Propositional Logic: A only if B

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This video shows how to evaluate conditional statements of the form "A only if B"

[@radhiaismael2714]

Thank you! I needed this clarification of what is the antecedant in 'only if' statements!

[@DontReadThisAgain]

I was struggling a bit with "Only if", thank you for clearing that up

[@AudiaLucus]

Very well explained to a problem that has been bugging me for some time

[@kojirouhattori8125]

INCREDIBLY MAKING SENSE

[@장용연-f6v]

Makes perfect sense. Many thanks

[@joncolumbino744]

helps a lot thanks!

[@mathsworld1421]

Thank you❤️

[@johnred1893]

I did not get it. U buying the puppy is the consequence of the action of me first promising to take care of it. So should me promising to take care of it actually be the antecedent and the buying a puppy the consequent that follows it !??

[@PrettyPatriciia]

+John Red nope :P Because the promise would be antecedent in this statement: I"ll buy you a puppy if you promise", AKA: If you promise, then I'll buy you a puppy The promise is a sufficient condition for the buying of a puppy And not the antecedent here: I'll buy you a puppy only if you promise" AKA: if the puppy was bought, then the promise has been made The promise is a necessary condition, for the buying of a puppy

[@bobbyyen6317]

me too, I have the same idea with you.

[@ef2b]

+John Red I see why it is tempting to think this way, but nope. Imagine that you promise to take care of the puppy. Is it certain that I will buy one? Nope. I could change my mind or I might not have the money. You promised, but sorry, no puppy. Knowing that you promised does not guarantee the purchase of the puppy. But, if I've purchased the puppy, it is absolutely certain that you've promised, since I made it a requirement. The structure of A => B is that when A is true, B is necessarily true. So, it must be in the order as described in the video. I think the tenses make this confusing. You might be happier if we say, "If I bought you a puppy, then you promised to take care of it," but the logic is the same for the tense in the video. Maybe it helps to think of this as the speaker declaring a contract. The contract is that, "I'll buy you a puppy only if you promise to take care of it." You agree to the contract, i.e., you say this is a true statement. You haven't promised yet, but you've accepted the contract. I buy the puppy. Now, you must make the promise, as agreed or else the contract is broken. Yes, I understand it isn't logical to reply to you two years late, but maybe someone else will come upon this.

[@FIREBALL_XL5]

@@ef2b thanks it worked after 3 years

[@ef2b]

@@FIREBALL_XL5 :-) Thanks for letting me know! Quite fun.

[@gaurishukla9177]

Hi! I have a doubt. in the puppy promise example.. if "I did not buy the puppy" is given, can we conclude anything definitely true about whether the promise was made or not??

[@josephsmy1994]

You're right, it's not a great example because our colloquial understanding of this agreement is closer to " if you make a promise then you'll get a puppy". If you promise then you get the puppy If you promise and you don't get the puppy - you got cheated. If you make no promise then you have no expectation either way of getting a puppy. Bad examples of colloquial use of "only if" is what makes this confusing in the first place. Here's a clear example of a conditional relationship with "only if" because it represents a physical fact. "You can make tea, only if you have water" If you can make tea, then it MUST be true that you have water. If you can't make tea, you may or may not have water. Truth table: T | W | T -> W T | T | T T | F | F F | T | T F | F | T The coin flip example is also confusing as we all understand a coin flip to be a bi-conditional. "Our team kicks off if the coin lands heads (if it doesn't land heads we obviously don't kick off)"

[@ostihpem]

Isn't "only if" in everyday language often meant as "if and only if"? If I say "I give u 1.000 bucks, but only if you smile" then there's no doubt that I mean: "If I give u 1.000 bucks, you do smile" AND "If you smile I give u 1.000 bucks". Or am I mistaken?

[@maxmax9050]

I think you have a point. The trick is that the logical form does not translate 1:1 into English, which is annoying and the cause of much confusion. In normal parlance, "only if" and "if and only if" and sometimes "if" are interchangeable when casually forming a conditional. But in a logical conditional, these phrases imply specific valid forms where the antecedent and consequent have an exact order within the sentence, and this fact is hidden because it is only implied by the middle conditional phrase. Let's say there is a situation where "I fall if I trip." "I trip _if_ I fall." "I trip _only if_ I fall." "I trip _if and only if_ I fall." These three statements make no sense in normal English. It sounds like you are saying that tripping is a result of falling, but that doesn't make any semantic sense. The middle statement is technically valid logically, but it is not clear why. But if we specify that: " *Antecedently* I trip _if_ *consequently* I fall." " *Antecedently* I trip _only if_ *consequently* I fall." " *Antecedently* I trip _if and only if_ *consequently* I fall." These three statements now make sense in English, and they all mean the same thing, and it is now clear why the middle statement makes technical sense logically, but the first and last conditionals are not in logical form and it is not clear why. But if finally we translate into logical form for the other two conditionals according to the rules formally specified by "if" and "iff": " *Consequently* I trip _if_ *antecedently* I fall." " *Antecedently* I trip _only if_ *consequently* I fall." " *Consequently* I trip _if and only if_ *antecedently* I fall." Only the middle statement makes sense logically and semantically despite all three having valid logical form, because "only if" signals that that the valid form of the conditional is such that the antecedent is phrased prior to the consequent formally. If I remove the bolded words, the statement indeed makes no sense in English, but it will still make sense logically, because "only if" _implies_ the antecedent is prior the consequent in the sentence as a formal rule.

[@electricimpulsetoprogramming]

@@maxmax9050 thank you!

[@PrettyPatriciia]

helpful thanks!!!!

[@briansalzano4657]

"You can go to the store only if you buy me something." If you can go to the store then you buy me something. The second sentence seems odd, but the antecedent is a necessary condition for something to be bought. Or "If the match is burning then there is oxygen in the room."