Question about example on p. 73 of LGB (unless/until)

[lsat_novice]

The following example is on page 73 of the Logic Games Bible:

"G cannot be cleaned until F is cleaned, unless F is cleaned second."

The book says that this can be diagrammed in the following way: (G -- F) --> F2 (imagine the 2 is a subscript).

I'm confused by this because:

Step 1: "G cannot be cleaned until F is cleaned" ... this contains "until" so I thought that this part of the sentence would be diagrammed G -- F. ("Until" negates the sufficient condition.)

Step 2: "Unless F is cleaned second." Because of "unless," I thought that this should negate the first part of the sentence. So I thought that (G -- F) should be turned into a negative. But the book doesn't do this... it keeps (G -- F) as it is in Step 1.

Can someone please explain?
Thank you!

[Jonathan Evans]

Hi!

Good question!

Here the "until" refers to the order of the variables G and F. This "until" is not part of the conditional structure.

Think of it like this:

• "G is cleaned after F unless F is cleaned second."

Notice that in the way that I phrased the rule above I have omitted the "until" without changing the meaning of the sentence, and the Unless Equation™ still works correctly:

1. Negate the sufficient condition: (F G) becomes (G F)
2. Keep the necessary condition intact: F2
3. (G F) F2

Conditional statements such as these are sometimes difficult to parse. In situations such as these, it helps to separate out the conditions and the conditional language that dictates what we do with them. Look at the example statement separated out thus:

• "G cannot be cleaned until F is cleaned" UNLESS "F is cleaned second"

The statements in the quotation marks above are the two conditions. The "unless" tells us what to do with them. Use the "unless" to determine which statement is sufficient and which is necessary. Then negate as needed according to the Unless Equation.

Does this make sense? Please follow up with further questions.

[lsat_novice]

Thanks so much for the detailed (and prompt!) explanation, Jonathan!

[SGD2021]

Hello,

In general, when we have two of those odd necessary conditional indicators (except, until, without, unless), in a sentence, would we be able to just pay attention to one of them as the main conditional and not apply the Unless Equation to the other?

I am still a bit confused about when we can just not pay attention to a second conditional indicator in a sentence, especially in light of the discussion about nested conditionals in the Logical Reasoning Bible on page 235 (2020-2021 edition), where it seems like you would always draw a diagram for all of the conditional statements in a sentence.

Why is "G cannot be cleaned until F is cleaned" not a nested conditional?

[Adam Tyson]

It actually CAN be treated that way, SGD2021, although doing so might cause more confusion than help (as can often be the case with nested conditionals). That portion of the relationship might be diagrammed this way:

G (F G)

If this rule appeared in a game in which G did not have to be included in the order, that would be a wise way to handle it. But if this was a more typical ordering game in which all the variables must be included somewhere in the order, there would be no "if" about G: it WOULD be included, and would have to be after F UNLESS F was 2nd (in which case, G could be 1st or could be after F). In that case, treating that "until" as a simple ordering rule rather than a conditional indicator would make sense. After all, if something is guaranteed to occur, why waste time and effort thinking about IF it occurs?

(Note for anyone following along: in the 2021 edition of the LGB, this example is #11 on pg 76)