There are some important topics that you should understand for deductive reasoning so that you are better equipped.
- Contradiction: An argument based on contradiction depends on the intersection of two terms. For example, you may say “Apples are red. This fruit is not red. Therefore, this fruit cannot be an apple”. This syllogism depends on a pair of contradictory terms; being red or not being red and being an apple or not being an apple.
- Contraries: Contraries are 2 terms that are opposites or that cannot be true. Proving that one of the terms is true is enough to disapprove the other. When establishing contraries, there are sometimes only two options. For instance, when coming to a fork in the road, you can either go to the left or the right. However, many times there are more than 2 possibilities. If there is a traffic light, it can be red, yellow, or green. Establishing that one of the terms is false is not enough to prove that the other is true. For example, saying “If the light is not red, so then it is green” would be wrong as there is the possibility it is yellow.
- Antecedent and Consequence: These arguments are based on the idea that if one thing happens then another follows. The relationship between terms is often at the center of a deductive argument. For example, a person discussing minimum wages in the government may say “If we raise wages, then we will have to levy new taxes to pay for them”. In this example, there is a concealed assumption, that being that the only way to pay for a new minimum wage is to levy taxes. While the syllogism is valid, you may question the truth of the initial premise by questioning an assumption.
- Cause and Effect: Cause-and-effect claims can be made about the future or the past. For example, you may say that your friend crashed because he did not change his tires. In this case, the premises are as follows:
Premise 1: If one does not change their tires, they might blow out and cause an accident
Premise 2: They got into an accident
Conclusion: They must have not changed their tires.
- However, beware! The syllogism above is invalid. The only way to prove the cause of an event in deductive reasoning is to rule out every possible cause. Therefore, the first premise would have to say that “the only way to get into an accident is by not having changed your tires”. Even though this claim would make the syllogism valid, it is false! It is very hard to make deductive arguments based on cause-and-effect claims, so most of these will be educated guesses.
One last thing before you leave! There are errors both of fact and of logic that can cause a syllogism to fall apart. These are called fallacies, and some may come across when you analyze deductive arguments or make some of your own, especially when your main premise does not apply to the case covered in the minor premise. Here are some fallacies that one may commit when making deductive claims:
- Equivocation: When you change your terms halfway through the syllogism, which is likely to happen when a word means two things or when two concepts are somewhat similar (ex. The new study shows that sleep is essential to good health, so you must take naps to be healthy)
- Either/or Fallacy: Involves insisting on a binary opposition of terms when there are multiple options (ex. Either you pay to help stray dogs or you are a bad person!).
- Faulty casual associations: When you assume without proof that an event was caused by one of multiple causes (ex. If a student cheats, they may pass the test. My friend passed the test, so they must have cheated).
For now, this is all I will share about deductive reasoning, I know it was a lot of information! In the next article post, I will talk about another major type of reasoning: inductive reasoning.