I mean, I'm a materialist so I do not believe in deities or souls or spirits, but I understand Hinduism can be atheistic, but I haven't read much on how that works.
There is a strong strand of empirical and rationalism based investigations in Hinduism articulated not only in Nyaya but also in Vaisesika and Nyaya schools of classical and medieval Hinduism.
The posts in this thread would be of interest
Place of Rational Inquiry in Dharmic Worldviews
Of specific substance :-
Posts 1, 2, 4, 15, 19, 24, 26, 66
and then the last page
Place of Rational Inquiry in Dharmic Worldviews
Posts 145, 146, 154, 156, 160.
In these posts I (and a few others) have traced the evolution of an early form of evidence and reason based inquiry that began in 500 BCE (appx.) to a sophisticated methodology of doing an evidence and reason based investigation and a sketch of a metaphysical system that has a very modern approach to things by about 900 CE.
Key points:-
(1)
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Arthashastra (1.2.11):- (200 BCE appx.)
Investigating by means of reasons - good and evil in the Vedic religion, profit and loss in the field of trade and agriculture, and prudent and imprudent policy in political administration, as well as their relative strengths and weaknesses - the study of critical inquiry (anviksiki) confers benefit on people, keeps their minds steady in adversity and prosperity, and produces adeptness of understanding, speech and action.
The study of critical inquiry is always thought of as a lamp for all branches of knowledge, a means in all activities, and a support for all religious and social duty.
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(2)
While commenting on the Nyayasutra (100 BCE-100 CE), Vatsyyana tries to explicate what is it that distinguishes his school from the others. He writes (translation by Dr. Ganeri):-
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Nyaya is the examination of things with the help of methods of knowing (pramana). It is an inference supported by observation and authority.This is called a critical proof (anviksa). A critical proof is the proof of things desired, supported by observation and authority. The discipline of critical inquiry is the one which pertains to it, and is also called the science of nyaya or writings on nyaya. But an inference that contradicts observation and authority is only bogus-nyaya.
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In a second set of important passages (which I paraphrase below) Vatsyayana lays out why its so important to learn the correct methods of knowing:-
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By cognition, a cognizer (jnani) grasps an object/objective/purpose/meaning (artha) in his conscious mind. This then creates either a desire for that object (artha) or an aversion from it. Then he makes an effort to either obtain it or to avoid it. Success is then the coming together of that activity with its reward (actually obtaining or avoiding the object (artha)) and the contentment one feels due to this. Such success can only be produced if the original cognition of the object and its qualities were veridical (as opposed to a mirage of water say). And veridical cognition can only be guaranteed if the cognition was obtained by an accredited method of knowing (pramana). Nyaya then, is the study of identifying when such accredited methods of knowing occurs and a systematic study of what is cognized through them.
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The word "artha" in Sanskrit is multivalent (just like dharma). It can mean:- meaning, purpose, one's goal, the thing that is one's goal. The correct cognition (jnana) of such an artha (from the mundane to the transcendental, like the Purushartha-s) can only be guaranteed if they cognized through an accredited means of knowing/cognition (pramana), and nyaya is the study of what methods do guarantee such a thing. Crucially, while Arthashastra used anviksiki to aid one to get to one's goals; Nyaya, Vatsyayana claims, also helps one to correctly perceive what those goals (artha-s) really are or should be. This transition makes Nyaya a normative philosophical school of thought in its own right.
(3) Mode of Inquiry
According to the philosophers of Nyaya, every investigation begins with the arising of a
doubt. The doubt can be mundane (Is this piece of information true?) to deeply spiritual/moral/philosophical (Is this right? What should I do?). Typical of the school, doubt, the font of all inquiry is very precisely defined in the sutra and then expanded upon in the commentary by several examples:-
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Doubt is the conflicting judgement about the precise character of an object. It arises from the recognition of properties common to many objects (viz. is the tall thing over there seen in the twilight a man or a post?) ; or of properties not common to any of the objects (viz. what kind of an entity is sound?) ; Conflicting testimony (viz. merely by study one cannot determine if the soul exists or not, as various texts say different things); and from irregularity of perception (mirage) and non-perception (not perceiving the presence of water in a vegetable).
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Nyaya also places great stress on
purpose of the inquiry. What purpose will be achieved if the doubt is resolved. Nyaya beleives that unmotivated inquiry is going to be fruitless as there will be no reason for making an honest effort for getting at a resolution.
Once the specific form of the doubt and the purpose of inquiry has been resolved one goes to what observational data is there. The definition of observational data (drstanta) is interesting:-
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An observational data is the thing about which an ordinary man and an expert entertain the same opinion.
(Like everyone agrees that smoke is co-located with fire in the case of a kitchen fire.)
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Thus one starts the investigation with instances of observation with which common man agrees.
An
established tenet is some theory or premise that is accepted by all parties interested in the investigation. This may be due to everyone truly agrees to it, or are curious to see if accepting it on a hypothetical basis leads to fruitful results or not.
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So far so good. Now comes the crucial
parts of the actual demonstration that resolves the doubt (avayava). There will be a lot of work on this by both Buddhists and later Nyaya scholars. But Gautama writes down the parts of the demonstration as
i) Preliminary statement of the thesis to be demonstrated that resolves doubt. (The hill is fiery).
ii) Citation of reason. ( Because it is smoky).
iii) Invoking an example ( As in a kitchen fire, where smoke is seen with fire in a kitchen.)
iv) Application to the present case . (Similarly smoke is seen in the hill.)
v) Conclusion:- Thus there is fire on the hill.
Nyaya claims that a proper method of knowing the truth can be guaranteed only if the conclusion can be established by the successful formulation of a demonstration in such a canonical step by step format. Vatsyayana emphasizes this in his commentry:-
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The means of acquiring knowledge reside in those demonstration steps. The preliminary statement of the thesis is an item of testimony (agama). The reason (hetu) is an item of inference. The example is an item of perception. The application is an item of analogical comparison. The final conclusion exhibits the possibility of all these coming together in a single thesis. Such is Nyaya par excellence. Fixing the truth depends on this.
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Continued...