What is the Material Conditional Paraphrasing in Logic?

[Shackleford]

I have the following book:

https://www.amazon.com/dp/0072401893/?tag=pfamazon01-20

I'm currently going over symbolization and truth-functional connectives.

I have a question considering a material conditional paraphrasing.

If Jones got the job then he applied for it.

Of course, you cannot state this backwards. If he applied for the job, then he doesn't necessarily have to have gotten the job.

The book paraphrased it as such:

Either it is not the case that Jones got the job or Jones applied for the job.

What is their basis for their paraphrasing? Are they basing it on the truth-functional value of "Jones got the job"? Either Jones got the job or he didn't.

If he didn't get the job, then we don't know if applied or not.
If he did get the job, then he applied for the job.

I have to admit it's a bit fuzzy for me in a few places. Looking ahead in the book, it seems a bit dry.

 

[apeiron]

You are dealing with a hierarchical situation of sets and subsets. So events on different spatiotemporal scales.

Applying for a job is the more global or general level of action, getting a job is a more local or specific action. And the smaller must always be found inside the larger.

So the serial nature of spoken language makes the two events seem to be of identical scale, and so confusable as to which is figure, which is ground. But logically, they are a hierarchy.

 

[Hippasos]

...

Of course, you cannot state this backwards. If he applied for the job, then he doesn't necessarily have to have gotten the job...

Trying to generalize and find a set for this particular example...

How would this logic be transformed to this particular case of "getting a job":

Let Jone's father be the king of Legoland.
Let Jones be the eldest son.
Did Jones apply for the next king?
Not necessarily, but he would probably still be next king of Legoland, unless he got involved in an accident or something other misfortune.

(and unless of course you don't consider being a king to be a job)

So how would the logic of "getting a job in general" be paraphrased so that it would stand also in this case?

What's the use of paraphrase some logic if it is not valid in some cases?

 

[Shackleford]

Trying to generalize and find a set for this particular example...

How would this logic be transformed to this particular case of "getting a job":

Let Jone's father be the king of Legoland.
Let Jones be the eldest son.
Did Jones apply for the next king?
Not necessarily, but he would probably still be next king of Legoland, unless he got involved in an accident or something other misfortune.

(and unless of course you don't consider being a king to be a job)

So how would the logic of "getting a job in general" be paraphrased so that it would stand also in this case?

What's the use of paraphrase some logic if it is not valid in some cases?

So, basically you're saying you have to use some intuition and infer that given the two ultimate possibilities - got or did not get the job - you have to either state explicitly he did not get the job, or, with how it's written, that he applied for the job, and thus inferring/use intuition that he got the job.

 

[apeiron]

(and unless of course you don't consider being a king to be a job)

?

That would be your answer. The general class would be "being born to". The dynasty is the set of which individuals are members. Unless the meet some accident.