## Logic

Statue of Aristotle

What makes logic important when studying Aristotle are two reasons. First of all, Aristotle essentially invented logic as we know it. Secondly, the deductive logical method which he came up with was applied to everything he did, and this comprehensive method of study is one of the reasons he was such a successful philosopher. At the end of one of his works on logic, Aristotle writes:

Of what we still have of Aristotle’s works, the two treatises of Aristotle on logic are the

All snakes are reptiles.

All reptiles are cold-blooded.

Therefore, all snakes are cold-blooded.

This would be considered a valid inference, because each of the two statements is true, and the “therefore” statement is true, and can also be derived from the other two statements. When using variables, this statement would be:

All A’s are B’s.

All B’s are C’s.

Therefore, all A’s are C’s.

If the first two statements are true, then the inference will always be correct.

---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

A inference may be wrong for one of two reasons. Either, one or more of the initial statements may be false, or there may be a false inference from two correct statements.

All humans are animals.

Some animals are birds.

Therefore, some humans are birds.

This would be an example of a false inference, because although the first two statements are true, the inference that comes from them is not an accurate statement. This means that, although the statements and inference may end up true, it doesn't always work so following setup is not good:

All A's are B's.

Some B's are C's.

Therefore, some A's are C's.

---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

Some humans are birds.

All birds have feathers.

Therefore, some humans have feathers.

In this case, the inference is correctly obtained from the statements, but as one of the statements is false, the inference is wrong. Otherwise this setup would work:

Some A's are B's.

All B's are C's.

Therefore, some A's are C's.

---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

Although Aristotle made enormous progress in the study of logic and it went unrivaled for long periods of time afterwards, it only covers the basics of what we know as logic today, and is inferior to modern deductive systems. Aristotle never dealt with sentences that didn't use "all," "no," and "some," such as "if, then" statements, and also didn't consider statements that had "all" "no" and "some," albeit not at the beginning. As Anthony Kenny writes about Aristotle's system of logic in his book,

*In the case of rhetoric there were many old writings on which to draw upon, but in the case of logic we had absolutely nothing at all to mention until we had spent much time in laborious research.*Of what we still have of Aristotle’s works, the two treatises of Aristotle on logic are the

*Prior Analytics*and the*Posterior Analytics*. The*Prior Analytics*deals with sets of statements that use letters as undefined variables in order to see whether a deduction from a certain set of statements is valid or not, while the*Posterior Analytics*applies this logical method to the sciences. Geometricians, especially Euclid, applied similar deductive methods to axioms to prove mathematical theorems. In his books, however, Aristotle essentially discusses what can be inferred from a certain set of truths. Using words such as “all,” “no,” and “some,” he made inferences from the true statements. For example:All snakes are reptiles.

All reptiles are cold-blooded.

Therefore, all snakes are cold-blooded.

This would be considered a valid inference, because each of the two statements is true, and the “therefore” statement is true, and can also be derived from the other two statements. When using variables, this statement would be:

All A’s are B’s.

All B’s are C’s.

Therefore, all A’s are C’s.

If the first two statements are true, then the inference will always be correct.

---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

A inference may be wrong for one of two reasons. Either, one or more of the initial statements may be false, or there may be a false inference from two correct statements.

All humans are animals.

Some animals are birds.

Therefore, some humans are birds.

This would be an example of a false inference, because although the first two statements are true, the inference that comes from them is not an accurate statement. This means that, although the statements and inference may end up true, it doesn't always work so following setup is not good:

All A's are B's.

Some B's are C's.

Therefore, some A's are C's.

---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

Some humans are birds.

All birds have feathers.

Therefore, some humans have feathers.

In this case, the inference is correctly obtained from the statements, but as one of the statements is false, the inference is wrong. Otherwise this setup would work:

Some A's are B's.

All B's are C's.

Therefore, some A's are C's.

---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

Although Aristotle made enormous progress in the study of logic and it went unrivaled for long periods of time afterwards, it only covers the basics of what we know as logic today, and is inferior to modern deductive systems. Aristotle never dealt with sentences that didn't use "all," "no," and "some," such as "if, then" statements, and also didn't consider statements that had "all" "no" and "some," albeit not at the beginning. As Anthony Kenny writes about Aristotle's system of logic in his book,

*An Illustrated Brief History of Western Philosophy*, "The rules would not permit one to determine, for instance, the validity of inferences containing premises such as 'every schoolchild knows some dates' or 'some people hate all policemen'. It was not until twenty-two centuries after Aristotle's death that this gap was filled."