I've been meaning to ask these questions. Two questions actually.
i) What role does faith play in cultivation?
ii) What role does gratitude play in cultivation?
... presumably cultivation on the Buddhist path :)
Faith is one of the Eleven Wholesome Dharmas of the One Hundred Dharmas (see entry for latter); it is also one of the Five Faculties (faith, vigor, mindfulness, concentration, and wisdom).
"Faith is necessary in whatever it is one does. One needs to have a sense of belief, an attitude of faith. First, one needs to have faith in oneself. What kind of faith? One needs to have faith that one certainly can become a Buddha. One has to believe that there is no difference between the Buddha and oneself. Yet that lack of difference is in one's Buddha-nature. Cultivation is still required in order to actually become a Buddha. If one cultivates, one will become a Buddha. In order to do so, one must have an initial belief in this principle.
"Second, not only is it necessary to believe that one can become a Buddha oneself, but also to believe that all people can become Buddhas. Moreover, not only can all people become Buddhas, one should believe that all living beings have the Buddha-nature and are capable of becoming Buddhas. If one has that kind of faith, then one should begin by following the rules oneself. To follow the rules means to hold the moral precepts. First one holds the precepts, and then one can become a Buddha. One does it oneself and also encourages others to do so as well.
"Faith must be solid, like a rock, firm and sturdy. Faith shouldn't be like a pile of ashes which seems to have some substance to it but which crumbles at the slightest disturbance. Don't be too soft. One's faith must be strong and solid." (HD 44 45)
THE IMPORTANCE OF FAITH
"Faith is the foundation of cultivation of the Way and the mother of merit and virtue, because it is capable of nourishing wholesome roots. The Buddhadharma is like a vast sea; only by faith can it be entered. Therefore, the single word 'faith' is the essence of escape from birth and death and is the wonderful means for returning to the source. It is a precious raft on the stream of affliction, a torch in the dark cave of ignorance, and a guide who leads us out of the path of confusion. It is a compass for those floundering in the waves on the sea of suffering, and a sagely teacher for those in the Three Paths (Arhat, Pratyekabuddha, and Bodhisattva) and Eight Difficulties ( ). It is the origin of awakening for the Four Kinds of Creatures born (from wombs, eggs, moisture, and transformation) within the Six Paths (see entry). Faith cannot be ignored. An author of ancient times said, 'If a man has no faith, I do not know what can be made of him.'
"Once two bhikshus were travelling to see Shakyamuni Buddha, the World-Honored One. As they travelled they became extremely thirsty but could not find any water. As they walked they happened upon a human skull containing water in which some small bugs were swimming, enjoying themselves tremendously. One of the bhikshus picked up the water and offered some to his companion. The companion replied, 'This water contains bugs, and the moral precepts do not permit drinking such water. I would rather die of thirst than to violate the precepts in order to stay alive.' After this incident he died of thirst.
"When the bhikshu who had drunk the water reached the place where the Buddha was residing, he bowed and said to the Lord, 'Your disciple was travelling in the company of another bhikshu who perished of thirst on the road. I hope the Buddha will be compassionate and rescue him.'
"The Buddha said to the bhikshu who had drunk the water, 'Because he stringently maintained the moral precepts and was so firm in his faith that he would not violate them even in the face of death, he received the awesome power of the Buddhas and arrived here before you. He has already seen the Buddha and heard the Dharma before you. He is a bhikshu who has true faith in the precepts." (WM 53-54; also S42 75-76)
Hymn of Faith
Faith is the source of the Way;
Faith is the mother of merit and virtue.
As they arise by faith,
All wholesome dharmas must by faith be nurtured.
Faith cuts the tangled web of doubt,
Escaping loves delusive flow,
And opens wide to reveal the true and unsurpassed Nirvana's road.
Faith has no stain or mar,
Bringing the turbid mind purification,
Eradicating pride,
Of all respect and reverence the foundation.
Within the Dharma Treasury
faith's jewel outshines the fairest gold;
Hence every conduct our hands by faith made pure receive and surely hold.
Faith is the healing source
By which our faculties are cleansed and quickened. Nothing can turn its force,
The solid power of faith cannot be broken.
And when by faith forever
From all affliction we depart,
The Buddha's merit will thus become the sole devotion of our hearts.
With faith the mind's unmoved,
Free from attachment to conditioned arising;
Disasters far removed,
In the tranquility of faith abiding.
The bliss of faith victorious!
Among the conducts of all worlds,
This faith alone is the one most rare and precious wish-fulfilling pearl.
Profoundly we believe:
Trusting the Buddhas and the Buddhas' Dharma,
Treading the Bodhi-Path,
Forever followed by all true disciples.
And to the Great Enlightenment
Our thoughts are joyfully inclined:
The Bodhisattvas with this deep heart of faith produce the Bodhi-Mind!
(RH 235)
1) Ch. syin , 2) Skt. sraddha, (prasada), 3) Pali saddha, 4) Alternate Translations: belief.
See also: One Hundred Dharmas, Five Types of Buddhist Study and Practice--Pure Land.
BTTS References: WM 53-54; FAS Ch10 ?; FAS-PI 184; FAS-PII(1) 139-140); FAS Ch11 184; FAS Ch22 4-6; AS 24; HD 44.
《�严�》上所说, 信为�元功德�'
Faith is Bodhi mind / Bodhicitta, or Buddha nature of all sentient beings
http://www.purifymind.com/BodhicittaQA.htm
Probably can explore The Platform Sutra of the Sixth Patriarch.
Only realizing and attaining Bodhi mind of the ten directions, gratitude is accomplished.
Samantabhadra cultivation of gratitude stated in Avatamsaka Sutra
http://www.tamqui.com/buddhaworld/Samantabhadra