8.5: Syllogisms

Syllogisms are an example of Deductive reasoning. Deductive reasoning derives specifics from what is already known. It was the preferred form of reasoning used by ancient rhetoricians like Aristotle to make logical arguments. A syllogism is an example of deductive reasoning that is commonly used when teaching logic. A syllogism is an example of deductive reasoning in which a conclusion is supported by major and minor premises. The conclusion of a valid argument can be deduced from the major and minor premises. A commonly used example of a syllogism is “All humans are mortal. Socrates is a human. Socrates is mortal.” In this case, the conclusion, “Socrates is mortal,” is derived from the major premise, “All humans are mortal,” and the minor premise, “Socrates is a human.” In some cases, the major and minor premises of a syllogism may be taken for granted as true. In the previous example, the major premise is presumed true because we have no knowledge of an immortal person to disprove the statement. The minor premise is presumed true because Socrates looks and acts like other individuals we know to be human. Detectives or scientists using such logic would want to test their conclusion. We could test our conclusion by stabbing Socrates to see if he dies, but since the logic of the syllogism is sound, it may be better to cut Socrates a break and deem the argument valid. Since most arguments are more sophisticated than the previous example, speakers need to support their premises with research and evidence to establish their validity before deducing their conclusion.

A syllogism can lead to incorrect conclusions if one of the premises isn’t true, as in the following example:

· All presidents have lived in the White House. (Major premise)

· George Washington was president. (Minor premise)

· George Washington lived in the White House. (Conclusion)

In the previous example, the major premise was untrue, since John Adams, our second president, was the first president to live in the White House. This causes the conclusion to be false. A syllogism can also exhibit faulty logic even if the premises are both true but are unrelated, as in the following example:

· Penguins are black and white. (Major premise)

· Some old television shows are black and white. (Minor premise)

· Some penguins are old television shows. (Conclusion)

Figure 17. Like in the game of Clue, real-life detectives use deductive reasoning to draw a conclusion about who committed a crime based on the known evidence. Sleepmyf – Lego detective – CC BY-NC-ND 2.0.