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p.4 All roads in the study of discovery lead back to the Greek mathematicians and philosophers of antiquity. In their study of the processes for solving problems, two were the main heuristic strategies, namely analysis and synthesis.
p.13-14 [Karl Popper]
"Accordingly I shall distinguish sharply between the processes of conceiving a new idea, and the methods and results of examining it logically... my view of the matter, for what it is worth, is that there is no such thing as a logical method of having new ideas, or a logical reconstruction of this process" [Pop34, P.134].
p.14 we should emphasize that Popper draws a clear division between two processes; amidst the conception of a new idea, and the systematic tests to which a new idea should be subjected to, and in the light of this division he advances the claim that not the first but only the second one is amenable to logical examination.
p.14 Popper's answer to this question [JLJ - the sources of our knowledge] is that we do not know or even hope to know about the sources of our knowledge, since our assertions are only guesses [Pop60b, p. 53]. Rather, the question and its answer should be the following: "How can we hope to detect and eliminate error? Is, I believe, By criticizing the theories or guesses of others" [Pop60b, p. 52]. This is the path to make knowledge grow: "the advance of knowledge consists, mainly, in the modification of earlier knowledge" [Pop60b, p. 55].
p.16 Although there is no precise methodology by which scientific discovery is achieved, as a form of problem solving, it can be pursued via several methodologies. The key concept in all this is that of heuristics, the guide in scientific discovery which is neither totally rational nor absolutely blind.
p.28 Broadly speaking, abduction is a reasoning process invoked to explain a puzzling observation. A typical example is a practical competence like medical diagnosis... Abduction is thinking from evidence to explanation, a type of reasoning characteristic of many different situations with incomplete information.
p.30 an abductive explanation is always an explanation with respect to some body of beliefs.
p.35 More precisely, we shall understand abduction as reasoning from a single observation to its abductive explanations, and induction as enumerative induction from samples to general statements. While induction explains a set of observations, abduction explains a single one. Induction makes a prediction for further observations, abduction does not (directly) account for later observations. While induction needs no background theory per se, abduction relies on a background theory to construct and test its abductive explanations.
p.45 According to Polya, a mathematician discovers just as a naturalist does, by observing the collection of his specimens (numbers or birds) and then guessing their connection and relationship [Pol54, p.47]. However, the two differ in that verification by observation for the naturalist is enough, whereas the mathematician requires a proof to accept her findings.
p.57 Haack... For her, the question we should be asking is whether a system is good and useful rather than 'logical', which after all is not a well-defined concept.
p.68 to model reasoning outside of mathematics, a richer format is needed.
p.149 Gardenfors' basic idea is that an explanation is, that which makes the explanandum less surprising by raising its probability... Explanations are propositions that effect a special epistemic change, increasing the belief value of the explanandum.
p.167 In this chapter, I present the philosophical doctrine known as pragmatism, as proposed by Charles Sanders Peirce, namely, as a method of reflexion with the aim at clarifying ideas and guided at all moments by the ends of the ideas it analyzes... The abductive formulation can... be seen as a process of belief acquisition by which a surprising fact generates a doubt that is appeased by a belief, an abductive explanation.
p.171 Peirce proposes abduction to be the logic for synthetic reasoning, that is, a method to acquire new ideas.
p.172-173 Peirce... In the context of perception he writes:
"The perceptual judgments, are to be regarded as extreme cases of abductive inferences" [CP,5.181].
p.173 In Peirce's epistemology, thought is a dynamic process, essentially an interaction between two states of mind: doubt and belief. While the essence of the latter is the "establishment of a habit which determines our actions" [SP,5.388], with the quality of being a calm and satisfactory state in which all humans would like to stay, the former "stimulates us to inquiry until it is destroyed" [CP,5.373], and is characterized by being a stormy and unpleasant state from which every human struggles to be freed:
"The irritation of doubt causes a struggle to attain a state of belief". [CP,5.374].
Peirce speaks of a state of belief and not of knowledge.
p.173 it is surprise that breaks a habit:
"For belief, while it lasts, is a strong habit, and as such, forces the man to believe until some surprise breaks up the habit". ([CP,5.524], emphasis of the author Aliseda).
And Peirce distinguishes two ways to break a habit:
"The breaking of a belief can only be due to some novel experience" [CP, 5.524 or "...until we find ourselves confronted with some experience contrary to those expectations." ([CP, 7.36], emphasis of the author Aliseda).
p.175 [Peirce]
'The action of thought is excited by the irritation of doubt, and ceases when belief is attained; so that the production of belief is the sole function of thought'. [CP, 5.394].
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