Making Logic Practical

Verbs other that "to be"

"All dogs bark" does not have the verb as to be. But we can change it to "All dogs are barking animals." What about "Some cats howl at night." Would be translated to "Some cats are animals that howl at night.

Aristotle's classic argument

All humans are mortal. Socrates is human. Therefore, Socrates is mortal. This would be translated into a standard form categorical syllogism as: All humans are mortalS. All "Socrateses" are humanS. Therefore, all "Socrateses" are mortalS.

Can logic prove anything?

Clinton is an ex-president. Reagan is an ex-president. Therefore, Reagan is Clinton. Translated into a standard form categorical syllogism would be "All Clintons are ex-presidents. All Reagans are ex-presidents. Therefore, all Reagans are Clintons. This breaks rule 2, which proves it is invalid and you cannot prove everything.

Logic and computers

Computers are often called logic machines. Does it have the human capacity for creativity, intuition and pattern recognition? One contemporary skeptic of computers becoming "like us" is Professor Hubert Dreyfus from UC-Berkeley. He has written "Mind over Machine" and "What Computers Still can't do: A Critique of Artificial Reason."

Using context to translate ordinary language

Ex: A dog is an animal. Clearly this means that all dogs are animals. "A dog is barking outside" refers to one dog. So we translate it to "Some dogs are animals that are barking outside."

Translating ordinary language into universal propositions

Ex: All dogs are animals can be translated to: Dogs are all animals, Dogs are animals, A dog is an animal, Any dogs is an animal, etc. These are all considered A propositions. E proposition No dogs are cats can be translated into No dog is a cat, Every dog is not a cat.

a typical argument

Ex: Athletes are strong, because people who exercise are strong and all jocks work out." Athletes are strong is the conclusion. We can translate it into "All athletes are strong people. The major term in our argument is "strong people," since it is the predicate term in our conclusion. The major premiss is "people who exercise are strong," since it contains the major term. We can translate the major premiss as "All people who exercise are strong people." The minor term in our argument is "athletes" since it is the subject term in our conclusion. The minor premiss is "All jocks work out." Jocks and athletes are synonyms and so are work out and exercise. The minor premiss becomes "All athletes are people who exercise."

Translating ordinary language into particular propositions

I proposition: Some dogs are brown animals. Can be translated into Lots of dogs are brown, Many dogs are brown, there are brown dogs. O proposition ex: Some dogs are not brown. Can be translated into Lots of dogs are not brown, Many dogs are not brown, etc.

ordinary language into standard form categorical syllogism

People who exercise are strong. All jocks work out. Athletes are strong. All people who exercise are strong people. All athletes are people who exercise. All athletes are strong people.

Translating singular propositions

Socrates is human is a singular proposition. We consider this as a statement about the "unit class" of all those who are 5th century B.C. Athenian philosopher Socrates. There is only one member of this class named Socrates. So Socrates is human becomes "All Socrateses are humans." Another example: "This book is interesting" would become "All this-books are interesting things."