So far we have been dealing with categorical arguments but there are other forms of arguments which are not categorical. Because, they have less or more propositions than the standard form categorical arguments. They include;
- The hypothetical syllogism
- The disjunctive syllogism
An enthymeme is a valid syllogism with one of the premises or conclusion suppressed.
There are basically three kinds of enthymeme depending on the part of the argument suppressed
- The first order enthymeme: this is one in which the major premise is omitted such that the only the minor premise and conclusion are stated
- The second order enthymeme: this is one in which the minor premise is omitted such that only the major premise and the conclusion are stated.
- The third order enthymeme: this is one in which the conclusion is suppressed in such a way that only the major premise and the minor premise are visible.
Schematically, the three orders of enthymeme can be summarized as follows
|enthymeme||major premise||Minor premise||Conclusion|
Expressing syllogism into their enthymematic order
To express a syllogism as an enthymeme of the first order, write the conclusion first then link it to the minor premise using “since or because” there by omitting the major premise. For the second order, do the same but just that you instead omit the minor premise.
To write the enthymeme of the third order, write the major premise first and then link it the minor premise using “and” there by omitting the conclusion.
All carnivores are animals
All lions are carnivores
Therefore all lions are animals
First order: all lions are animals since all lions are carnivores
Second order: all lions are animals because all carnivores are animas
Third order: all carnivores are animals and all lions are carnivores
- HYPOTHETICAL SYLLOGISM
This is one in which all the propositions are hypothetical or the major premise is hypothetical. There are two forms of hypothetical syllogism; the pure and the mixed hypothetical syllogism
- Pure hypothetical syllogism
This is a hypothetical syllogism whose propositions or premises are all hypothetical
If Shekinah works hard, she would pass her exam.
If she passes her exam, she would go to Europe.
Therefore if Shekinah works hard, she would go to Europe.
Valid form of hypothetical syllogism
For a hypothetical syllogism to be valid, the component parts of the premises should be related to the component parts of the conclusion.
- e. The antecedent of the major premise and the antecedent of the conclusion should be the same
- The consequence of the minor and that of the conclusion should be the same
- The consequence of the major premise should be the same as the antecedent of the major.
EXAMPLE: see example above
- The mixed hypothetical syllogism
This is a syllogism whose major premise is hypothetical while the minor premise and conclusion are categorical.
There are two forms of hypothetical syllogism: namely the modus ponens and the modus tollens
- Modus ponens
The word “ponens” comes from the Latin word “ponere” which means “affirm”. So the modus ponens means I affirm. It is therefore a syllogism whose minor premise affirms the antecedent of the major and the conclusion affirms the consequence of the major
Form of the valid modus ponens
If A is B then A is C OR if A is B then C is D
A is B A is B
Therefore A is C then C is D
If man is a free being then he is master of his destiny
Man is a free being
Therefore he is master of his own destiny
- Modus tollens
In an invalid modus tollens minor premise denies the antecedent of the hypothetical major premise while the conclusion denies the consequence of the hypothetical major premise.
If A is B, then C is D OR if A is B then A is C
A is not B A is not B
Therefore C is not D therefore A is not C
If Denuel is an engineer, then he can manufacture computers
Denuel is not an engineer
Therefore he cannot manufacture computers