Vaisheshika or Vaiśeṣika (Sanskrit: वैशेषिक) is one of the six orthodox schools of Hindu philosophy (Vedic systems) from ancient India. In its early stages, the Vaiśeṣika was an independent philosophy with its own metaphysics, epistemology, logic, ethics, and soteriology. Over time, the Vaiśeṣika system became similar in its philosophical procedures, ethical conclusions and soteriology to the Nyāya school of Hinduism, but retained its difference in epistemology and metaphysics.
The epistemology of Vaiśeṣika school of Hinduism, like Buddhism, accepted only two reliable means to knowledge: perception and inference. Vaiśeṣika school and Buddhism both consider their respective scriptures as indisputable and valid means to knowledge, the difference being that the scriptures held to be a valid and reliable source by Vaiśeṣikas were the Vedas.
Vaisheshika school is known for its insights in naturalism,  it is a form of atomism in natural philosophy. It postulated that all objects in the physical universe are reducible to paramāṇu (atoms), and one's experiences are derived from the interplay of substance (a function of atoms, their number and their spatial arrangements), quality, activity, commonness, particularity and inherence. According to Vaiśeṣika school, knowledge and liberation were achievable by complete understanding of the world of experience.
Although the Vaisheshika system developed independently from the Nyaya school of Hinduism, the two became similar and are often studied together. In its classical form, however, the Vaishesika school differed from the Nyaya in one crucial respect: where Nyaya accepted four sources of valid knowledge, the Vaishesika accepted only two.
Vaisheshika espouses a form of atomism, that the reality is composed of four substances (earth, water, air, fire). Each of these four are of two types, explains Ganeri, atomic (paramāṇu) and composite. An atom is that which is indestructible (anitya), indivisible, and has a special kind of dimension, called “small” (aṇu). A composite is that which is divisible into atoms. Whatever human beings perceive is composite, and even the smallest perceptible thing, namely, a fleck of dust, has parts, which are therefore invisible. The Vaiśeṣikas visualized the smallest composite thing as a “triad” (tryaṇuka) with three parts, each part with a “dyad” (dyaṇuka). Vaiśeṣikas believed that a dyad has two parts, each of which is an atom. Size, form, truths and everything that human beings experience as a whole is a function of atoms, their number and their spatial arrangements.
Vaisheshika postulated that what one experiences is derived from dravya (substance: a function of atoms, their number and their spatial arrangements), guna (quality), karma (activity), samanya (commonness), vishesha (particularity) and samavaya (inherence, inseparable connectedness of everything).
Hinduism identifies six Pramāṇas as epistemically reliable means to accurate knowledge and to truths: Pratyakṣa (perception), Anumāna (inference), Upamāna (comparison and analogy), Arthāpatti (postulation, derivation from circumstances), Anupalabdhi (non-perception, negative/cognitive proof) and Śabda (word, testimony of past or present reliable experts). Of these Vaiśeṣika epistemology considered only pratyakṣa (perception) and anumāna (inference) as reliable means of valid knowledge. Nyaya school, related to Vaiśeṣika, accepts four out of these six.
The earliest systematic exposition of the Vaisheshika is found in the Vaiśeṣika Sūtra of Kaṇāda (or Kaṇabhaksha). This treatise is divided into ten books. The two commentaries on the Vaiśeṣika Sūtra, Rāvaṇabhāṣya and Bhāradvājavṛtti are no more extant. Praśastapāda’s Padārthadharmasaṁgraha (c. 4th century) is the next important work of this school. Though commonly known as bhāṣya of Vaiśeṣika Sūtra, this treatise is basically an independent work on the subject. The next Vaisheshika treatise, Candra’s Daśapadārthaśāstra (648) based on Praśastapāda’s treatise is available only in Chinese translation. The earliest commentary available on Praśastapāda’s treatise is Vyomaśiva’s Vyomavatī (8th century). The other three commentaries are Śridhara’s Nyāyakandalī (991), Udayana’s Kiranāvali (10th century) and Śrivatsa’s Līlāvatī (11th century). Śivāditya’s Saptapadārthī which also belongs to the same period, presents the Nyāya and the Vaiśeṣika principles as a part of one whole. Śaṁkara Miśra’s Upaskāra on Vaiśeṣika Sūtra is also an important work.
According to the Vaisheshika school, all things that exist, that can be cognized and named are padārthas (literal meaning: the meaning of a word), the objects of experience. All objects of experience can be classified into six categories, dravya (substance), guṇa (quality), karma (activity), sāmānya (generality), viśeṣa (particularity) and samavāya (inherence). Later Vaiśeṣikas (Śrīdhara and Udayana and Śivāditya) added one more category abhava (non-existence). The first three categories are defined as artha (which can perceived) and they have real objective existence. The last three categories are defined as budhyapekṣam (product of intellectual discrimination) and they are logical categories.
1.Dravya (substance): The substances are conceived as 9 in number. They are, pṛthvī (earth), ap (water), tejas (fire), vāyu (air), ākaśa (ether), kāla (time), dik (space), ātman (self or soul) and manas (mind). The first five are called bhūtas, the substances having some specific qualities so that they could be perceived by one or the other external senses.
2.Guṇa (quality): The Vaiśeṣika Sūtra mentions 17 guṇas (qualities), to which Praśastapāda added another 7. While a substance is capable of existing independently by itself, a guṇa(quality) cannot exist so. The original 17 guṇas (qualities) are, rūpa (colour), rasa (taste), gandha (smell), sparśa (touch), saṁkhyā (number), parimāṇa (size/dimension/quantity), pṛthaktva (individuality), saṁyoga (conjunction/accompaniments), vibhāga (disjunction), paratva (priority), aparatva (posteriority), buddhi (knowledge), sukha (pleasure), duḥkha (pain), icchā (desire), dveṣa (aversion) and prayatna (effort). To these Praśastapāda added gurutva (heaviness), dravatva (fluidity), sneha (viscosity), dharma (merit), adharma (demerit), śabda (sound) and saṁskāra (faculty).
3.Karma (activity): The karmas (activities) like guṇas (qualities) have no separate existence, they belong to the substances. But while a quality is a permanent feature of a substance, an activity is a transient one. Ākāśa (ether), kāla (time), dik (space) and ātman (self), though substances, are devoid of karma (activity).
4.Sāmānya (generality): Since there are plurality of substances, there will be relations among them. When a property is found common to many substances, it is called sāmānya.
5.Viśeṣa (particularity): By means of viśeṣa, we are able to perceive substances as different from one another. As the ultimate atoms are innumerable so are the viśeṣas.
6.Samavāya (inherence): Kaṇāda defined samavāya as the relation between the cause and the effect. Praśastapāda defined it as the relationship existing between the substances that are inseparable, standing to one another in the relation of the container and the contained. The relation of samavāya is not perceivable but only inferable from the inseparable connection of the substances.
According to the Vaiśeṣika school, the trasareṇu are the smallest mahat (perceivable) particles and defined as tryaṇukas (triads). These are made of three parts, each of which are defined as dvyaṇuka (dyad). The dvyaṇukas are conceived as made of two parts, each of which are defined as paramāṇu (atom). The paramāṇus (atoms) are indivisible and eternal, they can neither be created nor destroyed. Each paramāṇu (atom) possesses its own distinct viśeṣa (individuality).
The measure of the partless atoms is known as parimaṇḍala parimāṇa. It is eternal and it cannot generate the measure of any other substance. Its measure is its own absolutely.