“ONLY” in logical reasoning

[jhtien]

In this example, “Only Apple Inc. has this kind of patent.” I know the diagram would be patent —> Apple. However, I also think the vice versa would work, in other words, if Apple Inc., then it must have this patent. Could you let me know if the above is right? Thank you.

[Jay Donnell]

Hi jhtien!


Let's have a talk about 'only,' what may legitimately hold the title as the most important and most devious word found on the LSAT.

The word 'only' implies a need or a requirement, as in: "Obi Wan, you're my only hope." With the use of only, it's clear that Mr. Kenobi is required to help Princess (and later, General) Leia get out of her bind.

The presence of 'only' is extremely likely to hold relevance to the question and answer, and is famously known for implying a massive degree of logical force.

The frustration from students stems primarily from the apparent variability in the use of the word. To help with that, here are a few of the more common uses and their conditional statement implications:

'Only if'

Of all the varieties of the word 'only' this format is likely the simplest. Plainly put, the phrase 'only if' always directly precedes the necessary condition. I always instruct my students (and as a force of habit I still do the same thing!) to circle the two word phrase, and draw the arrow ( -->) above the words to reinforce the idea that the following term will be on the right side of the arrow, aka the necessary condition.

Take the following conditional statement: If you live in a mansion, then you must be rich. ( LM --> R)

Using the phrase 'only if' we can form that same statement in either of the following ways:

You can live in a mansion only if you are rich.

AND

Only if you are rich can you live in a mansion.


In both sentences, the term 'rich' is the first variable to follow the phrase 'only if', so 'rich' becomes the necessary condition.

Both sentences are diagrammed as ( LM --> R )


The next two variations of 'only' can be a bit confusing, but let's take a stab at distinguishing them from each other.

'only'

vs

'the only'

The following two english sentences, though appearing different on the surface, are both identical in that they should be diagrammed as ( LM --> R )

Only rich people live in mansions.

The onlypeople who live in mansions are rich.

When the word 'only' is used on it's own, the first term to follow becomes the necessary condition.

When in the form of 'the only', the necessity implied by the term 'only' is diverted toward the latter term in the sentence.


In your referenced example, the version used of 'only' finds it on its own, so then the following term in line becomes the necessary.

If 'only Apple has this kind of patent', then having this kind of patent requires the use of Apple, or: ( P --> A).

The syntax of this particular example does seem to add to the ambiguity and mystery of the word only, but I want to stress why the above is the correct (and dare I say, the only) way that the statement should be diagrammed.

Take for example the identical structure, but slightly different example:

Only Tom's Grocery Store carries Jerry's Jelly.

That would mean that if you wanted to buy Jerry's Jelly, it would need to be at Tom's Grocery store, or: BJJ --> TGS

However, there is the chance that the jelly could be out of stock, so it's not a guarantee that going to Tom's guarantees you can buy Jerry's Jelly. It may very likely to be true that being at the store implies you can find the product, but it's not guaranteed, so the use of the arrow implying TGS --> BJJ would not be 100% true and therefore invalid.


That was a bit of a windy explanation but I hope it helps clear up some of the mystery behind the LSAT's biggest Super Villain!