What does belief in the Vedas or accepting the authority of the Vedas actually mean?
Vedas have some mythological stories like women accepting the boon of menstruation from Indra (YV II 5.1).
Then there are mantras that supposedly cure diseases (AV VI), bring rain (AV IV 15), etc.
Does belief in the Vedas mean (blindly) accepting everything that's stated in them?
Traditionally Hindus are the one who believe in Aparusheyatva of Vedas. Swami Prabhavananda says the following in book Spiritual Heritage of India.
The Vedas, on the other hand, are said to be apauruseya, which means divine in origin. In fact, in the words of Sayanacarya, the learned commentator on the Vedas, Yo vedebhyaH akhilaM jagat nirmAne — God created the whole universe out of the knowledge of the Vedas. That is to say, Vedic knowledge existed even before the creation of mankind. The authority of the Vedas does not depend upon anything external. They themselves are authority, being the knowledge of God. And, as we shall see later, their truth is verifiable by any spiritual aspirant in transcendental consciousness
Till we reach that state of transcendental consciousness (also can be called as state of Nirvikalpa Samadhi in Yoga terminology) or state of deep tapasya, vedas are to believed by an aspirant and can be verified later through Sadhana. Since Brahman (Ultimate Reality) is beyond senses and mind, we have to first believe visions or first hand experiences of Rishis and then later can verify them in state of transcendental consciousness.
Faith or belief is indeed everywhere. Sri Maheshwaranath Babaji, direct disciple of Mahavatar Babaji explains about Faith to Sri M in book "Jewel in the Lotus - Deeper aspects of Hinduism".
M: With all the knowledge that I have acquired from you, do you think that I will succeed in my path if I have not much faith in you? I ask this question purely out of academic interest. Please enlighten me about the proper place of faith in religious pursuits.
Master: Faith is nothing to laugh at. The entire world, including that of science, depends a great deal on faith.
At school, you study all about the universe in your science books. Since you are not in a position to explore what has been stated – for instance, that there are nine planets in our solar system that revolve round the sun – you accept it on faith. Of course, as you grow up, you might get an opportunity to find out for yourself whether what you have accepted on faith is true or not. But till then, you pin your faith on the sincerity of the scientist who stated it and the textbook that you read.
Would it not be foolish to deny the existence of the nine planets straightaway because you haven’t seen or you can’t see them? Of course, the really intelligent student wouldn’t either accept or deny it straightaway; he would accept it on faith till he finds a means to enquire into it first hand.
This is the kind of faith that is required of the earnest religious seeker. He has to merely suspend judgment about the truths the sages have uttered, after experiencing what is beyond the ordinary man’s capacity to explore. In the meanwhile, he should try to develop in himself the faculties that lie outside our sensory organs and conditioned thought. Once he has reached the same state as a sage who proclaimed a particular truth, he is at liberty to accept or discard it. One who denies a statement without enquiry builds a mental obstruction that blocks all knowledge. How can one seek something which one has denied off-hand?
You should also note that the word translated into English as ‘faith’ is, in the original Sanskrit, shraddha. Faith is not an accurate translation of shraddha. Indeed, there are many words in Sanskrit that do not have a one-to-one equivalence in English. Shraddha, apart from meaning faith and confidence in oneself, also means one-pointed attention, the sacred care given to one’s endeavor. When a person has unquestioned faith in his own capacity for achieving his goal, whether spiritual or temporal, he is not disturbed by negative thoughts that weaken the will and discourage the spirit. Not disturbed by any demoralizing thought, the person who has faith in himself persists in his efforts till the very end and attains what he sets out to do.
Swami Vivekananda also says the same. The Vedas can be verified in Super-conscious state of human soul.
We have to understand that this consciousness is only the name of one link in the infinite chain. Being is not identical with consciousness, but consciousness is only one part of Being. Beyond consciousness is where the bold search lies. Consciousness is bound by the senses. Beyond that, beyond the senses, men must go in order to arrive at truths of the spiritual world, and there are even now persons who succeed in going beyond the bounds of the senses. These are called Rishis, because they come face to face with spiritual truths.
The proof, therefore, of the Vedas is just the same as the proof of this table before me, Pratyaksha, direct perception. This I see with the senses, and the truths of spirituality we also see in a superconscious state of the human soul. This Rishi-state is not limited by time or place, by sex or race. Vâtsyâyana boldly declares that this Rishihood is the common property of the descendants of the sage, of the Aryan, of the non-Aryan, of even the Mlechchha.
Now, regarding stories, Mantras human and God names in Vedas, certain philosophers have explained them based on their understanding. For example, Adi Shankara says words like Indra, Varuna has objective counterparts which are eternal and they don't depend on birth and death in his Brahmasutra Bhashya of 1.3.28.
Each word of the Vedas has an objective counterpart, which is not an individual but a type. The word ‘cow’, for instance, has for its counterpart the object, which is a type and as such is eternal and does not depend on the birth or death of individuals belonging to that type. Similar is the case with words like Indra, Varuna, etc. Words representing the gods etc. have for their counterpart objects that are types and not individuals. Again Indra is the name of any one who would occupy that exalted position, like the word ‘king’ in ordinary parlance. So there is no contradiction to Vedic words. As a matter of fact, the world including the gods etc. have originated from Vedic words.
Jaimini Purva Mimamsa Sutras also explain extensively on same topic. Jaimini says these stories serve as a purpose to glorify the Yajna. So, they are just parts of Vedic injunctions. Jaimini refutes some objections through Arthavada.
अविद्यमानवचनात् ॥ १।२।३४॥ 34.
By reason of the description of that which does not exist..The objector says that the mantra describe those things which do not exist. For example चत्वारि शृङ्गात्रयाअस्य पादा देशीर्षे सप्तहस्तासाअस्य। (ऋ० म० ४ सू० ५८ ऋचा ३)
He refutes this in Sutra 46 through Arthavada.
अभिधानेऽर्थवादः ॥ १।२।४६॥
अभिधाने in the figurative description.
46. The figurative description is by way of अर्थवाद.
This is in reply to the objection contained in sâtra 34, The description of the thing not in existence is by way of figurative speech. See for the explanation of चत्वारि शृगा &c, in the भाष्य ।।
Even six orthodox Schools (Astika Schools) have varied allegiance to Vedas. Swami Viresananda say the following in introduction to Brahma Sutras.
The destructive criticism of everything in the old system by the Chârvâkas and others set the orthodox section to organize their belief on a more rationalistic basis and render it immune against all such criticism. This led to the foundation of the six systems of orthodox Hindu philosophy -orthodox in the sense that they accepted the authority of the Vedas in things transcendental - while there were others who did not accept this authority and therefore were dubbed heterodox, though otherwise they too were the outcome of Upanishadic thought. The acceptance of the authority of the Vedas by these orthodox schools, however, does not mean that they accepted them in toto . Their allegiance to the Vedas varied widely and often it was too loose, Of the six orthodox schools, viz. Nyâya, Vaiseshika, Sânkhya, Yoga, Purva Mimâmsâ and Uttara Mimâmsâ or Vedanta, the last two are intimately connected with the Vedas, which is one of the reasons why they are not mentioned in the Jaina and Buddhistic literature, while the others are mentioned.
Does belief in the Vedas mean (blindly) accepting everything that's stated in them?
So, in short six traditional schools themselves have different beliefs on certain portions of Vedas but they accepted Vedas in things transcendental. So, there can't be one answer for "belief in Vedas or their authority" and it varies with school to school.
This is a very very peculiar question.
For understanding the meaning of the mantras of Vedas,trivarna boys had to be initiated and then learn the six vedangas :Sikha,Kalpa,Nirukta,Chhanda,Jyotisha and Vyakarana.The had to study Vedas with extreme austerity for twelve consecutive years staying in the gurukula and ONLY then, some could understand the Vedas.
Sri Krishna says in Srimadbhagavatam (11/21/35)
वेदा व्रह्मात्मबिषयास्त्रिकाण्डविषया इमे। परोक्षवादा ऋषयः परोक्षो मम च प्रियम् meaning that the Vedas contain three pars : Karma, jnana and Upasana. The Seers have mentioned it in indirect ie hidden ways as that is dear to me.
The Vedic words are NOT sanskrit. We want to understand them without the required knowledge and sadhana and find out contradictions or meaninglessness. Ridiculous indeed! Were the meanings of the Vedamantras known to them who translated them to english or other languages? Absoltulely impossible--- according to Sri Sitaramdas Omkarnath (Omkarnath Rachanavali, vol 7, page 97). Our scriptures consider even the writing down of the Vedamantras as a sin!
Sri Ramakrishna once told Narendranath(later Swami Vivekananda) about Sraddha (faith):
Quoting Complete Work of Swami Vivekananda : Volume 1 / Lectures and Discourses / STEPS TO REALISATION:
The next qualification required is Shraddhâ, faith. One must have tremendous faith in religion and God. Until one has it, one cannot aspire to be a Jnâni. A great sage once told me that not one in twenty millions in this world believed in God. I asked him why, and he told me, "Suppose there is a thief in this room, and he gets to know that there is a mass of gold in the next room, and only a very thin partition between the two rooms; what will be the condition of that thief?" I answered, "He will not be able to sleep at all; his brain will be actively thinking of some means of getting at the gold, and he will think of nothing else." Then he replied, "Do you believe that a man could believe in God and not go mad to get him? If a man sincerely believes that there is that immense, infinite mine of Bliss, and that It can be reached, would not that man go mad in his struggle to reach it ?" Strong faith in God and the consequent eagerness to reach Him constitute Shraddha.
So the Vedas are beyond understanding of a unillumined soul. Believing in the Vedas in truest sense means believing in the essence of the Vedas.The very beginning sloka of the Srimadbhagatam explains it and that has been accepted by Sri Chaitanyadeva as per Srichaitanyacharitamrita. The essence of the Vedas is not whether Indra, Agni etc exists or not. Their essential message is the bold affirmation about the existence of the God Who is the embodiment of Existence-Wisdom-Bliss .So if someone really believes in the Vedas, he or she will get immersed in seeking God forgetting even the world.That is real believing.
And Sri Ramakrishna also used to say in His Kathamrita: One can not understand the true meaning of the holy scriptures without proper sadhana ie spiritual practice.