Fallacies of Immediate Inference:
Fallacies of immediate inference occur when the rules of different types of immediate inference are violated. One such fallacy is the fallacy of illicit conversion. This fallacy occurs when we make a simple conversion of an A-proposition.
The argument “All cats are mammals. Therefore, all mammals are cats” is fallacious. The term ‘mammal’ is distributed in the conclusion without being distributed in the premises. This fallacy is also committed when we convert an O- proposition.
Consider the following argument. “Some females are not aunts. Therefore, some aunts are not females.” In this argument the term ‘female’ is not distributed in the premise, but it is distributed in the conclusion. It can easily be noticed that in each of the above arguments, even though the premise is true, the conclusion is false.
Contraposition of I-proposition is also fallacious. Fallacies may occur when the rules of immediate inference based on the traditional square of opposition of propositions are violated. For example, in case of contrary relation from the falsity of one of the contraries we cannot infer the truth of the other.
So also in sub contrary relation from the truth of one the falsity of the other cannot be inferred. Violation of rules of inference in case of sub alternation and contradictory relations also lead to formal fallacies.
Mediate Deductive Fallacies:
Categorical syllogisms are the foremost forms of mediate deductive arguments. When any of the rules of categorical syllogistic argument is violated a fallacy is committed.
Fallacy of Four Terms:
A valid categorical syllogism, by definition, must have exactly three terms. An argument commits the fallacy of four terms, if it purports to be a valid categorical syllogism, but has four or more terms. So a purported categorical syllogism that contains more that three terms commits this fallacy.
The following argument commits the fallacy of four terms:
All men who write books are authors.
All educated men could write books.
Therefore, all educated men are authors.
Here the middle term is changed from actual writing of books to having the potentiality to write books. One who actually writes books is an author and one who does not write any book is not an author even if he or she has the potentiality to write books.
Sometimes a term is used in two different senses in an argument. In such a case we can say that the fallacy of equivocation is committed. We shall discuss this fallacy under the list of informal fallacies.
In a categorical syllogism the middle term must be distributed at least once in order to establish the relation between the major and minor terms in the conclusion. If the middle term is not distributed in at least one of the premises, there arises the fallacy of undistributed middle. This fallacy is committed in the following argument:
All dogs are mammals.
All cats are mammals.
Therefore, all cats are dogs.
Illicit Major and Illicit Minor:
If the major term or the minor term is distributed in the conclusion without being distributed in the respective premise the argument becomes fallacious. The following argument commits the fallacy of illicit major.
All dogs are mammals.
No cats are dogs.
Therefore, no cats are mammals.
The fallacy of illicit minor arises in the following example.
All voters are adults.
All voters are citizens.
Therefore, all citizens are adults.
Affirmative Conclusion from a Negative Premise:
In a categorical syllogism if one premise is negative the conclusion will be negative. So deriving an affirmative conclusion from a negative premise is fallacious. This fallacy is committed in the following argument.
All judges are educated.
Some lawyers are not judges.
Therefore, some lawyers are educated.
Any form of categorical syllogism with two negative premises commits this fallacy. The following argument illustrates this fallacy.
No birds are mammals.
No dogs are birds.
Therefore, no dogs are mammals.
In addition to these fallacies of categorical syllogism, one should guard oneself against two other common fallacies that might affect deductive arguments. These are the fallacies of affirming the consequent and denying the antecedent.
Fallacy of Affirming the Consequent:
In a deductive argument by affirming the consequent of a conditional or implicative proposition one cannot affirm or deny its antecedent. So any deductive
If A then B
The following argument commits this fallacy.
If Hari is in Kolkata, then he is in West Bengal.
Hari is in West Bengal.
Therefore, Hari is in Kolkata.
This argument is invalid. It can easily be imagined that even though the premises are true, the conclusion could be false. Hari might be in Malda.
Fallacy of Denying the Antecedent:
The fallacy consists in proceeding to argue by denying the antecedent of a conditional proposition. By denying the antecedent of a conditional proposition one cannot proceed to deny the consequent. So any argument of the following form is invalid:
If A then B
Therefore, not B
The following argument is invalid and it commits the fallacy of denying the antecedent.
If Asok is in Kolkata then he is in West Bengal.
Asok is not in Kolkata.
Therefore, Asok is not in West Bengal.
It can be notices that even though the premises are true, the conclusion might be false. Asok could be in Malda or any where in West Bengal other than Kolkata, which would make the premises true but the conclusion false.