Despite some surface similarities, Charles Peirce’s philosophy of mathematics, pragmaticism, is incompatible with both mathematical structuralism and fictionalism. Pragmaticism has to do with experimentation and observation concerning the forms of relations in diagrammatic and iconic representations ofmathematical entities. It does not presuppose mathematical foundations although it has these representations as its objects of study. But these objects do have a reality which structuralism and fictionalism deny.

This collection of essays discusses a central feature of European philosophy: the idea of a universal active power as the ultimate world-explanation.

In this article I bring to light a group of scientific and philosophical ideas and intellectual currents from the early era of the significs movement, contemporaneous with the origins of early analytic philosophy. Significs was a strong candidate for the science of language, meaning, and communication during the new century. Its heyday coincided with the forums of the Vienna Circle, yet its intellectual and cultural climate persisted until fading in the turmoil of the mid-century's analytic thought.

I will show that the semantic structure of a new imperfect-information propositional logic can be described in terms of extensive forms of semantic games. I will discuss some ensuing properties of these games such as imperfect recall, informational consistency, and team playing. Finally, I will suggest a couple of applications that arise in physics, and most notably in quantum theory and quantum logics.

The problem of intentional identity, as originally offered by Peter Geach, says that there can be an anaphoric link between an indefinite term and a pronoun across a sentential boundary and across propositional attitude contexts, where the actual existence of an individual for the indefinite term is not presupposed. In this paper, a semantic resolution to this elusive puzzle is suggested, based on a new quantified intensional logic and game-theoretic semantics (GTS) of imperfect information. This constellation leads to an expressive (...) intensional language with a property of informational independence, argued to produce a purely semantic explication to intentional identity statements. One consequence is that various extra-logical and pragmatic factors become of secondary concern; it is possible to solve the puzzle by logico-semantic methods, albeit somewhat radically renewed ones. (shrink)

Modern explainable AI methods remain far from providing human-like answers to ‘why’ questions, let alone those that satisfactorily agree with human-level understanding. Instead, the results that such methods provide boil down to sets of causal attributions. Currently, the choice of accepted attributions rests largely, if not solely, on the explainee’s understanding of the quality of explanations. The paper argues that such decisions may be transferred from a human to an XAI agent, provided that its machine-learning algorithms perform genuinely abductive inferences. (...) The paper outlines the key predicament in the current inductive paradigm of ML and the associated XAI techniques, and sketches the desiderata for a truly participatory, second-generation XAI, which is endowed with abduction. (shrink)

We study partiality in propositional logics containing formulas with either undefined or over-defined truth-values. Undefined values are created by adding a four-place connective W termed transjunction to complete models which, together with the usual Boolean connectives is shown to be functionally complete for all partial functions. Transjunction is seen to be motivated from a game-theoretic perspective, emerging from a two-stage extensive form semantic game of imperfect information between two players. This game-theoretic approach yields an interpretation where partiality is generated as (...) a property of non-determinacy of games. Over-defined values are produced by adding a weak, contradictory negation or, alternatively, by relaxing the assumption that games are strictly competitive. In general, particular forms of extensive imperfect information games give rise to a generalised propositional logic where various forms of informational dependencies and independencies of connectives can be studied. (shrink)

It is of common use in modern Venn diagrams to mark a compartment with a cross to express its non-emptiness. Modern scholars seem to derive this convention from Charles S. Peirce, with the assumption that it was unknown to John Venn. This paper demonstrates that Venn actually introduced several methods to represent existentials but felt uneasy with them. The resistance to formalize existentials was not limited to diagrammatic systems, as George Boole and his followers also failed to provide a satisfactory (...) symbolic representation for them. This difficulty points out issues that are inherent to the very nature of existentials. This paper assesses the various methods designed for the representation of existential statements with Venn diagrams. First, Venn’s own attempts are discussed and compared with other solutions proposed by his contemporaries and successors, notably Lewis Carroll and Peirce. Since disjunctives hold an important role in an effective representation of existentials, their representation is also discussed. Finally, recent methods for the diagrammatic representation of existing individuals, rather than mere existence, are surveyed. (shrink)

Charles Sanders Peirce: Logic Charles Sanders Peirce was an accomplished scientist, philosopher, and mathematician, who considered himself primarily a logician. His contributions to the development of modern logic at the turn of the 20th century were colossal, original and influential. Formal, or deductive, logic was just one of the branches in which he exercized … Continue reading Peirce’s Logic →.

We describe Peirce’s 1903 system of modal gamma graphs, its transformation rules of inference, and the interpretation of the broken-cut modal operator. We show that Peirce proposed the normality rule in his gamma system. We then show how various normal modal logics arise from Peirce’s assumptions concerning the broken-cut notation. By developing an algebraic semantics we establish the completeness of fifteen modal logics of gamma graphs. We show that, besides logical necessity and possibility, Peirce proposed an epistemic interpretation of the (...) broken-cut modality, and that he was led to analyze constructions of knowledge in the style of epistemic logic. (shrink)

Some have suggested that images can be arguments. Images can certainly bolster the acceptability of individual premises. We worry, though, that the static nature of images prevents them from ever playing a genuinely argumentative role. To show this, we call attention to a dilemma. The conclusion of a visual argument will either be explicit or implicit. If a visual argument includes its conclusion, then that conclusion must be demarcated from the premise or otherwise the argument will beg the question. If (...) a visual argument does not include its conclusion, then the premises on display must license that specific conclusion and not its opposite, in accordance with some demonstrable rationale. We show how major examples from the literature fail to escape this dilemma. Drawing inspiration from the graphical logic of C. S. Peirce, we suggest instead that images can be manipulated in a way that overcomes the dilemma. Diagrammatic reasoning can take one stepwise from an initial visual layout to a conclusion—thereby providing a principled rationale that bars opposite conclusions—and the visual inscription of this correct conclusion can come afterward in time—thereby distinguishing the conclusion from the premises. Even though this practical application of Peirce’s logical ideas to informal contexts requires that one make adjustments, we believe it points to a dynamic conception of visual argumentation that will prove more fertile in the long run. (shrink)

This paper presents an enrichment of the Gabbay–Woods schema of Peirce’s 1903 logical form of abduction with illocutionary acts, drawing from logic for pragmatics and its resources to model justified assertions. It analyses the enriched schema and puts it into the perspective of Peirce’s logic and philosophy.

This article investigates Charles Peirce’s development of logical calculi for classical propositional logic in 1880–1896. Peirce’s 1880 work on the algebra of logic resulted in a successful calculus for Boolean algebra. This calculus, denoted byPC, is here presented as a sequent calculus and not as a natural deduction system. It is shown that Peirce’s aim was to presentPCas a sequent calculus. The law of distributivity, which Peirce states in 1880, is proved using Peirce’s Rule, which is a residuation, inPC. The (...) transitional systems of the algebra of the copula that Peirce develops since 1880 paved the way to the 1896 graphical system of the alpha graphs. It is shown how the rules of the alpha system reinterpret Boolean algebras, answering Peirce’s statement that logical graphs supply a new system of fundamental assumptions to logical algebra. A proof-theoretic analysis is given for the connection betweenPCand the alpha system. (shrink)

We present a dynamic approach to Peirce’s original construal of abductive logic as a logic of conjecture making, and provide a new decidable, contraction-free and cut-free proof system for the dynamic logic of abductive inferences with neighborhood semantics. Our formulation of the dynamic logic of abduction follows the philosophical and scientific track that led Peirce to his late, post-1903 characterization of abductive conclusions as investigands, namely invitations to investigate propositions conjectured at the level of pre-beliefs.

Charles Peirce’s alpha system \ is reformulated into a deep inference system where the rules are given in terms of deep graphical structures and each rule has its symmetrical rule in the system. The proof analysis of \ is given in terms of two embedding theorems: the system \ and Brünnler’s deep inference system for classical propositional logic can be embedded into each other; and the system \ and Gentzen sequent calculus \ can be embedded into each other.

Peirce considered the principal business of logic to be the analysis of reasoning. He argued that the diagrammatic system of Existential Graphs, which he had invented in 1896, carries the logical analysis of reasoning to the furthest point possible. The present paper investigates the analytic virtues of the Alpha part of the system, which corresponds to the sentential calculus. We examine Peirce’s proposal that the relation of illation is the primitive relation of logic and defend the view that this idea (...) constitutes the fundamental motive of philosophy of notation both in algebraic and graphical logic. We explain how in his algebras and graphs Peirce arrived at a unifying notation for logical constants that represent both truth-function and scope. Finally, we show that Shin’s argument for multiple readings of Alpha graphs is circular. (shrink)

The paper proposes a way to naturalise Charles S. Peirce’s conception of the scientific method, which he specified in terms of abduction, deduction and induction. The focus is on the central issue of the economy of research in abduction and self-correction by error reduction in induction. We show how Peirce’s logic of science receives support from modern breakthroughs in computational neuroscience, and more specifically from Karl Friston’s statements of active inference and the Free Energy Principle, namely the account of how (...) organisms’ capacity to decrease the discrepancy between the expected value and actual outcomes entails the minimisation of errors in their hypotheses about the world. A scientific account of organisms’ capacity to choose policies and form expectations is aligned with Peirce’s theories of abduction and induction, and especially with the economy of research. The upshot is the recovery of Peirce’s theory of the logic of science in the context of active inquiry. (shrink)

This paper explores the intertwining of uncertainty and values. We consider an important but underexplored field of fundamental uncertainty and values in decision-making. Some proposed methodologies to deal with fundamental uncertainty have included potential surprise theory, scenario planning and hypothetical retrospection. We focus on the principle of uncertainty transduction in hypothetical retrospection as an illustrative case of how values interact with fundamental uncertainty. We show that while uncertainty transduction appears intuitive in decision contexts it nevertheless fails in important ranges of (...) strategic game-theoretic cases. The methodological reasons behind the failure are then examined. (shrink)

This important collection focuses on the nature and importance of biodiversity. The concept is clarified and its intrinsic and instrumental value are discussed. Even though the term biodiversity was invented in the 1980s to promote the cause of species conservation, discussions on biological diversity go back to Plato. There are many controversies surrounding biodiversity and a few of them are examined here: What is worthy of protection or restoration and what is the acceptable level of costs? Is it permissible to (...) kill sentient animals to promote native populations? Can species be reintroduced if they have disappeared a long time ago? How should the responsibilities for biodiversity be shared? This book will be of interest to philosophers of science and biologists, but also to anyone interested in conservation and the environment. (shrink)

Most public discussion has focused on those effects of genetic research that are considered in some way unwanted or unpleasant. For example, there has been much debate concerning the risks and the ethical appropriateness of genetic screening, gene therapy, and agricultural applications based on genetic techniques. It often claimed that genetic research may cause new problems such as genetic discrimination, stigmatization, environmental risks, or mistreatment of animals. Genes and Morality: New Essays adopts a critical attitude toward genetic research, on both (...) a theoretical and a practical level. It presents some of the most important problems in the ethics of genetic engineering, including the questions of genetic health and disease, genetic testing, responsibility for health, patenting non-human and human life, and problems related to the disclosure of genetic information. The aim of the book is to focus on real ethical and conceptual issues. Consider, for instance, the concept of genetic disease. As one of the contributors, Ingmar Pörn, writes, fear of genetic disease, or anxiety, is not itself a disease any more than fear of becoming unemployed is a disease. Alleviating such emotions is not a medical task to be discharged by drug therapy. The book also examines the philosophical foundations of these issues by discussing the most influential bioethical theories of today, including utilitarianism and principlism. (shrink)

Abstraction and generalization are two processes of reasoning that have a special role in the construction of scientific theories and models. They have been important parts of the scientific method ever since the nineteenth century. A philosophical and historical analysis of scientific practices shows how abstraction and generalization found their way into the theory of the logic of science of the nineteenth-century philosopher Charles S. Peirce. Our case studies include the scientific practices of Francis Galton and John Herschel, who introduced (...) composite photographs and graphical methods, respectively, as technologies of generalization and thereby influenced Peirce’s logic of abstraction. Herschel’s account of generalization is further supported by William Whewell, who was very influential on Peirce. By connecting Herschel’s scientific technology of abstraction to Peirce’s logical technology of abstraction—namely, diagrams—we highlight the role of judgments in scientific observation by hypostatic abstractions. We also relate Herschel’s discovery-driven logic of science and Peirce’s open-ended diagrammatic logic to the use of models in science. Ultimately, Peirce’s theory of abstraction is a case of showing how logic applies to reality. (shrink)

The Annual Biosemiotic Achievement Award was established at the annual meeting of the International Society for Biosemiotic Studies (ISBS) in 2014, in conjunction with Springer and _Biosemiotics_. It seeks to recognize papers published in the journal that present novel and potentially important contributions to biosemiotic research, its scientific impact, and its future prospects. Here the winner of the Biosemiotic Achievement Award for 2022 is announced: The award goes to Sigmund Ongstad for his article “Simple Utterances but Complex Understanding? Meta-studying the (...) Fuzzy Mismatch between Animal Semantic Capacities in Varied Contexts”. (shrink)

We propose a reconstruction of the constellation of problems and philosophical positions on the nature and number of the primitives of logic in four authors of the nineteenth century logical scene: Peano, Padoa, Frege and Peirce. We argue that the proposed reconstruction forces us to recognize that it is in at least four different senses that a notation can be said to be simpler than another, and we trace the origins of these four senses in the writings of these authors. (...) We conclude that Frege, and even more so Peirce, developed new notations not to make drawing logical conclusions easier but in order to answer the needs of logical analysis. (shrink)

Expressively equivalent logical languages can enunciate logical notions in notationally diversified ways. Frege’s Begriffsschrift, Peirce’s Existential Graphs, and the notations presented by Wittgenstein in the Tractatus all express the sentential fragment of classical logic, each in its own way. In what sense do expressively equivalent notations differ? According to recent interpretations, Begriffsschrift and Existential Graphs differ from other logical notations because they are capable of “multiple readings.” We refute this interpretation by showing that there are at least three different kinds (...) of such multiple readings. While readings of the first kind do not capture any essential difference among notations but only among vocabularies, corresponding to readings of the second and the third kind two general parameters according to which notations may differ are defined: linearity vs. non-linearity, and tabularity vs. non-tabularity. This answers the question of how there can be substantially different but expressively equivalent logical notations. (shrink)

We examine Charles S. Peirce's mature views on the logic of science, especially as contained in his later and still mostly unpublished writings. We focus on two main issues. The first concerns Peirce's late conception of retroduction. Peirce conceived inquiry as performed in three stages, which correspond to three classes of inferences: abduction or retroduction, deduction, and induction. The question of the logical form of retroduction, of its logical justification, and of its methodology stands out as the three major threads (...) in his later writings. The other issue concerns the second stage of scientific inquiry, deduction. According to Peirce's later formulation, deduction is divided not only into two kinds but also into two sub-stages: logical analysis and mathematical reasoning, where the latter is either corollarial or theorematic. Save for the inductive stage, which we do not address here, these points cover the essentials of Peirce's latest thinking on the l.. (shrink)

This article presents and defends an integrated view of the placebo effect, termed “affective-meaning-making” model, which draws from theoretical reflection, clinical outcomes, and neurophysiological findings. We consider the theoretical limitations of those proposals associated with the “meaning view” on the placebo effect which leave the general aspects of meaning unspecified, fail to analyze fully the role of emotions and affect, and establish no clear connection between the theoretical, physiological, and psychological aspects of the effect. We point out that a promising (...) way to overcome these limitations is given by grounding the placebo effect on Peirce’s theory of meaning, in which the role of the meaning constitution and change is placed in logical and objective structures. We also show the connection between our theoretical proposal and the appraisal theory and integrate it with emotion regulation. (shrink)

The background target of the research going into the present article is to forge an intellectual alliance between, on the one hand, active inference and the free-energy principle (FEP), and on the other, Charles S. Peirce’s theory of semiotics and pragmatism. In the present paper, the focus is on the allegiance between the nomenclatures of active and abductive inferences as the proper place to begin reaching at that wider target. The paper outlines the key conceptual elements involved in a naturalistic (...) rendering of Peirce’s late semiotic and logical notion of abductive reasoning. The target is a cognitive-biological model of abduction which preserves the functional integrity of an organism and fulfils the existential imperative for living beings’ evidence of existence. Such a model is an adaptation of Peirce’s late logical schema of abduction proposed in his largely unpublished works during the early 20th century. The proposed model is argued to be a feasible sketch also of recent breakthroughs in computational (sensu Bayesian) cognitive science. (shrink)

The pragmatic notion of assertion has an important inferential role in logic. There are also many notational forms to express assertions in logical systems. This paper reviews, compares and analyses languages with signs for assertions, including explicit signs such as Frege’s and Dalla Pozza’s logical systems and implicit signs with no specific sign for assertion, such as Peirce’s algebraic and graphical logics and the recent modification of the latter termed Assertive Graphs. We identify and discuss the main ‘points’ of these (...) notations on the logical representation of assertions, and evaluate their systems from the perspective of the philosophy of logical notations. Pragmatic assertions turn out to be useful in providing intended interpretations of a variety of logical systems. (shrink)

Peirce wrote in late 1901 a text on formal logic using a special Dragon-Head and Dragon-Tail notation in order to express the relation of logical consequence and its properties. These texts have not been referred to in the literature before. We provide a complete reconstruction and transcription of these previously unpublished sets of manuscript sheets and analyse their main content. In the reconstructed text, Peirce is seen to outline both a general theory of deduction and a general theory of consequence (...) relation. The two are the cornerstones of modern logic and have played a crucial role in its development. From the wider perspective, Peirce is led to these theories by three important generalizations: propositions to all signs, truth to scriptibility, and derivation to transformability. We provide an exposition of such proposed semiotic foundation for logical constants and point out a couple of further innovations in this rare text, including the sheet of assertion, correction as a dual of deduction and the nature of conditionals as variably strict conditionals. (shrink)

The theory of existential graphs, which Peirce ultimately divided into four quadrants , is a rich method of analysis in the philosophy of logic. Its $$\upbeta $$ β -part boasts a diagrammatic theory of quantification, which by 1902 Peirce had used in the logical analysis of natural-language expressions such as complex donkey-type anaphora, quantificational patterns describing new mathematical concepts, and cognitive information processing. In the $$\upbeta $$ β -quadrant, he came close to inventing independence-friendly logic, the idea of which he (...) found indispensable in fulfilling the tasks –. (shrink)

The following two articles comprise two sets of Charles Peirce’s manuscripts, “Recent Developments of Existential Graphs and their Consequences for Logic” (MS 498, MS 499, MS 490 & S-36, 1906) and “Assurance through Reasoning” (MS 669 & MS 670, 1911), written for the National Academy of Sciences meetings in 1906 and 1911. The papers are deposited at Houghton Library, Harvard University. Only some parts of MS 470 have been published before, and in somewhat defective form. Although “Assurance” follows “Recent Developments” (...) chronologically, given the expository style of the former it is recommended to be read before “Recent Developments”. As the title indicates, in the latter Peirce goes on to describe his latest discoveries concerning the method and the logic of existential graphs. The transcription reproduces all significant deletions that appear in the original sheets. Editorial comments and additions are given in brackets. [Alt.:] means the beginning of an alternative sequence. [Del. (shrink)

Clinical equipoise has been proposed as an ethical principle relating uncertainty and moral leeway in clinical research. Although CE has traditionally been indicated as a necessary condition for a morally justified introduction of a new RCT, questions related to the interpretation of this principle remain woefully open. Recent proposals to rehabilitate CE have divided the bioethical community on its ethical merits. This paper presents a new argument that brings out the epistemological difficulties we encounter in justifying CE as a principle (...) to connect uncertainty and moral leeway in clinical ethics. The argument proposes, first, that the methodology of hypothetical retrospection is applicable to the RCT design and that it can accommodate uncertainty. As currently understood, however, HR should give up its reliance on the assumption of uncertainty transduction, because the latter assumes the principle of indifference, which does not accommodate uncertainty in the right way. The same principle is then seen to distort also the received interpretations of CE. (shrink)

Scientific evidence and scientific values under risk and uncertainty are strictly connected from the point of view of Peirce’s pragmaticism. In addition, economy and statistics play a key role in both choosing and testing hypotheses. Hence we may show also the connection between the methodology of the economy of research and statistical frequentism, both originating from pragmaticism. The connection is drawn by the regulative principles of synechism, tychism and uberty. These principles are values that have both epistemic and non-epistemic dimension. (...) They concern both the decisions to test a hypothesis as well as inductive risk. The validity of this result stems from the values cost–benefit analysis imposes on scientific inquiry. Values associated with the economy of research are important not only in the pre-test phases of generating hypotheses but also when hypotheses are effectively tested. Peirce took these economic considerations to leave room for an interpretation of probability which is not only a frequentist and propensity-theoretic but also a conceptualist one referring to degrees of belief. We show that this leeway nonetheless agrees with the theory of the economy of scientific methods. (shrink)

It is well-known that by 1882, Peirce, influenced by Cayley’s, Clifford’s and Sylvester’s works on algebraic invariants and by the chemical analogy, had already achieved something like a diagrammatic treatment of quantificational logic of relatives. The details of that discovery and its implications to some wider issues in logical theory merit further investigation, however. This paper provides a reconstruction of the genesis of Peirce’s logical graphs from the early 1880s until 1896, covering the period of time during which he already (...) was acquainted with the works of his Johns Hopkins colleagues on the mathematical theory of graphs and was reaching the very first forms of his theory and method of... (shrink)

Abductive conclusions are drawn in a special, co-hortative mood. Abductive conclusions are representative interpretants that represent abduction as a form of reasoning that can convey a general conception of the truth. The truth is not asserted; abduction merely delivers the idea of a matter of course, rendering that idea comparatively simple and natural, hence assuring us of its justified assertibility. Hence abductive reasoning is at home in addressing ‘How Possible’-questions in science. Abductive reasoning concerns the question of how things might, (...) could or would conceivably be such that they can be plausibly asserted. Peirce took all reasoning to be diagrammatic and representable using the graphical method of logic. Yet no examples have previously been found in his large manuscript corpus of what such non-deductive graphs might look like. This paper proposes a new interpretation of a sole exception, a sketch of two graphs from a rejected page from 1903, which might be the only surviving example of Peirce’s abductive graphs. The proposed interpretation takes them to be representative interpretants of this special inverse type of inference. (shrink)

Peirce and Frege both distinguished between the propositional content of an assertion and the assertion of a propositional content, but with different notational means. We present a modification of Peirce’s graphical method of logic that can be used to reason about assertions in a manner similar to Peirce’s original method. We propose a new system of Assertive Graphs, which unlike the tradition that follows Frege involves no ad hoc sign of assertion. We show that axioms of intuitionistic logic can be (...) derived from AGs, and argue that AGs analyse and represent assertions and illocutionary content in a way which is motivated both by its logical properties and its historical connection with the ideas that led to the development of the graphical method. (shrink)

This paper examines the contemporary philosophical and cognitive relevance of Charles Peirce's diagrammatic logic of existential graphs (EGs), the ‘moving pictures of thought’. The first part brings to the fore some hitherto unknown details about the reception of EGs in the early 1900s that took place amidst the emergence of modern conceptions of symbolic logic. In the second part, philosophical aspects of EGs and their contributions to contemporary logical theory are pointed out, including the relationship between iconic logic and images, (...) the problem of the meaning of logical constants, the cognitive economy of iconic logic, the failure of the Frege–Russell thesis, and the failure of the Language of Thought hypothesis. (shrink)

This paper provides an analysis of the notational difference between Beta Existential Graphs, the graphical notation for quantificational logic invented by Charles S. Peirce at the end of the 19th century, and the ordinary notation of first-order logic. Peirce thought his graphs to be “more diagrammatic” than equivalently expressive languages for quantificational logic. The reason of this, he claimed, is that less room is afforded in Existential Graphs than in equivalently expressive languages for different ways of representing the same fact. (...) The reason of this, in turn, is that Existential Graphs are a non-linear, occurrence-referential notation. As a non-linear notation, each graph corresponds to a class of logically equivalent but syntactically distinct sentences of the ordinary notation of first-order logic that are obtained by permuting those elements that in the graphs lie in the same area. As an occurrence-referential notation, each Beta graph corresponds to a class of logically equivalent but syntactically distinct sentences of the ordinary notation of first-order logic in which the identity of reference of two or more variables is asserted. In brief, Peirce’s graphs are more diagrammatic than the linear, type-referential notation of first-order logic because the function that translates the latter to the graphs does not define isomorphism between the two notations. (shrink)

Are knowledge and belief pivotal in science, as contemporary epistemology and philosophy of science nearly universally take them to be? I defend the view that scientists are not primarily concerned with knowing and that the methods of arriving at scientific hypotheses, models and scenarios do not commit us having stable beliefs about them. Instead, what drives scientific discovery is ignorance that scientists can cleverly exploit. Not an absence or negation of knowledge, ignorance concerns fundamental uncertainty, and is brought out by (...) retroductive inferences, which are roughly characterised as reasoning from effects to causes. I argue that recent discoveries in sciences that coped with under-structured problem spaces testify the prevalence of retroductive logic in scientific discovery and its progress. This puts paid to the need of finding epistemic justification or confirmation to retroductive methodologies. A scientist, never frightened of unknown unknowns, strives to advance the forefront of uncertainty, not that of belief or knowledge. Far from rendering science irrational, I conclude that catering well for the right conditions in which to cultivate ignorance is a key to how fertile retroductive inferences arise. (shrink)