SYLLOGISTIC RULES AND SYLLOGISTIC FALLACIES

READ Copi/Cohen, pp. 261-264

8.2. THE FORMAL NATURE OF SYLLOGISTIC ARGUMENT

COMMENT: The purpose of this section is to introduce the concept of the formal nature of syllogistic argument. We will not do the Exercises for this section; however. it is essential that the concepts discussed here be fully understood.

1. [Copi/Cohen, 261] Is the following argument valid?

All martians are polygons.

All students are martians.

Therefore all students are polygons.

If you understood the point made in this section about the FORMAL nature of syllogistic argument, then you would know the answer--Yes, this argument is VALID. Is this argument SOUND? No, it is not. (I have been teaching over 30 years and I have seen very few students who are polygons and quite a few students who are not polygons, so it is false to say that "all students are polygons.")

You may have noticed that the students/martians/polygons argument uses terms which begin with the same letters as the sample argument in mood and figure AAA-1 at the top of 261. The two arguments on 261 are both of this form and both are valid--they are also sound. The "s/m/p" argument given above is FORMALLY the same as the examples on 261 (which is why the argument is valid), but of course the content is somewhat goofy, to say the least. Remember that syllogistic logic is concerned with analyzing the FORM of what we say and think, not the content.

2. [Copi/Cohen, 262] If you are very fast on your logical feet, you might be able to produce counter-arguments of the type described on this page, but as Copi/Cohen indicates, it is extremely difficult to produce such parallel arguments on the spur of the moment. There is another way to evaluate syllogistic arguments, slower perhaps, but much more reliable--in fact, it is foolproof, once its rules are mastered. That way is the subject of the next section.

8.3. VENN DIAGRAM TECHNIQUE

3. [Copi/Cohen, 264] The text presents a formal way of diagramming the two premises into a three-circle Venn diagram: The two circles on the top will be for the subject term (S--on left) of the conclusion and the predicate term (P--on right) of the conclusion. The bottom circle is for M, the middle term in the premises.

The method to show validity/invalidity is to diagram each of the premises onto the three-circle Venn diagram--BUT NOT THE CONCLUSION. The test for validity is to ask, after putting together the two premises= diagrams, whether the conclusion is already pictured in the three-cirle diagram--WITHOUT PUTTING IT THERE OURSELVES. IF WE SEE THE VENN DIAGRAM FOR THE CONCLUSION IN THE 3-CIRLE DIAGRAM FROM THE TWO PREMISES, THEN THE CATEGORIAL SYLLOGISM IS VALID. WHY? Because the conclusion is IMPLICIT in the premises and it can be made explicit validly.

MY SUGGESTION is that one first does three TWO-CIRCLE diagrams, one for each statement in the argument. One then copies ONLY the two diagrams for the two premises into the 3-circle diagram. Finally one checks the 2-circle diagram for the conclusion against the 3-circle diagram to see if the diagram for the conclusion is already in the 3-circle diagram. If so, the argument is valid; if not, invalid.

DO EXERCISES, pp. 272-273. In the first set you are just given the form (figure and mood) so you will need to write out the statements using S, P, and M for the major (P), minor (S) and middle (M) terms. Then do 3 separate 2-circle diagrams for the 3 statement. The major premise (All M is P) will need a 2-circle diagram with one circle marked M and the other marked P. The minor premise will need a diagram with one circle marked S and one M; and the conclusion, with S and P. When you next copy the major premise diagram (with two circles) into the three circle diagram, you need to match the terms--on the formal diagram on p. 272, you can see that the major premise, which we said had a two circle diagram with M and P, matches the two right circles (the bottom one being to the right of nothing!). The two minor premise circles are the two Aleft@ circles in the 3-circle diagram.

In the second set of exercises, mark your circles with the first letter of each term (rather than SPM). For example, #1 will have for the conclusion (identify this first--it follows Aso@) a two-circle diagram with I and F. The major term is F, so the major premise is ASome reformers are fanatics@ with a 2-circle diagram with R and F. The minor term is I, so the minor premise will have a 2-circle diagram with I and R.

TWO CIRCLE DIAGRAMS: Major premise: an x in the overlap of R & F.

Minor premise: shading (for empty) the part of R outside I.

When we put these two into the 3-circle diagram, which has I on the left top, F on the right top and R on the bottom, we will always do the universal premise first. So the minor premise put into the 3-circle diagram will have the part of R outside of I shaded, which will include part of the RF overlap that is outside of I (there is still an unshaded part of the RF overlap inside of I). Then we put in the diagram of the major premise, placing an x in the remaining open (unshaded) section of the RF overlap. Next we ask: does the conclusion diagram show in the 3-circle diagram at this point (WITHOUT PUTTING THE CONCLUSION=S 2-CIRCLE DIAGRAM INTO THE 3-CIRCLE DIAGRAM, IN WHICH CASE YOU WOULD ALWAYS FIND IT! AND ALL ARGUMENTS WOULD BE VALID!)

The 2-circle diagram of the conclusion shows an x in the overlap of I & F. We also find an x in the overlap of I& F in the 3-circle diagram from the two premises--it is in the subsection of the IF overlap that is still in R. THEREFORE, the argument is valid.