Deduction and Induction

Arguments are traditionally divided into two different types, deductive and inductive.

A deductive argument is one in which the conclusion follows necessarily from the premises; in other words, the premises support the conclusion in such a way that if they are assumed true, it is impossible that the conclusion be false.

An inductive argument is one in which the conclusion follows only probably from the premises; in other words, the premises support the conclusion in such a way that if they are assumed true, then, based on that assumption, it is only probable that the conclusion be true.

Three factors that bear upon the evaluation of an argument is inductive or deductive are the following:

· the occurrence of special indicator words – If, in drawing a conclusion the arguer uses words such as “probable,” “improbable,” “plausible,” “implausible,” “likely,” “unlikely,” or “reasonable to conclude,” the evaluator may take such indicators as reason for considering the argument inductive.

Neon has unstable isotopes. Therefore, since argon is similar in may ways to neon, it probably follows that argon has unstable isotopes, too.

On the other hand, if the arguer uses words such as “necessarily,” “certainly,” “absolutely,” or “definitely,” the evaluator may consider the argument deductive.

If a substance is a noble gas, it is inert. Therefore, since argon is a noble gas, it necessarily follows that it is inert.

· the nature of the inferential link between premises and conclusion – If this link is such that the conclusion follows necessarily from the premises, the argument is clearly deductive. To say that the conclusion follows “necessarily” means that the premises support the conclusion in such a way that if they are assumed true, it is absolutely impossible that the conclusion be false.

All saleswomen are extroverts. Judy Wage is a saleswoman. Therefore, she is extrovert.

On the other hand, if the conclusion does not follow necessarily from the premises but does probably, it is usually best to consider the argument inductive.

The vast majority of saleswomen are extroverts. Rose Liam is a saleswoman. Therefore, Rose Liam is an extrovert.

· The character or form of argument the arguer uses – Sometimes it happens that an argument contains no indicator words and the conclusion follows neither necessarily nor probably from the premises, that is, the premises provide no clear support for the conclusion, This situation points out the need for the third factor to be taken into account, which is the character or form of argumentation the arguer uses.

Five such types of argumentation that are typically deductive are the following:

Argument based on mathematics	An argument in which the conclusion depends on some purely arithmetic or geometric computation or measurement. A shopper may place two apples and the three oranges into a paper bag and then conclude that the bag contains five fruits. /A surveyor might measure a square piece of land and, after determining that it is 100 feet on each side, conclude that it contains 10,000 square feet.
Argument from definition	An argument in which the conclusion is claimed to depend upon the definition of some word or phrase used in the premise or conclusion. Claudia is mendacious, so she tells lies. / This paragraph is prolix, so it follows that it is excessively wordy.
Categorical syllogism	A syllogism in which each statement begins with one of these quantifiers: “all,” “no,” “some.” All lasers are optical devices. Some lasers are surgical instruments. Therefore, some optical devices are surgical instruments.
Conditional syllogism	A syllogism having a conditional statement for one or both of its premises. If quartz scratches glass, then quartz is harder than glass. Quartz scratches glass. Therefore, quartz is harder than glass.
Disjunctive syllogism	A syllogism having a disjunctive statement (“either… or”) for one or both of its premises. Either breach of contract is a crime or it is not punishable by the state. Breach of contract is not a crime. Therefore, it is not punishable by the state.

The following are typically inductive forms of argumentation. Inductive arguments are such that the content of the conclusion is in some way intended to go beyond the content of the premise. The premises of such an argument typically deal with some subject that is relatively familiar, and the conclusion then moves beyond this to a subject that is less familiar or that little is known about.

Prediction	The premises deal with some known event in the present or past, and the conclusion moves beyond this event to some event in the relative future. Because certain meteorological phenomena have been observed to develop over a certain region in the Pacific, a storm will occur there in the next several hours.
Argument from analogy	An argument that depends on the existence of an analogy, or similarity, between two things or state of affairs. Because of the existence of this analogy, a certain condition that affects the better known thing or situation is concluded to affect the similar lesser known thing or situation. From knowledge that his Mercedes car is an expensive car, I argue that your car, being a Mercedes, is also expensive.
Inductive generalization	An argument that proceeds from the knowledge of selected sample to some claim about the whole group. Because the members of the sample have a certain characteristic, it is argued that all the members of the group have the same characteristic. One may argue that because three oranges selected from a certain crate were especially tasty and juicy, all the oranges from that crate are especially tasty and juicy.
Argument from authority	An argument in which the conclusion rests upon a statement made by some presumed authority or witness. A lawyer may argue that the criminal committed no murder because an eyewitness testified to that effect under oath.
Argument based on signs	An argument that proceeds from the knowledge of a certain sign to knowledge of the thing or situation that the sign symbolizes. When driving on an unfamiliar highway, one might see a sign indicating the road makes several sharp turns one mile ahead. Base on this information, one might argue that the road does indeed make several sharp turns one mile ahead.
Causal inference	An argument that proceeds from knowledge of a cause to knowledge of the effect or conversely, from knowledge of an effect to knowledge of a cause. From the knowledge of the bottle of wine had been accidentally left in the freezer overnight, someone might concluded that it had frozen (cause to effect) Or, after tasting a piece of chicken and finding it dry and crunchy, one might conclude that it had been overcooked. (effect to cause)

Although every argument involves the claim that its premises provide evidence for the truth of its conclusion, only a deductive argument involves the claim that its premises provide conclusive evidence. In the case of deductive arguments the technical terms valid and invalid are used in place of correct and incorrect. A deductive is valid when its premises, if true, do provide conclusive evidence for its conclusion, that is, when premises and conclusion are so related that it is absolutely impossible for the premises to be true unless the conclusion is true also. Every deductive argument is either valid or invalid. The task of deductive logic is to clarify the nature of the relation between premises and conclusion in valid arguments, and thus to allow us to discriminate valid and invalid arguments.

An inductive argument, on the other hand, involves the claim, not that its premises give conclusive evidence for the truth of its conclusion, but only that they provide some evidence for it. Inductive arguments are neither valid nor invalid in the sense in which those terms are applied to deductive arguments. Inductive arguments may, of course, be evaluated as better or worse, according to the degree of likelihood or probability, which their premises confer upon their conclusions.