by TCA Srinivasa Raghavan
When the ebullient editor of this section in her usual cheerful way asked me if I would like to write anything for the International Women’s Day, I asked if something on formal logic would do.
What, she asked suspiciously.
Would you mind if I dealt with a propositional fallacy, I said.
What are you babbling about, she asked again.
So I explained it as follows.
We tend, I said, to make jumps in reasoning.
As for example when we say:
1. If today is Tuesday, I will write my column.
2. Today is Tuesday.
3. Therefore, I will write my column.
Or in a more generalised way:
1. If P, then Q.
2. Q.
3. Therefore P.
Truth is, I told her, the conclusion can be false even when the premises are correct. This is because we tend to confuse between what is necessary and what is sufficient.
For instance, it was never said that being a Tuesday is the only condition for writing a column. One must have the time, for one thing; a topic for another. And so on.
So what’s all this got to do with women, she asked belligerently.
In for a penny, in for a pound, so I soldiered on.
This is what it means, I said:
1. If wife, then woman
2. Womanhood.
3. Therefore wife=womanhood.
1 and 2 are both true, I said, but 3 does not follow automatically from them.
By now I had got her sufficiently riled and curious.
Please explain, she growled.
You see, the problem is one of overlaps.
A wife always a woman but that does not mean she always exhibits the characteristics of a woman: caring, gentle, sympathetic and so on.
In factthe moment a woman becomes a wife she loses most of these attributes of womanhood.
Fuzzy sets
It’s got to do with fuzzy sets, I droned on.
In set theory, these are sets whose elements don’t clearly belong to any one set. This is in contrast to normal or classical set theory where they either belong or do not belong to a set.
Before she could ask me to get out, I put forth another concept, Category Theory.
I am not very clear myself about it but what I do know is that it describes groups and the connections between them. You have something called a groupoid, in which everything is invertible.
You know, wife and woman being used interchangeably?
Are you suggesting I am not a woman, she asked.
Indeed you are, I said, but to everyone except your husband.
To him, darling,you are a bloody wife.
