Modus Ponens, Modus Tollens

القياس الاستثنائي

If I say: ‘‘whenever I pray, I‘m happy’ and one day I didn’t pray, can I say I was not happy that day?

Logically speaking, No.

Welcome to القياس الاستثنائي or repetitive syllogism.

So, when I say: ‘‘whenever I pray, I‘m happy.’, it only proves that my praying makes me happy, it doesn't prove that if I don't pray, I feel sad. It works one way only. وجودا not عدما. In reality, it may or may not be true that I left pray and felt bad, however, it will be a coincidence as it doesn't necessarily make a valid conclusion. To prove that skipping prayer makes me unhappy, I have to make another statement : Every time I don't pray, I feel bad.

Let’s go back to the original statement and see how many conclusions we can draw from them. Turns out, there are only 4 ways:

Get H. Afridi’s stories in your inbox

Join Medium for free to get updates from this writer.

Remember me for faster sign in

(> means conclusion)

1. ‘whenever I pray, I‘m happy’. And I prayed this morning’> I’m happy.
2. ‘whenever I pray, I‘m happy’ And I didn't pray this morning’> undecided
3. ‘whenever I pray, I‘m happy’ And I’m happy’ >undecided
4. ‘whenever I pray, I‘m happy’ And I’m not happy’ > I haven’t prayed.

Notice that only the first and last are valid conclusions that I can bet on. The rest are undecided. The second one is undecided bcs I never claimed that I am NOT happy when I skip prayer. Third is undecided because there could be other reasons for being happy besides prayer. So if there are only two valid conclusions in a conditional claim like this, what are they called and how are they written? The first is Modus Ponens. The last is Modus Tollens.

Here’s how they may be written in shorthand:

(Remember A: I pray | B: I’m happy)

1. if A > B. However, A. Conclusion: B (Modus Ponens)
2. if A > B. However, not B. Conclusion: not A (Modus Tollens)

Now, Imagine I want to be brief and need one sentence to convey the meaning of these two sentences: I’m happy when I pray and I'm not happy when I don't. I say: I’m not happy unless when I pray. This is very strong and then we can say:

I’m not happy unless when I pray. And I didn’t pray this morning’ >I'm not happy. So we have the conclusion. it is no longer undecided.

You must have noticed that Quran and Hadith usually uses this structure : ‘no, except/unless’ to make it stronger.

Taufeeq!