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Hasty Generalization and Secundum Quid

The size of the sample is too small to support the conclusion. “[This] type of argument [goes] under varied terms for the fallacy like over-generalization, glittering generality, accident, converse accident, or secundum quid (neglect of qualifications). Typically, however, two types of fallacies are emphasized. One is an inductive fallacy that occurs in statistical reasoning from a selected sample to a wider population. The other has to do with overlooking qualifications to a defeasible generalization.” (Douglas N. Walton, Argumentation Methods for Artificial Intelligence in Law, p. 39) By contrast, see “Slothful Induction and Ad Hoc Escapism“.

Examples
  1. "After only one year the alternator went out in Mr. O'Grady's new Chevrolet. Mrs. Dodson's Oldsmobile developed a transmission problem after six months. The obvious conclusion is that cars made by General Motors are just a pile of junk these days." (Hurley, Logic, 1991: p. 142)
  2. "Iraq boasts quite a long history of intermarriage and intercommunal cooperation. But a few years of this hateful dialectic soon succeeded in creating an atmosphere of misery, distrust, hostility, and sect-based politics. Once again, religion had poisoned everything." (Hitchens, god is not Great: p. 27. Emphasis in original.)
  3. "[Y]our opponent might argue that her client's future lost profits are $2 million, based on profits from one prior year. But if that year's profits were unusually high, her generalization is based on data that is deficient in both quantity (only one instance) and quality (an atypical year)." (Waicukauski, Sandler, and Epps, The Winning Argument: p. 50)
  4. "Madame Luna predicted in 1980 the fall of Russian communism; so, Madame Luna is a reputable psychic. The argument can be revised as: One observed prediction of Madame Luna has come true; so, all of Madame Luna's predictions must come true." (Holowchack, Critical Reasoning and Philosophy, p. 80.)
  5. "Here is a gentleman of the medical type, but with the air of a military man. Clearly an army doctor, then. He has just come from the tropics, for his face is dark, and that is not the natural tint of his skin, for his wrists are fair. He has undergone hardship and sickness, as his haggard face says clearly. His left arm has been injured. He holds it in a still and unnatural manner. Where in the tropics could an English army doctor have seen much hardship and gotten his arm wounded? Clearly in Afghanistan." (Sherlock Holmes in Sir Arthur Conan Doyle's A Study in Scarlet.)
  6. "We arrived at the park gate at 7:25 P.M., at which time the cashier gleefully took our admission money. Upon entering the zoo and walking across the bridge, we heard the loudspeaker state that the zoo building were closing at 8:00 P.M. and that the zoo itself would close at 8:30 P.M. We went to the ticket counter and asked if we could get a pass for the following day. The answer was "no." It is easy to see that Calgary is anything but friendly, but, rather, out to rake off tourists for all they can get." (Johnson & Blair, Logical Self-Defense, p. 70.)
Critique
"[W]e may expose a fallacy in generalization by proving: 1) That the relative size of the unobserved part of the class is so large as to discredit the generalization. 2) That the members observed are not fair examples of the class. 3) That there are exceptions to the general rule or statement. 4) That it is highly improbably that such a general rule or satement is true." (Foster, Argumentation and Debating, 1908, p. 146.) Note: in some cases, a formal proof would require a mathematical calculation. This is the subject of probability theory. More often, common sense should suffice.

Hasty Generalization versus Secundum Quid

"Traditionally, [secundum quid] has been the term used for all Hasty Generalizations, but modern treatments have drawn the distinction between the hasty inductions of the last section and the failure to accomodate relevant exceptions. It is the latter that interests us here. Secundum quid means 'in a certain respect' and refers to qualification that may be attached to a generalization. What is the case in a certain respect may not hold generally. Sometimes a close association to an issue or perspective may blind us to reasonable exceptions to a general rule." (Tindale, Fallacies and Argument Appraisal, p. 154.)

Essential versus Accidental Properties

"The source of this fallacy's persuasive power is its resemblance to valid arguments in which individual cases do fall under a general rule. The point to remember is that a generalization is designed to apply only to individual cases that properly fall under it. It is not designed to apply to special cases. It is certainly valid to argue that, since all men are mortal, Socrates is mortal. But it would be incorrect to argue: 'Since horseback riding is healthful exercise, Mary Brown ought to do more of it because it will be good for her heart condition.' What is good for someone in normal health does not apply where special health problems exist. The fallacy of sweeping generalization is also referred to as the fallacy of accident, to emphasize the irregularity of particular cases to which generalizations do not apply." (Engel, Fallacies and Pitfalls of Language, p. 72.)

Anecdotal Evidence

"One typical form of hasty conclusion occurs when the arguer uses anecdotal evidence. Evidence is anecdotal, as contrasted with systematic, when it takes the form or recounting an experience, often in story form, of one person or a few people... There is a difference between using a story to illustrate a thesis in a premise that has already been established and using a story to prove a point. We refer to the latter situation when we allude to the dangers of anecdotal evidence." (Johnson & Blair, Logical Self-Defense, pp. 71-2.)
Comment
"The fallacy of hasty generalization needs to be understood not simply as a flaw or error in one type of reasoning, but as a kind of scalar fallacy where reasoning is pushed forward from one of five levels to another." (Walton, Argumentation Schemes for Presumptive Reasoning, p. 164.)
  1. Argument from Example: "This [one] F is a G." Here, one case is cited as an example of illustration of something that shares both properties F and G.
  2. Particular Claim: "Some F are G." This type of claim is not really a generalization (or much of one), because one instance is enough to verify it.
  3. Plausible (Defeasible) Generalization: "Typically, F are G." This type of claim is defeasible. It says that normally you can expect F to be G in a typical case, but an F may fail to be a G in an exceptional case.
  4. Inductive Generalization: "Most [many] F's are G's." This type of claim is based on data that is collectible and/or countable. "How many?" is a very important consideration. Where a specific number (normally expressed as a fraction between 0 and 1) is given, the claim is called a statistical generalization.
  5. Universal Generalization: "All F are G." This type of claim is falsified by any (even a single) counter-instance — any case of something that is F but not a G.
On the tendency to generalize too hastily...
"In spite of all the powers and advantages of generalization, men require no incitement to generalize; they are too apt to draw hasty and ill-considered inferences. As Francis Bacon said, our intellects want not wings, but rather weights of lead to moderate their course. The process is inevitable to the human mind; it begins with childhood and lasts through the second childhood. The child that has once been hurt fears the like result on all similar occasions, and can with difficulty be made to distinguish between case and case. It is caution and discrimination in the adoption of general conclusions that we chiefly have to learn, and the whole experience of life is one continued lesson to this effect. Baden Powell has excellently described this strong natural propensity to hasty inference, and the fondness of the human mind for tracing resemblances real or fanciful. 'Our first inductions,' he says, 'are always imperfect and inconclusive; we advance towards real evidence by successive approximations: and accordingly we find false generalization the besetting error of most first attempts at scientific research. The faculty to generalize accurately and philosophically requires large caution and long training; and is not fully attained, especially in reference to more general views, even by some who may properly claim the title of very accurate scientific observers in a more limited field. It is an intellectual habit which acquires immense and accumulating force from the contemplation of wider analogies. Hasty and superficial generalizations have always been the bane of science, and there would be no difficulty in finding endless illustrations. Between things which are the same in number there is a certain resemblance, namely in number, but in the infancy of science men could not be persuaded that there was not a deeper resemblance implied in that of number." (Jevons, The Principles of Science, 1874, pp. 278-9.)
On the amplified temptation to generalize for advocates...
"As Walton points out, a problem that arises with arguments based on generalization is that 'some people who are passionately committed to a viewpoint tend to overlook qualifications that are needed in a specific case.' Showing someone who holds to absolutes that exceptions may be warranted can be one of the more difficult tasks we take on as arguers." (Tindale, Fallacies and Argument Appraisal, p. 154.)
On the failure to account for negative instances...
" Another fallacy that can occur when you use argument by generalization is the failure to account for negative instances. Examples that do not conform to the general pattern cannot be ignored. If the evidence reveals that many pit bulls are violent and a few are not (i.e., there are negative instances), it would be invalid to conclude that all pit bulls are violent. It would, on the other hand, be valid to generalize by adding an appropriate qualifying term such as 'most' — 'most pit bull are violent.' To make a valid argument, you must qualify the inductive argument to account for any negative instances." (Waicukauski et al., The Winning Argument, pp. 50-1.)
On the general reliability of generalizing, so to speak.
"The received wisdom has it that hasty generalization is a fallacy, a sampling error of one sort or another. The received wisdom may be right, but if it is, individual human agency is fallacy-ridden in degrees that would startle even the traditional fallacy-theorist. Bearing on this question in ways that suggest an answer different from the traditional one is the fact that the individual's hasty generalization seem not to have served his cognitive and practical agendas all that badly. Upon reflection, in the actual cases in which a disposition towards hasty generalization plays itself out, the generalization are approximately accurate, rather than fallacious errors, and the decisions taken on their basis are approximately sound, rather than exercises in ineptitude. Not only is the individual agent a hasty generalizer, he is a hasty generalizer who tends to get things right." (Gabbay, Jurgen & Woods, Handbook of the Logic of Argument and Inference, p. 16.)
On the necessity of generalizing before one dies...
"At what point in time does the hasty generalization become the educated surmise? Were historians to wait until all the evidence was in before making a generalization, they would never write a word. As Edward Hallet Carr wrote in his What is History? historians who want to publish anything have to start writing before they have finished the research. ... All the evidence will never be in because all the evidence can never be in. ... Professional historians have developed methods to improve upon the largely unsupported surmise, but if they want to publish in their lifetimes, they have to make some generalizations that are, simply put, hasty. We pride ourselves on the thoroughness of our research. But the fact is that we jump to conclusions all the time. Sometimes they are inadequate, while on other occasions they are acceptable." (Hoffer, The Historians' Paradox, pp. 133-4.)