In Indian inferential logic, any claim that “where X is, Y is” is supported by two structured sets of instances. The sapakṣa — the “similar locus” — is the set of cases where the property being established (the sādhya) is known to be present, and where the reason being offered (the hetu) is also present. The kitchen, the iron-foundry: places where fire is known to be present and where smoke is also observed. The vipakṣa — the “dissimilar locus” — is the set of cases where the property is known to be absent. The lake at dawn: a place where fire is known to be absent, and where smoke is also absent. Both sets are needed. The sapakṣa shows the reason accompanying the property; the vipakṣa shows the reason absent when the property is absent.
A reason that appears in the sapakṣa but also in the vipakṣa is doing no work — its presence does not discriminate. A reason that fails to appear in the sapakṣa is doing no work for a different reason. The two-set discipline is what distinguishes inference from accidental co-occurrence. Pervasion (vyāpti, N2) is established by surveying both sets and finding the structure right.
Where English Falls Short
Machine learning has positive and negative training data, and statistics has control groups, so the structure is recognisable in English. What is missing is the normative force. ML positive and negative sets are descriptive — these are the labels we happen to have. The Nyaya treatment is prescriptive — these are the kinds of instances that must be surveyed for the inference to be valid, and the failure modes of each are named.
In particular, the Indian frame foregrounds a question ML practice often elides: are there counter-instances we have not seen? A reason can pass the sapakṣa test on every instance we have and still fail because the vipakṣa search was thin. The classic Nyaya example asks whether a reason that has only been surveyed in some loci can be relied on as pervading — and the answer, repeatedly, is that the vipakṣa must be canvassed systematically. Casual observation in passing does not meet the test.
Where it Shows Up
Training data design. Most failure modes in ML come from inadequate negative instance sets. Models that learn to detect cats by being shown many cats but few non-cats end up with reason structures that pass the sapakṣa and fail the vipakṣa — they classify almost anything as a cat. The Nyaya discipline asks whether the dissimilar locus has been canvassed at the same depth as the similar locus.
A/B test interpretation. The treatment group is the sapakṣa; the control is the vipakṣa. A lift in treatment is suggestive; a lift in treatment together with a flat control is what actually carries the inference. Many product teams report the treatment effect without examining whether the control behaved as expected, which is a vipakṣa-side failure.
Counterexample search in research synthesis. When summarising “what we know about X,” the sapakṣa (papers where X is found) is easy. The vipakṣa (papers where the conditions for X were present but X did not appear) is harder, and its absence in the synthesis is a hidden invalidity.
Eval rubric design. “When does the model succeed?” is the sapakṣa question. “Under what conditions does the model fail when it should not?” is the vipakṣa question. Many AI evals have rich positive batteries and thin negative ones.
Safety testing. Red-teaming is a structured vipakṣa search — the discipline of finding the conditions under which a system fails. A safety claim that has only been tested against the sapakṣa (the cases where the system worked) is unsupported in the Nyaya sense.
Diagnostic Question
“Have I canvassed thevipakṣaat the same depth as thesapakṣa— and have I actually looked for the cases where the property was absent and the reason should have been absent too?”
IKS Roots
The Sanskrit terms are sapakṣa (सपक्ष), literally “with the same side,” and vipakṣa (विपक्ष), literally “with the opposite side.” Both are technical terms within the structure of anumāna (inferential cognition). Their formal role appears in the analysis of any inference: the reason (hetu) must be present in the sapakṣa and absent in the vipakṣa — and the technical machinery for testing this becomes the heart of Navya-Nyaya from Gangesha onward. The set of fallacies of the reason (hetvābhāsa) is partly defined by failures at the sapakṣa-vipakṣa level: anaikāntika (where the hetu appears in both), asiddha (where it appears in neither), and so on. See N5 for one of these (satpratipakṣa).
See also N2 (vyāpti — the relation these instance sets are used to establish) and N1 (the wider pramāṇa frame).
Further Reading
Bimal Krishna Matilal, Logic, Language and Reality (Motilal Banarsidass), for the integration of sapakṣa-vipakṣa into the broader theory of inference. Stephen Phillips, Classical Indian Metaphysics, for the Navya-Nyaya elaboration. The Anumana-khanda of Gangesha’s Tattvacintamani is the canonical technical treatment, available in modern translation.