# The author uses the word "immediacy" (line 39) most likely in order to express

GAM on February 27, 2020

grammar of applying logic rules

I am having an issue understanding the rules due to the malleability of the english language. For example, the term "only if" is supposed to introduce a necessary condition. However, you could make a grammatically correct sentences which states that "only if there is smoke is there fire" AND "There is smoke only if there is fire". Grammatically and verbally these two statements mean the exact same thing, but according to the rules of logic presented they mean totally different things. I am having difficulty internalizing the rule when it does not work with the english language.

SamA on February 28, 2020

Hello @GAM,

I really like the example that you are using here. However, I would argue that these sentences do have a different meaning. Once you understand that, you will start to get the hang of conditional reasoning. I'll explain why your example actually proves the "only if" rule that you are talking about.

"Only if there is smoke there is fire."
I'll rephrase this: Fire needs smoke. There is no fire without smoke.
F - - - - - -> S
no S - - - - - > no F

Can smoke exist without fire? Yes. There is nothing in this sentence to suggest that smoke needs fire. The necessary condition can exist without the sufficient condition, but not the other way around. This is why fire is sufficient and smoke is necessary.

"There is smoke only if there is fire."
In this case, smoke needs fire. There is no smoke without fire. Do you see how this is the opposite of the first sentence? "Only if" introduces fire, and fire is necessary for smoke.
S - - - - - - -> F
no F - - - - - - > no S

Can fire exist without smoke? Yes it can. Your sentence does not prohibit that. "Only if" has once again introduced the necessary condition.

Here is a third example that might clear things up. You will sometimes come across "if and only if." In this case, each condition is both sufficient and necessary.

"There is smoke if and only if there is fire." We represent it with a double arrow.
S < - - - - - - > F
no S < - - - - - - - > no F

This is like combining your two other sentences.
Fire needs smoke.
Smoke needs fire.

I am guessing that this is what you were thinking of when you said that those two sentences have the same meaning. However, each sentence was only half of this reasoning.
1. F - - - - -> S
2. S - - - - -> F
Combined, we get: S < - - - - -> F