Scientific reasoning is an exploratory dialogue that can always be resolved into two voices or two episodes of thought, imaginative and critical, which alternate and interact. [P.B. Medawar, Induction and Intuition in Scientific Thought (New York, NY: Routledge, 1969, 2009), 46]
The process by which we come to formulate a hypothesis is not illogical but non-logical, i.e. outside logic. (p. 46)
This elementary theory is supported by a metatheory which specifies the rules o deduction or statement-transformation (“logical syntax”) and adjudicates upon the meanings of the empirical terms which it employs, i.e. says what they stand for (“semantics”). … We assert a postulate and take an axiom for granted, but hypotheses we merely venture to propose. (p. 47)
For scientists and all those involved in the scientific industries, it seems almost obvious that science is about finding out the truths of nature. With the failure of logical positivism and pure inductivism, the hypothetico-deductive model is adopted as the way science is done. And in a certain sense, they are right. Modern science largely functions according to the hypothetico-deductive model. But saying that is so does not indicate to us the nature of science and the relation of science to truth. Such a model is blind to the obvious paradigms of thought science operates in, for this model is blind to the fact that what may seem obvious and a reasonable assumption or prediction is paradigm-dependent, and will thus change when paradigms shift.
It is therefore on the one hand true that [normal] science operates according to the hypothetico-deductive model, and on the other hand true that whatever is discovered is paradigm-dependent in terms of its truth value. Also, since science is paradigm-dependent, all "truths" so discovered are descriptions of reality according to the paradigm. In other words, they are true, but only secondarily so. Scientific truths at best are reflections of truth, refracted through their governing paradigms. In that, they necessarily partake of the problem with induction, where there is simply no foolproof way to prove an inductive argument to be correct, as just because 100 black swans are seen does not mean all swans are black.
P.B. Medawar rightly points out the problem with pure inductivism. However, it is one thing to see the problems with inductivism, and another thing to escape the problem of induction. For since science necessarily argues from the particular to the general, induction plays a role in scientific reasoning, even under the hypothetico-deductive model. For in testing a hypothesis, one uses induction to prove that the experiment results (particular) necessarily say something about the systems being tested in general. For example, testing the hypothesis that a certain chemical causes an increase in an incidence of cancer requires one to believe that the experimental results is indicative of the general case of the presence of this chemical to the incidence of cancer. Without induction, one can only say that the experimental results of a positive correlation of high concentrations of this chemical with the incidence of cancer only applies to the experimental subjects. Without induction, one cannot conclude that this positive correlation would also be true in others that are not the experimental subjects, no matter how large or representative the sample size for the experiment is.
Therefore, while science works with the hypothetico-deductive model, we must understand that this is scientific methodology on the surface, which does not indicate to us the true nature of science or even a full understanding of the scientific method either. Rather, as we look at the history of science, we can come to recognize the paradigmatic nature of science, which undergirds the entire scientific enterprise.