10 Apr 2010
03 Oct 2013

Categorical Logic


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 dog.

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.

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