Chapter 12, page 254
You have probably encountered syllogistic reasoning without actually having realized so. Many logic puzzles are based upon the syllogism. For instance:
- Premise 1: All dogs are mammals
- Premise 2: All mammals are animals
- Conclusion: All dogs are animals
Have a look at the following logic puzzles and decide whether or not the conclusion is valid or invalid: in other words, whether it follows logically from the two premises without the need for any further information.
- If today is Tuesday, then I have a criminal law seminar. If I have a criminal law seminar, then I will pack Smith and Hogan in my bag. Therefore, if today is Tuesday, I will pack Smith and Hogan in my bag.
This is a valid and believable syllogism. The conclusion follows logically from the two premises without any need for further information.
- All mice in England eat sunflower seeds. Some rodents eat sunflower seeds. Therefore, some rodents are mice in England.
Although this seems believable, it is not a valid syllogism. It assumes the piece of information that all mice are rodents. If the second premise was ‘some horses eat sunflower seeds’ it would obviously not follow that ‘some horses are mice in England’.
- All lawyers are highly intelligent. Some lawyers are not polite. Therefore, no polite people are highly intelligent.
This syllogism is both invalid and unbelievable. It would follow that some highly intelligent people are not polite, but not the converse: that it is not possible to be both highly intelligent and polite.