Logic of discovery, abduction and types of explanatory models

The facts. A likeness of motion of Mars in an elliptic orb

Conclusion

Verify virtual predictions about the latitudes and parallaxes based on hypothesis (CP 2.96)

In some passages Peirce writes about abduction as more significant stage of inquiry. “All the ideas of science come to it by the way of Abduction.” (CP 5.145) Abduction not only suggests explanatory hypothesis, but can design an explanatory theory for facts, it is the instrument of learning (CP 5.171). And it is justified by the Last Judgement of the whole understanding (CP 5.145).

The problem of control of abduction is enclosed in the subject matter of pragmatism (“the question of pragmatism …is nothing else than the question of the logic of abduction” CP 5.196). Peirce writes about the guiding principles of economy. Abduction should obey the economy rules of money, time, thought, vitality and energy. Economy presupposes that verification will be conducted with the appraisal of the cost of experiment, the assessment of the value of a hypothesis and significance of the effects of hypothesis on other investigations. (CP 7.220, NEM 4:38) Economy destines the best hypothesis in the case when there is a list of possible hypotheses-explanation, in so-called situation of IBE (CP 5.600, 6.528)

Concerning the connection between pragmatism and abduction starts the discourse of the goal of abduction. The aims of abduction are abolishment of surprise in the sense of controversy with expectations, disposal of all unclear ideas, help in clear apprehension of complicated ideas by engendering conceptions and theories and forming a habit of positive expectation that will not be disillusioned. This is a part of huge evolutionary process from the state of indeterminacy, original chaos, where there was no regularity, nothing existed or really happened to regularity of existing objects in the world, events in regular flow of time. (CP 5.197, CP 5.206, CP 5.590, CP 1.411).

Peirce has remarks about the most general and primary abductions. These are the hypotheses with which we should start as pre-stage of inquiry. The first is that surprising facts with which we are coping can be rationalized. The second hypothesis is that such kind of rationalization can be realized by us. (CP 7.219)

It is worth mentioning here that Peirce emphasizes that first hypotheses are the object of hope. Strangely it may look comparing to the requirement that most and foremost is that hypothesis must be “capable of being subjected to experimental testing” (CP 7.220) and there are hypotheses that cannot be verified, as taken for granted hopes guiding rationalization practice. Desperate hope of knowing anything about real world is foundation for principal hypothesis of existence of reality. (PMSW 175) So, let us assume that provisional hierarchy of hypotheses may be constructed. The upper levels of hypotheses are guiding principle for all the scientific practice, but they can be justified only by practice. It looks similar to some kind of circle in the reasoning as in the case of justification of induction, when it is stated that the principle of uniformity of nature is confirmed by discovering laws of regularities which are in presence because there is uniformity in nature and so on. Peirce honestly confesses that some most fundamental hypotheses can be justified only in times when there will be no necessity in abduction, because it will have gained such results that there will be no surprising, unexpected laws. Peirce suggests to use two arguments in support of a hypothesis: instinctive (kinship of mind and the truth) and reasoned (inductions). (CP 7.220, CP 1.121). Inductive justification refers to effective experience of abductive rational regulation of scientific inquiries in past as ground for hope that abductive principle will continue to guide practice effectively. (EP 2:299) It should be noted that Peirce clearly understood the hypothetical character of his claim about unity of mind and matter, but Peirce does not discard hypothesis and even avows that in his understanding abduction directs us to monism in philosophy. (CP 5.581)

Peirce reverts to the theme of seeming groundlessness of some hypotheses. Suddenness of appearance of some crucial hypotheses has great consequences in the progress of knowledge. Science which evolutions gradually by the huge amount of work dedicated to “some good, solid, well-trained labor of observation and inference”, accounts for much of scientific research, of achievements (CP 1.108). But breakthrough discoveries are characterized as advance by leap thanks to new way of reasoning about observations or new observational source. Abduction can suggest new way of thinking about already known and really new facts from the point of view of new relation of facts, of focusing on something that was unperceived earlier. And these hypotheses are the case of surprising openings. (CP 1.109)

Peirce appeals to the metaphor of bridge over the chasm of ignorance and erroneous beliefs to the ultimate aim of science which people started to build from primordial times through joint efforts. The structure - bridge material in metaphor - consists of spontaneous guesses of instinctive reason. Each board, continuing the metaphor of a bridge construction, equals to each new concept is the result of abduction. Deduction and induction look like design of the bridge and some props, they just make indefinite structured definitely. The aim of deduction - explication, the goal of induction is evaluation. (CP 6.475)

Not only leaps are the characteristic of some hypotheses, but their unexpected high probability of being true. Despite the fact that “abduction is, after all, nothing but guessing.” (CP 7.219), it is really very successful guessing. The evidence of these successful trials is the fact that mind can choose a hypothesis in consequence of finite number of guesses in spite of strictly innumerable quantity of possible explanatory hypotheses (CP 7.219). The philosopher often describes his feeling of wonder connected with this amazing human ability: “the frequency with which that turns out to be an actual fact is to me quite the most surprising of all the wonders of the universe”. (CP 8.238) Peirce explains this emboldening fact by referring to the fundamental nexus between evolution of mind and matter: “man divines something of the secret principles of the universe because his mind has developed as a part of the universe and under the influence of these same secret principles”. (CP 7.46) From the evolutionary point of view, human capacity of successful guessing (“guessing instinct”) is corresponding to specific capacities which provide an evolutionary advantage being effective adaptations (aeronautic and musical powers of birds). (CP 7.48)

Peirce contraposes his own evolutionary thesis to transcendentalist explanation (or its very arbitrary version) of Mind/Laws of nature coherence. Peirce claims that there is rationality in nature, people do not project their impressions into object, to nature, but discover already existing natural laws. Natural laws, according to Peirce, are not fiction, created by human mind using space-time organizing schemes, but the reality, the fact. People mark insistent generalized percepts, form predictions from generalizations. Evolutionism of Peirce is reflected in his statement that human mind is well adopted to the search for regularities in reality because they have great significance for survival. (CP 8.146) Anyway, special human attention to regularities does not mean that there are no objectively existing laws. In this sense Peirce is not Kantian: relatively speaking, the order of nature is not established by mind, organizing the chaotic matter of senses. Peirce declares that laws of nature are independent from people. This thesis is justified by Peirce appealing to verification of predictions. (CP 8.145-8.156) Peirce has the realistic representation of the world: things exist independently of people.(W 3: 27) The world according to Peirce is in state of disenchantment (Entzauberung, using the term of Shiller and Weber): “…according to my notions there can be no mystery in the universe, in the sense of a real fact to which no approach to knowledge can ever be gained. For a reality is an idea that insists upon proclaiming itself, whether we like it or not.” (CP 8.156) Here is the ground for the conception of the aim of abduction as abolishment of all the surprise (“our inquiry to rationalize” CP 7.220).

Personal hypothesis of Peirce which grounds his evolutionary hypothesis is that human mind as a continuous being correspond to continuous being of nature. For Peirce, every continuum is conscious and living. Well, nature is a conscious continuum. Universe which started its existence by pure chance directs itself to the state of full determinacy by laws. Things and all continuous beings as humans gain habits and make universe more stable. (PMSW 176, W 5:293)

Belief in reality of natural laws corresponding to developed guessing instinct fits with specific scientific ethos in the life of professional researches. Inspired by the majesty of truth which has the whole power over the world, scientists are actuated “on condition of submissive observation” (CP 8.136) to interpret the truth that opened to them due to resemblance of their minds to the truth. Scientists are developing in bringing mind in accordance with cosmical truth, progressing by small discoveries saving awareness of little knowledge.

Rising higher in the level of coverage hypotheses, Peirce puts forward the hypothesis of structure of the three categories: Firstness (Quality/question of condition of having meaning concerning signs), Secondness (Relation/issue of truth-conditions of signs), Thirdness (Representation/problem of defining conditions for transferring meaning from one signs to others) (PMSW 167). Peirce stated that three types of reasoning correspond to three Categories (W 4:588, W 5:294) As it was mentioned before, three types of reasoning constitute system of formal logic, but “formal logic must not be too purely formal; it must represent a fact of psychology, or else it is in danger of degenerating into a mathematical recreation.” (W 4:421) Peirce embeds evolutionary principle, inner dynamics in the structure of reality that is why he presumes that hypothetical proposition “if A, then B” containing belief revision from belief stated in premise to belief in conclusion is more fundamental than categorical propositions. Peirce integrates his understanding of logic, psychology and laws of evolution of reality in such a scheme, exploring “the nature of mental processes first as a phenomenology of the human mind and then as a system of categories” (W 4:422-423, W 3:329-330, W 3:338):

Table 3

There are some problems concerning interpretation of induction as forming concept. Because, as it is already known from previous paragraphs, sometimes Peirce attributes this function to abduction. The role of hypothesis explicitly formulated as search for causes should be noticed, because it is the rare case than conditional structure of hypothesis is interpreted as causal one.

There are two additional personal hypotheses of Peirce that play significant role in his system.

Peirce writes that the basis of the system of a philosophy should be the principle of absolute chance, named by Peirce tychism (from ancient Greek word Tyche, chance). Tychism engendered evolutionary cosmology where mind and nature are recognized as products of growth. Peirce confessed that his understanding of evolution of matter has traces of the influence of Schelling: matter as “mere specialized and partially deadened mind”. The general law of mental action, mind is for Peirce the idea of continuity (synechism), of continuous dissemination of ideas with loss of intensity and gain of more cohesion with other ideas and its effect on close related items connected by affectability. Peirce concocts the accordance scheme of three classes of inferences (deduction, induction and abduction) and three modes of action of the human consciousness. Deduction corresponds to already formed habit that trigger reactions on special stimuli, induction matches to the unity of sensations gathered in general idea uniting sensations with one reaction, establishing habit. Hypothesis as induction from qualities in this case of perception, it connects number of reactions on special occasion. It should be noticed that mental laws has no universality and necessity, otherwise it has a potential of spontaneity, it has needful uncertainty for the possibility of forming new hypotheses. For Peirce, mental phenomena are governed by a living conscious continuum of feeling pervading ideas, perceptions and feelings. The supreme law of ideas requires their mutual influence on each other.

Tychism is justified by abduction. The uniformity presupposes that necessary law can be the result of another law, fortuitous distribution (chance1) can be consequence of other fortuitous distribution (chance2). So we have radical dualism, but abduction suggests to use monistic guiding principles qua heuristics as often as possible. Let us assume that the first entity was law. It could not beget chance. But if the First was chance, it could cause some kind of regularity, the first sprout of law. For Peirce, originary irregularity is a more effective way of explanation of the development than originary law in part because there will be no problems with the principle of sufficient reason. Chaos does not need justification. “First of all Chawos [Gap] came into being.” (CP 7.521)

Abduction is a very dynamic concept in the system of Peirce, so even incomplete list of abduction mentions as in this work should be somehow classified. The following table tries to highlight creative aspects.

Table 4

Separately worth saying that philosophical hypotheses could have great influence on AI and psychology, but the reasons for this claim may become more clear after the last chapter which describes themata approach of Holton.

Abduction Studies: Great Expectations

/This subchapter is devoted to overview of some trends in Abduction Studies, starting from articles on historical-philosophical appraisal of Peirce's thought, then referring to some articles on the issue of correct classification of abduction and finally mentioning some strictly logical applications of abduction.

Modern pundits focus on fundamental distinctions between induction and abduction, noticing that abduction is fundamental irreducible type of inference. Scholars focus on quotations that underscore extreme value of abduction in Peirce's system of logic as science of reasoning and guiding scientific inquiry: “All that makes knowledge applicable comes to us viв abduction. [. . .] Not the smallest advance can be made in knowledge beyond the stage of vacant staring, without making an abduction at every step” (HP 2:899-900, 1901), “the whole fabric of our knowledge is one matted felt of pure hypothesis” (HP 2:900, 1901). Psychological explanations are admitted but the accent is on the thesis that abduction itself presents “a pure rational doctrine of how a discovery ought to take place” (CP 2.107). A particular emphasis is brought to shift in the representation of deduction, induction and abduction as stages of scientific inquiry with accentuating the role of two deductive subprocesses, theorematic (demonstration, mathematical reasoning including such a significant operation of thought as hypostatic abstraction proposing new entities through conceptual changes) and corollarial (logical analysis, explication of hypothetical state of things). Researchers stress the importance of dual role both in science and logic which is reflected in titles of deduction, induction and abduction as three “types” or “grades” or “orders” (MS 756, 1, c. 1906, MS 843, 1908, MS 752, 1914, MS 905, 1908). The interrogatory mood of abductive conclusion is also a subject matter of studying. Separately worth noting the fact that there is a strong connection between diagrammatic reasoning and abductions. Special consideration is paid to the evaluation procedure. Distinguishing a priori acceptability of hypotheses and a posteriori acceptability, scientists indicate features of hypotheses that should be examined first (easy falsifiability, simplicity, amazement). The self-referent characteristic of justification of retroduction by means of hypotheses (MS 328, 46, c. 1905, W 1, 280-283; MS 328, c. 1905) is recorded in addition to deductive (CP 2.786) and inductive (W 1:280-283; MS 328) justifications, justification through history of science (inductive justification, too). The list of first, upper hypotheses is broadened after careful consideration, so, Ur-abduction postulating the principle that nature is explainable, basis of all explanations, and hypothesis confirming possibility reaching the truth are included in it. The capacity of abduction to make a single notion of high degree of abstractness from plurality of propositions is under scrutiny. Another line of research is connected with psychological investigations and development of Peirce's intuitions. For instance, the process of abductive argument is itself divided to subprocesses of perceptual judgement that has no problem of justification because its truth is not questioned and process of suggesting hypothesis. Concerning the insights about habitual nature of abductions, of progressing in forming habits scientists add, basing on textual evidences, ethical and esthetical considerations for generating hypotheses. (CP 5.35-36, 108, 130, 1903; HP 2: 826-827, 833, 1904; HP 2:1028, 1902). The problem of involvement of unconscious elements in abduction is surprising solved by the argument of community agreement in successful guessing. In addition to famous holistic potential of abduction, unifying experience, scholars supplement order, division of problems and economic solutions which are the characteristics of successful abductions.

IBE interpretations of abduction emphasize the role of context, background knowledge and define abduction as description of scientific practice. This thesis is presented as contraposition to AI formal and content-free descriptions. Abduction in this interpretation registers a set of heuristics (for instance, heuristic “consider alternative hypotheses”). Interestingly, there are evidences for assuming that the presence of alternative hypotheses can reduce errors in reasoning.

Direct research on the field of logic of discovery in abductive theory is worked out in strategic rules realized in inquiries guided by abduction but elaborated in methodeutic. Methodeutic (Speculative Rhetoric) is a part of trivium with Speculative Grammar studying meanings of signs and Critic dedicated to the problems of analysis of arguments. Methodeutic solves the problem of descriptive and normative discrepancy in abduction. Rules of abduction, its realization in scientific practice present so-called logica utens and they are the product of logica docens, logician's analysis of stages of scientific inquiry, reasons for conducting research and its aims. One of these rules is principle of simplicity of hypothesis provided that simplicity is understood as simplicity for human mind, helping to make unclear ideas more comprehensible.

Game-theoretic approach opens up new opportunities in analyzing creative potential of abduction calling Peirce the predecessor of game theory. The game of twenty questions and three guesses suggested by Peirce as analogy for dialogue of nature and science, his offer to test cheap in experimental realization hypotheses first, principle of new financing of new fields of research are the object of interest for economists of science. Interestingly, the game of twenty questions shines the light on the philosophical aspect of abduction which is sometimes neglected, specifically, relations between different laws of nature which are the object of peculiar discoveries. Game-theoretic approach also help to elucidate the role of mathematics to encourage abductions, videlicet function of economy of research, explicating consequences of hypotheses, making useful conceptualizations. This approach contributes to clarification of the principle of economy of research: scientist according to Peirce should use each and every means and heuristics that can economy efforts to save thought powers as the most valuable resource. The loftiest of our instinctive powers, using the term of Peirce (CP 7.48), faculty of guessing, ability to anticipate the future, think strategically in the conditions of necessary economy of research due to scarcity of resources is the evolutionary gift not from the point of view of our adaptation to nature, but, as economical theorist underlines, for the progress of our social world.

Due to the fact that renaissance of abduction has elicited a great deal of criticism, there is need for defense. One of the great examples presenting abduction as methodology of discovery is the article of Sami Paavola. In this article answers to standard criticism are given. Firstly, the problem of relevant hypothesis in the scheme of argument started by “The surprising fact, C, is observed…”: critics postulate that incredibly large amount of hypotheses can be subsumed in this scheme, but not being really explanatory hypothesis. Paavola notices that only hypotheses explaining surprising effect are relevant. Secondly, the creative aspect of abduction calls into question because some scholars surmise that hypothesis is a product of abduction, so the role of abduction is intermediate between discovery and justification. The author of the article states that abduction is an example of logic oriented not on error avoidance, but risky enough attainment of excellence of reasoning destined by strategies. The advantages of strategic thinking about abductions as stages of scientific inquiry are numerous: possibility of choice between different directions of inquiry, involved temporal dynamic, goal-directedness, holistic approach to assessment of series of steps in strategies. As a result, strategically sound hypotheses take into account all the relevant information, have explanations for and arguments for acceptance of this particular hypothesis, start heuristically from surprising, little facts-details and can relate to exceptions. Abduction in this sense is a technique of analyzing conceptual issues in discoveries. Paavola attracts attention to passage from Peirce's writing which is of particular significance in the framework of topic of this research: “It is true that the different elements of the hypothesis were in our minds before; but it is the idea of putting together what we had never before dreamed of putting together which flashes the new suggestion before our contemplation” (CP 5.181). Hypothesis precisely is the synthesizing and organizing mental act which structures some pre-given by previous experience knowledge. Paavola underscores the pattern which will be discussed later relating to the thematic analysis of Holton: “How I interpret this idea from the strategic viewpoint is that a hypothesis suggested can in itself be something old and even well known.” Paavola refers to the Hanson's reconstruction of logic of discovery started by retroductive inference detecting anomaly, then outlining a kind of explanation H and finally presenting an organized pattern of concepts. It should be mentioned, that strategy in Hanson's interpretation indicates different types of explanations and there is a situation of choice. The real challenge for modern scholars dedicating their works to Peirce's heritage is the problem of classification of different abductions. The principle that organizes classification reflects understanding of notion of abduction, of researcher's preference between explanatory, creative and subsuming functions of abduction.

For example, A. Aliseda understands abduction as a process of forming explanations, as inversed deduction. So, the structure of abductive inference is presented as Given a (background) theory T (a set of formulae) and a formula (observation) E (T E),

an abduced item C is an explanation if

(1) TЎИC |= E

(2) C is consistent with T

(3) C is `minimal'

(4) C has some restricted syntactical form (usually an atomic formula or a conjunction of them).

C may be fact, rule, new theory.

As for classification, the scientist proposes three basics of logical division:

1) the kind of reasoning involved - deductive and statistical abduction

2) the kind of observation triggering the abduction

Abductive Novelty:

T П--E, T П ¬E

E is novel. It cannot be explained (T П E), but it is consistent with the theory (T П ¬E).

Abductive Anomaly:

T П E, TЃЛ¬E

E is anomalous. The theory explains rather its negation (TЃЛ¬E).

3) the kind of explanations produced (facts, rules, or theories)

One of the most cited classification of abductive inferences is a classification of Gerhard Schurz. He understands abduction as inference to the best explanation, search strategy for finding unobserved cause or explanatory reasons of observed phenomena. Philosopher explicitly distinguishes selective and creative abductions. He focuses mostly on creative abductions because of their role in the history of science. As far as concepts and theoretical models are the products not only of scientific, but also speculative abductions, Schurz suggests justification criteria for distinction (explanatory unification, independent testability). It is important to note that philosopher writes that each inference has justificatory (inferential) and strategic (discovery) function, so it explains the necessity of remarks about justification of abduction. Of course, abduction is to more degree inference with developed strategic function. In his classification Schurz combines a number of questions: psychological aspect of abduction (cognitive mechanisms that guide abduction - “drivers”), context of justification (the type of evidence in explanandum) and creative aspect, abduction in quantitative and qualitative background knowledge context. Philosopher states that for all kinds of abduction even for theoretical model abductions (on condition of specified theory in the background) general formal patterns and algorithms can be generated.

Table 5. Patterns of abduction (Schurz), titles in italics - (Hoffmann)

Table 6

The significance of the Schurz' classification of abduction will become obvious if we step back to the problem stated in the line of discussion of AI impact on logics of discovery. There was a need for description how some inquiries lead to discoveries of new entities, unobservable levels of reality, unification theories. So, abductions should be included in AI programs. Moreover, this classification thanks to appeal to background knowledge is in accordance with achievements of cognitive psychology, proving that this factor is of crucial importance.

Hoffmann proposes expanded version of the system of eleven patterns of abduction of Schurz. In his vision Hoffmann extracts fifteen forms with special attention to the targets of inference, distinction between selective, educational abduction (psychologically creative in the scope of personal life, in learning) and historically creative (real discoveries in the history of science). Hoffmann pays special attention to theoretical-model abduction which he defines as the most important kind. Such an appraisal is connected with view that theoretical-model abduction is a preliminary stage of all abductive inferences. Scholar says that two conditions are in need for this type of abduction. The first condition is system of representation including language with established ontology, syntax, semantics. Furthermore, representation system ensures operation rules for transforming covered laws, concepts, entities. Second condition of theoretical-model abduction is “theoric transformation” - possibility to find a new aspect, perspective of the problem to solve it, reframing of problem space, changing vision (the Greek “theoria” means “vision”). It can be assumed that reframing can be related to the change of methodological perspective (as in example of Desargues's theorem with shift from measurement of length to a perspective representation) or, suggest for the purposes of this study, to the change of metaphysical preconceptions, for example. The process of creating new theoretical-model abductions is called by Hoffmann “meta-diagrammatic abduction”. The concept of theoric transformation may be developed by advances from gestalt psychology with its detailed theory of solution of problems requiring insights.

Table 7. Possible forms of abduction (Hoffmann)

There are great achievements in the direction of formalization of some creative abductive procedures. To name a few, there is an article dedicated to the modeling of abduction generating hypotheses unifying empirical correlations by the usage of common cause principle using Bayes net modeling. In this work modelled inference can make use-novel prediction, i.e. predict unknown at the time of prediction phenomenon. The stereotypical presentation of abduction as inverse deduction (fallacious modus ponens) was rethought in new scheme of interrelations of three basic inference types and their inverse versions. The scheme is presented in the triangle dynamical structure of interaction of abduction, deduction and induction and inverse types of reasoning:

Figure 1. The dynamical interaction of abduction, deduction and induction and their inverse kinds

Some logicians elaborate adaptive abduction logic as a kind of defeasible reasoning. They differentiate theoretical and practical abductions, as locating potential explanations of a given explanandum and extending one's knowledge in a defeasible way respectively. Owing to this approach there is a formalization of revised systems of patterns of Schurz:

Table 8. Formal representation of abductive patterns

The application of tools of paraconsistent logics towards abductive inferences is of particular interest. It sets out to dealing with not obvious explanations, even including possible contradictions. Abductions are differed as creative (responsible for generation new hypotheses) and explicative (constituting explanation for yet non deducible unexpected fact). Within the framework of this approach the problems of existence of different explanations for one surprising phenomenon and difference in the strength and relevance are explicitly stated. The unifying power of abduction is used in databases for forming integrated versions of ontologies.

To date, there are a lot of different formalizations of abduction which is understood and divided in various ways. Scholars distinguish philosophical and computational, epistemic and projectual abductions, explanatory and instrumental (goal-oriented abduction including means to achieve a goal as explanandum), explanatory and not explanatory, factual and theoretical, creative and selective. Philosophers of science indicate that abduction becomes an object of interest from the point of view that it represents some special type of reasoning. Task of investigation of intrinsic mechanisms of generation of hypotheses becomes more popular. So, the Big Question of abduction or “the fundamental problem of contemporary epistemology” as Hintikka calls it, is now especially relevant. Some specialists propose the generalizing scheme of framework of abduction studies (it is known as Hintikka-Kapitan's four theses). Supplemented by material of previous paragraphs it can be presented in this way:

1. Inferential Thesis

Abduction is inferential process / processes. (Textual evidence: (CP 2.623)

2. Thesis of Purpose

Abduction as a crucial part of scientific inquiry presupposing generation and selection of hypotheses. So understood abduction tends “to recommend a course of action”.

(CP 7.220, CP, 5.602)

Practical abduction is directed to filling the gaps in belief-system or database.

3. Comprehension Thesis

Scienti?c abduction includes all the operations whereby theories are engendered.

(CP 5.145)

4. Autonomy Thesis

Abduction is a kind of reasoning which is neither deduction nor induction

(CP 5.171, CP 7.218, CP 8.209)

This situation of a variety of perspectives on abduction issue can be explained by the fact that abduction has no strict substantialist definition, but for the reason that it has lots of functions and applications, it inspires different practices. Second explanatory strategy for comprehension of abduction phenomenon is based on thesis that abduction is the closest type of reasoning to the real process of reasoning. Third possible elucidation refers to the cognitive turn in logic concentrating on issues of making progress in analyzing and evaluating information processing.

Modern classifications of abduction can serve for computational theories of discovery as paradigm for division types of discoveries. Game-theoretic and interrogatory interpretations of abduction can also be realized as programs. The creative potential of abduction is also depicted in the approach of paraconsistent logics to abduction, because it provides means to analysis of explanations in antagonistic mode. Defeasible models of abduction are in need for psychology.

The most important for the aims of this work is focus in classifications on creative potential of abduction.

The Big Question of abduction and its renaissance (because original theory of abduction was forgotten from the beginning to the second half of the twentieth century) are the hallmarks of validity of hypothesis proposed in the first chapter: the time for Hypothesis-Abduction-Retroduction prominence is coming. Especially since Peirce suggested hypothesis substituting “computational mind”: human mind endowed by guessing instinct as the coworker of nature in the destination to make world more regular.

3. Explanations: unexpected source of new ideas

Explanations are not so often realized as a creative tool. One of the insights on discovering powers of explanation is interpretation of abduction as generation of explanatory hypotheses. More often explanations are understood as organizational instrument in the scheme of science. There were debates in history of philosophy of science dedicated to the problems of distinguishing tasks of explanation and comprehension, methodological connection of explanation and prediction, but this discussion is out of scope in this work. During this chapter the possible synthesis of ideas of Peirce and Holton will be presented after presentation of some psychological and classical philosophical classifications of explanations.

Explanations as crucial part of educational, scientific, philosophical and social practice are the object of research for different disciplines. Philosophers prefer to analyze explanations as the products of some theories following positivistic tradition of context of justification, comparing explanations and predictions. Psychologists focus on explanations as processes, consider practice of creating explanations as a part of personal development, and investigate influence of capacity to make explanations on cognitive development.

Question of efficiency assessment is of paramount importance for all disciplines, so the problems of evaluation of simplicity of explanations, their predictive and unification power are very significant for scholars. But the problem of classification of explanations is the question that began to attract more and more attention in the 21st century. It is connected with the issue of proper definition of explanation, because now explanation is understood as family term for phenomena of very distinguished nature. There is a demand for interdisciplinary common vocabulary where explanation will play a huge role. Such a formulation of the goal is itself a good explanation why scholars refer to quasi-Aristotelian scheme or complicated physical concepts in their pursuits of correct classification of explanations: Aristotelian metaphysics is a common root of many modern sciences; physics is the guarantor and paradigm of the scientific method.

Cognitive psychologists with their emphasis on the problem of generating explanations provide required attention to the problem of pre-established schemes of the mind. Of course, nobody in the field of psychology states that there is an analogue of transcendental apparatus containing three or more modes of explanations, but there is some correlation between age, health, level of development of mental capacities and ease of setting some explanatory types, but not others. Going forward, functional explanations are the most affordable explanations. Before applying to the aforementioned quasi-Aristotelian typology of explanations, let us consider some other classifications which use as principle of division either structural or functional features.

i. Principle of division by “discipline”

How- and why- questions

This typology is good at conventional division of scientifically (how-) and philosophically (why-) oriented questions.

Anyway, there are a lot of counterexamples: famous “how possible?” in Kantian system of critiques and presence of why- questions in physics.

ii. Artificial metatheory of explanation with principle of division corresponding to different kinds of relationship of asymmetric dependence or generation (structural division).

1. Causal explanations

Search for the cause(s) for an event or property as explanans.

2. Subsumption / unification explanations

Explanations subsume the explanandum under an explanatory pattern (for example, law / counterfactual-supporting generalization)

The type of mathematical explanations and explanations concerning formal relationships.

3. Mechanism-based explanations

Explanations include description of causal mechanisms, their part-whole relations, operations of components, principle of organization (for example, hierarchical).

iii. Structural and functional explanations.

iv. Division based on modality dependence: “how possibly” and “how actually” explanations with subdivision of both types to other types.

v. Aristotelian system of explanation with distinction between four causes

1. Mechanistic explanations

Explanations dedicated to the analysis of parts and processes(“material” and “efficient” causes).

2. Teleological or functional explanations

Explanations specifying functions or goals (“final cause”).

3. Formal explanations

Explanations attributing to kinds, categories, membership, normative statements (“formal cause” and “final cause” in cases of explanations referring to norms).

Psychologists clearly understand the problem of heterogeneity of explanations. The task of complete and sufficiently general classification is realized. The great problem for psychologists is division between causal and non-causal (typical for logic and mathematical explanations) types.

The most influential classification of explanations in philosophy of science is the Hempel one, which solves this problem. Hempel creates covering-law model of explanation including two prominent ideal type-models: Deductive-Nomological Model (D or D-N) and Probabilistic-Statistical (P or I-S) Model.

Explanatory arguments have such a form:

Table 9

Deductive-Nomological explanations are not always causal. The D-N model allows to deductive subsumption of general laws under more abstract principles. Hempel is epistemological optimist: he considers that there is a hierarchy of explanations with increasing level of inclusiveness and comprehensiveness, so in the long-term each fact that has no explanation nowadays will be explained. This dynamics is itself explained by the fact that each time the broader law is discovered, it applies to more phenomena. The depth, breadth and scope of covering laws increase. Moreover, D-N explanation can be referred to future and past events.

Probabilistic explanations are statements about proportion of objects that have some quality. As Hempel underlines, the distinction between two types is logical. D-N explanations claim about all the elements of certain class, P explanations refer to the proportion of the class. Hempel also stresses the fundamental irreducible character of probabilistic explanations which are typical for quantum mechanics and genetics.

The scheme of Hempel caused a wave of criticism. For example, Salmon is in opposition to the understanding of typology of explanations proposed by Hempel (just two types of explanations: deductive-nomological (D-N) explanations and inductive-statistical (I-S) explanation). He dubbed the claim that “scientific explanations are arguments” a third dogma of empiricism. From the point of view of Salmon, scientific explanations show “how events and statistical regularities fit into the causal network of the world”. Salmon argues that explanations are not deductive arguments, because the latter cannot cope with irrelevancies that are neutral relatively to the validity of the deductive argument. Being understood as causal arguments, explanations have no retrodictive power, just predictive, in other case it will be fault of explaining from effects, not causes. The other point of critique is the requirement of total evidence, relevant for deductive and inductive arguments. In comparison with inductive arguments which have the requirement of total evidence, I-S explanations of Hempel have the requirement of maximal specificity (it claims for the reference class of the individual in a statistical explanation to be narrow enough to eliminate subsequent relevant partition). Salmon proposes his criterion - the requirement of the maximal class of maximal specificity (just those considerations that are relevant to the explanandum are contained in the explanans) - according to it, the reference class is determined by taking account of all relevant considerations, but that it is not irrelevantly divided. The explanation model, which Salmon suggests, is called the statistical-relevance (S-R) model with stress on relevant information and it outlines comprehension of explanation as an aggregation of relevant considerations. Statistical explanation is expressed by of a probability distribution over a homogeneous partition (no further relevant partition) of an initial reference class. This probability distribution employs an analogue for sufficient and necessary conditions required for functional explanation. Firstly, S-R model launches statistical regularities for a relevant partition of a given reference class into maximal homogeneous subclasses, secondly S-R explanations explain individual events on the basis of statistical dependencies (improbable coincidences when dependent events occur in conjunction with a probability higher than the product of probabilities counted separately, so-called principle of the common cause of Reichenbach).