⁂ Concepts · Knowledge · No. 48
Inference

Fire detection: what is measured is heat, and what is reported is fire.

Inference

Moving from what you have to what you do not - concluding one thing on the strength of another.

Theme
Knowledge, truth and reason
Tradition
Cross-tradition
Term
अनुमान · anumāna
Term fixed
c. 330 BC

In plain terms

You see smoke and conclude there is fire. Nothing about the smoke is fire, and you did not see the fire. Something got you across the gap.

What carries you is a general connection: where there is smoke, there is fire. That connection has to be reliable, or the crossing fails. And it has to be applied correctly - smoke on a stage or steam from a kettle will trip it.

Every piece of knowledge that goes beyond what is directly present depends on this and nothing else. Everything about the past, everything about other people's minds, everything about what will happen, everything from an instrument. Which makes inference the most heavily used mechanism in the whole of knowledge, and the one whose failures are hardest to notice from inside.

As a philosopher would put it

A deductive inference is truth-preserving: if the premises are true the conclusion cannot be false. Non-deductive inference is ampliative - it says more than the premises guarantee - and buys content at the cost of certainty. Every interesting inference is of the second kind.

The Nyāya analysis is unusually careful about what makes it work. The relation required is vyāpti, pervasion: wherever the mark is present the thing inferred is present, established by observed co-presence, absence of counterexample, and the absence of any defeating condition. The five-membered demonstration - thesis, reason, example, application, conclusion - includes an instance, which Aristotle's syllogism does not, and Nyāya's catalogue of hetvābhāsas, pseudo-reasons, is a systematic theory of exactly how inference goes wrong.

Hume's problem sits underneath the whole subject. The general connections that carry every ampliative inference are themselves established by inference from experience, which is circular - and no one has produced an answer that is generally accepted.

Where you meet it

Nobody at NASA sees most of the world's wildfires. Satellite instruments detect them by measuring radiance in two infrared bands, comparing a candidate pixel against its neighbours, and flagging it when the difference exceeds a threshold that varies with time of day, land cover and viewing angle.

What is measured is heat. What is reported is fire. Between them sits a general connection established from ground-truthed cases, plus a list of known defeaters - gas flares, hot bare soil, sun glint off water, factory roofs - each of which produces the mark without the thing.

That is the smoke-and-fire inference industrialised, with the pervasion relation written down and the pseudo-reasons enumerated. The system publishes a confidence value with every detection because the inference is ampliative and everybody knows it. And the failures are exactly the ones Nyāya catalogued: a mark present where the thing is absent, and a defeating condition unnoticed.

What is actually disputed

Whether ampliative inference can be justified.

Hume's argument is that any attempt to justify the move from observed to unobserved must appeal to the uniformity of nature, which is itself known only from observation, so the justification is circular. Two and a half centuries of replies - pragmatic vindication, inductive intuition, Bayesian coherence, Popper's proposal to abandon justification for falsification - have each attracted committed defenders and none has closed the question.

A quieter dispute concerns whether deduction and non-deductive inference are really the same kind of thing. On one view they are points on a spectrum of strength. On another, deduction is a matter of what follows and non-deductive inference is a matter of what to believe, which are different subjects that share a word - and the Buddhist epistemologists, who treat inference as concerned with exclusion rather than with entailment, arrive at something closer to the second.

Commonly confused with

  • Intuition 1641 Both deliver conclusions. Inference has traceable steps and intuition does not, which is the whole difference.

Defined against

  • Perception The two are the standard pair in almost every epistemology: what is present to you, and what you get to from it

Philosophers

  • Aristotle The first formal treatment of what follows from what
  • Vasubandhu The Buddhist analysis of the mark and its conditions
  • David Hume The problem that no ampliative inference is justified
  • John Stuart Mill The methods for identifying causes from patterns of occurrence
  • Charles Sanders Peirce The three-way division into deduction, induction and abduction

Works

Schools

Related concepts

Deduction c. 330 BC · Induction c. 330 BC · Abduction 1878 · Pramāṇa c. 200 · Reason c. 500 BC

Aristotle's syllogistic is the first formal treatment in Europe; the Nyāya analysis of anumāna, with its five-membered demonstration and its requirement of a pervasion relation, is developed independently and is in some respects more careful.