A material theory of induction

tags

Problem of Induction

Notes

1. Introduction.

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we have failed, not because of lack of effort or imagination, but because we seek a goal that in principle cannot be found.

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I will develop an account of induction with no universal schemas. Instead inductive infer- ences will be seen as deriving their license from facts.

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‘‘All induction is local.’’

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2. The Material View.

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In a material theory, the admissibility of an induction is ultimately traced back to a matter of fact, not to a universal schema. We are licensed to infer from the melting point of some samples of an element to the melting point of all samples by a fact about elements: their samples are generally uniform in their physical properties.

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There are no corresponding facts for the induction on wax, so the formal similarity between the two inductions is a distraction.

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my principal contention is that all induction is like this. All inductions ultimately derive their licenses from facts pertinent to the matter of the induction.

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3. A Little Survey of Induction.

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3.1. Universality Versus Successful Functioning. My principal argument for a local material theory of induction is that no inductive inference schema can be both universal and function successfully.

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3.2. First Family: Inductive Generalization.

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3.3. Second Family: Hypothetical Induction.

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3.3.1. Exclusionary Accounts.

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3.3.2. Simplicity.

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our decisions as to what is simple or simpler depend essentially upon the facts or laws that we believe to prevail. These facts dictate which theoretical structures may be used and the appeal to simplicity is really an attempt to avoid introducing theoretical structures unsuited to the physical reality governed by those facts or laws.

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picking the simplest curve can only make sense evidentially if we make the right choices for the variables and family of functions. And we make those choices correctly if we think that the variables and function hierarchy selected somehow map onto the basic physical reality at hand.

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If our system is one describing growth, we would quickly look to fitting exponential functions since they are the functions that figure in the laws governing growth. In that case, we would certainly prefer an exponential curve over, say, a quintic curve that fitted as well,

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In short, we have no universal scheme or universal formal rules that define what is simpler or simplest.

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3.3.3. Abduction: Inference to the Best Explanation.

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Consider, for example, a controlled study of the healing efficacy of prayer. A theist would readily accept divine intervention as the best explanation of a positive result in the study. An atheist however would conjecture some as yet unnoticed flaw in the experimental design as the best explanation and may even deny that divine intervention would count as an explanation at all. The difference depends fully on their differences over the facts that prevail.

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modern day astronomers would no doubt not avail themselves of Newton’s explanatory repertoire. He proposed ([1692] 1957, first letter) that the planets have just the right velocities to produce stable orbits since they were ‘‘impressed by an intelligent Agent.’’

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3.3.4. Reliabilism.

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In an uncooperative world, no method can succeed.

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3.4. Third Family: Probabilistic Accounts.

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What makes matters more complicated is that Bayesianism asserts that the same notion of degrees of belief and the same calculus should be applied in all cases, including those in which no stochastic processes deliver convenient chances.

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Bayesianism is vacuous until we ascribe some meaning to the probabilities central to it. Until then, they are just mathematical parameters.

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presumed that a degree of belief p in some outcome A makes us indifferent to which side of a bet we take in which winning $(1-p) is gained if A obtains and $p is lost if A fails.

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easy to see that these material facts would obtain in some contexts, such as if we are making wagers on horses at a racetrack.

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other contexts in which it is hard to see how these material facts could be made to obtain. How might our beliefs in big bang versus steady state cosmology be converted into the relevant sorts of wagers?

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Bayesian confirmation theory seems to be the most general of all the systems currently in favor. The reason is that it is a rather weak system. We get very little from it until we specify what might need to be a quite large number of conditional probabilities (the likelihoods) and these are determined by the factual properties of the relevant system.

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a mythical prior probability distribution, formed in advance of the incorporation of any evidence, decides how any evidence we may subsequently encounter will alter our beliefs.

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4. Inductions Too Local to Categorize.

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the more universal the scope of an inductive inference schema, the less its strength.

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5. The Control of Inductive Risk.

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5.1. Strategies in a Formal and Material Theory.

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5.2. The Portability and Localization of Inductive Risk.

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transporting of inductive risk from a schema to a fact, the relevant material postulate.

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5.3. Demonstrative Induction as a Limiting Case.

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If we can reduce inductive risk by transporting it from the schemas into the material postulates, might we eliminate it entirely? We can, in a limiting case in which the material postulate and the evidence taken together deductively entail the hypothesis at issue.

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6. The Problem of Induction Eluded?

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6.1. The Analog of Hume’s Problem for the Material Theory.

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We shall see that Hume’s problem can be set up quite easily for a formal theory, since a formal theory separates factual content from formal schemes. I will argue that the absence of this separation in a material theory results in the same considerations failing to generate a comparable problem for a material theory.

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6.2. Comparison.

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The regress described here is far from the fanciful meta- meta-meta-inductions remote from actual inductive practice required by a formal theory. It merely describes the routine inductive explorations in science. Facts are inductively grounded in other facts; and those in yet other facts; and so on.

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What remains an open question is exactly how the resulting chains (or, more likely, branching trees) will terminate and whether the terminations are troublesome.

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They may just terminate in brute facts of experience that do not need further justification, so that an infinite regress is avoided.

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must await the ever elusive clarification of the notion of brute facts of experience and of whether the notion even makes sense.

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The closest we have come to a fatal difficulty in the material theory is a regress whose end is undecided but with the real possibility of benign termination: a fatal difficulty has not been forced. Contrast this with the analogous outcome in a formal theory: a regress whose beginning is prob- lematic and whose end, an assured infinity, is disastrous.

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7. Conclusion.

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