My question is doesn’t the verse that tells us to send salawat upon the prophet (pbuh) only tell us to send it on him? If that is the case, then why is it wajib to add his household (آل محمد)? Isn't this itself a form of innovation and bid’ah? Regarding saying “اشهد ان علیا ولی الله” in the adhan, scholars have said: “If it is said with the intention of being mustahabb, it has thawab and rewards, and if one says it with the intention of it being part of the adhan, it is haram because it is bid’ah and innovation. Having said this, can we say that adding the household of the prophet (pbuh) to the end of the salawat is only considered mustahabb and no more because of the fact that the verse only mentions sending salawat upon the prophet (pbuh) without making any mention of his household (Indeed Allah and His angels bless the Prophet; O you who have faith! Invoke blessings on him and invoke Peace upon him in a worthy manner). This is while one can neither claim that the term ‘prophet’ covers the Ahlul-Bayt, nor that the pronoun at the end of the verse covers them as well, in order to say that the verse has indirectly asked us to do so. In other places of the Quran it is possible to interpret certain terms in a way so that they cover the Ahlul-Bayt as well, such as the terms ‘Ulul-Amr’ and ‘Imam’, but that isn't the case with the term ‘prophet’ in this verse; it is only used to refer to prophet Muhammad (pbuh). So, considering all of this, can we say that sending salawat upon the family of the prophet (pbuh) isn't part of the salawat and is only mustahabb and not wajib?
Please give me a theological and philosophical response without making any references to Sunni or Shia hadiths, because I already know all of them.
Not only isn't adding the household of the prophet (pbuh) to the end of the salawat bid’ah, but it is in total accordance with what the Quran, hadiths, the mind and irfan tell us, the reason being:
1- Bid’ah refers to when something that isn't part of religion is considered part of it. We don’t see sending salawat upon the prophet (pbuh) and his household as bid’ah, because it is something that hadiths from the prophet (pbuh) and the imams tell us to do.
2- Allah (swt) has instated different duties for his servants, pointing to their obligation in general and seldom getting into the details. He hasn’t mentioned all of the specifics and conditions of these duties in the Quran. In order to comprehensively learn everything that He wants from us, we have no choice but to refer to the true addressees and interpreters of the Quran, the infallibles (meaning the prophet (pbuh) and the imams).
On this basis, when the prophet (pbuh) himself interprets the verse for us and says that what is meant is that his household has to be mentioned next to him, it means that this is actually what the Quran is ordering us to do.
3- In addition to the apparent meaning of verses, the verses of the Quran also have deeper and more profound meanings that the prophet (pbuh) and the imams after him can only inform us of; although the apparent meaning of “النبی” or “prophet” only covers Prophet Muhammad (pbuh), but hadiths tell us that its inner and deeper meaning covers his household as well.
4- Quranic verses introduce the prophet (pbuh) and his household as one truth. There are hadiths that disclose that the prophet (pbuh) and his household are from one ‘light’. This is why in gnosis, this one light is referred to as ‘The Muhammadian Truth’ or the ‘First Emanation’. In this case, how can one send salawat upon the prophet (pbuh), but leave out his household?! In other words, salawat and blessings upon the household of the prophet (pbuh) is the same as sending it upon the prophet himself; both are the manifestation of one reality.
One final point is that reciting the salawat isn't absolutely wajib, rather it is only wajib in certain cases, such as in the tashahud of prayer. Of course, in the cases in which it is wajib, it is mandatory to add the household of the prophet (pbuh). In the cases of it being mustahabb, adding the household is also mustahabb and not adding it makes the salawat incomplete.
In order for the answer to become clear, several points must be considered:
1- Bid’ah means for something which isn't part of religion to be considered part of it. It has also been proven (in other discussions) that the prophet’s (pbuh) and imams’ (as) actions and sayings are all part of and constitute religion. Keeping this in mind, what you claimed about how adding the household of the prophet (pbuh) to the salawat is bid’ah is false, because even if we assume that it hasn’t been mentioned in the Quran as you put it, it indeed has been mentioned in hadiths from the prophet (pbuh) and the imams (as), making it part of religion. What jurisprudents mean when they say that adding “اشهد ان علیا ولی الله” with the intention of it being part of the adhan is bid’ah, is that they haven’t found any Quranic or hadithic proof that shows this to be part of the adhan (thus, they say since there is no religious proof that it is part of the adhan, we can't say it is, or add it with the intention of it being part of it). To make it short, it is Islam (the Quran, traditions and other Islamic sources) as a whole that determines whether or not something is part of religion or not, not only the Quran; the Quran is one reference for this, but not the only one.
2- All of the different obligations and duties Allah (swt) has instated for us, such as taharah, prayer, fasting, Hajj, jihad, khums, zakat, etc., have all been mentioned in the Quran; the only thing is that they have only been pointed to, without many of their details being explained. Only some of the conditions and parts of these obligations have been expressed in a general way. For instance, the necessity of prayer has been mentioned in the Quran, also some of its conditions have also been mentioned, but what should be said in the ruku and sujud of the prayer, recitation, the tasbihat arba’ah, how to make wudhu, ghusl and tayammum etc. haven’t been explained in detail at all.
The method Muslims used in the advent of Islam was to refer to the prophet (pbuh) and ask him in order to learn of these details and put them to practice.
This was the case with the ‘salawat’ at that time as well. After the verse “ان الله و ملائکته یصلون علی النبی یا ایها الذین آمنوا صلوا علیه و سلموا تسلیما” was revealed, the Muslims went to the prophet (pbuh) and asked him how they were supposed to send salawat upon the prophet (pbuh), and as has been narrated in numerous hadiths by both Shia and Sunni sources (mutawatir), the prophet (pbuh) answered: “Say: “اللهم صل علی محمد و آل محمد کما صلیت علی ابراهیم و...”; this is how the Muslims learned to send salawats upon the prophet (pbuh).
In other words, Allah (swt) has introduced his prophet (pbuh) as the true interpreter and clarifier of the Quran, and he (the prophet) has interpreted the abovementioned verse by saying that what is meant by reciting salawat is to say: “اللهم صل علی محمد و آل محمد”. Conclusion: Adding the household of the prophet (pbuh) to the salawat is understood from the Quran itself.
3- In addition to its ‘apparent’ meaning and surface, there are deeper and more profound meanings that only the infallibles are aware and can inform us of. Therefore, it can be said that those hadiths that tell us to add the household of the prophet (pbuh), are actually informing us of the deeper meaning of the verse. In other words, they are telling us that although the meaning of ‘prophet’ or ‘النبی’ only refers to the Prophet Muhammad (pbuh) in normal circumstances, but here covers the Ahlul-Bayt as well, which is a deeper meaning than the normal one.
4- It can be inferred from Quranic verses that Allah (swt) looks at the prophet (pbuh) and his household as one truth and reality. For instance, in the verse of ‘Purification’ or ‘تطهیر’, Allah (swt) says: “انما یرید الله لیذهب عنکم الرجس اهل البیت و یطهرکم تطهیرا”; in this verse Allah (swt) has addressed them as one reality.
Another example would be the verse of Mawaddah or love: “قل لا اسئلکم علیه اجرا الا المودة فی القربی”; when Allah (swt) refers to the love of the household of the prophet (pbuh) as the reward for prophet’s (pbuh) endeavors and efforts, it comes to show that the two never part in His eyes.
Another example is the verse of Mubahalah or malediction: “قل تعالوا ندعوا ابنائنا و ابنائکم و نسائنا و نسائکم و انفسنا و انفسکم...”. As you can see, in this verse, Imam Ali (as) has been regarded as the prophet’s self, and the verse tells us that being the victor in this mubahalah is totally contingent upon all of those mentioned being present.
5- There are various hadiths that tell us that the prophet (pbuh) and his progeny are one light. Take this example: The prophet (pbuh) of Islam says: “I was created from God’s light, and my Ahlul-Bayt were created from my light.”
6- Arefs refer to the prophet (pbuh) and his progeny as “The Muhammadian Truth” or “The First Emanation” which is one reality with different manifestations.
7- In the eyes of normal people, those who share the same beliefs and ideas and are in no conflict with each other, neither in practice nor in thoughts and belief, are all considered one and in other words, people look at them with the same view.
Conclusion: Not only isn't adding the household of the prophet (pbuh) to the salawat not bid’ah, but is in total accordance with the Quran and hadiths and even the view of normal people. Sending salawat upon the prophet (pbuh) is the same as sending it upon the Ahlul-Bayt and both are manifestations of one reality. The last point is that reciting salawat isn't wajib absolutely and rather becomes wajib only in certain cases, like in the tashahud of prayers. Of course, when the salawat does become wajib, it must be recited with the “آل محمد”, and in the cases in which it is mustahabb, adding “آل محمد” will also be mustahabb.
 Tafsir Nemouneh, vol. 17, pg. 419.
 For further information, see: Sending salawat upon the prophet (pbuh) and his progeny, Question 428.
 Biharul-Anwar, vol. 89, pp. 90-95.
 Biharul-Anwar, vol. 15, pg. 20.
 Tahrirul-Wasilah, vol. 1, pg. 143, tashahud, issue 1.