Prior Analytics by Aristotle: Summary & Interpretation

Instructor: Michelle Penn

Michelle has a J.D. and is getting her PhD in history.

In ''Prior Analytics'', Aristotle outlines three different figures of syllogisms, which have been very important for the study of logic. In this lesson we will learn about the three different figures and look at examples of each type.

Aristotle and Today

Mathematician George Boole, whose work is given credit for our modern information age
George Boole picture

Greek philosopher Aristotle wrote Prior Analytics around 350 B.C. It is hard to imagine that his writings could be that relevant today. But what if I told you that Prior Analytics had helped to create our modern information age, including all the advances the internet has brought? It's true, Prior Analytics especially influenced George Boole, who used Aristotle's logic in Prior Analytics to create what is called Boolean Algebra. Boolean Algebra was used to develop electronics and create modern programming languages. Perhaps, like George Boole, you will find that Aristotle's writings have previously unrealized applications!



In Prior Analytics, Aristotle makes his argument using syllogism. A syllogism is a logical argument made up of three parts- two premises and one conclusion.

Aristotle says that a premise is 'something affirming or denying one thing or another.' Aristotle called the first premise major premise and the second premise the minor premise. So for example, if A=B and B=C, then A=C, Aristotle would call A=B the major premise, B=C the minor premise, and A=C the conclusion.

Because writing out different examples call take up a lot of spaces, scholars have developed formulas to write about Aristotle's syllogisms. The letter 'a' is used to symbolize all, for example if we wanted to say 'All humans are animals' in code, we could write AaB.

The capital A represents humans, the capital B animals, and the lowercase a represents that all humans are animals.

To represent 'no', scholars use the letter 'e'. So to represent 'no humans are horses' we could write AeB.

'Some' is represented by 'i'. So to write 'some humans are kind,' we would write AiB.

Finally, 'o' represents 'some are not'. So to write 'some humans are not kind', we would represent that with AoB.

Let's look at how these shortcuts are used to represent Aristotle's Prior Analytics.

The First Figure

Aristotle wrote that 'if A is predicated of every B and B of every C, it is necessary for A to be predicated of every C.' In other words, the general outline of the first figure is that A states something (making A the predicate) about B (making B the subject), and B (predicates) and C (subject), then A (predicate) and C (subject). So if all men are animals (AaB), and all animals are mortal (BaC), then all men are mortal (AaC).

The first figure has four types in total, they have been expressed in code:

AaB and BaC =AaC

AeB and BaC =AeC

AaB and BiC =AiC

AeB and BiC =AoC

As you can see, we can also make sentences with negatives and when somethings are true for some and not for others. For example, let's write out an example of the second type, AeB and BaC =AeC. One example of this could be: if no man is a bird, and all birds are swans, then no man is a swan. Can you try making your own examples for each the formulas of the first figure?

The Second Figure

Aristotle defines the second figure as 'Whenever the same thing belongs to all of one subject, and to none of another, or to all of each subject or to none of either.'

A simpler way of expressing the general form of the second figure is A (predicate) and B (subject), and A (predicate) and C (subject), then B (predicate) and C (subject).

The four variations of the second figure are written as follows:

AaB and AeC = BeC

AeB and AaC =BeC

AeB and AiC = BoC

AaB and AoC = BoC

Let's look at one example of the formula AaB and AeC = BeC : if all swans are birds, and if no swans are cardinals, then birds are not necessarily cardinals. Try writing a syllogism of your own using a type from the second figure.

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