How does bringing Binyamin to Egypt prove that the brothers are not spies?

Question

In Bereishit 42:19-20 Yosef says that by allowing one of them to be imprisoned and the rest returning and bringing back their other brother, this would prove that they are not spies.

I've read various Mikra'ot Gedolot commentaries, and I understand the Midrash that says that they entered via separate gates to look for Yosef. Because they didn't all enter in one gate, Yosef accused them of being spies. So, I understand how he arrives at his accusation.

But, in reading the commentaries, I'm not seeing anything that explains the connection of bringing down their other brother absolves them of the spy accusation.

In light of @robev's comment, I'm adding some extra clarification of a nuance I see in various verses. I originally concentrated on Bereishit 42:16 where Yosef says that he will test to see if what the brothers said - namely, that they were all brothers of the same family and all they did was come to buy food - was true. If they couldn't do that, then they were spies.

However, when the brothers relay the story to Ya'akov in verse 34 they say that Yosef said, "In this way I will know that you are not spies, but you are honest people."

There's a bit of a nuance I see in this second verse. To me, it implies not just proving that they were correct in their claim, but they also had to prove that Yosef's claim that they were spies was wrong.

Thus, in providing defense to the accusation, they may have had to do both according to Yosef's demand, (in most U.S. court cases, (and perhaps, in halacha, as well) as I understand, when the defense provides proof that his claim is right, it doesn't necessarily counter the accusation, and it may not be a defense at all.) or, to my original claim, that the proof of their original claim that they were brothers of one family contradicted Yosef's claim.

Answer 1

Until about 200 years ago (around the time of the founding of the United states) most of the world had barbaric laws which were twisted and favoured those with power. Thank G-d we have grown up unaware of this in 1st world modern day society. It says Earlier in Bereishit 12,15 that Pharoh kidnapped Avrahams wife Sarah, so Egypt wasn't exactly "just" rather corruption was the norm.

The brothers were just trying to get food, so that meant doing whatever Yosef wanted corrupt or not, so they'd Bring Binyomin, it was Pikuach Nefesh. They thought Yosef was illegitimately framing them Bereishis 42,30: דבר האיש אדני הארץ אתנו קשות ויתן אתנו כמרגלים את הארץ that the brothers recounted to Yaakov how Yosef spoke harshly to them as if they were spies (and we weren't).

This is what the Ramban explais Bereishit 42,9 was Yosefs agenda:

בראות יוסף את אחיו משתחוים לו זכר כל החלומות אשר חלם להם וידע שלא נתקיים אחד מהם בפעם הזאת כי יודע בפתרונם כי כל אחיו ישתחוו לו בתחילה מן החלום הראשון והנה אנחנו מאלמים אלומים כי "אנחנו" ירמוז לכל אחיו אחד עשר ופעם שנית ישתחוו לו השמש והירח ואחד עשר כוכבים מן החלום השני וכיון שלא ראה בנימן עמהם חשב זאת התחבולה שיעליל עליהם כדי שיביאו גם בנימין אחיו אליו לקיים החלום הראשון תחילה ועל כן לא רצה להגיד להם אני יוסף אחיכם ולאמר מהרו ועלו אל אבי וישלח העגלות כאשר עשה עמהם בפעם השניה כי היה אביו בא מיד בלא ספק ואחרי שנתקיים החלום הראשון הגיד להם לקיים החלום השני ולולי כן היה יוסף חוטא חטא גדול לצער את אביו ולהעמידו ימים רבים בשכול

Basically Yosef had an agenda to fulfill his dream which was a prophecy that all his brothers should bow down to him like the first dream of the 11 sheaves. Therefore he made up an excuse in order for Binyomin to come and bow down which he did in 43,26 along with all the brothers.
He then detained Binyomin and did not reveal himself straight away in order to eventually Bring Yaakov to bow down to him like the second dream of the Sun Moon and Stars which were his father mother and 11 brothers bowing down to him. This didn't quite work as he revealed himself prematurely, but Yaakov eventually did in Bereishis 47,31 willingly.

Answer 2

The Malbim 42:16 explains that initially Yosef wanted all the brothers to stay and when he says "send one from you ,and he will bring your brother ". He meant that they wpuld send a messenger with a document asking Binyamin to come down,this would definitively prove that they weren't spies,since the brother wpuld not have any interaction with him.

However the Malbim notes that Yosef put them into custody for 3 days since they would not submit to Yosefs test. So Yosef gives another option to save their lives . They would have to leave one of the "brothers" to see if they indeed are brothers ,if they aren't brothers then the others would jusy leave and never come back,but if they are truly brothers they will come back for their brother.

So the Malbim is saying that Yosef is trying to corroborate the words of the brothers to see if they are indeed brothers ,to prove defentitlvy that they are spies using his first test idea of holding all brothers he was not able to do based off the belief in God,he would not hold them against their will. So with the second test at least he will be able to prove that at least they are brothers.

Answer 3

In addition to the other excellent answers, Yosef would also be motivated to know if these were the same men who sold him into slavery out of envy.

Knowing that at this point his youngest full brother would most likely be the favorite of their father, he shows great favor to that one (with a greater portion of food at dinner) and sees no jealousy, and then puts that same one into danger (the well-known frame-up) to see if they will stick their necks out for him or throw him under the bus.

Once they have passed these tests, Yosef knew that they had changed for the better, and makes himself known to them.