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).
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.
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.
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.
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.
Categorical syllogisms are named as such because they divide things up into categories. These form groups which can be analyzed using set theory and displayed using Venn diagrams.
There are six rules that categorical syllogisms must obey:
- All syllogisms must contain exactly three terms, each of which is used in the same sense.
- The middle term must be distributed in at least one premise.
- If a major or minor term is distributed in the conclusion, then it must be distributed in the premises.
- No syllogism can have two negative premises.
- If either premise is negative, the conclusion must be negative.
- No syllogism with a particular conclusion can have two universal premises.
When you hear people talking about syllogisms without describing what type of syllogism, they often mean categorical syllogisms.
Categorical syllogisms are sometimes viewed as being a ‘spatial reasoning’ as it divides the world up into ‘spaces’. This is creating a 3D image of the categories, or sets.
The basic flaw that often appears is the an assumption that if you have one characteristics of a group, you have all of the characteristics of the group. This leads people into stereotyping and comments such as ‘Oh, they are all like that.’
Whenever you hear a generalization (all, never, some, most, etc.) there is a good chance that there is a categorical syllogism in there that you can challenge.
On the other hand, you can create your own categorical syllogisms, which will often go unchallenged.