Conditionals: Only A is B and the like

mkang89

So far, I have treated Only A is B as B-->A. So far so good.
Recently, I have come across this question:
Does the statement "only A is B" deny other necessary conditions?
If so, does that amount to A--> (anything not B ) a false statement (such as A-->C)?

Here's why I pose the above question.
The word 'only' seems to imply exclusivity. Take this example: "Only you are the winner of this competition."
(and in this competition, it is possible to have multiple winners. It just happens to be that you are the only winner
I lay this down to rule out 'context' issue)

To me, this sounds like "winner of this competition --> you" and nobody else.
This would logically mean that winner --> (anyone who is not you) be false.

Similarly, if I were to say
"Only A assures B"
1. does this rule out other sufficient conditions? (I am assuming A assures B = A-->B)
2. does this render (anything not A) --> B a false statement?
For example, Let us assume C-->A; given the statement above, would saying C-->B a false statement?

Related to this question is does this amount to bi-conditional? My gut tells me no, but I am uncertain.
Assuming (only A is B = B-->A and no other necessaries) is true, this does not necessarily mean A = B, since there could
be other elements within B that is not A.

Jane1990

@mkang89

I think "Only A is B" is different from "Only A assures B".

"Only A is B" (B -> A) does not necessarily preclude other necessary conditions. For instance, "Only the best regional swimmers will participate in the state competition" does not preclude "To participate in the state competition, one must be 16 years or older":

Participate in the state competition -> best regional swimmers
Participate in the state competition -> 16 years or older.

So, to elaborate on your example ("Only you are the winner of this competition"), this still does not preclude "To win this competition, one must participate in this competition", for instance. There can be other necessary conditions that may not contradict the original statement.

"Only A assures B", however, might be a bi-conditional as you suggested, although I am not 100% certain. "Only" introduces a necessary condition, and so would "assure", which I think is being used in the same context as "guarantee".

Example: "Only success assures happiness" - if it were a bi-conditional, it should translate to the following statements:
1. One is happy if, and only if, one is successful
2. One is successful if, and only if, one is happy
3. If one is not happy, then one is not successful
4. If one is not successful, then one is not happy

This is interesting. Where have you seen "Only A assures B" on the LSAT? I would love to take a look at the specific example.

mkang89

@Jane1990
Thsanks for the reply
I can't exactly remember which pt it was but it had to do with
Perdect market economy and maximum utility. It was something like
Only perfect matket economy ensures maximum utility. It came with an additional qualifier 'though others may achieve maximum utility as well' which makes the statement a non-biconditional, i think.

I wanted to know what the statement would mean without the 'although others possible' part.

So this is how i understood your reply: existence of only does not preclude other possibilities.
Only A is B:
only is simply a necessary indicator, nothing mich more
Only A assures B:
Also in this case, only is a necessary qualifier. In this case it does seem to rule out other sufficient, since it is biconditional?

cribcracker

I read 'only' in the context you've given to mean: perfect market economy is sufficient for maximum utility, and it is the only thing which, by itself, ensures maximum utility. The qualifier then elaborates by acknowledging there are other combinations of factors which are sufficient for max utility. This seems like a slightly nebulous proposition from a theoretical standpoint, since any other factors which are jointly sufficient to cause something could be thought of as one sufficient condition.

So, I think this is an example of the word 'only' requiring the reader to use their intuition to arrive at the intended meaning. In this case, and in my best guess, the meaning is something like, "If perfect market economy, then maximum utility. However, if less-than-perfect market economy, it is still possible that max utility exists."

So in this case, it seems that 'only', along with the qualifier, alludes to the possibility of other sufficient conditions, and, as you say, denies bi-conditionality.

Another example (from a song) of 'only' being used in a way that defies the strict logical operator paradigm, "I'm only sweet when I'm high", translation: Only when I'm high, am I sweet/If I'm sweet, then I'm high.

You guys are right, this is really interesting. Would love to hear what anyone thinks!

Jane1990

@atviolin hahaha the song reference, and thank you for your insight!

@mkang89
Wow - "Only perfect market economy ensures maximum utility, though others may achieve maximum utility as well" is a really interesting statement. It is NOT a bi-conditional in my opinion, and here is why:

"Ensure" is being used as part of the sufficient condition itself. The sufficient condition is "Ensure maximum utility", rather than just "maximum utility". Thus, the first conditional statement goes as:

If "maximum utility is ensured", then "perfect market economy".
(Contrapositive: If not "perfect market economy", then "maximum utility is not ensured".)

This statement still holds true even with the latter phrase "though others may achieve maximum utility as well". According to the contrapositive, even if it is not "perfect market economy", "maximum utility" itself is not necessarily precluded from ever happening - it is just not ensured.

I am thinking about whether "ensure" is also being used a necessary condition indicator. I will write more when I can clarify my thoughts.

cribcracker

@Jane1990 Fascinating! So you would argue that 'only' in that sentence is the primary logical indicator, not 'ensure'?

My argument would be that 'ensures' indicates a sufficient-necessary relationship in exactly the same way that 'requires' does, while 'only', in this context, doesn't function as a strict logical operator.

Jane1990

As a reminder to myself, here are the necessary condition indicators: then, must, only, only if, only when, depends, requires.

@atviolin

"Ensure"/"Assure" is tricky in that it has a nuance of time delay. The definition of "ensure" is "make certain that (something) shall occur". Similarly, the definition of "assure" is "make (something) certain to happen".

Because of that subtle nuance, or the ambiguity of, time, I don't think ensure/assure qualifies as a necessary condition indicator. For instance, given "perfect market economy", I am not sure whether "maximum utility" would be ensured immediately or eventually.

So, if I were to translate "Perfect market economy ensures maximum utility" into a conditional statement, maybe I should be indicating the time as well:

If "perfect market economy", then "maximum utility" at some point.
(Contrapositive: If "no maximum utility" now or ever, then "not perfect market economy".)

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So, to go back to the example I wrote in my first response, the statement "Only success assures happiness" will not translate into the bi-conditional statements. It will only translate into:

1. If "assures happiness", then "success"
2. If "no success", then "happiness not assured"
3. If "success", then "happiness at some point"
4. If "no happiness now or ever", then "no success"

What do you think?

cribcracker

I looked up the original question (PT 39, S4Q23) and, in context, it is MUCH easier to understand in the way you have described.

Jane1990

@atviolin Thanks for providing the question!