On the basis of the sāṅkhya philosophy of acintya-bhedābheda-tattva, which maintains that the Supreme Lord is simultaneously one with and different from His creation, Lord Caitanya taught that the most practical way for the mass of people to practice sānkhya-yoga meditation is simply to chant the holy name of the Lord. He taught that the holy name of the Lord is the sound incarnation of the Lord and that since the Lord is the absolute whole, there is no difference between His holy name and His transcendental form. Thus by chanting the holy name of the Lord one can directly associate with the Supreme Lord by sound vibration. As one practices chanting this sound vibration, one passes through three stages of development: the offensive stage, the clearing stage and the transcendental stage. In the offensive stage of chanting one may desire all kinds of material happiness, but in the second stage one becomes clear of all material contamination. When one is situated on the transcendental stage, one attains the most coveted position—the stage of loving God. Lord Caitanya taught that this is the highest stage of perfection for human beings.
(Sri Caitanya Caritamrta------preface).

Lord Caitanya Mahāprabhu adopted the mood of Lord Śiva, for He is Śiva also. According to the philosophy of acintya-bhedābheda-tattva, Lord Śiva is not different from Lord Viṣṇu, but still Lord Śiva is not Lord Viṣṇu, just as yogurt is nothing but milk and yet is not milk nevertheless. One cannot get the benefit of milk by drinking yogurt. Similarly, one cannot get salvation by worshiping Lord Śiva. If one wants salvation, one must worship Lord Viṣṇu. This is confirmed in the Bhagavad-gītā (9.4): mat-sthāni sarva-bhūtāni na cāhaṁ teṣv avasthitaḥ. Everything is resting on the Lord, for everything is His energy, yet He is not everywhere. Lord Caitanya’s adopting the mood of Lord Śiva is not extraordinary, but one should not therefore think that by worshiping Lord Śiva one is worshiping Lord Caitanya. That would be a mistake.
(Sri Caitanya Caritamrta------1:7:100------purport).

The Brahma-sūtra states that according to the principle of śakti-śaktimator abhedaḥ, the living entity is simultaneously one with and different from the Supreme Personality of Godhead. Qualitatively the living entity and the Supreme Lord are one, but in quantity they are different. According to Śrī Caitanya Mahāprabhu’s philosophy of acintya-bhedābheda-tattva, the living entity and the Supreme Lord are accepted as one and different at the same time.
(Sri Caitanya Caritamrta------2:6:163------purport).

The Māyāvādīs imagine themselves to be the Supreme. They imagine that the Supreme has no personal form and that all His forms are imaginary like the will-o’-the-wisp or a flower in the sky. Both Māyāvādīs and those who imagine forms of God are misguided. According to them, worship of the Deity or any other form of the Lord is a result of the conditioned soul’s illusion. However, Śrī Caitanya Mahāprabhu confirms the conclusion of Śrīmad-Bhāgavatam on the strength of His philosophy of acintya-bhedābheda-tattva. That philosophy holds that the Supreme Lord is simultaneously one with and different from His creation. That is to say, there is unity in diversity. In this way Śrī Caitanya Mahāprabhu proved the impotence of fruitive workers, speculative empiric philosophers and mystic yogīs. The realization of such men is simply a waste of time and energy.
(Sri Caitanya Caritamrta------2:9:360------purport).

The Supreme Personality of Godhead is always transcendental to this material creation. Nārāyaṇaḥ paro ’vyaktāt: “Nārāyaṇa, the Supreme Personality of Godhead, is always transcendental.” He is not a creation of this material world. Without realizing spiritual knowledge, one cannot understand that the transcendental form of the Lord is always beyond the creative energy. The example of the sun and the sunshine is given. The sunshine is not the sun, but still the sunshine is not separate from the sun. The philosophy of acintya-bhedābheda-tattva (simultaneously one and different) cannot be understood by one who is fully under the influence of the external energy. Consequently a person under the influence of the material energy cannot understand the nature and form of the Personality of the Absolute Truth.
(Sri Caitanya Caritamrta------2:25:118------purport).

When the living entity wants to enjoy by imitating the Supreme Personality of Godhead, his desire is called māyā, and it puts him in the material atmosphere. A living entity who wants to enjoy on his personal account and not cooperate with the Supreme Lord is engaged in materialistic life. As soon as he dovetails his enjoyment with the Supreme Personality of Godhead, he is engaged in spiritual life. An example may be cited here: The different limbs of the body cannot enjoy life independently; they must cooperate with the whole body and supply food to the stomach. In so doing, all the different parts of the body enjoy equally in cooperation with the whole body. That is the philosophy of acintya-bhedābheda, simultaneous oneness and difference. The living entity cannot enjoy life in opposition to the Supreme Lord; he has to dovetail his activities with the Lord by practicing bhakti-yoga.
(Srimad Bhagavatam------3:29:35-------purport).

This confirms the philosophy of acintya-bhedābheda-tattva ("simultaneously one and different") propounded by Lord Śrī Caitanya Mahāprabhu. The Supreme Personality of Godhead is simultaneously different and nondifferent from this cosmic manifestation. In a previous verse it has been explained that the Supreme Personality of Godhead, like the root of a tree, is the original cause of everything. It was also explained how the Supreme Personality of Godhead is all-pervasive. He is present within everything in this material manifestation. Since the energy of the Supreme Lord is nondifferent from Him, this material cosmic manifestation is also nondifferent from Him, although it appears different. The sunshine is not different from the sun itself, but it is simultaneously also different. One may be in the sunshine, but he is not on the sun itself. Those who live in this material world are living on the bodily rays of the Supreme Personality of Godhead, but they cannot see Him personally in the material condition.
(Srimad Bhagavatam------4:31:16-------purport).

In this verse the philosophy of acintya-bhedābheda—simultaneous oneness and difference—is described. The living entity is eternal (nitya) like the Supreme Personality of Godhead, but the difference is that the Supreme Lord is the greatest, no one being equal to or greater than Him, whereas the living entity is sūkṣma, or extremely small. The śāstra describes that the magnitude of the living entity is one ten-thousandth the size of the tip of a hair. The Supreme Lord is all-pervading (aṇḍāntara-stha-paramāṇu-cayāntara-stham [Bs. 5.35]). Relatively, if the living entity is accepted as the smallest, there should naturally be inquiry about the greatest. The greatest is the Supreme Personality of Godhead, and the smallest is the living entity.
(Srimad Bhagavatam------6:16:9-------purport).

In Bhagavad-gītā the Supreme Personality of Godhead has explained that the material energy and spiritual energy both emanate from Him. The material energy is described as me bhinnā prakṛtir aṣṭadhā [Bg. 7.4], the eight separated energies of the Lord. But although the eight gross and subtle material energies—namely, earth, water, fire, air, ether, mind, intelligence and false ego—are stated to be bhinnā, separate from the Lord, actually they are not. As fire appears separate from wood and as the air flowing through the nostrils and mouth of the body appear separate from the body, so the Paramātmā, the Supreme Personality of Godhead, appears separate from the living being but is actually separate and not separate simultaneously. This is the philosophy of acintya-bhedābheda-tattva propounded by Śrī Caitanya Mahāprabhu. According to the reactions of karma, the living being appears separate from the Supreme Personality of Godhead, but actually he is very intimately related with the Lord. Consequently, even though we now seem neglected by the Lord, He is actually always alert to our activities. Under all circumstances, therefore, we should simply depend on the supremacy of the Supreme Personality of Godhead and thus revive our intimate relationship with Him. We must depend upon the authority and control of the Supreme Personality of Godhead.
(Srimad Bhagavatam------7:2:43-------purport).

The word param means "the supreme cause," and aparam means "the effect." The supreme cause is the Supreme Personality of Godhead, and the effect is material nature. The living entities, both moving and nonmoving, are controlled by the Vedic instructions in art and science, and therefore they are all expansions of the external energy of the Supreme Personality of Godhead, who is the center as the Supersoul. The brahmāṇḍas, the universes, exist during the duration of a breath of the Supreme Lord (yasyaika-niśvasita-kālam athāvalambya jīvanti loma-vilajā jagad-aṇḍa-nāthāḥ [Bs. 5.48]). Thus they are also within the womb of the Supreme Personality of Godhead, Mahā-Viṣṇu. Nothing, therefore, is separate from the Supreme Lord. This is the philosophy of acintya-bhedābheda-tattva.
(Srimad Bhagavatam------7:3:33-------purport).

True oneness, however, is not equivalent to the conception of the Māyāvādīs. The true understanding is that the differences are manifested by the energy of the Supreme Personality of Godhead. The seed is manifested as a tree, which displays varieties in its trunk, branches, leaves, flowers and fruits. Śrīla Bhaktivinoda Ṭhākura has therefore sung, keśava tuyā jagata vicitra: "My dear Lord, Your creation is full of varieties." The varieties are one and at the same time different. This is the philosophy of acintya-bhedābheda-tattva.
(Srimad Bhagavatam------7:9:31-------purport).

When one is completely in knowledge of ahaṁ brahmāsmi, he thinks, "I am part of the Supreme Lord, my body is made of His material energy, and therefore I have no separate existence. Yet although the Supreme Lord is spread everywhere, He is different from me." This is the philosophy of acintya-bhedābheda-tattva. An example given in this regard is that of the aroma within the earth. In the earth there are aromas and colors, but one cannot see them. Actually we find that when flowers grow from the earth, they appear with different colors and aromas, which they have certainly gathered from the earth, although in the earth we cannot see them. Similarly, the Supreme Lord, by His different energies, spreads throughout one's body and soul, although we cannot see Him.
(Srimad Bhagavatam------7:9:35-------purport).

Simply by raising one's staunch faith in Kṛṣṇa and His instructions, one can understand reality without a doubt (asaṁśayaṁ samagraṁ mām). One can understand how Kṛṣṇa's material and spiritual energies are working and how He is present everywhere although everything is not Him. This philosophy of acintya-bhedābheda, inconceivable oneness and difference, is the perfect philosophy enunciated by the Vaiṣṇavas. Everything is an emanation from Kṛṣṇa, but it is not that everything must therefore be worshiped. Speculative knowledge cannot give us reality as it is, but will continue to be nefariously imperfect. So-called scientists try to prove that there is no God and that everything is happening because of the laws of nature, but this is imperfect knowledge because nothing can work unless directed by the Supreme Personality of Godhead.
(Srimad Bhagavatam------7:15:58-------purport).