Premises are supposed to provide reason to believe conclusions. Under what circumstances do premises succeed in doing this? How do we distinguish good from bad arguments?
An argument is deductive if and only if its premises are intended to provide “an inescapable absolutely foolproof guarantee of the truth” (Rescher 1964, 57) of the conclusion. An argument is inductive if and only if its premises attempt to provide good but less than conclusive evidence for the conclusion.
Example deductive argument: The shirt is blue all over. ∴ The shirt is not red all over. Example inductive argument: The postman has always come by at 2pm before. ∵ The postman will come by at 2pm today.
The symbol ‘∴’ signals a deductive inference. The symbol ‘∵’ signals an inductive inference.
Deductive or Inductive? The plaque on the leaning tower of Pisa says that Galileo performed experiments there. Therefore, Galileo did indeed perform experiments there. There were pry marks around the lock on the rear door. There were deposits of mud near the rear threshold. Therefore, the burglar entered through the rear door. If global warming is not arrested, then hurricanes will become more intense. Global warming will not be arrested. Therefore, hurricanes will become more intense.
A deductive argument is valid if and only if its premises succeed in providing incontrovertible reason to believe the conclusion. A deductive argument is invalid if and only if it is not valid.
How can we tell whether an argument is valid or invalid? If an argument is invalid, then there is a conceivable scenario in which the premises are all true and the conclusion is false. If there is no such scenario, then the argument is valid.
Valid or invalid? If Socrates was a philosopher, then he wasn’t a historian. Socrates wasn’t a historian. ∴ Socrates was a philosopher. All men are mortal. Socrates is a man. ∴ Socrates is mortal.
Valid or invalid? If Col. Mustard is the murderer, then the murder weapon is the wrench. The murder weapon is not the wrench. ∴ Col. Mustard is not the murderer. Every plant has nine toes. President Obama is a plant. ∴ President Obama has nine toes.