Arrangement of Middle Terms in Syllogisms

The Shirt Collar vs the Bow Tie Arrangement

On page 262 of the book entitled "A Concise Introduction to Logic" Copyright 2012 by Patrick J. Hurley provides a figure of a shirt collar or Oxford shirt collar which is used to display the four possible arrangement of middle terms in a syllogism. The Oxford collar is shown at the top of the figure, where the circles correspond to the middle terms, two for each line, and where the numbers correspond to the figure of a categorical syllogism. :

As described by Hurley, and borrowed from page 262, there are four figures as shown in Table I:

Table I
Figure 1	Figure 2	Figure 3	Figure 4
M P	P M	M P	P M
S M	S M	M S	M S
------	------	------	-----
S P	S P	S P	S P

As can be seen the middle M terms in the Figures correspond to the circles in the Oxford Shirt figure. Alternatively, if the left part of the figure is superimposed onto the right half, the bow tie arrangement is obtained. This arrangement of terms produces a much simpler figure that can be drawn in one step instead of two separate pieces. In addition, the Ms can be read as either 1, 2, 4, 3 or 1, 2, 3, 4. Also coincidentally, the bow tie fits perfectly well under the shirt collar as shown in the above figure.

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