This is definitely not acceptable, because his great Prophet departed when the Islamic society was in its worst situation. From one side two powerful empires of Rome and Iran were threatening the Islamic government—proved by Prophet’s emphasis on equipping Jeish al-Osama.  On the other hand, the hypocrite and the Jews were making troubles for the nation every day.

It’s obvious that in such a chaos, not even an ordinary ruler would leave the society without a successor, so how our logic would accept that prophet Muhammad (Pbuh) had left the society without assigning his successor and caliph? More than anyone else, his highness cared about Muslim and attended their grief. And for their welfare did not spare any efforts.

This holy verse: (لقد جاءكم رسول من أنفسكم عزيز عليه ما عنتّم حريص عليكم‏بالمؤمنين رؤوف رحيم) التوبة  128 is the best evidence for us.

Moreover, believing so is the biggest insult o Prophet Muhammad (Pbuh); implying that the prophet had put the society into jeoparody with this decision. As Dr. Ahmad Amin, the Egyptian scholar explicitly asserts: Prophet Muhammad (pbuh) departed without assigning his successor or the conditions for him, he had exposed the Islam society to the most difficult and hazardous problems:

« توفّي رسول‏اللَّه - صلّى اللَّه عليه وآله - ولم يعيّن من يخلفه ، ولم يبيّن كيف يكون اختياره ، فواجه المسلمون أشقّ مسألة وأخطرها! » فجر الاسلام : 225 . . 

Also, Ibn Khaladoon says: it’s impossible to leave a society without leader; since it’s the cause of fight among people and politicians. Thus in every society there’s a vital need to assign a ruler in order to prevent the chaos:

« فاستحال بقاؤهم فوضيّ دون حاكم يزع بعضهم عن بعض واحتاجوا من أجل ذلك إلى الوازع وهو الحاكم عليهم » مقدّمة ابن خلدون ص 187 .