In Hinduism, what exactly is a lie? And is lying adharma?
First lying is adharma; although you may not be hurting someone else, you are hurting yourself.
One should always tell the truth, but one should never tell a harsh truth. A harsh truth is a truth that is hurtful or cause offense in some way or perhaps feeds your own ego (this is really being hurtful to your own self).
This does not mean you should lie. You can say something that can be interpreted in several ways, or an evasive answer, or reply with another question (example: 'Who am I to know about that?'), or you can be silent. This is supported in scripture.
In your 3 examples:
1) not a lie; unless you are gaining some unknown advantage by saying so.
2) Morally wrong. Completely.
3) Depends on why you are doing. If you're trying to avoid a harsh truth, then no. If you're just lying with your actions instead of words, then yes it is a lie. A lie is a lie is a lie, doesn't matter if you use words or actions.
Swami Nikhilananda in his writings on Hindu ethics says:
Besides the objective duties based on the castes and stages of life, there are laid down the common duties of men, the sadharanadharma, which are the foundation of the moral life. Manu, the lawgiver, enumerates these common duties as follows: steadfastness (dhairya), forgiveness (kshama), good conduct (dama), avoidance of theft (chauryabhava), control of the senses (indriyanigraha), wisdom (dhi), learning (vidya), truthfulness (satya) and absense of anger (akrodha)...the aim of Hindu ethics is to enable a man ultimately to conquer his lower self and attain freedom from passion, desire, and attachment.
All Hindu philosophers regardless of their conceptions of the supreme end of man, admit the empirical reality of the individual, endowed with volition, desire, will, conscience or consciousness of duty, emotion, etc. The goal of Hindu ethics is to train these faculties in such a way that they shall lead the individual to the realization of Moksha, or Liberation. Therefore all the schools of philosophy have described the virtues and their opposites in detail. It is expected of the moral agent that he should follow the former and shun the latter. We propose to discuss the virtues and their opposites according to the classification of Nyaya and of Patanjali's system.
Vatsyayana, in his commentary on the Nyaya aphorisms, classifies will as impious (papatmika) and auspicious (subha). The impious will leads to unrighteousness (adharma), and the auspicious will, to righteousness (dharma). Righteousness, it is necessary to add, is conductive to the Highest Good, whereas unrighteousness produces evil. The purpose of ethics is to subdue the impious and to manifest the righteous will.
Unrighteousness may take three forms, namely, physical, verbal, and mental, depending upon the condition of its functioning. Physical unrighteousness manifests itself asa cruelty (himsa), theft (steya), and sexual perversion (pratisiddha maithuna); verbal unrighteousness, as falsehood (mithya), rudeness (katukti), insinuation (suchana), and gossip (asambaddha); mental unrighteousness, as ill-will (paradroha), covetousness (paradravyabhipsa), and irreverance (nastikya).
The practice of continence, highly extolled by all the philosophers and mystics of India, implies, besides the literal meaning of the vow, abstention from lewdness in thought, speech, and action through any of the sense-organs. Through the practice of this virtue, one develops the capacity for subtle spiritual perception.
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