Why We Use the Term "Vedic" in Our Name
The word Veda has its Sanskrit root vid, which means "to know", or simply "knowledge". The word Veda also has three root meanings, representing its connection with the power of God, namely; 1) that Vedic knowledge is eternal; 2) Veda is the essential knowledge itself, which means that it provides knowledge of God, or that we can know the Supreme through the Veda; and 3) Veda gives the most desirable thing to the souls, which is the Divine Bliss that comes from our connection with God.
As most scholars on Vedic philosophy know, when you say Vedas you refer to the original four Vedas: the Rig, Yajur, Sama, and Atharva Vedas. From the four main Vedas are branches or appendices called Brahmanas, which relate to rituals and ceremonies. From these are derived the Aranyakas. The Upanishads are the appendices (the secret and esoteric knowledge) of the Aranyakas. When you say Veda (without the s) you not only refer to the four Vedas, but also to the Brahmanas, Aranyakas, and Upanishads, or all the texts that are considered Shruti. Shruti is considered the original revealed knowledge, which was unveiled to self-realized sages. The remaining parts of Vedic literature consist of the Mahabharata and Bhagavad-gita, the Ramayana, and the Puranas. These are the Itihasas or histories and supplemental portions of the Vedic literature, which they call Smriti, or that which is remembered. When we say "Vedic literature", it refers to both Shruti and Smriti in a general way. However, some scholars think that the Shruti is the genuine Vedic portions of this philosophy and more important than the Smriti. So some may object to the use of the word "Vedic" to refer to that which includes all of the Vedic texts, both Shruti and Smriti. However, this is not an accurate view according to the Vedic texts themselves.
For example, the Brihadaranyaka Upanishad (4.5.11) also relates: "The Rig, Yajur, Sama, and Atharva Vedas, the Itihasas, Puranas, Upanishads, verses and mantras, sutras, and the spiritual knowledge and explanations within, all emanate from the Supreme Being." It not only says it once, but the Brihadaranyaka Upanishad says it again (2.4.10) as follows: "As from a fire kindled with wet fuel, clouds of smoke issue forth, so, my dear, verily, from this glorious great God has been breathed forth the Rig-veda, the Yajur-veda, the Sama-veda, Atharvanagirasa, Itihasas, Puranas, science of knowledge, mystic doctrines or Upanishads, pithy verses, aphorisms, elucidations and commentaries. From Him, indeed, are all these breathed forth." Thus, they all have importance in presenting Vedic information, and one should not be biased toward one set of shastra or scripture to exclude the other. Therefore, to leave out the supplemental portions of the Vedic literature would deprive the reader of an enormous amount of Vedic knowledge and elaborated explanations. In this way, if anyone feels the "Vedic" tradition includes only the four Vedas up to the Upanishads, the Vedic tradition itself shows this as a wrong view, and that all of the ancient texts which support the Vedic conclusion are also Vedic and should be considered as such.
The Mahabharata (Adi Parva 1.267) explains the necessity of understanding Vedic knowledge with the help of the Puranas: "One should expand and accept the meaning of the Vedas with the help of the Itihasas and Puranas. The Vedas are afraid of being mistreated by one who is ignorant of the Itihasas and Puranas." This is quite similar to what is related in the Prabhasa-khanda (2.93) section of the Skanda Purana, where it is said, "I consider the Puranas equal to the Vedas. . . The Vedas feared that their purport would be distorted by inattentive listening, but their purport was established long ago by the Itihasas and Puranas. What is not found in the Vedas is found in the smritis. And what is not found in either is described in the Puranas. A person who knows the four Vedas along with the Upanishads but who does not know the Puranas is not very learned." In this way, we should understand that one's education in Vedic culture and science is not complete if one excludes the understanding and knowledge given in the Puranas and the Itihasas. It is the Puranas which more fully explain that which is found in the four Vedas.
To further verify this point, in the Naradiya Purana Lord Shiva is quoted as saying to his wife Parvati that, "I consider the message of the Puranas to be more important than that of the Vedas. All that is in the Vedas is in the Puranas without a doubt." So I relate this simply for those who feel that there should be some further distinction between Shruti and Smriti and may object to the use of the term "Vedic" within our name--The Vedic Friends Association--although many parts of the Vedic literature point to the need for using the Puranas and other portions of the Smritis to more fully understand the depths of Vedic knowledge.
Furthermore, some of the greatest of spiritual authorities, like Shankaracarya, Ramanujacarya, Madhvacarya, and others, have presented Smriti as valid evidence of spiritual truths and wrote commentaries on Bhagavad-gita. In fact, Madhvacarya, in his commentary on the Vedanta-sutras (2.1.6), quotes the Bhavishya Purana, which states: "The Rig-veda, Yajur-veda, Sama-veda, Atharva-veda, Mahabharata, Pancaratra, and the original Ramayana are all considered Vedic literature. The Vaishnava supplements, the Puranas, are also Vedic literature." This would obviously mean that the knowledge within them is also Vedic. Even the Chandogya Upanishad (7.1.4) mentions the Puranas as the fifth Veda. The Srimad-Bhagavatam (1.4.20) also clearly agrees with this: "The four divisions of the original sources of knowledge (the Vedas) were made separately. But the historical facts and authentic stories mentioned in the Puranas are called the fifth Veda." Therefore, why should we argue with these conclusions? Actually, when it comes to understanding the verdict of the Vedic tradition, we should understand it as presented by the Vedic authorities and the tradition itself rather than depending on other standards.