Irreducibility and unity of the three forms of inference

Laudan, as we have seen, holds that all methods could be reduced to quantitative induction; on the other hand, Francis Reilly188 argues that through the continuous application of inductive testing the inquirer becomes more qualified to select better hypotheses, and because of his increased experience, his mind is sharpened by more accurate selective instinct for truth. But this conclusion, in my view, implies underestimation of the

185 _{See Losee John, (2004), An Introduction in Scientific Progress and Convergence upon Truth, pp. 100-}

101.

186

See Strawson P. F. (1952), Introduction to Logical Theory, pp. 254-257, where Strawson examines the two propositions: 1. The probability that a sample matches a given population increases with the size of the sample and 2. The probability that a population matches a given sample increases with the size of the sample, and he concludes that proposition 2 is false.

187

Ian Hacking in Mellor (1980), Science Belief and Behavior, pp. 141-160, discusses the single case problem and holds the same. Peirce even in his later writings states it clearly: ‘An individual inference must be either true or false, and can show no effect of probability; and therefore in reference to a single case considered in itself, probability can have no meaning’ (CP 2.661. 1910).

188

See Reilly Francis (1970), Charles Peirce’s Theory of Scientific Method, pp. 72-80, where he discusses this aspect of Peirce’s self-corrective method.

originative function of abductive inference or even reduction of abduction to induction. Therefore it has to be explored whether the three forms of inference are irreducible or not.

First, it is apparent the difference between the necessary deduction and the other two types of inference, because it is analytic and necessary true, since is the application of the rule, as explained with the syllogism BARBARA, while both induction and abduction are synthetic sorts of inference and inversions of deduction. Deductive inference is always necessary true, therefore deduction is a method applied in mathematics. Even in the statistical or probable deduction applied in scientific inquiry, the conclusion is true, because the syllogism lends the probability of the rule to the conclusion. Moreover, deduction, as a typical inference of formal logic, can deal only with abstract or mathematical entities, whereas induction and abduction deal with real physical phenomena, as both of them are based on data of experience. But in Peirce’s schema, as we have seen, deduction can be used for tracing out the necessary consequences of a hypothesis experimentally.

Furthermore, induction is a generalization from a number of cases of which something is true and inference that the same thing is true for the whole class, while abduction is where we find some very curious event, which would be explained by the supposition that it was a case of a certain rule. In other words, in induction we synthesize to find the rule, while in abduction we synthesize to classify the case under a class of events. Another difference is that induction is reasoning from particulars to the general law, while abduction is reasoning from effect to cause. Induction cannot possibly yield any hypothesis about the causes of the phenomena nor can it introduce new entities189.

However, the crucial difference between abduction and induction concerns the unobserved facts, for induction infers the existence of phenomena such as we have observed in similar cases, whereas by abduction we conclude the existence of a fact quite different from anything observed, from which something that is observed would necessarily result; therefore abduction supposes something, which would be impossible for us to observe directly (unobservables). The consequence of this difference is that inductive inferences can be directly verified, while abductive inferences can only be indirectly verified; therefore induction is stronger sort of inference than abduction. We cannot verify directly e.g. the existence of Napoleon, the kinetic theory of gases, uncertainty theory, DNA mechanisms

189

In the second part of this work by appealing to Lavoisier’s method I am going to show how abduction can introduce new entities (i.e. oxygen).

etc., but only through their effects, while we can directly verify the existence of a chemical substance, of a close to earth planet, etc.

From all the above differences it is apparent that the three forms of inference cannot be reduced to one sort, and only in some cases abduction can be reduced to induction (e.g. when concerns observed facts), but in most cases, when the inference concerns effects of unobserved entities, abduction cannot be reduced to induction. Therefore, Peirce argues that different sciences use different types of techniques and reasoning: Sciences such as zoology, mineralogy and chemistry are purely inductive, while geology, biology, history, archaeology etc. are mostly sciences of hypothesis or abductive. But, in my opinion, modern theories of sciences such as in physics, chemistry, biology and astronomy use a mixture of induction and abduction supporting one another.

The last critique of Laudan concerns the view that Peirce does not provide a technique of generating better hypothesis that the refuted one190, a position that also Losee and Van Fraassen adopt in like fashion191. Therefore I am going to discuss here Peirce’s proposal for the solution of that problem, i.e. of finding better alternative theory than the refuted one.

As I said, after the inductive phase and according to the testing results the inquirer is able to characterize his explanatory hypothesis as: proved, partially proved, unworthy of further investigation, in need of modification, highly dubious and so forth. In any case, positive or negative inductive verification contributes to the forward progress of scientific inquiry. Even the case of negative verification (falsification) contributes to the progress of inquiry more, since it excludes certain useless avenues previously open, is instructive with reference to the next hypothesis, as it points to more fruitful areas for future modified hypotheses after new abductions; while the whole process increases both the background knowledge and the skill of the inquirer. The latter can be used as a basis for forming a more accurate, revised hypothesis with more truth-content. In other words, when the hypothesis

190

Laudan Larry (1981), Peirce and the Trivialization of the Self-Corrective Thesis, on p. 239, argues: ‘Given that an hypothesis is refuted, qualitative induction provides specifies no technique for generating an alternative, which is closer to the truth than the refuted hypothesis’.

191

Van Fraassen in (2000), The False Hopes of Traditional Epistemology, concludes: ‘Peirce could see no way to demonstrate that the ones (hypotheses) we then come up with will be increasingly better in some concrete sense. Nor could he show that if this process is carried out under varying historical circumstances, the results will converge!’. See also Losee John (2004), pp. 100-101: ‘given that an hypothesis has been refuted, qualitative induction specifies no technique for discovering an alternative H´ which is (or is likely to be) closer to the truth than the refuted H’.

is falsified or is need of modification, the increased scientists’ skill and background knowledge contributes to generating a better hypothesis than the refuted one, as the scientist becomes familiar with the certain regularity.

Moreover, the experimental predictions of the new hypothesis will be predesignated more reliably and with more experience and skill, and as a result they will provide better experimental tests. Therefore all the three stages form a dialectical unity, where each one is complementary to another and contributes to the correction of the others. In this way Peirce’s proposed method can overcome both the weakness of induction that cannot yield any hypothesis about the causes of the phenomena and introduce new entities, and the weakness of the traditional Hypothetico-Deductive method (HD) that lacks in accuracy and epistemic austerity.

Particularly, Peirce with his notion ‘induction corrects its premises’ provided a technique for drawing better hypotheses, as he implied a way of modifying the hypotheses by correcting the premises of abductive inference, that is, by returning to the minor premise of the abductive inference and modify it, as explained with my example of salt. To the choice of the new modified hypothesis contribute: the consideration of some criteria of admissibility of the hypotheses (economy of research), in association with the pragmatic maxim (consequences of a hypothesis) and the development of the scientific skill through scientific community192. The hope to find in the long run the right hypothesis – after a continuous process of deducing the predictions from each suggested hypothesis, testing inductively these predictions and re-modifying the hypothesis – is based upon this conception, but not on ‘inarticulate faith’ or a priori ‘intuition’ that Peirce so thoroughly discredited. Furthermore, as I said, what is valid for the individual investigator is also true for the community of inquirers, since each member is informed about the work of the other member, shares in his experience and learns from his failures and as result the whole community proceeds gradually and fallibly towards the approximate representation of the natural regularities.

192

In the second part of this work by appealing to Lavoisier’s method I am going to show how the scientists’ skill and the consideration of the different criteria of admissibility can contribute to the selection of better hypotheses than the refuted one.