QuestionsCan we be certain of anything?Induction by elimination
Can we be certain of anything?Through experience, with care

Induction by elimination

Francis Bacon 1561 · 1626Knowledge is power: observe and experiment.
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What it claims

Induction by elimination finds the true cause of a phenomenon (its "form", Bacon says), far more surely than induction by simple enumeration.

Why

A single contrary case rules out a hypothesis; by eliminating whatever is absent when the phenomenon is present, the cause remains.

In short

"Induction by elimination" is an argument by Francis Bacon (Novum Organum, I, 105 and II, 11-20 (1620)) on the question "Can we be certain of anything?" (answer: through experience, with care). Its claim: Induction by elimination finds the true cause of a phenomenon (its "form", Bacon says), far more surely than induction by simple enumeration. According to AskPhilosophy's logic check (Z3 solver), the argument is valid only if one grants a premise the author leaves unstated (P4, P5). AskPhilosophy presents 4 objections, 1 of them with a documented reply, and the original text behind each premise, checked word for word.

Novum Organum, I, 105 and II, 11-20 (1620)
Valid with an implicit premise

Take a modern example: "all the swans I have seen are white, so all swans are white". Bacon calls this kind of reasoning, by simple enumeration, a "childish" induction, because a single contrary instance (a black swan) is enough to ruin it. He proposes to turn the difficulty around: since a single contrary instance is enough to rule out a hypothesis, let us use it. To find the cause of heat, we draw up three tables: cases where there is heat, neighbouring cases where there is none, cases where it increases or decreases. Then we eliminate every explanation that fails a single one of these tests. What remains is the cause. His own attempt, his "first vintage", concludes that heat is a motion.

P1A single contrary instance is enough to rule out a hypothesis about the cause of a phenomenon.
P2We can gather, in the manner of a history and without premature speculation, the instances where the phenomenon is present, the closely related ones where it is absent, and those where it varies: these are the three tables.
P3With these tables, we rule out every explanation that is absent where the phenomenon is present, present where it is absent, or that does not vary with it. Only one remains.
P4 · implicit premiseThe true cause was among the explanations examined, and these were well defined: the one that remains is therefore the cause, in the cases studied.
P5 · implicit premiseA cause found in the cases studied holds everywhere and always: nature follows the same laws in the cases we have not observed.
Therefore induction by elimination finds the true cause of a phenomenon (its "form", Bacon says), far more surely than induction by simple enumeration.

click a premise to reject it

If you accept every premise, logic forces you to accept the conclusion. So the debate is about the premises.
Checked by a logic solver: the premises cannot all be true while the conclusion is false.
Without the implicit premise: Without P4, the computer finds a case where all explanations but one have been ruled out, but the true cause was not on the list: the survivor is wrong. Without P5, the cause is found for the cases studied, but nothing guarantees it holds for the others.
Valid with two implicit premises, and every premise is indispensable. The negative part is very solid: ruling out a hypothesis contradicted by a fact is flawless reasoning (P1). The weakness lies in the positive part: for the survivor to be the true cause, the right answer must have been on the list (P4), and what holds for the cases studied must hold elsewhere (P5). Bacon himself sees the difficulty of P4 (NO II, 19); P5 is what Hume will attack.
Analogy. A detective has five suspects. One was abroad, another in hospital, three do not have the key: only one is left. The reasoning is strong, on one condition: that the culprit really is among the five. Bacon has his own image too: the true scientist is neither the ant that hoards nor the spider that spins its web out of itself, but the bee that gathers and then transforms.

Objections

4

Each objection is a conversation: click to see who replies and where the debate stands.

Objection anticipated by Bacon attacks premise 4

But if our notions of simple natures (the elemental, the heavenly, the rare…) are still vague and ill-defined, how can the exclusion be accurate?

Bacon replies
Bacon
Since truth will sooner come out from error than from confusion, Bacon allows the mind, once the three tables have been drawn up and weighed, to venture a first, provisional positive interpretation: his "first vintage". On heat, it concludes that heat is a motion.
The debate goes on (our summary) Just before (II, 19), Bacon admits that exclusion cannot be perfect at the start, and he announces more powerful aids for the understanding. But Book II breaks off unfinished before giving them all. The "vintage" answers the problem of vague notions by accepting a provisional hypothesis; it does not guarantee that the true cause was on the list (P4).
Hume 1748 · attacks premise 5

Every conclusion drawn from experience assumes that the future will resemble the past. Yet that resemblance cannot be proved by experience without arguing in a circle. Bacon's tables show what happened in the cases observed: nothing more. Believing that the cause found will hold tomorrow is a habit, not a proof.

no reply
No reply possible: objection raised in 1748, after the author's death (1626).
The debate goes on (our summary) The objection does not target Bacon alone: it hits all experimental science. Bacon, like his successors, takes for granted that nature has constant laws. Hume's problem is still debated today (see Hume's argument on induction).
Kant 1787 · attacks premise 2

Observations made at random, according to no preconceived plan, never yield a law. Reason must question nature as a judge questions witnesses: with its own questions, designing its experiments according to its principles. So gathering facts "without premature speculation" is not enough: a question and a principle must come first.

no reply
No reply possible: objection raised in 1787, after the author's death (1626).
The debate goes on (our summary) Kant does not reject Bacon: in the same preface he credits "Bacon of Verulam" with partly prompting, partly stimulating the revolution of experimental physics. What he objects to is the idea of neutral observation. Bacon, for his part, wanted "experience duly ordered" (NO I, 82) and allowed a provisional hypothesis (NO II, 20).
Karl Popper 1934 · attacks premise 4

The list of possible explanations is never complete: there are always infinitely many. Elimination can therefore never prove a theory true. Science advances by bold conjectures that we try to refute; a theory that survives is not proved, only not yet refuted.

no reply
summary: their text is not yet in our corpus
No reply possible: objection raised in 1934, after the author's death (1626).
The debate goes on (our summary) Popper keeps Bacon's strongest idea: the asymmetry between confirming and refuting (P1). He draws a more modest conclusion from it: science does not find "the true form", it rules out errors. Both agree on the decisive role of the contrary instance.
What today's voices say
Criticize it
Karl PopperAgainst the idea that science starts from piling up observations: it starts from conjectures.