This book employs a new eco-cognitive model of abduction to underline the distributed and embodied nature of scientific cognition. Its main focus is on the knowledge-enhancing virtues of abduction and on the productive role of scientific models. What are the distinctive features that define the kind of knowledge produced by science? To provide an answer to this question, the book first addresses the ideas of Aristotle, who stressed the essential inferential and distributed role of external cognitive tools and epistemic mediators (...) in abductive cognition. This is analyzed in depth from both a naturalized logic and an ecology of cognition perspective. It is shown how the maximization of cognition, and of abducibility – two typical goals of science – are related to a number of fundamental aspects: the optimization of the eco-cognitive situatedness; the maximization of changeability for both the input and the output of the inferences involved; a high degree of information-sensitiveness; and the need to record the “past life” of abductive inferential practices. Lastly, the book explains how some impoverished epistemological niches – the result of a growing epistemic irresponsibility associated with the commodification and commercialization of science – are now seriously jeopardizing the flourishing development of human creative abduction. (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)

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examine Charles S. Peirce's mature views on the logic of science, especially as contained in his later and still mostly unpublished writings.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)

One of our purposes here is to expose something of the elementary logical structure of abductive reasoning, and to do so in a way that helps orient theorists to the various tasks that a logic of abduction should concern itself with. We are mindful of criticisms that have been levelled against the very idea of a logic of abduction; so we think it prudent to proceed with a certain diffidence. That our own account of abduction is itself abductive is methodological (...) expression of this diffidence. A second objective is to test our conception of abduction's logical structure against some of the more promising going accounts of abductive reasoning. We offer our various suggestions in a benignly advisory way. The primary targets of our advice is ourselves, meant as guides to work we have yet to complete or, in some instances, start. It is possible that our colleagues in the abduction research communities will find our counsel to be of some interest. But we repeat that our first concern is to try to get ourselves straight about what a logic of abduction should encompass. (shrink)

1 INTRODUCTION Above the other titles he might justly have claimed, Charles S. Peirce prized the title 'logician'. He expressed in several places his ...

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)

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)

Peirce believed that inquiry involves three types of reasoning—abduction, deduction, and induction. While Peirce’s beliefs about reasoning, especially abduction, changed over time, in his mature work the following picture of reasoning emerges: abduction generates and chooses hypotheses to test; deduction determines the entailments of a hypothesis; induction ascertains whether the evidence accords with the hypothesis in question.1 Peirce both identified abduction and coined the word.2 His concept of abduction is one of the most original contributions he made to the study (...) of reasoning. It is also one of the most poorly understood. Peirce’s concept of abduction has been distorted by contemporary... (shrink)

I argue against the tendency in the philosophy of science literature to link abduction to the inference to the best explanation (IBE), and in particular, to claim that Peireean abduction is a conceptual predecessor to IBE. This is not to discount either abduction or IBE. Rather the purpose of this paper is to clarify the relation between Peireean abduction and IBE in accounting for ampliative inference in science. This paper aims at a proper classification—not justification—of types of scientific reasoning. In (...) particular, I claim that Peireean abduction is an in-depth account of the process of generating explanatory hypotheses, while IBE, at least in Peter Lipton's thorough treatment, is a more encompassing account of the processes both of generating and of evaluating scientific hypotheses. There is then a two-fold problem with the claim that abduction is IBE. On the one hand, it conflates abduction and induction, which are two distinct forms of logical inference, with two distinct aims, as shown by Charles S. Peirce; on the other hand it lacks a clear sense of the full scope of IBE as an account of scientific inference. (shrink)

An agent-centered, goal-directed, resource-bound logic of human reasoning would do well to note that individual cognitive agency is typified by the comparative scantness of available cognitive resources—information, time, and computational capacity, to name just three. This motivates individual agents to set their cognitive agendas proportionately, that is, in ways that carry some prospect of success with the resources on which they are able to draw. It also puts a premium on cognitive strategies which make economical use of those resources. These (...) latter I callscant-resource adjustment strategies,and they supply the context for an analysis of abduction. The analysis is Peircian in tone, especially in the emphasis it places on abduction’signorance-preservingcharacter. My principal purpose here is to tie abduction’s scarce-resource adjustment capacity to its ignorance preservation. (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)

In three comprehensive volumes, Logic of the Future presents a full panorama of Charles S. Peirce’s most important late writings. Among the most influential American thinkers, Peirce took his existential graphs to be a significant contribution to human thought. The manuscripts from 1895–1913, with many of them being published here for the first time, testify to the richness and open-endedness of his theory of logic and its applications. They also invite us to reconsider our ordinary conceptions of reasoning as well (...) as the conventional stories concerning the evolution of modern logic. This first volume of Logic of the Future is on the historical development, theory and application of Peirce’s graphical method and diagrammatic reasoning. It also illustrates the abundant further developments and applications Peirce envisaged existential graphs to have on the analysis of mathematics, language, meaning and mind. (shrink)

This book offers a novel perspective on abduction. It starts by discussing the major theories of abduction, focusing on the hybrid nature of abduction as both inference and intuition. It reports on the Peircean theory of abduction and discusses the more recent Magnani concept of animal abduction, connecting them to the work of medieval philosophers. Building on Magnani's manipulative abduction, the accompanying classification of abduction, and the hybrid concept of abduction as both inference and intuition, the book examines the problem (...) of visual perception together with the related concepts of misrepresentation and semantic information. It presents the author's views on caricature and the caricature model of science, and then extends the scope of discussion by introducing some standard issues in the philosophy of science. By discussing the concept of ad hoc hypothesis generation as enthymeme resolution, it demonstrates how ubiquitous the problem of abduction is in all the different individual scientific disciplines. This comprehensive text provides philosophers, logicians and cognitive scientists with a historical, unified and authoritative perspective on abduction. (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.

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)

When one tries to determine what the iconic dimension of thought consists in for Peirce and what its range is, one might have the impression that his remarks on this matter are inconsistent. For instance, on the one hand he writes the following: Remember it is by icons only that we really reason, and abstract statements are valueless in reasoning except so far as they aid us to construct diagrams. The sectaries of the opinion I am combating seem, on the (...) contrary, to suppose that reasoning is performed with abstract "judgments," and that an icon is of use only as enabling me to frame abstract statements as premisses. In an apparently similar fashion, Peirce argues that the predicate of a... (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.