Hasty Generalization to an Inverse

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© 2011-2019 by Zack Smith. All rights reserved.

Hasty Generalization to an Inverse

An argument is constructed where because P implies Q, it is just assumed that therefore NOT P implies NOT Q as well.

  • Proposition P implies Proposition Q.
  • Therefore it is wrongly assumed that NOT P implies NOT Q. ]]


We cannot find skilled people to hire therefore skilled people are not available. This type of fallacy may be expressed from the outset in the NOT P therefore NOT Q form.

  • P = We can find skilled people.
  • Q = There are enough available.

This is a commonplace form of the fallacy, usually meaning the arguer wants to fixate on a narrow cause of not finding, when in reality it may be that:

  • They are not considering older workers.
  • They are not considering workers who are citizens (they prefer foreigners).
  • They are not considering workers who will work only 40 hours.

Let P be infection; Q is disease. An arguer might try to claim that because P implies Q, it is also the case that NOT P (lack of infection) implies NOT Q (lack of disease). If there is no infection I do not have any disease. This is a narrow view. P can be false and yet Q is still true, for example a person can have a disease without an infection ever having caused it, such as because of:

  • Smoking
  • Obesity
  • Cancer
  • Genetics
  • Chemical exposure

If am using software with bugs (P) I will observe computer malfunctions (Q). Here the NOT P therefore NOT Q form assures the arguer that if his software has no bugs he will not observe any problem. This is a narrow view. A computer can malfunction for many reasons, of which software bugs are but one. Other causes include:

  • Mistakes by the user
  • Hardware failure of the computer
  • Hardware failure of a connected device
  • Virus or trojan horse infection
  • Internet connection problems
  • Cosmic rays causing memory errors

If the candidate did not win the election (NOT Q), that's because voters did not like the candidate (NOT P). But in reality elections are also lost because of

  • Rigging of election machines (especially electronic voting machines)
  • Rigging of the vote-counting process
  • Ballot stuffing
  • Vote buying
  • Redistricting
  • Voter suppression and intimidation


The arguer is ignoring the possibility that many things besides NOT P that can imply NOT Q. The two examples above provide specific weaknesses.

Typically the arguer is exhibiting:

  • Naivete: He believes the simplistic claims of experts or non-experts saying that only X causes Y.
  • Lack of creative thinking: He can only imagine certain causes.
  • Eagerness to blame: A specific cause or person or group of people regardless of contrary evidence.