Question

Categorical syllogisms examples

Answer 1

Description The basic form of the categorical syllogism is: If A is part of C then B is a part of C. (A and B are members of C). Major premise The major premise (the first statement) is a general statement of the form 'All/none/some A are B', for example: All men are mortal. This statement is not challenged and is assumed to be true. Minor premise The minor premise (the second statement) is also a statement about inclusion and is also assumed to be true. It is usually a specific statement, for example: Socrates is a man. It may also be a general statement with a reduced scope. Thus, for example, when the major premise takes the format of 'all', the minor premise may be 'some'. The minor premise is also assumed to be true. Conclusion The conclusion is a third statement, based on a combination of the major and minor premise. Socrates is mortal. From the truth of the first two statements, a truth is created in this third statement. The trouble is that this 'truth' is not always true -- yet it often appears to be quite a logical conclusion. Example This is a logically valid statement: All New Yorkers are happy Some people live in New York Some people are happy This is because and unspoken fourth fact: that a portion of New Yorkers are people (there are also dogs and cats there who may be considered New Yorkers!). Here is another one that seems quite reasonable: All dogs have four legs. All animals have four legs. All dogs are animals. Note how this is potentially invalid because all dogs and all animals are both members of the set of things with four legs. The following syllogism has exactly the same structure: All dogs have four legs. All chairs have four legs. All dogs are chairs.