Making a Case
To make a good case for a conclusion, an argument must have two features. The conclusion must follow from the premises and the premises must at least be more likely to be true than not. Arguments can be challenged either by suggesting that the premises do not entail or support the conclusion, or that one or more of the premises is false or unsupported.
Deductive Categorical Arguments
In a good deductive argument, the truth of the premises is supposed to guarantee the truth of the conclusion. But not all deductive arguments are of the same kind. A deductive argument about categories is an argument about what or who belongs to what category. One can know if Socrates is a member of the category of things that are mortal by reasoning that Socrates is a man and that all men are mortal.
Jesus uses the same sort of reasoning to assert that anyone who receives one of his disciples receives him, and anyone who receives him receives his Father (Matt 10:40). If you belong in the first category, you automatically belong in the last one.
Categorical arguments are also deployed against Jesus. In one of many Sabbath controversies, the religious leaders claim that Jesus is not from God. The two premises for their argument (one explicit, the other, implicit) are (1) All people from God are Sabbath keepers (2) Jesus does not keep the Sabbath. Therefore, (3) Jesus is not from God (John 9:16). The argument goes wrong at some point, but exactly how?
First, one can ask: assuming the premises are true, would the conclusion follow? Upon consideration, it appears it would. Hence, it passes the first test. If it goes wrong, it must be because one or more of its premises are false. Someone might suggest that (1) is at fault. But, instead, Jesus implies that (2) is false. His reply indicates that it is he—and not the Pharisees—who knows when the Sabbath is kept. The grossly distorted version of the Sabbath advanced by the opposition is almost unrecognisable. Hence, Jesus is in full compliance with the Sabbath and (2) is false. If so, the argument is a bad one.
Deductive Propositional Arguments
Another kind of deductive argument uses propositions as its basic unit. Assessing the merits of these arguments requires acquiring the capacity to recognise good patterns. For example, the pattern called modus ponens looks like this: If p, then q. p. Therefore, q. The pattern is so recognisable that conclusions from it are almost automatic. If I say, “if it’s an apple, it grew on a tree” and then say, “it is an apple,” the conclusion, “it grew on tree,” follows almost as spontaneously as breathing. Its cousin, modus tollens, is almost as identifiable. Replacing the second premise with “it didn’t grow on a tree” would yield the conclusion, “it isn’t an apple.”
Paul deploys the latter sort of pattern in his letter to the Roman church. He writes:
If our unrighteousness brings out God’s righteousness more clearly, what shall we say? That God is unjust in bringing his wrath on us? (I am using a human argument.) Certainly not! If that were so, how could God judge the world? (Romans 3:5–6)
In this passage Paul is arguing against a conditional statement, namely, ‘if our unrighteousness brings out God’s righteousness more clearly, then God is unjust in bringing his wrath on us.’ To make his case, he uses another conditional. If that were so, he says, then God would be unable to judge the world. Since God can judge the world, it cannot be the case that if our unrighteousness brings out God’s righteousness more clearly, then God is unjust in bringing his wrath on us. The pattern Paul is following is modus tollens (if p, then q. Not q. Hence, not p). Notice that the complexity of the parts can increase without deviating from the pattern. In Paul’s argument, the ‘p’ of the pattern is itself a conditional statement.
Inductive Testimonial Arguments
Inductive arguments are assessed in similar fashion to their deductive counterparts. One assesses the support offered for a conclusion and the merits of the premises offered as support. However, inductive arguments can’t guarantee the truth of their conclusions. Instead, the most a good inductive argument can establish is that the conclusion is more likely true than not.
A Christian’s knowledge of historical facts depends on the testimony of witnesses. An inductive argument from testimony begins with the claim that someone has claimed something. For example, we might begin with, “Luke tells us that Jesus of Nazareth rose from the dead.” To defend this claim, some historical evidence must be forthcoming supporting claims such as Luke really wrote his gospel, there really was such a person, and we have reliable copies of what he wrote.
But just because someone says something, it doesn’t follow that he believes it. So, we’d also need to say, “Luke sincerely believes that Jesus rose from the dead.” Supporting this claim involves ruling out some reason he might have for lying. Was Luke motivated by fear of reprisal or obtaining a profit?
But even this isn’t enough to support the claim that Jesus rose from the dead. One must also claim that “Luke knows what he is talking about.” If Luke had no access to witnesses and got all his information from someone he met down the pub, we wouldn’t take him seriously. So, part of the argument relies on the expertise of the witness. As it turns out, Luke had ample access to first-hand testimony and meticulously records various accounts from eyewitnesses.
When someone tells us something sincerely and knows what they are talking about, we have some reason to think what they say is true. So, we have a good inductive case for the resurrection from the gospels.
However, inductive arguments can admit additional evidence, which can lower the likelihood of the truth of the conclusion. Famously, David Hume rejected the conclusion even while accepting the other premises of the argument. Hume accepts that miracle reports can be attested by credible expert witnesses but says that it doesn’t follow that miracles occur. He reasons that even the best witness testimony cannot provide sufficient evidence for the occurrence of a miracle. We will return to Hume’s challenge in a future post.
Inductive Causal Arguments
Making the case for one event bringing about another is perhaps the most common form of argument in everyday conversation. We argue about what caused the pound to plumett, who’s to blame for our woes, and what diet causes the best health. Unfortunately, the frequency of its use is not accompanied by the simplicity of its nature. Causal arguments are notoriously difficult to make and defend.
Nonetheless, some idea of their components helps us know what we must do to make them. It also helps us limit our confidence appropriately when we defend them. A simple causal claim might be something like the following: regular Bible reading causes an increase of joy in believers. Now, this might be a trivial truth, one which every believer accepts without argument. But suppose someone challenges it. How can we make a case?
The nature of the claim requires demonstrating the causal connection between joy and Bible reading. First, we’d have to show that believers who read their Bibles regularly are more likely to have increased joy. To obtain such information, one would need to survey a sample population of believers and generalise to all believers. If one can establish some data, which is not as easy as it sounds as we have discovered from the inaccuracy of polling, we may have a case for the correlation of regular Bible reading and increased joy. But, as we know, correlation does not equal causation.
To make the case for the causal relationship, we’d have to rule out alternatives. We’d have to show that the causal relationship is not the other way around. Does joy increase Bible reading? We’d also have to rule out an alternative cause. Perhaps people with increased joy all attend a regular worship service and that is what is causing their joy. Ruling out alternatives is perhaps the most difficult component of a causal argument. In consequence, many scientific arguments only conclude with strong correlation and stop short of claiming causation.
What I have offered is only a very cursory glance at the enormous body of knowledge we possess about logic. If you are interested in learning the details, there are many good introductory books available. I personally teach from Patrick Hurley’s A Concise Introduction to Logic, which is in its 13th edition, published by Cengage Learning. It has lots of exercises and contains most logics commonly deployed in argumentation. Recently, Christian authors have written good introductions to logic, including Travis Dickinson’s Logic and the Way of Jesus: Thinking Critically and Christianly, and T. Ryan Byerly’s Introducing Logic and Critical Thinking: The Skills of Reasoning and the Virtues of Inquiry. In this post I have drawn from biblical examples offered in Nance and Wilson’s Introductory Logic and Intermediate Logic both of which are published by Canon Press.