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A Historical Introduction to the
Philosophy of Science

Ch. 10: Inductivism v. the Hypothetico-Deductive View of Science

Book cover: A Historical Introduction to the Philosophy of Science by John Losee

The following is a summary of the tenth chapter of John Losee's book, A Historical Introduction to the Philosophy of Science (fourth edition), with some ancillary notes.

Philosophers discussed in this chapter: John Stuart Mill (1806–73); William Stanley Jevons (1832–82)

Mill's Inductivism

(p. 133) Inductivism posits that:

  1. scientists discover laws and theories by generalizing inductively from observations and experiment
  2. scientists justify scientific laws and theories with evidence using inductive principles

(pp. 133–4) Mill's four inductive methods are:

  1. Method of Agreement
  2. Method of Difference (most important)
  3. Method of Concomitant variations
  4. Method of Residues

Losee objects that with Mill's Method of Difference:

  1. no two instances are exactly alike bar one circumstance (e.g., place, time)
  2. not all circumstances are equally relevant (e.g., handling method versus sunspot activity)

(p. 134) Mill responded that considering only a small number of circumstances is justified by experience.

(p. 135) Losee notes that prior to applying Mill's Method of Difference schema, the scientist must devise a hypothesis about which circumstances are relevant for controlled experimentation.

Mill saw his Method of Agreement limited by:

  1. not knowing all of the relevant circumstances
    [LA: e.g., poor school performance due to socio-economics and not race]
  2. different causes may give the same effect (e.g., B caused a in 1 and 3, and D caused a in 2)

Mill suggested varying the circumstances in order to increase the probability of cause.

(pp. 135–6) Mill thought the possibility of the plurality of causes is not a problem for his Method of Difference when applied to a single instance.

Losee objects that Mill's reference to 'a cause in this instance' contradicts his notion of a cause as an invariant set of circumstances preceding a particular effect.

(p. 136) Jevons objects that Mill unjustifiably assumed that a correlation in a single experiment will happen in other experiments (contradicting the principle of inductive inference).

In spite of Mill's overstatement on the inductive method, he agreed with Whewell on the importance of hypothesis generation.

Mill described two types of multiple causation:

  1. various causes continue to produce their own separate effects

  2. resultant effect is other than the effects produced separately:

    1. resultant effect is the 'vectorial sum' of the causes present (Composition of Causes)
    2. resultant effect differs in kind from the otherwise separate effects

(pp. 136–7) Mill held his four inductive methods can be applied to types 1. and 2.b. above, but not to type 2.a. (Composition of Causes).

(p. 137) Mill thought they cannot be applied to Composition of Causes cases (e.g., vectorial addition of separate forces along a parallelogram) as same motion can be generated from infinitely many sets of forces.

(p. 138) For Composition of Causes cases, Mill recommended the Deductive Method in three stages:

  1. formulation of a set of laws (by induction from observation or by hypothesis)
  2. deduction of a statement of resultant effect from a combination of laws
  3. complete verification by deductive consequences agreeing with observations and no other hypothesis entailing same consequences
A System of Logic by John Stuart Mill

For an example of complete verification, Mill cited Newton's inverse-square law of gravitation. But neither Newton nor Mill tried to prove that there is no other possible successful hypothesis [LA: this problem formulated later as the 'Duhem–Quine Underdetermination Thesis'].

In other cases, Mill recognized that a future theory may deduce successfully what a current theory deduces (e.g., Young and Fresnel's wave theory of light) in addition to explaining what is currently not explained.

(p. 139) Although Mill recognized the importance of deductive methods for science, he thought the justification of theories is done by using inductive logic alone.

Mill distinguished casual relations from accidental relations in that casual relations are both invariable (constantly conjoined) and unconditional (necessary).

(pp. 139–40) Mill suggested a relation is unconditional if it will continue as long as the ultimate laws of nature persevere. His test for an unconditional relation is:

  1. vary the conditions for the invariable sequence (leaving ultimate laws of nature constant)
  2. if the effect fails under some variations, then the relation is not unconditional

(e.g., day does not cause night)

(p. 140) Losee objects that Mill has not specified which laws are the ultimate laws of nature.

Mill vacillated between all four of his inductive methods being capable of proving causal connection and only his Method of Difference.

For Mill's Method of Difference to prove causal connection, he requires proof that a connection is both invariable and unconditional. Mill's attempted proof is that:

  1. the positive and negative instances differ in just one relevant circumstance
  2. the principle of universal causation is true

Philosophers of science accept that Mill failed to justify 1. as he failed to show that no other circumstance could be relevant to occurrence and non-occurrence.

And Mill failed to justify 2. as he failed to escape the vicious circle of trying to prove the law of universal causation.

(p. 141) Mill attempted to prove the law of universal causation as a necessary truth from the fact that it has has no exception in an extremely wide variety of observed circumstances.

Losee objects that pointing to no exceptions to date is not a (formal, logical) proof that it could not be otherwise. Without a proof of the necessity of the law of universal causation, Mill failed to show how the Method of Difference proves causal connections.

Jevons' Hypothetico-Deductive View

(pp. 141–2) Jevons rejected Mill's arguments that theories are justified by inductive logic. For Jevons, a hypothesis is justified by:

  1. demonstrating it is not inconsistent with other well-confirmed laws
  2. showing its consequences are consistent with observations

Contra Mill, 2. requires deductive reasoning, not inductive.

Questions to Consider:

  1. Did Mill overstate the importance of inductive methods in scientific discovery?
  2. Is the Method of Difference an inductive method or, more realistically, a deductive method?
  3. Was Mill right to think that justifying scientific hypotheses only requires inductive reasoning?
  4. How useful is Mill's test for casual relations vis-à-vis accidental relations?

Copyright © 2022–3

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