Deductive Reasoning

I. Definition

Deductive reasoning, or deduction, is one of the two basic types of logical inference. A logical inference is a connection from a first statement (a “premise”) to a second statement (“the conclusion”) for which the rules of logic show that if the first statement is true, the second statement should be true.

Specifically, deductions are inferences which must be true—at least according to the rules. If you assume that the premise (first statement) is true, then you can deduce other things that have to be true. These are called deductive conclusions.

Examples:

Premise: Socrates is a man, and all men are mortal.
Conclusion: Socrates is mortal.

Premise: This dog always barks when someone is at the door, and the dog didn’t bark.
Conclusion: There’s no one at the door.

Premise: Sam goes wherever Ben goes, and Ben went to the library.
Conclusion: Sam also went to the library.

Each of these miniature arguments has two premises (joined by the “and”). These are syllogisms, which provide a model for all deductive reasoning. It is also possible to deduce something from just one statement; but it isn’t very interesting; for example, from the premise “Socrates is a man,” you can certainly deduce that at least one man exists. But most deductions require more than one premise.

You’ll also notice that each premise contains a very general claim–something about “all men” or what the dog “always” does. This is an extremely common feature of deductions: their premises are general and their conclusions are specific.

In each case, the deductive reasoning is valid, meaning that the conclusion has to be true–if the premises are true. The logical relation between premise and conclusion is airtight. However, you always have to be careful with deductive reasoning. Even though the premise and conclusion are connected by an airtight deduction, that doesn’t necessarily mean the conclusion is true. The premises could be faulty, making the conclusions invalid.

Premises are often unreliable. For example, in the real world no dog is 100% reliable, so you can’t be certain that the premise “the dog always barks” is true. Therefore, even though the connection is a logical certainty, the actual truth of each statement has to be verified through the messy, uncertain process of observations and experiments.

There’s another problem with deductive reasoning, which is that deductive conclusions technically don’t add any new information. For example, once you say “All men are mortal, and Socrates is a man,” you’ve already said that Socrates is mortal. That’s why deductions have the power of logical certainty: the conclusion is already contained within the premises. That doesn’t mean deductive reasoning isn’t useful; it is useful for uncovering implications of what you already know—but not so much for developing really new truths.

II. Deductive Reasoning vs. Inductive Reasoning

While deductive reasoning implies logical certainty, inductive reasoning only gives you reasonable probability. In addition, they often move in opposite directions: where deductive reasoning tends to go from general premises to specific conclusions, inductive reasoning often goes the other way—from specific examples to general conclusions.

Examples of inductive reasoning:

Premise: No one has ever lived past the age of 122.
Conclusion: Human beings probably all die sooner or later.

Premise: So far, I’ve never seen someone come to the door without my dog barking.
Conclusion: My dog will probably bark when the next person comes to the door.

Premise: Sam has been following Ben around all day.
Conclusion: Sam will probably go to the library this afternoon when Ben goes.

Induction allows us to take a series of observations (specific premises) and extrapolate from them to new knowledge about what usually happens (general conclusion) or what will probably happen in the future. This seems extremely useful!

III. Quotations about Deductive reasoning

Quote 1

“In the hypothetico-deductive scheme the inferences we draw from a hypothesis are, in a sense, its logical output. If they are true, the hypothesis need not be altered, but correction is obligatory if they are false.” (Peter Medawar)

Peter Medawar wasn’t the clearest writer around, but he won a Nobel Prize for his part in inventing modern organ transplantation. In this quotation, he explains the importance of deductive reasoning in science; science normally advances through incorrect deductions! If we reason logically and our predictions turn out untrue, we know that there is something wrong with our premises, which motivates new theories from which we can deduce new conclusions to test. For example, if the Earth were flat (premise) then you’d be able to reach its edge (conclusion); since we never reach the edge (the conclusion is wrong), it can’t be flat (the premise is untrue) — which means it’s probably a sphere (new theory). In other words, unlike the popular idea that science is a kind of faith, there are no beliefs in real science—except the belief in the scientific method of making and testing hypotheses with reason and evidence.

Quote 2

“An ideally rational progression of thought will finally bring you back to the point of departure where you return aware of the simplicity of genius, with a delightful sensation that you have embraced truth, while actually you have merely embraced your own self.” (Vladimir Nabokov)

In this quote, the novelist Vladimir Nabokov explains his skeptical attitude toward deductive reasoning. He points out what we already discussed–that deductions get their certainty from the fact that they don’t add any new information. Nabokov extends this idea to rationality in general, but in this quotation he seems to be talking specifically about deductive reasoning.

IV. The History and Importance of Deductive Reasoning

Deductive reasoning is more formalized than induction, but its history goes way back before the origins of formal philosophy. It’s possible that the earliest form of deductive reasoning was math. All of mathematics is one big pile of deductions. It starts with some very general rules defining the sequence of whole numbers, and then deduces all sorts of conclusions from there. Math by itself may not teach us about the world; its conclusions are already buried in its premises, and therefore it doesn’t technically produce new information. However, mathematical deductions have progressed so far from their premises that recently it has become a source of new physical theories, such as with ‘string theory’—a trend that bothers many physicists. But in combination with observation and experimentation, math and deduction have always been powerful tool for understanding and manipulating the world. People all over the world have known about this power since prehistoric times.

Ever since then, mathematicians and philosophers have been working out the formal rules for what counts as a valid deduction. Their work allows us to distinguish good deductive reasoning from sloppy or misleading arguments, and forms the backbone of formal logic.

V. Deductive reasoning in Popular Culture

Example 1

“It is a capital mistake to theorize before one has data. Insensibly one begins to twist facts to suit theories, instead of theories to suit facts.” (Sherlock Holmes)

Sherlock Holmes famously uses the word “deduction” a lot. But if you pay attention to his logic, you’ll find that it’s almost always inductive rather than deductive; the word “deduction” is being misused. This quote is a well-known summary of Holmes’s method, and as you can see it describes inductive reasoning rather than deductive reasoning. Theories are general, whereas data is specific; therefore, if you start from data and move to theory, you’re moving from specific to general, which suggests that you’re dealing with induction rather than deduction. The definitive proof, though, is in the fact that Sherlock always comes up with stories that are probable, and often very convincing, but not logically certain. Sherlock Holmes never gives us a deductive syllogism; he gives only inductive stories.

Example 2

“It’s not complicated; faster is better. And iPhone 5 downloads fastest on AT&T 4G.”

This is an example of a deductive syllogism in an advertisement. Or, actually, only the two premises are given and the listener is expected to automatically deduce the conclusion. The first premise is a general law: faster is better. The second premise applies the law to a particular situation. And the implied conclusion is obvious: the iPhone is better. This conclusion is so obvious that it doesn’t need to be stated — another demonstration of the fact that deductive conclusions are already contained in the premises, as discussed earlier.