Sorting It All Out
Categorical logic is a branch of reasoning
that involves the sorting of people, places, things, events, or ideas
into various groups, with each group being identified in terms of some
characteristic common to all members of that group. With things
thus sorted, we can then identify and analyze areas of overlap and
relatedness (or lack thereof). For example, we categorize dogwoods
as plants, and dogs as animals. We further categorize both plants
and animals as living things. However, we also observe that there is
no overlap between plants and animals; they go about the living process in distinctly different
ways. Since anything that's an animal cannot be a plant, and vice
versa, we can conclude that no dog is a dogwood, and no dogwood is a
Categorical reasoning is extremely useful.
Indeed, we use it much of the time when we're in "figuring stuff out"
mode. For instance, an engine mechanic begins to diagnose a
problem by discerning whether the specific symptoms represent an
electrical, mechanical, or fuel fault. A quality-control inspector must
figure out whether a product flaw has resulted from materials,
production, engineering, or executive policy. A murder
investigator must consider opportunities, means, and motives to commit
the crime, and determine which of the suspects possessed all three.
But few of us take the time to consider exactly how and why the logic
works, and so we are probably not aware that the reasoning itself can
fail through misuse.
To study categorical logic, we'll make use of a
number of tools. First, we'll examine precisely what makes a
categorical argument work. Next, we'll adapt what we've already
learned about symbolic logic to deal with general and particular
quantitative concepts like all, no, and some.
Then, we'll see how various kinds of categorical statements are
interrelated. Finally, we'll take a graphic look at categories
using Venn diagrams.
Next: Categorical Syllogism