Incorrect Logical Reasoning

Logic can be a tricky thing.  Consider the following example from the ChangingMinds website:
Statement 1: All men are animals
Statement 2: Some animals are aggressive
Conclusion: Some men are aggressive
Seems perfectly reasonable at first glance, doesn't it?

Except it's not.  Here's the same reasoning, with one word changed:
Statement 1: All men are animals
Statement 2: Some animals are female
Conclusion: Some men are female
Which is clearly not true.  As the site explains,
The conclusion of the example falls into the traps of making the assumption that the 'aggressive animals' and 'men' subsets necessarily overlap, whereas there is no necessity for this in statements one and two. Although the conclusion could be true it does not have to be true.
As they suggest, drawing a Venn diagram can make things more clear:



In this case, the inner circles may or may not overlap, and we don't have enough information to make a definitive conclusion.

Statements like the first one here are often used by politicians and religious leaders to trick people into thinking that something is a fact, when really, it is completely unknown and/or unprovable.

Watch out for traps like this, and always think carefully when following the reasoning of others.

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