Popper is well known for rejecting a logic of discovery, but he is only justified in rejecting the same type of logic of discovery that is denied by consequentialism. His own account of hypothesis generation, based on a natural selection analogy, involves an error-eliminative logic of discovery and the differences he admits between biological and conceptual evolution suggest an error-corrective logic of discovery. These types of logics of discovery are based on (...) principles of plausibility that are used in the generation as opposed to the preliminary evaluation of hypotheses. The normative relevance of these principles is grounded in the distinction between strategic and definitory rules. (shrink)
In this paper, I want to substantiate three related claims regarding causal discovery from non-experimental data. Firstly, in scientific practice, the problem of ignorance is ubiquitous, persistent, and far-reaching. Intuitively, the problem of ignorance bears upon the following situation. A set of random variables V is studied but only partly tested for (conditional) independencies; i.e. for some variables A and B it is not known whether they are (conditionally) independent. Secondly, Judea Pearl’s most meritorious and influential algorithm for causal (...)discovery (the IC algorithm) cannot be applied in cases of ignorance. It presupposes that a full list of (conditional) independence relations is on hand and it would lead to unsatisfactory results when applied to partial lists. Finally, the problem of ignorance is successfully treated by means of ALIC, the adaptive logic for causal discovery presented in this paper. (shrink)
Traditional logical empiricist and more recent historicist positions on the logic of discovery are briefly reviewed and both are found wanting. None have examined the historical detail now available from recent research on Darwin, from which there is evidence for gradual transition in descriptive and explanatory concepts. This episode also shows that revolutionary research can be directed by borrowed metascientific objectives and heuristics from other disciplines. Darwin's own revolutionary research took place within an ontological context borrowed from non (...) evolutionary predecessors with methodological objectives borrowed from and justified by their success in Newton's physics. The logic of discovery is not a special form of inference from observation to theory, but rather a theory of the rationality of research, including principles bearing upon the rational choice of problems, or epistemic objectives, and heuristic, or means to solving the problems. Such choices can be justified only locally in the context of a relatively stable background ontology and substantive epistemology, not globally for all science. (shrink)
The distinction between the context ofdiscovery and the context of justificationrestricts philosophy of science to the rationalreconstruction of theories, and characterizesscientific discovery as rare, theoreticalupheavals that defy rational reconstruction. Kuhnian challenges to the two contextsdistinction show that non-rational elementspersist in the justification of theories, butgo no further to provide a positive account ofdiscovery. A gradualist theory of discoverydeveloped in this paper shows, with supportfrom ecological cases, that discoveries areroutinely made in ecology by extending modelsto new domains, or by making (...) additions toearlier models. The logic of discovery isphilosophically accessible once it isappreciated that model truth is presumed, evenif counterfactually, in ecologists' applicationof models. A gradualist view shows thatmodels' heuristic power routinely leads todiscoveries. (shrink)
In his influential paper, 'Why Was the Logic of Discovery Abandoned?', Laudan contends that there has been no philosophical rationale for a logic of discovery since the emergence of consequentialism in the 19th century. It is the purpose of this paper to show that consequentialism does not involve the rejection of all types of logic of discovery. Laudan goes too far in his interpretation of the historical shift from generativism to consequentialism, and his claim (...) that the context of pursuit belongs to neither discovery nor justification is based on narrow interpretations of the contexts of discovery and justification. As a result, Laudan draws unwarranted conclusions concerning both the early and contemporary defenders of a logic of discovery. A methodological logic of discovery - which involves self-corrective methods of hypothesis generation that promote the long-term goals of science and which require consequential support for justification - is a type of logic of discovery that survives the shift to consequentialism. (shrink)
A widely endorsed thesis in the philosophy of science holds that if evidence for a hypothesis was not known when the hypothesis was proposed, then that evidence confirms the hypothesis more strongly than would otherwise be the case. The thesis has been thought to be inconsistent with Bayesian confirmation theory, but the arguments offered for that view are fallacious. This paper shows how the special value of prediction can in fact be given Bayesian explanation. The explanation involves consideration of the (...) reliability of the method by which the hypothesis was discovered, and thus reveals an intimate connection between the 'logic of discovery' and confirmation theory. (shrink)
Although on opposite sides of the logic of discovery debate, Laudan and Simon share a thesis of divorce between discovery (invention) and justification (appraisal); but unlike some other authors, they do not base their respective versions of the divorce-thesis on the empirical/logical distinction. Laudan argues that, in contemporary science, invention is irrelevant to appraisal, and that this irrelevance renders epistemically pointless the inventionist program. Simon uses his divorce-thesis to defend his account of invention, which he claims to (...) be non-inductive--so evading the problem of induction. Underlying both authors' positions are inadequate conceptions of inductive inference. Laudan here ignores the role in contemporary science of plausibility arguments, which provide a crucial link between invention and appraisal, and thence an epistemic rationale for inventionism. Simon's account of invention does covertly call upon inductive principles from the context of appraisal, and this is what gives his program epistemic import; otherwise he would be vulnerable to Laudan's "no rationale" critique. The tensions in both authors reveal the falsity of the divorce-thesis, and the essential function of induction in both appraisal and invention of hypotheses. (shrink)
There is renewed interest in the logic of discovery as well as in the position that there is no reason for philosophers to bother with it. This essay shows that the traditional, philosophical arguments for the latter position are bankrupt. Moreover, no interesting defense of the philosophical irrelevance or impossibility of the logic of discovery can be formulated or defended in isolation from computation-theoretic considerations.
Proofs and Refutations is essential reading for all those interested in the methodology, the philosophy and the history of mathematics. Much of the book takes the form of a discussion between a teacher and his students. They propose various solutions to some mathematical problems and investigate the strengths and weaknesses of these solutions. Their discussion (which mirrors certain real developments in the history of mathematics) raises some philosophical problems and some problems about the nature of mathematical discovery or creativity. (...) Imre Lakatos is concerned throughout to combat the classical picture of mathematical development as a steady accumulation of established truths. He shows that mathematics grows instead through a richer, more dramatic process of the successive improvement of creative hypotheses by attempts to 'prove' them and by criticism of these attempts: the logic of proofs and refutations. (shrink)
There are various ``classical'' arguments against abduction as a logic of discovery,especially that (1) abduction is too weak a mode of inference to be of any use, and (2) in basic formulation of abduction the hypothesisis already presupposed to be known, so it is not the way hypotheses are discovered in the first place. In this paper I argue, by bringing forth the idea of strategies,that these counter-arguments are weaker than may appear. The concept of strategies suggests, inter (...) alia, that many inferential moves are taken into account at the same time. This is especially important in abductive reasoning, which is basically a very weak mode of inference. The importance of strategic thinking can already be seen in Charles S.Peirce's early treatments of the topic, and N.R.Hanson's later writings on abduction although they did not use the concept of``strategies.'' On the whole, I am arguing that the focus should be more on methodological processes, and not only on validity considerations, which have dominated the discussion about abduction. (shrink)
This article compares the features of a logic of discovery for the "friends of discovery" and for Karl Popper. It argues that the account given by Popper is the same as that of the "friends of discovery." The comparison will unsystematically exhibit that Popper proposes such a logic and will submit that the epistemological significance of a logic of discovery is to be sought in a configuration of ideas and transactions deemed regulated by (...) or mirroring rationality rather than in creative processes as such. (shrink)
New computer systems of discovery create a research program for logic and philosophy of science. These systems consist of inference rules and control knowledge that guide the discovery process. Their paths of discovery are influenced by the available data and the discovery steps coincide with the justification of results. The discovery process can be described in terms of fundamental concepts of artificial intelligence such as heuristic search, and can also be interpreted in terms of (...)logic. The traditional distinction that places studies of scientific discovery outside the philosophy of science, in psychology, sociology, or history, is no longer valid in view of the existence of computer systems of discovery. It becomes both reasonable and attractive to study the schemes of discovery in the same way as the criteria of justification were studied: empirically as facts, and logically as norms. (shrink)
One important problem in the philosophy of science is whether there can be a normative theory of discovery, as opposed to a normative theory of justification. Although the possibility of developing a logic of scientific discovery has been often doubted by philosophers, it is particularly interesting to consider how the basic insights of a normative theory of discovery have been turned into an effective research program in computer science, namely the research field of machine learning. In (...) this paper, I introduce some current research on statistical models to a philosophical audience. In particular, I will stress those features of statistical models that make them plausible computational counterparts of scientific theories. After noticing how these models allow for the main kinds of inference that are a trademark of scientific theories, I will focus on the problem of learning statistical models from data. The analysis will show how machine learning is casting new light on traditional problems in the philosophy of science. More precisely, I will explore the implications of some results in statistical learning with respect to the role of simplicity in theory choice and to the role of scalability (as a formal property of induction) in making scientific discovery effective. (shrink)
First encounters : Jesuit logica in the late Ming and early Qing -- Haphazard overtures : logic in nineteenth-century Protestant writings -- Great expectations : Yan Fu and the discovery of European logic -- Spreading the word : logic in late Qing education and popular discourse -- Heritage unearthed : the discovery of Chinese logic -- Textbooks on logic adapted from Japanese, 1902-1911 -- Logical terms in early-twentieth-century textbooks.
In this paper we will show Peirce’s distinction between deduction, induction and abduction. The aim of the paper is to show how Peirce changed his views on the subject, from an understanding of deduction, induction and hypotheses as types of reasoning to understanding them as stages of inquiry very tightly connected. In order to get a better understanding of Peirce’s originality on this, we show Peirce’s distinctions between qualitative and quantitative induction and between theorematical and corollarial deduction, passing then to (...) the distinction between mathematics and logic. In the end, we propose a sketch of a comparison between Peirce and Whitehead concerning the two thinkers’ view of mathematics, hoping that this could point to further inquiries. (shrink)
Summary The recent turn to the âcontext of discoveryâ and other âpostmodernistâ developments in the philosophy of science have undermined the idea of a universal rationality of science. This parallels the fate of the classical dream of a logic of discovery. Still, justificational questions have remained as a distinct perspective, though comprising both consequential and generative justification â an insight delayed by certain confusions about the (original) context distinction. An examination of one particular heuristic strategy shows its local (...) rationality; even as an efficient procedure of hypothesis generation, it carries probative weight. It will be explored in which respects such a strategy can be normative or contain normative elements. (shrink)
This book deals with questions everyone should become acquainted with when studying logic. It, however, has nothing in common with current introductions to logic, which are actually introductions to a particular logic paradigm, mathematical logic. There is nothing wrong with this, except that at present such paradigm is a problematic one. For mathematical logic, on the one hand, is inadequate for the use for which it was originally designed – to give mathematics the most secure (...) foundation – and, on the other hand, has found no crucial alternative use. This fact is almost invariably passed over in silence in current introductions to logic. This is as it could be expected, for people working within a given paradigm tend to consider it as the only possible one and cannot conceive of any alternative. But to read only such introductions will give a rather narrow view of the subject. In this book mathematical logic is presented as being not ‘The Logic’ but rather a particular logic paradigm, with some basic limitations. An alternative logic paradigm is outlined, meant to remove such limitations, in which logic is supposed to be a logic of discovery and justification a part of discovery. With respect to mathematical logic, the alternative paradigm involves a different view of the relation of logic with nature. Logic is a continuation of the problem solving procedures with which biological evolution has endowed humans and all organisms generally. The alternative paradigm also involves a different view of the relation of logic with method. Method is the source of logic. To implement the alternative paradigm, a number of basic discovery procedures are discussed. By their very nature, discovery procedures do not form a closed set, given once for all, but rather an open set, which can always be expanded. Those considered in this book, however, are especially important. This book is not intended to replace any introduction to mathematical logic but rather to be read parallel to it. Its aim is, on the one hand, to put mathematical logic into perspective, on the other hand, to show that an alternative paradigm is possible and to outline it. I hope it will give the reader a better feel of what logic really is. (shrink)
Springer link: http://www.springer.com/philosophy/logic+and+philosophy+of+language/book/978-94-007-6090-5 -/- This volume examines the limitations of mathematical logic and proposes a new approach to logic intended to overcome them. To this end, the book compares mathematical logic with earlier views of logic, both in the ancient and in the modern age, including those of Plato, Aristotle, Bacon, Descartes, Leibniz, and Kant. From the comparison it is apparent that a basic limitation of mathematical logic is that it narrows down the scope (...) of logic confining it to the study of deduction, without providing tools for discovering anything new. As a result, mathematical logic has had little impact on scientific practice. -/- Therefore, this volume proposes a view of logic according to which logic is intended, first of all, to provide rules of discovery, that is, non-deductive rules for finding hypotheses to solve problems. This is essential if logic is to play any relevant role in mathematics, science and even philosophy. To comply with this view of logic, this volume formulates several rules of discovery, such as induction, analogy, generalization, specialization, metaphor, metonymy, definition, and diagrams. A logic based on such rules is basically a logic of discovery, and involves a new view of the relation of logic to evolution, language, reason, method and knowledge, particularly mathematical knowledge. It also involves a new view of the relation of philosophy to knowledge. This book puts forward such new views, trying to open again many doors that the founding fathers of mathematical logic had closed historically. (shrink)
It is noted that Popper separates the creation of concepts, conjectures, hypotheses and theories—the context of invention—from the testing thereof—the context of justification—arguing that only the latter is susceptible of rigorous logical analysis. Efforts on the part of others to shift or eradicate the demarcation established by this distinction are discussed and the relationship of these considerations to the claims of “strong artificial intelligence” is pointed out. It is argued that the mode of education of scientists, as well as reports (...) of celebrated scientists, support Popper's judgement in this matter. An historical episode from Faraday's later career is used to illustrate the historiographical strength of Lakatos' “methodology of research programs.”. (shrink)
This paper offers a refutation of J. C. Pinto de Oliveira's recent critique of revisionist Carnap scholarship as giving undue weight to two brief letters to Kuhn expressing his interest in the latter's work. First an argument is provided to show that Carnap and Kuhn are by no means divided by a radical mismatch of their conceptions of the rationality of science as supposedly evidenced by their stance towards the distinction of the contexts of discovery and justification. This is (...) followed by an argument to the effect that the fact that Carnap's own work concentrated on formal aspects of scientific theories does not licence the conclusion that he thought historical investigations and concerns irrelevant for what we nowadays would rightly call "philosophy of science". (shrink)
Llull and Leibniz both subscribed to conceptual atomism, the belief that the majority of concepts are compounds constructed from a relatively small number of primitive concepts. Llull worked out techniques for finding the logically possible combinations of his primitives, but Leibniz criticized Llull’s execution of these techniques. This article argues that Leibniz was right about things being more complicated than Llull thought but that he was wrong about the details. The paper attempts to correct these details.
A semantic analysis of mass nouns is given in terms of a logic of classes as many. In previous work it was shown that plural reference and predication for count nouns can be interpreted within this logic of classes as many in terms of the subclasses of the classes that are the extensions of those count nouns. A brief review of that account of plurals is given here and it is then shown how the same kind of interpretation (...) can also be given for mass nouns. (shrink)
The aim of this paper, is to provide a logical framework for reasoning about actions, agency, and powers of agents and coalitions in game-like multi-agent systems. First we define our basic Dynamic Logic of Agency ( ). Differently from other logics of individual and coalitional capability such as Alternating-time Temporal Logic (ATL) and Coalition Logic, in cooperation modalities for expressing powers of agents and coalitions are not primitive, but are defined from more basic dynamic logic operators (...) of action and (historic) necessity. We show that STIT logic can be reconstructed in . We then extend with epistemic operators, which allows us to distinguish capability and power. We finally characterize the conditions under which agents are aware of their capabilities and powers. (shrink)
We extend the ordinary logic of knowledge based on the operator K and the system of axioms S₅ by adding a new operator Uφ, standing for "the agent utters φ", and certain axioms and a rule for U, forming thus a new system KU. The main advantage of KU is that we can express in it intentions of the speaker concerning the truth or falsehood of the claims he utters and analyze them logically. Specifically we can express in the (...) new language various notions of lying, as well as of telling the truth. Consequently, as long as lying or telling the truth about a fact is an intentional mode of the speaker, we can resolve the Liar paradox, or at least some of its variants, turning it into an ordinary (false or true) sentence. Also, using Kripke structures analogous to those employed by S. Kraus and D. Lehmann in  for modelling the logic of knowledge and belief, we offer a sound and complete semantics for KU. (shrink)
In this paper we show that the Hilbert system of agency and ability presented by Dag Elgesem is incomplete with respect to the intended semantics. We argue that completeness result may be easily regained. Finally, we shortly discuss some issues related to the philosophical intuition behind his approach. This is done by examining Elgesem's modal logic of agency and ability using semantics with different flavours.
In the present paper we prove that the poset of all extensions of the logic defined by a class of matrices whose sets of distinguished values are equationally definable by their algebra reducts is the retract, under a Galois connection, of the poset of all subprevarieties of the prevariety generated by the class of the algebra reducts of the matrices involved. We apply this general result to the problem of finding and studying all extensions of the logic of (...) paradox (viz., the implication-free fragment of any non-classical normal extension of the relevance-mingle logic). In order to solve this problem, we first study the structure of prevarieties of Kleene lattices. Then, we show that the poset of extensions of the logic of paradox forms a four-element chain, all the extensions being finitely many-valued and finitely-axiomatizable logics. There are just two proper consistent extensions of the logic of paradox. The first is the classical logic that is relatively axiomatized by the Modus ponens rule for the material implication. The second extension, being intermediate between the logic of paradox and the classical logic, is the one relatively axiomatized by the Ex Contradictione Quodlibet rule. (shrink)
The paper presents a logical treatment of actions based on dynamic logic. This approach makes it possible to reflect clearly the differences between static and dynamic elements of the world, a distinction which seems crucial to us for a representation of actions.Starting from propositional dynamic logic a formal system (DLA) is developed, the programs of which are used to model action types. Some special features of this system are: Basic aspects of time are incorporated in DLA as far (...) as they are needed for our purpose. Names for states and for instants are simulated by formulas. It is possible to express formally that a formula is satisfiable or valid. A special program is introduced to reflect developments which are not caused by an official agent but by external influences. (shrink)
Heuristic is a central concept of Lakatos' philosophy both in his early works and in his later work, the methodology of scientific research programs (MSRP). The term itself, however, went through significant change of meaning. In this paper I study this change and the ‘metaphysical' commitments behind it. In order to do so, I turn to his mathematical heuristic elaborated in Proofs and Refutations. I aim to show the dialogical character of mathematical knowledge in his account, which can open a (...) door to hermeneutic studies of mathematical practice. (shrink)
Attention is drawn to the fact that what is alternatively known as Dummett logic, Gödel logic, or Gödel-Dummett logic, was actually introduced by Skolem already in 1913. A related work of 1919 introduces implicative lattices, or Heyting algebras in today's terminology.
Peirce algebras combine sets, relations and various operations linking the two in a unifying setting. This paper offers a modal perspective on Peirce algebras. Using modal logic a characterization of the full Peirce algebras is given, as well as a finite axiomatization of their equational theory that uses so-called unorthodox derivation rules. In addition, the expressive power of Peirce algebras is analyzed through their connection with first-order logic, and the fragment of first-order logic corresponding to Peirce algebras (...) is described in terms of bisimulations. (shrink)
Peirce algebras combine sets, relations and various operations linking the two in a unifying setting. This paper offers a modal perspective on Peirce algebras. Using modal logic as a characterization of the full Peirce algebras is given, as well as a finite axiomatization of their equational theory that uses so-called unorthodox derivation rules. In addition, the expressive power of Peirce algebras is analyzed through their connection with first-order logic and the fragment of first-order logic corresponding to Peirce (...) algebras is described in terms of bisimulations. (shrink)