— 12 — Inductive Reasoning

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TFY C10: Inductive Reasoning: How Do I Reason from Evidence?

PCT C8 Inductive reasoning

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TFY C10 Induction;

Chapter Ten Inductive Reasoning

Inductive reasoning is a method used to discover new information or supply missing information. When we reason inductively, we observe, test, and investigate in a systematic manner known as the empirical or scientific method. Exercises and discussion in this chapter show you how induction uses sensory observation, enumeration, analogical reasoning, pattern discovery, causal reasoning, reasoning from hypotheses and through statistics and probability. A short writing application asks you to research some facts and form hypotheses about them. Concluding readings by science writer Ferris Jabr and novelist Kurt Vonnegut show us how empirical studies can be reported.

TPCT Ch. 8: Inductive Reasoning

TPCT Ch. 8: Inductive Reasoning – Summary:

Numerative Induction

  • An inductive argument is intended to provide only probable support for its conclusion, being considered strong if it succeeds in providing such support and weak if it does not.
  • Inductive arguments come in several forms, including enumerative, analogical, and causal. In enumerative induction, we argue from premises about some members of a group to a generalization about the entire group. The entire group is called the target group; the observed members of the group, the sample; and the group characteristics we’re interested in, the relevant property.
  • An enumerative induction can fail to be strong by having a sample that’s too small or not representative. When we draw a conclusion about a target group based on an inadequate sample size, we’re said to commit the error of hasty generalization.
  • Opinion polls are enumerative inductive arguments, or the basis of enumerative inductive arguments, and must be judged by the same general criteria used to judge any other enumerative induction.

Analogical Induction

  • In analogical induction, or argument by analogy, we reason that since two or more things are similar in several respects, they must be similar in some further respect. We evaluate arguments by analogy according to several criteria: (1) the number of relevant similarities between things being compared, (2) the number of relevant dissimilarities, (3) the number of instances (or cases) of similarities or dissimilarities, and (4) the diversity among the cases.

Causal Arguments

  • A causal argument is an inductive argument whose conclusion contains a causal claim. There are several inductive patterns of reasoning used to assess causal connections. These include the Method of Agreement, the Method of Difference, the Method of Agreement and Difference, and the Method of Concomitant Variation.
  • Errors in cause-and-effect reasoning are common. They include misidentifying relevant factors in a causal process, overlooking relevant factors, confusing cause with coincidence, confusing cause with temporal order, and mixing up cause and effect.
  • Crucial to an understanding of cause-and-effect relationships are the notions of necessary and sufficient conditions. A necessary condition for the occurrence of an event is one without which the event cannot occur. A sufficient condition for the occurrence of an event is one that guarantees that the event occurs.
Inductive reasoning, also known as induction or inductive logic, is a type of reasoning that involves moving from a set of specific facts to a general conclusion. It uses premises from objects that have been examined to establish a conclusion about an object that has not been examined
It can also be seen as a form of theory-building, in which specific facts are used to create a theory that explains relationships between the facts and allows prediction of future knowledge. The premises of an inductive logical argument indicate some degree of support (inductive probability) for the conclusion but do not entail it; i.e. they do not ensure its truth.
Induction is used to ascribe properties or relations to types based on an observation instance (i.e., on a number of observations or experiences); or to formulate laws based on limited observations of recurring phenomenal patterns.
Induction is employed, for example, in using specific propositions such as:
This ice is cold. (Or: All ice I have ever touched has been cold.)
This billiard ball moves when struck with a cue. (Or: Of one hundred billiard balls struck with a cue, all of them moved.)
…to infer general propositions such as:
All ice is cold.
All billiard balls move when struck with a cue.
Another example would be:
3+5=8 and eight is an even number. Therefore, an odd number added to another odd number will result in an even number.
Note that mathematical induction is not a form of inductive reasoning. While mathematical induction may be inspired by the non-base cases, the formulation of a base case firmly establishes it as a form of deductive reasoning.

Many philosophers[who?] believe that the ability to use inductive reasoning is essential for understanding and that it accumulates from observation and ideas which are the fabric of insight. Many philosophical[says who?] topics such as morality and faith are explained using inductive reasoning.