Diagramming

[ericha3535]

Hello,
how would you diagram such statement like:
A -> B, unless C
(like #18 from LR4, Dec 2010)
Or more simply:
if I am fat then I eat 10000 calories a day unless I exercise.

THanks!

[christine.defenbaugh]

That's an interesting question ericha3535! First, I'll say that this particular phrasing is pretty rare. Even in the example you cite, the first 'if' clause merely sets the stage for the discussion, and as such, including it in the the formal logic diagramming is not strictly necessary to solve that question.

That being said, there are a number of ways to express this kind of complex conditional expression, but the most useful is to simply see that there are two separate sufficient clauses and a single necessary clause. As such, it can be expressed as:

X and Y --> Z

The two 'if' statements are linked with an 'and' because they are nested ideas, not independent ones. To take (and twist!) your analogy a bit, consider the statement "If I eat 10000 calories, then I will gain weight unless I work out."

Translating the 'unless' to 'if not', this statement has three pieces:

If I eat 10000 calories and
If I don't work out
Then I will gain weight

C and ~WO --> GW
~GW --> ~C or WO

Note that if you translate 'unless' by replacing it with an arrow and negating the other clause, this would end up as:

If I eat 10000 calories and
If I do not gain weight
Then I must work out.

C and ~GW --> WO
~WO --> ~C or GW

Though these look a bit different, they are actually logically equivalent statements.

As important as it is to understand how to correctly diagram formal logic, it's also critical to realize when and where diagramming is both unnecessary and potentially confusing. Before tying yourself in knots to diagram a particularly tricky phrasing, take a step back to see if the conditional involved is really at play in the question. You just might find, as in PT62, S4, Q18, that you don't actually need it.

Please let me know if this answered your question!

[ericha3535]

Thanks for the quick reply!
I have an additional question.
If you look Matt's answer to this question in forum,
he actually diagrammed it out which makes a perfect sense except about first premise:

He diagrammed the first statement as:
If determined about sentient beings -> Intelligent.

But this does not resemble the diagram that you provided.
According to your rules, which was extremely helpful, the first statement should have been diagrammed as:
If there is sentiment + Determine about it -> As intelligent as us.

So Matt's diagram seems to lack a sufficient condition.
Is it ok to do so or is it an exception?

Thanks for your help!

[christine.defenbaugh]

Great question! This is exactly what I meant before about how in that particular question, the first sufficient clause is really just laying the foundation for the rest of the discussion.

Take yourself out of strict mathematical translations for a moment, and look at what that stimulus is all about. The discussion is about aliens, how smart they might be, in what circumstances we could discover them, communicating with them, etc. All of that interesting stuff is only allowed, though, in a universe where sentient aliens actually exist. If there are no sentient aliens, then all of that discussion is pretty pointless!

So that first 'if' clause just sets that up. Technically, yes, it is a sufficient condition. But we're really not that concerned about it, it's just defining the boundaries of the discussion. There's absolutely nothing wrong with including it into your formal logic diagramming of the stimulus, but once you work through the entire thing, you'll see that we never really engage with the idea again after including it in the first statement.

It is sort of akin to starting a discussion with "Okay, if we could all fly..." then launching into a set of conditional relationships that are true in the universe where we can all fly. That original condition of 'if we can fly' surrounds the entire conversation.

Matt's diagramming on that question focuses on the meat of the conditionals within the universe where sentient alien life exists.

Please let me know if this helps clear that issue up!