Faulty generalization

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A faulty generalization is an informal fallacy wherein a conclusion is drawn about all or many instances of a phenomenon on the basis of one or a few instances of that phenomenon. It is similar to a proof by example in mathematics. [1] It is an example of jumping to conclusions. [2] For example, one may generalize about all people or all members of a group from what one knows about just one or a few people:

Contents

Expressed in more precise philosophical language, a fallacy of defective induction is a conclusion that has been made on the basis of weak premises, or one which is not justified by sufficient or unbiased evidence. [3] Unlike fallacies of relevance, in fallacies of defective induction, the premises are related to the conclusions, yet only weakly buttress the conclusions, hence a faulty generalization is produced. The essence of this inductive fallacy lies on the overestimation of an argument based on insufficiently-large samples under an implied margin or error. [2]

Logic

A faulty generalization often follows the following format:

The proportion Q of the sample has attribute A.
Therefore, the proportion Q of the population has attribute A.

Such a generalization proceeds from a premise about a sample (often unrepresentative or biased), to a conclusion about the population itself. [3]

Faulty generalization is also a mode of thinking that takes the experiences of one person or one group, and incorrectly extends it to another.

Inductive fallacies

Hasty generalization

Hasty generalization is an informal fallacy of faulty generalization, which involves reaching an inductive generalization based on insufficient evidence [3] —essentially making a rushed conclusion without considering all of the variables or enough evidence. In statistics, it may involve basing broad conclusions regarding a statistical survey from a small sample group that fails to sufficiently represent an entire population. [1] [6] [7] Its opposite fallacy is called slothful induction, which consists of denying a reasonable conclusion of an inductive argument (e.g. "it was just a coincidence").

Examples

Hasty generalization usually follows the pattern:

  1. X is true for A.
  2. X is true for B.
  3. Therefore, X is true for C, D, E, etc.

For example, if a person travels through a town for the first time and sees 10 people, all of them children, they may erroneously conclude that there are no adult residents in the town.

Alternatively, a person might look at a number line, and notice that the number 1 is a square number; 3 is a prime number, 5 is a prime number, and 7 is a prime number; 9 is a square number; 11 is a prime number, and 13 is a prime number. From these observations, the person might claim that all odd numbers are either prime or square, while in reality, 15 is an example that disproves the claim.

Alternative names

The fallacy is also known as:

When referring to a generalization made from a single example, the terms fallacy of the lonely fact, [8] or the fallacy of proof by example, might be used. [9]

When evidence is intentionally excluded to bias the result, the fallacy of exclusion—a form of selection bias—is said to be involved. [10]

See also

Related Research Articles

Fallacies of definition are the various ways in which definitions can fail to explain terms. The phrase is used to suggest an analogy with an informal fallacy. Definitions may fail to have merit, because they: are overly broad, use obscure or ambiguous language, or contain circular reasoning; those are called fallacies of definition. Three major fallacies are: overly broad, overly narrow, and mutually exclusive definitions, a fourth is: incomprehensible definitions, and one of the most common is circular definitions.

<span class="mw-page-title-main">Fallacy</span> Argument that uses faulty reasoning

A fallacy is the use of invalid or otherwise faulty reasoning in the construction of an argument that may appear to be well-reasoned if unnoticed. The term was introduced in the Western intellectual tradition by the Aristotelian De Sophisticis Elenchis.

Deductive reasoning is the mental process of drawing deductive inferences. An inference is deductively valid if its conclusion follows logically from its premises, i.e. it is impossible for the premises to be true and the conclusion to be false.

The genetic fallacy is a fallacy of irrelevance in which arguments or information are dismissed or validated based solely on their source of origin rather than their content. In other words, a claim is ignored or given credibility based on its source rather than the claim itself.

Circular reasoning is a logical fallacy in which the reasoner begins with what they are trying to end with. Circular reasoning is not a formal logical fallacy, but a pragmatic defect in an argument whereby the premises are just as much in need of proof or evidence as the conclusion, and as a consequence the argument fails to persuade. Other ways to express this are that there is no reason to accept the premises unless one already believes the conclusion, or that the premises provide no independent ground or evidence for the conclusion. Circular reasoning is closely related to begging the question, and in modern usage the two generally refer to the same thing.

The term Inductive reasoning is used to refer to any method of reasoning in which broad generalizations or principles are derived from a body of observations. This article is concerned with the inductive reasoning other than deductive reasoning, where the conclusion of a deductive argument is certain given the premises are correct; in contrast, the truth of the conclusion of an inductive argument is at best probable, based upon the evidence given.

Anecdotal evidence is evidence based only on personal observation, collected in a casual or non-systematic manner.

<span class="mw-page-title-main">Logical reasoning</span> Process of drawing correct inferences

Logical reasoning is a mental activity that aims to arrive at a conclusion in a rigorous way. It happens in the form of inferences or arguments by starting from a set of premises and reasoning to a conclusion supported by these premises. The premises and the conclusion are propositions, i.e. true or false claims about what is the case. Together, they form an argument. Logical reasoning is norm-governed in the sense that it aims to formulate correct arguments that any rational person would find convincing. The main discipline studying logical reasoning is logic.

A statistical syllogism is a non-deductive syllogism. It argues, using inductive reasoning, from a generalization true for the most part to a particular case.

<span class="mw-page-title-main">Logical form</span> Form for logical arguments, obtained by abstracting from the subject matter of its content terms

In logic, the logical form of a statement is a precisely-specified semantic version of that statement in a formal system. Informally, the logical form attempts to formalize a possibly ambiguous statement into a statement with a precise, unambiguous logical interpretation with respect to a formal system. In an ideal formal language, the meaning of a logical form can be determined unambiguously from syntax alone. Logical forms are semantic, not syntactic constructs; therefore, there may be more than one string that represents the same logical form in a given language.

In logic and philosophy, a formal fallacy, deductive fallacy, logical fallacy or non sequitur is a pattern of reasoning rendered invalid by a flaw in its logical structure that can neatly be expressed in a standard logic system, for example propositional logic. It is defined as a deductive argument that is invalid. The argument itself could have true premises, but still have a false conclusion. Thus, a formal fallacy is a fallacy where deduction goes wrong, and is no longer a logical process. This may not affect the truth of the conclusion, since validity and truth are separate in formal logic.

Logic is the formal science of using reason and is considered a branch of both philosophy and mathematics and to a lesser extent computer science. Logic investigates and classifies the structure of statements and arguments, both through the study of formal systems of inference and the study of arguments in natural language. The scope of logic can therefore be very large, ranging from core topics such as the study of fallacies and paradoxes, to specialized analyses of reasoning such as probability, correct reasoning, and arguments involving causality. One of the aims of logic is to identify the correct and incorrect inferences. Logicians study the criteria for the evaluation of arguments.

In logic and mathematics, proof by example is a logical fallacy whereby the validity of a statement is illustrated through one or more examples or cases—rather than a full-fledged proof.

Appeal to the stone, also known as argumentum ad lapidem, is a logical fallacy that dismisses an argument as untrue or absurd. The dismissal is made by stating or reiterating that the argument is absurd, without providing further argumentation. This theory is closely tied to proof by assertion due to the lack of evidence behind the statement and its attempt to persuade without providing any evidence.

An argument is a series of sentences, statements, or propositions some of which are called premises and one is the conclusion. The purpose of an argument is to give reasons for one's conclusion via justification, explanation, and/or persuasion.

Slothful induction, also called appeal to coincidence, is a fallacy in which an inductive argument is denied its proper conclusion, despite strong evidence for inference. An example of slothful induction might be that of a careless man who has had twelve accidents in the last six months and it is strongly evident that it was due to his negligence or rashness, yet keeps insisting that it is just a coincidence and not his fault. Its logical form is: evidence suggests X results in Y, yet the person in question insists Y was caused by something else.

Argument from analogy or false analogy is a special type of inductive argument, where perceived similarities are used as a basis to infer some further similarity that has not been observed yet. Analogical reasoning is one of the most common methods by which human beings try to understand the world and make decisions. When a person has a bad experience with a product and decides not to buy anything further from the producer, this is often a case of analogical reasoning since the two products share a maker and are therefore both perceived as "bad". It is also the basis of much of science; for instance, experiments on laboratory rats are based on the fact that some physiological similarities between rats and humans implies some further similarity.

As the study of argument is of clear importance to the reasons that we hold things to be true, logic is of essential importance to rationality. Arguments may be logical if they are "conducted or assessed according to strict principles of validity", while they are rational according to the broader requirement that they are based on reason and knowledge.

References

  1. 1 2 Bennett, Bo. "Hasty Generalization". logicallyfallacious.com. Retrieved 2019-12-05.
  2. 1 2 Dowden, Bradley. "Hasty Generalization". Internet Encyclopedia of Philosophy. Retrieved 2019-12-05.
  3. 1 2 3 Nordquist, Richard. "Logical Fallacies: Examples of Hasty Generalizations". ThoughtCo. Retrieved 2019-12-05.
  4. ↑ Dowden, Bradley. "Fallacies — Unrepresentative Sample". Internet Encyclopedia of Philosophy. Retrieved 2019-12-05.
  5. ↑ Fischer, D. H. (1970), Historians' Fallacies: Toward A Logic of Historical Thought, Harper torchbooks (first ed.), New York: HarperCollins, pp. 110–113, ISBN   978-0-06-131545-9, OCLC   185446787
  6. ↑ "Fallacy: Hasty Generalization (Nizkor Project)". Archived from the original on 2008-12-17. Retrieved 2008-10-01.
  7. ↑ "Fallacy". www.ditext.com. Retrieved 2019-12-05.
  8. ↑ Fischer, David Hackett (1970). Historians' Fallacies: Toward a Logic of Historical Thought . HarperCollins. pp.  109–110. ISBN   978-0-06-131545-9.
  9. ↑ Marchant, Jamie. "Logical Fallacies". Archived from the original on 2012-06-30. Retrieved 2011-04-26.
  10. ↑ "Unrepresentative Sample". Archived from the original on 2008-04-15. Retrieved 2008-09-01.
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