An Introduction to Inductive and Deductive Logic

Fixing Flawed Thinking

We often suppose that the other guy’s thinking is flawed, without even considering whether the real problem is actually with our own thinking. We tend to elevate our limited observations and our plausible opinions to the level of sure facts and infallible conclusions. Faith indeed has a part in logic, but too often we give it the wrong part. We know what we want to believe, and we conclude that it therefore must be true. But t’ain’t necessarily so. We need to recognize what method of reasoning we are using, and what are the limits of that method of reasoning.

Two Methods Of Reasoning

Reasoning can run in two opposite directions. Deductive reasoning moves from a general premise to a more specific conclusion. Inductive reasoning moves from specific premises to a general conclusion. These two methods of reasoning will produce two different kinds of results.

Inductive Reasoning

Let’s look at inductive reasoning first. Inductive reasoning moves from the particular to the general. It gathers together particular observations in the form of premises, then it reasons from these particular premises to a general conclusion. The most common form of inductive reasoning is when we collect evidence of some observed phenomena (e.g. examining 10,000 dogs for fleas), then we draw a general conclusion about all such phenomena based on our collected evidence (e.g. whether all dogs have fleas). In an inductive argument, the conclusion goes beyond what the premises actually say. For example, if I observe 10,000 dogs, and every dog has fleas, I may conclude “All dogs must have fleas.” The conclusion is a conjecture or a prediction. Further evidence may support or deny my conclusion. The 10,001st dog may not have fleas. Therefore, with an inductive argument, anyone can affirm all my premises (10,000 dogs with fleas, yet deny my conclusion (all dogs have fleas) without involving himself in any logical contradiction. What I say in my conclusion is possible, It may even seem very probable. Nevertheless, it is not a necessary conclusion. If someone said, “Some dogs may have fleas, but I don’t believe all dogs have fleas,” there is no logical response I could make. The logical certainty of my conclusion is entirely dependent upon my correct interpretation of the evidence and the consistency of the evidence with the remainder of the phenomena which was not, is not, or may never be observed. Maybe I had fleas, and I inadvertently transferred them to each of the 10,000 dogs, so the 10,000 dogs actually had no fleas except when I examined them. I would have to examine all dogs at all times under thoroughly monitored conditions in order to “prove” my conclusion. But this would be an impractical task. Therefore it is unlikely my conclusion will ever be proven. It can, however, be disproven. Find one dog without fleas. Then you will be left with the conclusion which I should have arrived at to begin with, “Some dogs have fleas.” Maybe most dogs, or nearly all dogs have fleas. But all I know for certain is that some dogs have fleas. Remember, an inductive argument concludes more than the premises actually warrant.

We use inductive reasoning all of the time. It is very useful. But we must recognize its limits. Most inductive reasoning is not based upon exhaustive evidence, and therefore the form is incomplete. (10,000 dogs is not all dogs.) Unless the evidence or observations are exhaustive (I examine all dogs for fleas), the conclusion is only a guess. It may be a good guess. The strength of the inductive argument is increased as it approaches completeness. If the evidence I accept represents all possibilities within the whole, my inductive conclusion will be correct. The more I can demonstrate that the evidence is truly representative, the more compelling will my conclusion be. “10,000 dogs of every age and variety chosen at random from every country on the earth were examined under controlled conditions, and all of them had fleas. Therefore, it seems likely that all dogs have fleas.”

Deductive Reasoning

Deductive reasoning moves from the general to the particular. It takes a general premise and deduces particular conclusions. A “valid” deductive argument is one in which the conclusion necessarily follows from the premise. (All dogs have fleas. This is a dog. Therefore this dog has fleas.) The premise may not be “true” but the form of the argument is nevertheless “valid”. (If all dogs do have fleas, and if this is a dog, then this dog must necessarily have fleas.) An “invalid” deductive argument will contain something in the conclusion wholly new and independent from those things mentioned in the premise of the argument. (If all dogs have fleas, then my dog must have ticks. But ticks are not mentioned in the premise.) Sometimes it is not so obvious that something new has been introduced in the conclusion. (Only man is a rational being. Therefore, no woman is a rational being. This argument equivocates on the meaning of “man.” In the premise, the word “man” means mankind, including woman. In the conclusion, the word “woman” is used to designate that portion of mankind which is of the female gender as distinguished from the male portion called “man.” So a new concept, a distinction in gender, is introduced in the conclusion.)

Everything in the conclusion of a valid deductive argument must also be contained in the premises. (There are rules about how these things are arranged, but that is beyond our purposes here.) Therefore all valid deductive reasoning is by its nature actually circular reasoning or “begging the question.” That does not mean the conclusion is worthless. (If Johnny rides the bus 96 minutes every morning and 96 minutes every evening, five days a week, and if Johnny sleeps 8 hours every day, then Johnny spends the equivalent of one awake day [16 hours] on the bus every week. The conclusion is entirely contained in the premises, but the conclusion restates those premises in a way which causes us to understand more fully the consequences of riding the bus so much.)

The truth (or verity) of the conclusion of a deductive argument is dependent upon two things: the correctness (or validity) of the form of the argument, and the truth (or verity) of the premise. The validity of the form is determined by the application of established rules. So the only weakness of a deductive argument is the truth value (verity) of its premises. Your conclusions are only as good as your premises. Or, to put it another way, your presuppositions will always determine your conclusions.

More on inductive and deductive reasoning — Elementary Lessons in Logic: Deductive and Inductive by Ludwig von Mises Institute

Sources of Deductive Premises

If one believes all the premises in a valid deductive argument, he must believe the conclusion. The premise of a deductive argument may come from several sources. In order to evaluate the truth of the deductive argument, it is important to recognize the source of its premises.

The conclusion of an inductive argument may be used as the premise of a deductive argument. The weakness of most inductive arguments is that they begin with incomplete premises. (10,000 dogs is not all dogs.) One may arrive at a false inductive conclusion (All 10,000 dogs examined had flees, therefore all dogs have fleas.). He may use this false conclusion as the premise of a valid deductive argument (Since all dogs have fleas, therefore this dog must have fleas). If the premise is false, the conclusion is false. (This dog may indeed have fleas, but it is not a necessary consequence of the fact that all dogs have fleas, because all dogs do not necessarily have fleas, only 10,000 dogs had fleas at the time they were tested.) Scientists commonly arrive at inductive conclusions on the basis of inadequate information, then argue deductively from their induction.

More on inductive and deductive reasoning — The Art of Reasoning: An Introduction to Logic and Critical Thinkingby David Kelley

Invalid and False Inductive argument:

All living creatures have a genetic code.
Therefore all living creatures are genetically related.

Valid but False Deductive Argument:

All living creatures are genetically related.
Man is a living creature.
Therefore man is genetically related to all other living creatures.

The premises of a deductive argument may come from a direct observation. If the observations are correct, you may rely upon the conclusion. (Barring the most extraordinary circumstances, that locomotive will eventually pass over these tracks. Unless I move off of these tracks, that locomotive will eventually pass over me, barring the most extraordinary circumstances.)

The premise of a deductive argument may come from emotional feelings. Often the emotional premise is implied, not expressed, therefore must be discerned. (If you truly loved me you would never talk to me that way. The implied premise is that true love constantly prohibits certain kinds of speech.)

Some derive their premise for their deductive argument from their practical circumstances. (If that government program provides me with a job, then that government program is good. The implied premise is that anything which provides jobs is good.)

Often we find a definition as the premise of a deductive argument. (A pencil, by definition, is a long cylindrical writing instrument containing a thin piece of graphite for writing. This is a long cylindrical writing instrument containing a thin piece of graphite for writing. Therefore this, by definition, is a pencil.) If the definition is correct, and the argument is valid, then the conclusion is true.

To the Christian, the Bible provides an immense resource of true statements which he may use as premises in valid deductive arguments to arrive at true conclusions.

The whole counsel of God, concerning all things necessary for his own glory, man’s salvation, faith, and life, is either expressly set down in Scripture, or by good and necessary consequences may be deduced from Scripture: unto which nothing at any time is to be added, whether by new revelations of the Spirit, or traditions of men. Westminster Confession of Faith, I,6

(Divers weights and a false balance are abominations unto the Lord. {Proverbs 20:23; 11:1} If unbacked currency is a divers weight and unearned interest is a false balance, then such currency and such interest are abominations unto the Lord.)

More on inductive and deductive reasoning — Logic, Inductive and Deductive by William Minto

Induction and Deduction Compared

The conclusion of an inductive argument can be proven false by finding one contrary example. (All 10,000 dogs have fleas, therefore all dogs have fleas. Find one dog without fleas and this conclusion is proven false.) But the inductive conclusion can never be proven true unless you exhaust all particulars of the premise. (All you actually know is that some dogs have fleas. You have to examine all dogs to conclude all dogs have fleas.)

The conclusion of a valid deductive argument cannot be proven false unless its premises are also proven false, and it cannot be proven true unless its premises are also proven true. In other words, truth or falsehood is dependent upon the premises.

Induction is generally future oriented. It gathers specific information, then draws a general conclusion which predicts what you will find in the future. (All 10,000 dogs examined had fleas. Therefore I predict you will continue to find all dogs have fleas.) This conclusion is testable by future observation. Some try to “predict” the unobservable past, such as a forensic detective who investigates crimes, or a speculative scientist who investigates the origins of the universe. These types of “predictions” are untestable.

Deduction is generally past or present oriented. Presumably, its premises are already tested. It draws from general information, then extracts a specific conclusion which proves the past or present truth. The Bible is a source of true premises by which someone can prove the unobservable past (creation, lives of the patriarchal fathers) or the unobservable future (the first coming of Christ, the destruction of Jerusalem).

Both inductive and deductive arguments require faith. An inductive argument requires faith in its conclusion, while a deductive argument requires faith in its premises.

We suggest starting your logic journey with The Fallacy Detective: Thirty-Eight Lessons on How to Recognize Bad Reasoning (for ages 12 and up).