Nyaya and Vaisheshika: Pramanas, Padartha and Inference
Pramāṇas and padārthas
Nyāya lists four pramāṇas: pratyakṣa (perception), anumāna (inference), upamāna (comparison/analogy) and śabda (reliable testimony). Vaiśeṣika analyses reality into padārthas: dravya (substance), guṇa (quality), karma (action), sāmānya (universal), viśeṣa (particularity), samavāya (inherence), with abhāva (absence) added later. The two schools combine as Nyāya-Vaiśeṣika.
Inference
Anumāna requires pakṣa (subject), sādhya (what is proved), hetu (reason) and vyāpti (pervasion). Nyāya's five-membered form is pratijñā, hetu, udāharaṇa, upanaya, nigamana. A good hetu must be present in the pakṣa, pervaded by the sādhya, and absent from contrary cases.
Worked example
'This hill has fire' (pratijñā); 'because it has smoke' (hetu); 'wherever smoke, there fire, as in a kitchen' (udāharaṇa); 'this hill has such smoke' (upanaya); 'therefore this hill has fire' (nigamana). The reasoning is only as strong as vyāpti; a smoky-hill counterexample or a faulty reason (e.g. mistaking haze for smoke) breaks it.
Traps
Do not define upamāna as mere comparison of two known things; it is knowledge of a name through similarity. Śabda is testimony from a reliable speaker, not any rumour. Validity of inference is not the same as truth of conclusion. Do not omit abhāva when a sevenfold padārtha list is expected.