b) Write an essay on the square of opposition.

The square of opposition is a chart that was introduced within classical (categorical) logic to represent the logical relationships holding between certain propositions in virtue of their form. The square, traditionally conceived, looks like this:

The four corners of this chart represent the four basic forms of propositions recognized in classical logic:

A propositions, or universal affirmatives take the form: All S are P.
E propositions, or universal negations take the form: No S are P.
I propositions, or particular affirmatives take the form: Some S are P.
O propositions, or particular negations take the form: Some S are not P.

Given the assumption made within classical (Aristotelian) categorical logic, that every category contains at least one member, the following relationships, depicted on the square, hold:

Firstly, A and O propositions are contradictory, as are E and I propositions. Propositions are contradictory when the truth of one implies the falsity of the other, and conversely. Here we see that the truth of a proposition of the form All S are P implies the falsity of the corresponding proposition of the form Some S are not P. For example, if the proposition “all industrialists are capitalists” (A) is true, ______ ____ ____ ____ __________ ___ ___.
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