Q&A for How to Understand Syllogisms

If A=B and B=C then A=C. This works fairly well though sometimes the order is mixed up. To use one of their examples "All birds are animals. Turkey vultures are birds. Turkey vultures are animals." birds=A animals=B turkey vultures=C. So if A=B and C=A then C=B

"A" means universal affirmative, "E" means universal negative, "I" means particular affirmative and "O" means particular negative.

Nope. A syllogism has three parts, including a conclusion. These two statements might be considered two premises. If a conclusion was added, such as "Some mammals are engineers.", the three statement would together make a syllogism.

The third statement (the conclusion) would be false if either of the arguments used for it were false, or if the arguments do not necessarily imply the conclusion.

Though this form of logistics isn't used nearly as much as fallacies (ad hominem, tu quoque, ad baculum, ad populum, etc.), it can pretty much be summed up as "common sense," which is a general indicator of intelligence. For example, knowing that all men are mortal (major premise) and that Socrates is a man (minor premise), we may validly conclude that Socrates is mortal. Syllogistic arguments are usually represented in a three-line form: all men are mortal; Socrates is a man; therefore, Socrates is mortal.

The third statement is not necessarily true, because that series of statements does not form a syllogism. Here is an example of a syllogism. All humans love dogs. John is a human. John loves dogs.

If in two syllogisms the middle terms are the same, or of the same category, then their figures are the same.

This is an invalid syllogism, whilst the two premises are valid, they do not necessarily imply the conclusion. Elephants being a member of a larger group, of which some members are white, does not necessarily imply that any elephants are white.