Discussion of then and only then, and how it's biconditional

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timmydoeslsat
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Discussion of then and only then, and how it's biconditional

Postby timmydoeslsat » Thu Aug 04, 2011 3:41 pm

A then, and only then, B.

If A ---> Then B

How is B, logically speaking, being pulled into a concept of it being sufficient for anything? I would argue that we do not know anything about what happens if B.

Am I incorrect in believing that this is language of bi-conditionality?

kaiser
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Re: Discussion of then and only then, and how it's biconditional

Postby kaiser » Thu Aug 04, 2011 3:46 pm

If I were you, I would take the focus off the word "then" and place it on the word "if". A typical biconditional phrase would be "if and only if". You see this type of terminology many times, including exactly as quoted. I have never seen it given as you have it, with the focus on the word "then". I've never seen the LSAT use the term "then and only then", nor do I think this phrase indicates a biconditional. So lets say:

"I will go to the party if, and only if, you do"

The term "if" indicates a sufficient condition. Part of the above phrase would indicate that I will go to the party if you do

You --> Me

But there is also the term "only if" which, as we know, is an indicator of a necessary condition. So another part of the above sentence is that I will go to the party only if you do:

Me --> You

So in the same phrase, you are given 2 conditional relationships, one signified by "if" and the other signified by "only if". We either both go to the party together, or neither of us go, because each one of us is both sufficient and necessary for the other.

Hope this makes sense.

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timmydoeslsat
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Re: Discussion of then and only then, and how it's biconditional

Postby timmydoeslsat » Thu Aug 04, 2011 4:31 pm

PT 43 Section 3 Q 17

It is used there.

kaiser
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Re: Discussion of then and only then, and how it's biconditional

Postby kaiser » Thu Aug 04, 2011 5:50 pm

Ok well it still isn't a biconditional statement. "Then and only then" indicates that a necessary condition is brought about AND that the sufficient condition tha brought it about is the only sufficient condition with the power to do so. In no way does the necessary condition guarantee the sufficient in such a case. So "then and only then" is not at all biconditional, whereas "if and only if" is biconditional for the reasosns above. Make sense?

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timmydoeslsat
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Re: Discussion of then and only then, and how it's biconditional

Postby timmydoeslsat » Thu Aug 04, 2011 6:26 pm

Oh, I know that if and only if is a bi-conditional statement.

However, I have seen posts on here, if you look in previous searches of bi-conditionality, that talk about then and only then.

It seems like if what you said is in fact the case, a person would not be able to fully address the implications of what that statement says.

kaiser
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Re: Discussion of then and only then, and how it's biconditional

Postby kaiser » Thu Aug 04, 2011 6:32 pm

Wait a sec. I was wrong. "Then and only then" is biconditional as well. Let's use another example.

"The Yankees must win the world series. Then, and only then, will I be happy"

So if the yankees win the series, I will be happy. We also know that there is no other sufficient condition that will lead to my happiness. So if I say I am happy, you can at deductively that the yankees won the world series. They must come hand in hand or not at all. My apologies om the mistake earlier. Then and only then indeed indicates a biconditoonal statement.

KapTeacherBobby
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Re: Discussion of then and only then, and how it's biconditional

Postby KapTeacherBobby » Thu Aug 04, 2011 7:31 pm

timmydoeslsat wrote:A then, and only then, B.

If A ---> Then B

How is B, logically speaking, being pulled into a concept of it being sufficient for anything? I would argue that we do not know anything about what happens if B.

Am I incorrect in believing that this is language of bi-conditionality?


A then and only then B

=

A then B AND A only then B

"A then B" means IF A, THEN B (A is sufficient for B or B is necessary for A)

"A only then B" means "only when I have A will I have B" or in other words, A is necessary for B: IF NO A, THEN NO B (A is necessary for B or B is sufficient for A)

A is the only way we can have B. So, IF B happens, then we know A has also happened.

They are biconditional in the same way that IF AND ONLY IF is.

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timmydoeslsat
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Re: Discussion of then and only then, and how it's biconditional

Postby timmydoeslsat » Thu Aug 04, 2011 8:28 pm

So it is the case that "only then" introduces a sufficient condition?

I assume it does.

KapTeacherBobby
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Re: Discussion of then and only then, and how it's biconditional

Postby KapTeacherBobby » Sat Aug 06, 2011 2:31 pm

timmydoeslsat wrote:So it is the case that "only then" introduces a sufficient condition?



Whenever a sufficient condition is introduced, a necessary condition is automatically also introduced (and vice-verse).

For example, we can say that the statement "IF A THEN B" introduces the sufficient condition "A" through the word "IF." However, if A is sufficient for B, then B's occurence is necessary for A's (A cannot happen without B).

"A ONLY THEN B" directly tells you that A is necessary (not sufficient) for B because we can rephrase it to "ONLY when I have A will I have B"....therefore, I NEED A for B. If I don't have A, I won't have B:

If not A--> not B;

but this also means:

If B-->A,

which means that B is sufficient for A.

Let me know what questions you have.

The key thing to note in these biconditional statements is that the two things are a matched set; they occur together or not at all.




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