DEDUCTIVE AND INDUCTIVE ARGUMENTS

Deductively valid arguments are arguments in which the premises guarantee the truth of the conclusion. If the premises the true, the conclusion must also be true. Deductive arguments have a formal structure, which can be put into symbolic form. Deductive arguments are either valid or invalid based on their structure or form, so they are sometimes called formal arguments. We looked at some basic deductively valid argument forms: modus ponens, modus tollens, disjunctive syllogism and dilemma. We also looked at two formal fallacies; denying the antecedent and asserting the consequent.

You can put any set of premises and any conclusion into a valid deductive argument and know that the conclusion is true if the premises are. If Socrates is human and hemlock is fatal to all human beings, it follows as a matter of logic that Socrates will die after drinking the hemlock. If Socrates drinks the hemlock and seems no the worse for wear, then one of our premises must be false. Either he's not really a human being - maybe he's a god in human disguise or an alien - or it's not true that hemlock is fatal to all human beings. Maybe he didn't really drink the hemlock. Maybe some human beings have an immunity to hemlock. Whatever the case, we know that one of our premises must be false, because if the premises were true, the conclusion would have to be. If the premises are not true, nothing can be deduced about the truth of the conclusion.

Inductively strong arguments only guarantee the truth of the conclusion with a certain degree of probability. If the premises are true, then the conclusion is probably true, perhaps with 99.999999999% certainty, but there is a logical possibility that it's false. Why not just go with deductive arguments then? Take the following example: "If the defendant had the means, motive and opportunity to commit the crime, then he is guilty. He had the means, motive and opportunity to commit the crime, therefore he is guilty." That's modus ponens and a deductively valid argument. But how do you know the second premise is true? The prosecutor gains nothing by casting his argument in deductive form, because what matters is the strength of inductive evidence, not the formal structure of his argument. It's more natural to argue, "The defendant had the means, motive and opportunity to commit the crime, therefore he is guilty to a reasonable doubt. Most arguments are inductive in nature and attempting to stuff them into a formal deductive structure is counter-productive.

Logicians reserve the terms valid and invalid for deductive arguments but refer to inductive arguments as strong or weak. Like deductive arguments, they can go wrong in two ways: weak premises or faulty logic. If one of the premises is false or doubtful, then the conclusion doesn't logically follow. Or, all of the premises may be true and well grounded in evidence, but they still don't support the conclusion. Suppose someone argues, "The rich hardly pay any taxes, therefore any tax reform plan should exclude them. This might be a good argument if the premise was true, but it's not. For example, the top 20% pay 95% of all Federal income taxes, whereas the bottom 40% pay nothing or get money back. The flaw in this argument is a faulty premise. On the other hand, suppose someone argues, "Margaret Sanger, the founder of Planned Parenthood, was a white supremacist and promoted abortion as a means of keeping keeping the 'less desirable' races from breeding. Abortion is a eugenics project." The premise is actually true in this case, but doesn't support the conclusion. Just because Planned Parenthood was founded on eugenicist principles doesn't mean it operates on those principles today. To conclude something about a thing based on its origin is called the genetic fallacy.