Disjunctive Syllogism
Disjunctive Syllogism includes ‘OR’, which means either the first or second or the third, or the nth. If even one of them is present, the argument shall be valid.
Two alternative arguments can be presented as follows.
- Either A or B
- Not A.
- Therefore, B
Similarly, a three-alternative argument can be as follows.
- Either A or B or C
- Not A
- Not B
- Therefore, C
An example of valid Disjunctive Syllogism is as follows.
- John is either in the office or at home
- John is not in the office
- Therefore, he is at home
The following argument is also valid.
- The college teacher must have either a Masters or a PhD
- The college teacher does not have a PhD
- Therefore, he has the Master’s degree
However, the following Disjunctive Syllogism can be valid or invalid.
- Either A or B
- A
- Therefore, Not B
The above argument is valid only if OR is exclusive, meaning there is nothing common between A and B. Accordingly, the following argument shall be invalid.
- The college teacher must have either a Masters or a PhD
- The college teacher has a master’s degree
- Therefore, he is NOT a PhD
The above argument fails since a PhD usually includes a Master’s degree. Hence, a above structure of a disjunctive syllogism is valid only when both alternatives are mutually exclusive.
The appropriate argument, which can be valid even in both the inclusive and exclusive cases, can be expressed as follows.
- Either A or B
- not-A
- Therefore, B
In some institutes, a Masters degree is not a requirement for a PhD. For instance, in India, you can enrol for the PhD directly after your BE or B Tech. However, the above structure of the argument is always valid. For example, if the teacher does not have a PhD, he must have a Master’s degree. However, if he does not have a Master’s degree (because a Master’s degree was not mandatory for a PhD), he will surely have a PhD.
