (or someone else’s) Passover and before the mainline Passover. If we use the word “Passover” without further qualification, the disjunction between “before” and “after” needs to be inclusive from our vantage point—making room that both could be true—insofar as Passover was not celebrated simultaneously by all people.
“Dogmatism concerning the date of Passover is not possible.”
Q. You’re currently writing a book on “symbolic logic.” Can you give us a brief explanation of symbolic logic?
Earlier, we talked about formal logic, which deals with the form of an argument (whether the form is valid or invalid). Throughout the centuries, logicians have developed a system of symbols to stand in for the sentences and phrases in logical syllogisms. When you’re using symbols, it begins to look a lot like mathematics, and indeed, there is a lot of similarity between symbolic logic and math. Both logic and math draw conclusions which follow necessarily, if you’re following the process correctly.
Symbolic logic often uses letters (A, B, C, etc.) to stand for entire sentences, and it uses symbols for logic words and phrases such as “if-then,” “either-or,” “and,” “not,” and “therefore.”
As you mentioned, I am writing a book on symbolic logic. Why is symbolic logic important to study? Why should somebody—maybe someone overhearing our conversation—study symbolic logic? Ultimately because it explores a part of God’s creation. It is shorthand for more cumbersome ways of expressing complex ideas. It clarifies relationships that may come up in other forms of logic if these other forms are too weak to handle certain complexities at all.
“Why should somebody—maybe someone overhearing our conversation—study symbolic logic? Ultimately because it explores a part of God’s creation.”
There is no global unanimity in the symbols used, though they come out to express the same fundamental rationality. To get a basic understanding of formal and symbolic logic, the chapters on those topics in a general textbook in logic will suffice for a superficial overview. However, I hope that a superficial overview should not become the standard for philosophically-oriented apologetics. What I’m really wishing for is that more people interested in apologetics would be sufficiently fascinated by these topics to devote some serious study to this discipline.
