Shaykh ul-Islaam Ibn Taymiyyah said in his book "an-Nubuwwaat" - a refutation of al-Baqillani on some of his views on the subject of Prophethood and Miracles - so he said in Volume 1, page 255 (tahqeeq by at-Tawiyaan):

And the intent here is that these (people) they made this to be the foundation of their religion and their faith, and they made inspection (an-nadhar) of this evidence to be an obligatory consideration upon every single person (mukallaf), and (they held) that anyone who does not look into this evidence, then either his faith is invalid, and as such he is a disbeliever - based upon the view of one faction amongst them - or he is sinful upon the saying of others, or he is a blind-follower who has no knowledge of his religion, but his blind-following will benefit him, and he will become a believer through it, without being disobedient.

And all three sayings are futile, because they branch off from a foundation which (is itself) futile - which is that (to them) the inspection, reflection (an-nadhar) which is the foundation of the religion, is this inspection of this evidence (i.e. their rational demonstration through jism, 'arad and hudooth). The scholars of the Muslims know by necessity that the Messenger did not call the creation to this reflection (nadhar), and nor (call them) by this evidence, neither the generality of the creation, and nor the specific ones amongst them. Thus it is impossible for this to be a condition for faith and knowledge.

What is this evidence? It is the evidence that demonstrates the created nature of the universe through the use of basic underlying notions (borrowed from the Greek philosophers) such as Aristotle's substance (jawhar) and accident ('arad), and the Atomism theory (the indivisible particle). And it is called "hudooth ul-ajsaam", a specific and intricate rational demonstration of the createdness of the universe that these people made binding. We have covered this elsewhere and you should go through this article where it is mentioned in more detail.

And this became the foundational principle of the entire religion to these people (the Jahmiyyah, Mu'tazilah, Ash'ariyyah and Maturidiyyah) - and around this foundational principle did they build their formulation of their creed - and thus they fell into what they fell into. And when they say "Usool ud-Deen", the foundations of the religion, this is what they mean by it - the rational validation of their faith, and in this they have simply "borrowed" or been influenced by the Mu'tazilah - with subsidiary differences that they argue upon.

The verifier (of "an-Nubuwwaat") brings some quotations from the Ash'arite Mutakallimoon (Theologians) in the notes and a quote from Abu Mansoor al-Maaatureedee:

From al-Maatureedee in "at-Tawheed" (p. 129):

There is no path to knowledge of Him, except through [the method] of the [rational demonstration of the] universe providing evidence for Him...

And what they mean here is their Kalaam theology, what they have laid down as being the rational demonstration of the createdness of the universe.

And Abu Hamid al-Ghazaalee in "Tahaafut al-Falaasifah" (p.197):

...So it has become clear that anyone who does not believe in "hudooth ul-ajsaam", then there is no basis for his belief in the creator, fundamentally (i.e. at all)...

And as-Saawee says in "Sharh Jawharat ut-Tawheed" (p.61):

... And the truth that is to be depended upon is that he is a believer, but sinful by abandoning reflection (an-nadhar)...

He means a person who does not inspect and look at this rational proof of theirs by way of the createdness of bodies through the demonstration of a'raad (incidental attributes) and hawaadith (events, occurrences).

And Abu Bakr al-Baqillani makes this "nadhar" (argument by way of rational evidence through inspection) to be the first obligation, and he declares it obligatory upon each person to know the specifics of this rational demonstration, as occurs in his book "al-Insaaf" and also in "at-Tamheed".

And Ibn Fawrak (another prominent Ash'ari Scholar) holds it to be obligatory as indicated in the book "ash-Shaamil Fee Usool ud-Deen", as does Abu Ishaaq al-Isfaraa'eenee in the book "Sharh ul-Maqaasid".

And Abdul-Qahir al-Baghdadi, another prominent Ash'ari scholar makes the rational and intellectual inspection to be a condition for the validity of a person's faith.

He says in "Usool ud-Deen" (p.269):

From [being] a condition of the validity of faith - in our view [meaning the Ash'ariyyah] - is preceding knowledge with the intellectual foundations in Tawheed, Hikmah and 'Adl, and (in) establishing the Prophethood and Messengership, and belief (in) the Sharee'ah of islaam...

And al-Juwaynee (al-Imaam ul-Haramayn) says in "ash-Shaamil Fee Usool id-Deen" (p. 115):

Observation (an-nadhar) and inference (al-istidlaal) that lead to acquaintance of Allaah, the Sublime, are two obligations...

And what they mean by inspection and deduction of evidence is their rational demonstration, through their rational proof of al-Jawhar al-Fard.

This view is held by the majority of the Ash'arite Theologians - and there others who do not hold it to be obligatory or a condition of the validity of faith, but it is a position held by the majority of them.

And some of them speak of the disbelief (kufr) of the one who does not go into this inspection and deduction of evidence, whilst having had time to do that.

Al-Juwaynee says in "ash-Shaamil fee Usool id-Deen" (p. 122):

... And if time passed by - from the time that religious obligations applied to him - in which he had the capacity for an-nadhar (inspection and deduction of proof, rationally) leading to knowledge, and he did not inspect, despite there being no preventive barriers and he passed away after the time in which this was possible for him - then he is put alongside the disbelievers...

So some of them went to extremes as you can see.

Ibn Hajr al-Asqalani's Refutation of the Ash'aris on This Issue

Ibn Hajr al-Asqalani documented this view of the Ash'aris and refuted it with just a single verse and hadeeth. You can see that here. And Abu Ja'far as-Samnaanee, a prominent Ash'ari, turned away from the above view of the Ash'arites as Ibn Hajr explains, and he held on to this verse and hadeeth as proof to show that the ma'rifah (innate knowledge) of Allaah is in the fitrah already, and thus a person with intact sound fitrah does not need the rational demonstration that the Mu'tazilites and Ash'arites concocted. And Ibn Hajar al-Asqalani quotes the saying of as-Samnaanee (Fath ul-Baree 13/97):

...one of the issues of the Mu'tazilah that remained in the (Ash'ari) madhhab...

Imaam an-Nawawee's Refutation of the Asha'rite Theologians on This Issue

Commenting on the hadeeth, "I have been ordered to fight the people until they testify that there is none worthy of worship except Allaah (alone) and until they believe in me and what I have brought..." (Saheeh Muslim), an-Nawawee says in his Sharh of Saheeh Muslim (1/210-211):

In (the hadeeth) is a clear evidence for the madhhab of the muhaqqiqeen (those verifying what is correct) and the majority amongst the Salaf and the Khalaf that when a person believes in the religion of Islaam with a firm and resolute belief devoid of any doubt, that this is sufficient for him, and he is a believer amongst the Muhawahhideen. [And that] it is not obligatory upon him to learn the evidences of the Theologians and knowing Allaah, the Exalted, through them. [This being] in opposition to the one who made it obligatory and made it a condition of a person being from the the people of the qiblah [and who] claimed that he does not have the ruling [applicable to] the Muslims except through this. And this madhhab is the saying of many of the Mu'tazilah and some of our associates, the Theologians (Mutakallimoon), and it is a manifest error...

So it is apparent that the Ash'aris simply "borrowed" (again) from the Mu'tazilah, or were influenced by them in their foundations. And this is why it is said, the Ash'ariyyah are the effeminates (eunuchs) of the Mu'tazilah - being neither here nor there. And amongst themselves they differ in the details of this foundational principle of their madhhab - the issue of an-nadhar wal-istidlaal and their rational demonstration through "hudooth ul-ajsaam".