Hypothetical Syllogism These are arguments of the form: If A then B. If B then C. Therefore, if A then C.
Constructive Dilemma. These are of the form: If A then B, and if C then D. Either A or C. Therefore, either B or D.
In other words, there’s a choice between two options—if you pick one or the other option, then either of the two effects will happen.
EXAMPLE of Hypothetical Syllogism: If Louie goes to the concert, he’ll miss the ball game. If Louie misses the ball game, he won’t get a chili dog. Therefore, if Louie goes to the concert, he won’t get a chili dog.
EXAMPLE of Constructive Dilemma:
If I go to Miami, I can get some vacation, but if I stay home I can visit with relatives. Either I’ll go to Miami or I’ll stay home. Therefore, either I’ll get some vacation or I’ll visit with relatives.
The argument is valid The premises are actually true .
To check soundness: First check for validity. If the premises were true, is the conclusion forced to be true (it couldn't be false)? If so, the argument is valid. Next check for the truth of the premises. If the premises really were true, the argument is sound .
However, if either condition is not met, then the argument is unsound .
An argument can be unsound if it is valid but doesn’t have true premises. It can be unsound if it has true premises, but is invalid. Or both. If either or both conditions are not met, the argument is unsound.
Predictions : In predictions, an argument is made about the future based on past or present evidence.
Arguments about the past based on present evidence (also known as retrodiction): In these arguments, an inference is drawn about what happened at some earlier point in time based on current evidence.
Cause and effect reasoning: Here it is claimed that an event (effect) is based on one or more causal factors. Given the existence, then, of the causal factor, the effect should follow.
Arguments based on analogy: This argument rests on a comparison, from which it is claimed that a characteristic true of the one term in the equation will also be true of the other. In law this usually involves the application of a precedent or legal principle.
Statistical reasoning: These arguments draw from sample studies or statistical reasoning, from which an inference is drawn about the targeted population.