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.

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)

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)

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)

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 distinguish three aspects of medical diagnosis: generating new diagnostic hypotheses, selecting hypotheses for further pursuit, and evaluating their probability in light of the available evidence. Drawing on Peirce’s account of abduction, we argue that hypothesis generation is amenable to normative analysis: physicians need to make good decisions about when and how to generate new diagnostic hypothesis as well as when to stop. The intertwining relationship between the generation and selection of diagnostic hypotheses is illustrated through the analysis of a (...) detailed clinical case study. This interaction is not adequately captured by the existing probabilistic, decision-theoretic models of the threshold approach to clinical decision-making. Instead, we propose to conceptualize medical diagnosis in terms of strategic reasoning. (shrink)

This paper compares Peirce’s and Hintikka’s logical philosophies and identifies a cross-section of similarities in their thoughts in the areas of action-first epistemology, pragmaticist meaning, philosophy of science, and philosophy of logic and mathematics.

Exploring the early development of an area of medical literature can inform contemporary medical debates. Different methods of inference include deduction, induction, abduction, and inference to the best explanation. I argue that early shaken baby research is best understood as using abduction to tentatively suggest that infants with unexplained intracranial and ocular bleeding have been assaulted. However, this tentative conclusion was quickly interpreted, by some at least, as a general rule that infants with these pathological signs were certainly cases of (...) abuse. Rather than focusing on inductive arguments, researchers today may be better off focusing on making a compelling inference to the best explanation. (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)

Peirce aspired for the completeness of his logic cum the theory of signs in his 1903 Lowell Lectures and other late manuscripts. Semeiotic completeness states that everything that is a consequence in logical critic is derivable in speculative grammar. The present paper exposes the reasons why Peirce would fall short of establishing semeiotic completeness and thus why he would not continue seeking a perfect match between the theories of grammar and critic. Some alternative notions are then proposed.

Recent logic and linguistic literature suggest that certain forms of denial cannot be reduced to a simple assertion of negation. In particular, the existence of mathematical and empirical conjectures offers a basis for refuting Frege’s thesis of equivalence between denial and assertion of negation. Following this line of thought we develop a formal framework with two primitive illocutionary operators for assertion and denial, where denial is not a simple negation of assertion. We introduce a semantics for the operators mentioned above. (...) Finally, we discuss the relations between asserted and denied contents. (shrink)

Peirce made repeated attempts to clarify what he understood as abduction or creative reasoning in scientific discoveries. In this article, we draw on past and recent scholarship on Peirce’s later accounts of abduction to put a case for how teachers can apply his ideas productively to elicit and guide student creative reasoning in the science classroom. We focus on (a) his rationale for abduction, (b) conditions he recognised as necessary to support this speculative reasoning, (c) pragmatic strategies to guide inquiry (...) and test conjectural hypotheses, and (d) his growing recognition of creative dimensions to reasoning beyond abductive inference-making. We illustrate this case through examples of a guided inquiry approach to student claim-making in the science classroom. (shrink)

In this paper, we argue that one way to approach what is known in the literature as the “Trust Gap” in Medical AI is to focus on explanations from an Explainable AI (xAI) perspective. Against the current framework on xAI – which does not offer a real solution – we argue for a pragmatist turn, one that focuses on understanding how we provide explanations in Traditional Medicine (TM), composed by human agents only. Following this, explanations have two specific relevant components: (...) they are usually (i) social and (ii) abductive. Explanations, in this sense, ought to provide understanding by answering contrastive _why-questions_: “Why had P happened instead of Q?” (Miller in AI 267:1–38, 2019) (Sect. 1 ). In order to test the relevancy of this concept of explanation in medical xAI, we offer several reasons to argue that abductions are crucial for medical reasoning and provide a crucial tool to deal with trust gaps between human agents (Sect. 2 ). If abductions are relevant in TM, we can test the capability of Artificial Intelligence systems on this merit. Therefore, we provide an analysis of the capacity for social and abductive reasoning of different AI technologies. Accordingly, we posit that Large Language Models (LLMs) and transformer architectures exhibit a noteworthy potential for effective engagement in abductive reasoning. By leveraging the potential abductive capabilities of LLMs and transformers, we anticipate a paradigm shift in the integration of explanations within AI systems. This, in turn, has the potential to enhance the trustworthiness of AI-driven medical decisions, bridging the Trust Gap that has been a prominent challenge in the field of Medical AI (Sect. 3 ). This development holds the potential to not only improve the interpretability of AI-generated medical insights but also to guarantee that trust among practitioners, patients, and stakeholders in the healthcare domain is still present. (shrink)

This paper proposes to recover the topic of the philosophy of scientific method from its late nineteenth-century roots. The subject matter of scientific method sprouted from key inferential ingredients identified by Charles Peirce. In this paper, the historical path is traversed from the viewpoint of contemporary Cognitive Structural Realism (CSR). Peirce’s semiotic theory of methods and practices of scientific inquiry prefigured CSR’s reliance on embodied informational structures and experimentation upon forms of relations that model generic scientific domains. Three results are (...) shown to follow from this convocation: (i) a naturalization of Peirce’s interconnected abductive, deductive and inductive stages of the logic of science, here characterized de novo in terms of CSR. (ii) a perspective to scientific modeling that incorporates processes of abstraction and generalization as originated from Peirce’s logic of science, and (iii) diagrammatic reasoning as a pivotal method in analyzing scientific reasoning in experimental practices. (shrink)

This paper aims, above all, to invite a direct reading of the article that Charles S. Peirce published in 1908 with the title “A Neglected Argument for the Reality of God.” More than a century after its original publication, that article by Peirce has not lost its relevance: its careful reading continues to provide a lot to think about. To this end, my presentation is organized in six sections: 1) introduction; 2) presentation of “A Neglected Argument for the Reality of (...) God”; 3) the notion of reality; 4) the heart of the “Neglected Argument”; 5) contemporary discussion: a response to Oya ; and 6) conclusion. (shrink)

What understanding of mathematical objectivity is promoted by Peirce’s pragmatism? Can Peirce’s theory help us to further comprehend the role of intersubjectivity in mathematics? This paper aims to answer such questions, with special reference to recent debates on mathematical practice, where Peirce is often quoted, although without a detailed scrutiny of his theses. In particular, the paper investigates the role of intersubjectivity in the constitution of mathematical objects according to Peirce. Generally speaking, this represents one of the key issues for (...) the philosophy of mathematical practice, whereas – with regard to Peirce – these two aspects (intersubjectivity and objectivity) have been studied for a long time, but mostly as unrelated topics. To reconstruct the connection between Peirce’s reflection on intersubjectivity and the objectivity of mathematical theories, the paper is divided into three parts: (1) the first part introduces Peirce’s view of mathematics; (2) the second analyzes his peculiar “pragmatist realism,” which overcomes common dichotomies in the philosophy of mathematics; (3) the third illustrates the role that Peirce attributes to intersubjectivity in science, and investigates to what extent the intersubjective dimension is also essential in mathematics. (shrink)

Journal Name: Semiotica Issue: Ahead of print.

Reasoning in medicine requires the critical use of a clinical methodology whose validity must be evaluated as well as its limits. In the last decade, an increasing amount of evidence has shown severe limitations and flaws in the conduct of prognostic studies. The main reason behind this fact is that prognostic judgments are at high risk of error. In this paper we investigate the pragmatic and illocutionary aspects of different forms of linguistic acts and judgments involved in clinical practice. More (...) specifically, we analyze the role of uncertainty with regard to ‘particular’ clinical judgments and its relation with ‘general’ evidence. Focusing on how prognostic judgments are formulated and justified, our main purpose is to highlight the explication, the structure and the limits of prognosis from a linguistic and epistemological perspective. (shrink)

The roles of abductive inference in dynamic heuristics allows scientific methodologies to test novel explanations for the world’s ways. Deliberate reasoning often follows abductive patterns, as well as patterns dominated by deduction and induction, but complex mixtures of these three modes of inference are crucial for scientific explanation. All possible mixed inferences are formulated and categorized using a novel typology and nomenclature. Twenty five possible combinations among abduction, induction, and deduction are assembled and analyzed in order of complexity. There are (...) five primary categories for sorting these inferential procedures: fallacies, non-scientific procedures, quasi-scientific procedures, scientific procedures, and scientific heuristics. (shrink)

Peirce’s Pheme directs interpretation of narratives via a “series of surprises” (ep2:154). The indexical and iconic elements inherent in Phemes are particularly potent in forcing attention and depicting relevant events. Index intrudes upon interpreters’ consciousness to notice the unexpected consequence; but icons exploit vividness. As imperatives, Phemes compel particular behaviors (1906: ms295). When narratives are portrayed in pictures, interpreters remember happenings in which Phemes feature surprising percepts, evoking an attentional response, and securing a confluence of events in memory. Findings from (...) children’s narrations demonstrate that events represented by Phemes are more often included in children’s retellings, because surprising images command active participation. This viewpoint impels listeners to build episodes, ascribing meanings across events, and proposing rationale for novel outcomes. (shrink)