A categorical syllogism is a simple argument that contains only three categorical propositions, of which the first two are called premises and the third is called the conclusion. Any valid categorical syllogism contains three terms, namely: major term, minor term, and middle term, and each of them must appear exactly but not in the same proposition.
Example 1:
All Filipinos are Asians.
All Cebuanos are Filipinos.
Therefore, all Cebuanos are Asians.
The major term is defined as the predicate of the conclusion. In the example above, the major term is “Asians” because it is the predicate term of the conclusion.
The minor term is the subject term of the conclusion. In the example above, the minor term is “Cebuanos”.
The middle term is the term that occurs in the premises but not in the conclusion. Hence, in the example above, the middle term is “Filipinos”.
In any standard form of a categorical syllogism, the premise that contains the major term must be stated first, which is then called the major premise, followed by the minor premise, which contains the minor term, and then the conclusion.
Going back to the example above, “All Filipinos are Asians” is the premise that contains the major term “Asians”. The proposition “All Cebuanos are Filipinos” is the premise that contains the minor term; hence, it is the minor premise. The conclusion which contains the minor and major terms must be stated last. In short, in a standard form of a categorical syllogism, the order of the premise should be:
However, not all arguments are stated in their standard form. In some cases, the standard order of the terms is not followed, so the structure is hard to determine. Also, it could happen that the basic structure is concealed in a long paragraph so that not only that the structure is difficult to determine but also the validity itself. Logicians solved this problem this way: though the argument is not arranged in a standard form, it is still possible to determine its structure through the clues given by the logical indicators.
Premise indicators: For, Granted that, As indicated by, Since, As shown by, The facts are, Because, For the reason that, Assuming that, Inasmuch as, In view of, and the like.
Conclusion Indicators: Therefore, Thus, Leads to the belief that, Hence, In conclusion, It may be deduced that, So, Proves that, Implies that, Consequently, It follows that, Entails that, For this reason, Indicate that, Then, It is evident that, It must be that, and the like.
Now, if the statement starts with any of the indicators (either premise or conclusion indicators), then it means that the statement that follows is a premise or a conclusion.
Exercises
- Some preachers are people of unfailing vigor. No preachers are non-
intellectuals. Therefore, some intellectuals are persons of unfailing vigor.
- Some metals are rare and costly substances, but no welder’s materials are non-metals. Hence, some welder’s materials are rare and costly substances.
- Some oriental nations are non-belligerents. Since all belligerents are allies either of the United States or of the Soviet Union, and some oriental nations are not allies either of the united states of Soviet Union.
- Some non-drinkers are athletes, because no drinkers are persons in perfect physical condition, and some people in perfect physical condition are not non-athletes.
- All things inflammable are unsafe things, so all things that are safe are non-explosives, since all explosives are flammable things.
- All worldly goods are changeable things, for no wordly goods are things immaterial, and no material things are unchangeable things.
- All those who are neither members nor guests of members are those who are excluded; therefore, no conformists are either members or guests of members, for all those who are included are conformists.
- All mortals are imperfect beings, and no humans are immortal, whence it follows that all perfect beings are non-humans.
- All things are non-irritants; therefore no irritants are invisible objects, because all visible objects are absent things.
- All useful things are objects no more than six feet long, since all difficult things to store are useless things, and no objects are six feet long are easy things to store.