Is it possible to combine different logics into a coherent system with the goal of applying it to specific problems so that it sheds some light on foundational aspects of those logics? These are two of the most basic issues of combining logics. Paranormal modal logic is a combination of paraconsistent logic and modal logic. In this paper, I propose two further combinatory developments, focusing on each one of these two issues. On the foundational side, I combine paranormal modal logic (...) with normal modal logic, resulting into a paraconsistent and paracomplete multimodal logic dealing with the notions of plausibility and certainty. On the application side, I combine this logic with Reiter’s default logic, resulting into an inductive and consequently nonmonotonic paraconsistent and paracomplete logic able to represent some key inductive principles. (shrink)

Induction, conceived as the class of rational non-truth preserving inferences, has been a perennial problem in philosophy. Aside from the problem of justification of induction, a less debated issue is the problem of properly describing inductive inferences. The purpose of this book is to conceptually investigate this descriptive problem of induction from the standpoint of the nonmonotonic logical tradition raised inside the field of Artificial Intelligence in the last thirty years. As we try to show, an essential part of (...) this enterprise involves the analysis of a pragmatically oriented notion of probability, called by us inductive plausibility. This in turn is made from the viewpoint of paraconsistency ? which according to some is the unavoidable companion of nonmonotonicity ? and modal logic. We therefore put forward a nonmonotonic, paraconsistent and modal approach to induction and plausibility. The book shall be useful to philosophers, logicians and computer scientists interested in the problem of induction in general and in the logical analysis of induction and plausibility in particular. (shrink)

Here the author of How to Solve It explains how to become a "good guesser." Marked by G. Polya's simple, energetic prose and use of clever examples from a wide range of human activities, this two-volume work explores techniques of guessing, inductive reasoning, and reasoning by analogy, and the role they play in the most rigorous of deductive disciplines.

A number of single- and dual-process theories provide competing explanations as to how reasoners evaluate conditional arguments. Some of these theories are typically linked to different instructions—namely deductive and inductive instructions. To assess whether responses under both instructions can be explained by a single process, or if they reflect two modes of conditional reasoning, we re-analysed four experiments that used both deductive and inductive instructions for conditional inference tasks. Our re-analysis provided evidence consistent with a single process. In (...) two new experiments we established a double dissociation of deductive and inductive instructions when validity and plausibility of conditional problems were pitted against each other. This indicates that at least two processes contribute to conditional reasoning. We conclude that single-process theories of conditional reasoning cannot explain the observed results. Theories that postulate at least two processes are needed to account for our findings. (shrink)

Hempel's paradox of the ravens arises from the inconsistency of three prima facie plausible principles of confirmation. This paper uses Carnapian inductive logic to (a) identify which of the principles is false, (b) give insight into why this principle is false, and (c) identify a true principle that is sufficiently similar to the false one that failure to distinguish the two might explain why the false principle is prima facie plausible. This solution to the paradox is compared with a (...) variety of other responses and is shown to differ from all of them. (shrink)

The plausible reasoning class (called the JSM-reasoning in honour of John Stuart Mill) is described. It implements interaction of three forms of non-deductive procedures  induction, analogy and abduction. Empirical induction in the JSM-reasoning is the basis for generation of hypotheses on causal relations (determinants of social behaviour). Inference by analogy means that predictions about previously unknown properties of objects (individual’s behaviour) are inferred from causal relations. Abductive inference is performed to check on the explanatory adequacy of generated hypotheses. To (...) recognize rationality of respondents’ opinion deductive inference is used. Plausible reasoning, semantics of argumentation logic and deductive recognition of opinion rationality represent logical tool for cognitive sociology problems. (shrink)

The orthodox view about sensitivity and induction has it that beliefs formed via induction are insensitive. Since inductive knowledge is highly plausible, this problem is usually regarded as a reductio argument against sensitivity accounts of knowledge. Some adherents of sensitivity defend sensitivity against this objection, for example by considering backtracking interpretations of counterfactuals. All these extant views about sensitivity and induction have to be revised, since the problem of sensitivity and induction is a different one. Regardless of whether we (...) allow backtracking interpretations of counterfactuals, some instances of induction yield insensitive beliefs whereas others yield sensitive ones. These results are too heterogenous for providing a plausible sensitivity-account of inductive knowledge. Induction remains a serious problem for sensitivity accounts of knowledge. (shrink)

This paper tries to extend Hintikka's inductive logic so that we can confirm a causally necessary statement. For this purpose, a joint system of inductive logic and logic of causal modalities is constructed. This system can offer a plausible explication of the distinction between nomic and accidental universality, as well as a good formulation of a causal law. And the transition from actuality to causal necessity is construed, in this system, as essentially probabilistic; i.e. no statements about actuality (...) can entail a necessary statement, but certain statements about actuality can single out a most probable causal law. (shrink)

I here aim to show that a particular approach to the problem of induction, which I will call “induction by direct inference”, comfortably handles Goodman’s problem of induction. I begin the article by describing induction by direct inference. After introducing induction by direct inference, I briefly introduce the Goodman problem, and explain why it is, prima facie, an obstacle to the proposed approach. I then show how one may address the Goodman problem, assuming one adopts induction by direct inference as (...) an approach to the problem of induction. In particular, I show that a relatively standard treatment of what some have called the “Reference Class problem” addresses the Goodman Problem. Indeed, plausible and relatively standard principles of direct inference yield the conclusion that the Goodman inference (involving the grue predicate) is defeated, so it is unnecessary to invoke considerations of ‘projectibility’ in order to address the Goodman problem. I conclude the article by discussing the generality of the proposed approach, in dealing with variants of Goodman’s example. (shrink)

2014 Reprint of 1954 American Edition. Full facsimile of the original edition, not reproduced with Optical Recognition Software. This two volume classic comprises two titles: "Patterns of Plausible Inference" and "Induction and Analogy in Mathematics." This is a guide to the practical art of plausible reasoning, particularly in mathematics, but also in every field of human activity. Using mathematics as the example par excellence, Polya shows how even the most rigorous deductive discipline is heavily dependent on techniques of guessing, (...) class='Hi'>inductive reasoning, and reasoning by analogy. In solving a problem, the answer must be guessed at before a proof can be given, and guesses are usually made from a knowledge of facts, experience, and hunches. The truly creative mathematician must be a good guesser first and a good prover afterward; many important theorems have been guessed but no proved until much later. In the same way, solutions to problems can be guessed, and a god guesser is much more likely to find a correct solution. This work might have been called "How to Become a Good Guesser."-From the Dust Jacket. (shrink)

Pre-analytically at least some of our inductions seem to be possessed of rational justification. This comment would apply, for instance, to my present induction, ‘If that climber high on the Flatirons falls he will be killed,’ not to mention such more momentous inductions as, ‘If a full-scale nuclear war breaks out there will be greater destruction than in World War II.’ Notoriously, however, a few Humean reflections seem to strip even the most plausible of our inductions of all possible rational (...) justification, leaving them mere bare psychological faits accomplis: in effect, section V of the Enquiry's ‘Sceptical Solution of these Doubts.’. (shrink)

The purpose of this paper is twofold. First we want to extent a specific paranormal modal logic in such a way as obtain a paraconsistent and paracomplete multimodal logic able to formalize the notions of plausibility and certainty. With this logic at hand, and this is our second purpose, we shall use a modified version of Reiter‘s default logic to build a sort of inductive logic of plausibility and certainty able to represent some basic principles of epistemic (...) inductive reasoning, such as a negative autoepistemic principle, an `error-prone feature of induction' principle and a confirmation by enumeration principle. (shrink)

Current practice in logic increasingly accords recognition to abductive, presumptive or plausible arguments, in addition to deductive and inductive arguments. But there is uncertainty about what these terms exactly mean, what the differences between them are (if any), and how they relate. By examining some analyses ofthese terms and some of the history of the subject (including the views of Peirce and Cameades), this paper sets out considerations leading to a set of definitions, discusses the relationship of these three (...) forms of argument to argumentation schemes and sets out a new argumentation scheme for abductive argument. (shrink)

With respect to inductive reasoning, there are at least two broad projects that have been of interest to philosophers. The first project is that of accurately describing paradigmatic instances of inductive reasoning in the sciences and in everyday life. Thus, we might ask, of some particular historical episode, how exactly Newton, or Darwin, or Einstein arrived at some conclusion on the basis of the evidence that was before him. The second project is one of justification. The task here (...) is that of showing why paradigmatic inductive reasoning is good reasoning, or why skeptical challenges which purport to undermine the legitimacy of such reasoning fail to do so. As I understand it, this second, justificatory project prominently includes, but is not limited to, the task of either solving or dissolving Hume’s skeptical critique of induction.[1] Neither of these projects is trivial. Indeed, many think that we are currently far from successfully completing either one. But in any case, it would seem that the descriptive project has a certain priority to the justification project. After all, how could one justify our inductive practices, or defend them against skeptical challenge, in the absence of some reasonably detailed and accurate description of those practices? Given this apparent priority, it is a striking fact that the justification project has often been pursued in the absence of any significant attention to the project of accurate description. In particular, a great deal of the traditional discussion of Hume’s problem of induction has proceeded against the background of hopelessly crude models of our actual inductive practice—a fact sometimes acknowledged by participants in such discussions themselves. Plausibly, the thought which underlies this procedure is the following: whatever force Hume’s critique ultimately possesses, that force is not tied to the specific content of the general rules or principles that we follow in reasoning inductively. Rather, the force of Hume’s critique depends on our following any general rules or principles at all.. (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)

I present a solution to the epistemological or characterisation problem of induction. In part I, Bayesian Confirmation Theory (BCT) is discussed as a good contender for such a solution but with a fundamental explanatory gap (along with other well discussed problems); useful assigned probabilities like priors require substantive degrees of belief about the world. I assert that one does not have such substantive information about the world. Consequently, an explanation is needed for how one can be licensed to act as (...) if one has substantive information about the world when one does not. I sketch the outlines of a solution in part I, showing how it differs from others, with full details to follow in subsequent parts. The solution is pragmatic in sentiment (though differs in specifics to arguments from, for example, William James); the conceptions we use to guide our actions are and should be at least partly determined by preferences. This is cashed out in a reformulation of decision theory motivated by a non-reductive formulation of hypotheses and logic. A distinction emerges between initial assumptions--that can be non-dogmatic--and effective assumptions that can simultaneously be substantive. An explanation is provided for the plausibility arguments used to explain assigned probabilities in BCT. -/- In subsequent parts, logic is constructed from principles independent of language and mind. In particular, propositions are defined to not have form. Probabilities are logical and uniquely determined by assumptions. The problems considered fatal to logical probabilities--Goodman's `grue' problem and the uniqueness of priors problem are dissolved due to the particular formulation of logic used. Other problems such as the zero-prior problem are also solved. -/- A universal theory of (non-linguistic) meaning is developed. Problems with counterfactual conditionals are solved by developing concepts of abstractions and corresponding pictures that make up hypotheses. Spaces of hypotheses and the version of Bayes' theorem that utilises them emerge from first principles. -/- Theoretical virtues for hypotheses emerge from the theory. Explanatory force is explicated. The significance of effective assumptions is partly determined by combinatoric factors relating to the structure of hypotheses. I conjecture that this is the origin of simplicity. (shrink)

Inductive reasoning is a fundamental and complex aspect of human intelligence. In particular, how do subjects, given a set of particular examples, generate general descriptions of the rules governing that set? We present a biologically plausible method for accomplishing this task and implement it in a spiking neuron model. We demonstrate the success of this model by applying it to the problem domain of Raven's Progressive Matrices, a widely used tool in the field of intelligence testing. The model is (...) able to generate the rules necessary to correctly solve Raven's items, as well as recreate many of the experimental effects observed in human subjects. (shrink)

To clarify the proper role of values in science, focusing on controversial expert responses to Covid-19, this article examines the status of (in)convenient hypotheses. Polarizing cases like health experts downplaying mask efficacy to save resources for healthcare workers, or scientists dismissing “accidental lab leak” hypotheses in view of potential xenophobia, plausibly involve modifying evidential standards for (in)convenient claims. Societies could accept that scientists handle (in)convenient claims just like nonscientists, and give experts less political power. Or societies could hold scientists to (...) a higher bar, by expecting them not to modify evidential standards to avoid costs only incidentally tied to error. (shrink)

The place of induction in the framing and test of scientific hypotheses is investigated. The meaning of 'induction' is first equated with generalization on the basis of case examination. Two kinds of induction are then distinguished: the inference of generals from particulars (first degree induction), and the generalization of generalizations (second degree induction). Induction is claimed to play a role in the framing of modest empirical generalizations and in the extension of every sort of generalizations--not however in the invention of (...) high-level hypotheses containing theoretical predicates. It is maintained, on the other hand, that induction by enumeration is essential in the empirical test of the lowest-level consequences of scientific theories, since it occurs in the drawing of "conclusions" from the examination of empirical evidence. But it is also held that the empirical test is insufficient, and must be supplemented with theorification, or the expansion of isolated hypotheses into theories. Refutation is not viewed as a substitute for confirmation but as its complement, since the very notion of unfavorable case is meaningful only in connection with the concept of positive instance. Although the existence of an inductive method is disclaimed, it is maintained that the various patterns of plausible reasoning (inductive inference included) are worth being investigated. It is concluded that scientific research follows neither the advice of inductivism nor the injunction of deductivism, but takes a middle course in which induction is instrumental both heuristically and methodologically, although the over-all pattern of research is hypothetico-deductive. (shrink)

In several early 19th century works, Mary Shepherd articulates a theory of causation that is intended to respond to Humean skepticism. I argue that Shepherd's theory should be read in light of the science of the day and her conception of her place in the British philosophical tradition. Reading Shepherd’s theory in light of her conception of the history of philosophy, including her claim to be the genuine heir of Locke, illuminates the broader significance of her attempt to reinstate reason (...) as the source of scientific knowledge. Reading Shepherd's theory in light of the science of the day helps make plausible her claim that there are robust natural kinds in nature, defined by their causal powers: this is precisely what then-recent advances in chemistry hold. (shrink)

The Drosophila compound eye is an excellent experimental system for analysing fate induction of identifiable single cells. Each ommatidium, a unit eye, contains eight photoreceptors (R1‐R8), and the differentiation of these photoreceptors occurs in the larval eye imaginal disc in discrete steps: first R8 is determined, then R2/R5, R3/R4, R1/R6 and finally R7. Induction of R7, in particular, has been extensively studied at the molecular level. The R8 photoreceptor presents on its surface a ligand, Bride of Sevenless, that binds and (...) activates Sevenless receptor tyrosine kinase in the R7 precursor. Autophosphorylated Sevenless initiates a Ras1‐mediated cascade, which eventually activates transcription factors in the nucleus via Raf1 and MAP kinases, resulting in R7 development. However, recent studies indicate that Sevenless (Sev) functions just to neuralize the cell and has no role in R7 fate determination per se. It appears that the R7 fate may represent the lowest rung of a ‘neuronal ground state’, which is attained without any specific inductive cue. It is plausible that the R7 precursor is actively prevented from taking on the neuronal fate and this inhibition is removed by activation of Sev. (shrink)

So simple and imperfect as it may appear this book has made use of knowledge on invention and discovery accumu lated during a lifetime. Those persons who would be tempted to emphasize only its imperfections should read the correspondence exchanged between Cantor and Dedekind at the end of the nineteenth century; they would then realize how difficult it was, even for an outstanding man, the creator of the set theory, to propose impeccable results in a completely new field. The field (...) I have chosen here is plausibility. I have proposed an intuitive, some would say a naive, presentation as I want to reach as large an audience as possible and because I personally believe that it is easier to axiomatize a mathematical theory precisely than to dis cover it and enunciate its key theorems. Professor Polya said: "The truly creative mathematician is a good guesser first and a good prover afterward. " For centuries a formalized generalized logic was found necessary and many attempts have been made to build it. vi Preface Mine is based on plausibility which covers with precision a wider field than probability and makes the formalization of analogy and generalization possible. As Laplace said: "Even in the mathematical sciences, our principal instru ments to discover the truth are induction and analogy. "* The examples of application I have chosen are not des cribed in detail. (shrink)

C-Inductive arguments are arguments that increase the probability of a hypothesis. This can be contrasted with what is called a P-Inductive argument. A P-inductive argument is an argument that shows the overall probability of a hypothesis to be more probable than not. In this paper, we put forth a C-inductive argument for the truth of the Catholic hypothesis (CH). Roughly, we take CH to be the hypothesis that the core creedal beliefs found within the Catholic Tradition (...) are true. Specifically, we argue that we would expect the Miracle of Fátima on CH, but, we wouldn’t expect it as much on ~CH. In order to establish this thesis, we first discuss the basics of confirmation theory. Second, we give the historical context of the Miracle of Fátima. Third, we briefly survey and then reject two possible non-supernatural explanations of the apparent miracle. Doing this will help make plausible that the Miracle of Fátima is actual evidence that a hypothesis needs to predict. Fourth, we give the details as to why we should expect the Miracle of Fátima more on CH than ~CH. Finally, we argue that miracles that occur in Protestant contexts, generally don’t carry the same evidential weight for a Protestant hypothesis as the Miracle of Fátima carries for CH. (shrink)

According to Seungbae Park, two versions of the pessimistic induction argument against scientific realism, what he calls the "absolute" and "relative" versions, each fail for the same reason. Depending on whether their respective premises refer to distant or recent past theories, either each premise is implausible, or the conclusion does not probably follow from them. I suggest that Park has misconstrued the sort of argument his pessimist interlocutors rely on. When properly recast, the absolute and relative versions of the argument (...) become deductive rather than inductive. The result in each case is an argument that, contra Park, has both a plausible premise and a conclusion that follows from it. (shrink)

John Foster presents a clear and powerful discussion of a range of topics relating to our understanding of the universe: induction, laws of nature, and the existence of God. He begins by developing a solution to the problem of induction - a solution whose key idea is that the regularities in the workings of nature that have held in our experience hitherto are to be explained by appeal to the controlling influence of laws, as forms of natural necessity. His second (...) line of argument focuses on the issue of what we should take such necessitational laws to be, and whether we can even make sense of them at all. Having considered and rejected various alternatives, Foster puts forward his own proposal: the obtaining of a law consists in the causal imposing of a regularity on the universe as a regularity. With this causal account of laws in place, he is now equipped to offer an argument for theism. His claim is that natural regularities call for explanation, and that, whatever explanatory role we may initially assign to laws, the only plausible ultimate explanation is in terms of the agency of God. Finally, he argues that, once we accept the existence of God, we need to think of him as creating the universe by a method which imposes regularities on it in the relevant law-yielding way. In this new perspective, the original nomological-explanatory solution to the problem of induction becomes a theological-explanatory solution. The Divine Lawmaker is bold and original in its approach, and rich in argument. The issues on which it focuses are among the most important in the whole epistemological and metaphysical spectrum. (shrink)

We formalise a notion of dynamic rationality in terms of a logic of conditional beliefs on (doxastic) plausibility models. Similarly to other epistemic statements (e.g. negations of Moore sentences and of Muddy Children announcements), dynamic rationality changes its meaning after every act of learning, and it may become true after players learn it is false. Applying this to extensive games, we “simulate” the play of a game as a succession of dynamic updates of the original plausibility model: the (...) epistemic situation when a given node is reached can be thought of as the result of a joint act of learning (via public announcements) that the node is reached. We then use the notion of “stable belief”, i.e. belief that is preserved during the play of the game, in order to give an epistemic condition for backward induction: rationality and common knowledge of stable belief in rationality. This condition is weaker than Aumann’s and compatible with the implicit assumptions (the “epistemic openness of the future”) underlying Stalnaker’s criticism of Aumann’s proof. The “dynamic” nature of our concept of rationality explains why our condition avoids the apparent circularity of the “backward induction paradox”: it is consistent to (continue to) believe in a player’s rationality after updating with his irrationality. (shrink)

Recently, there has been a resurgence of scholarly criticisms regarding the plausibility of the Roman Catholic doctrine of the Papacy. Broadly speaking, these problems include scholarly criticisms of the scriptural passages which Roman Catholic theologians claim support the papacy, historical discrepancies regarding apostolic succession from the Apostle Peter, and a priori intuitions about the moral nature of those who attain Papal Status. In this paper, I respond to these objections by utilizing Swinburne’s C-inductive strategy (Bayesian Confirmation Theory) – (...) found in his text, The Existence of God – and conclude that overall, there is a strong P-Inductive argument for the Papacy. First published 2019 (online). Now published in The Heythrop Journal, Volume 63, Issue 4, Page 531-546, July 2022. (shrink)

This essay discusses and criticizes Richard Swinburne's inductive argument for the existence of God. In his The Existence of God, Swinburne aims at showing that the existence of God is more probable than not. This is an argument taking into consideration the premises of all traditional arguments for the existence of God. Swinburne uses the phenomena and events that constitute the premises of these arguments as evidence in an attempt to show that his hypothesis is more probably true than (...) nor. Swinburne pursues this task by way of applying Bayes' theorem. The aim of this essay is normative - to judge the strength of Swinburne's argument for the existence of God. My primary objections towards Swinburne is that he professes a subjective concept of probability, that he relies too heavily on simplicity as a virtue of plausible and probable hypotheses and that his concept of God involves an incoherent picture of God's nature. I question not only the actual success of Swinburne's project but what his argument, if it had been successful, would have been able to establish. (shrink)

This paper explains what’s wrong with a Hume-inspired argument for skepticism about induction. Hume’s argument takes as a premise that inductive reasoning presupposes that the future will resemble the past. I explain why that claim is not plausible. The most plausible premise in the vicinity is that inductive reasoning from E to H presupposes that if E then H. I formulate and then refute a skeptical argument based on that premise. Central to my response is a psychological explanation (...) for how people judge that if E then H without realizing that they thereby settled the matter rationally. (shrink)

This paper naturalizes inductive inference by showing how scientific knowledge of real mechanisms provides large benefits to it. I show how knowledge about mechanisms contributes to generalization, inference to the best explanation, causal inference, and reasoning with probabilities. Generalization from some A are B to all A are B is more plausible when a mechanism connects A to B. Inference to the best explanation is strengthened when the explanations are mechanistic and when explanatory hypotheses are themselves mechanistically explained. Causal (...) inference in medical explanation, counterfactual reasoning, and analogy also benefit from mechanistic connections. Mechanisms also help with problems concerning the interpretation, availability, and computation of probabilities. (shrink)

The prospect of cognitive enhancement well beyond current human capacities raises worries that the fundamental equality in moral status of human beings could be undermined. Cognitive enhancement might create beings with moral status higher than persons. Yet, there is an expressibility problem of spelling out what the higher threshold in cognitive capacity would be like. Nicholas Agar has put forward the bold claim that we can show by means of inductive reasoning that indefinite cognitive enhancement will probably mark a (...) difference in moral status. The hope is that induction can determine the plausibility of post‐personhood existence in the absence of an account of what the higher status would be like. In this article, we argue that Agar's argument fails and, more generally, that inductive reasoning has little bearing on assessing the likelihood of post‐personhood in the absence of an account of higher status. We conclude that induction cannot bypass the expressibility problem about post‐persons. (shrink)

Common probability theories only allow the deduction of probabilities by using previously known or presupposed probabilities. They do not, however, allow the derivation of probabilities from observed data alone. The question thus arises as to how probabilities in the empirical sciences, especially in medicine, may be arrived at. Carnap hoped to be able to answer this question byhis theory of inductive probabilities. In the first four sections of the present paper the above mentioned problem is discussed in general. After (...) a short presentation of Carnap''s theory it is then shown that this theory cannot claim validity for arbitrary random processes. It is suggested that the theory be only applied to binomial and multinomial experiments. By application of de Finetti''s theorem Carnap''s inductive probabilities are interpreted as consecutive probabilities of the Bayesian kind. Through the introduction of a new axiom the decision parameter can be determined even if no a priori knowledge is given. Finally, it is demonstrated that the fundamental problem of Wald''s decision theory, i.e., the determination of a plausible criterion where no a priori knowledge is available, can be solved for the cases of binomial and multinomial experiments. (shrink)

In this two-parts paper we present paranormal modal logic: a modal logic which is both paraconsistent and paracomplete. Besides using a general framework in which a wide range of logics  including normal modal logics, paranormal modal logics and classical logic can be defined and proving some key theorems about paranormal modal logic (including that it is inferentially equivalent to classical normal modal logic), we also provide a philosophical justification for the view that paranormal modal logic is a formalization of (...) the notions of skeptical and credulous plausibility. (shrink)

Necessity holds that, if a proposition A supports another B, then it must support B. John Greco contends that one can resolve Hume's Problem of Induction only if she rejects Necessity in favor of reliabilism. If Greco's contention is correct, we would have good reason to reject Necessity and endorse reliabilism about inferential justification. Unfortunately, Greco's contention is mistaken. I argue that there is a plausible reply to Hume's Problem that both endorses Necessity and is at least as good as (...) Greco's alternative. Hence, Greco provides a good reason for neither rejecting Necessity nor endorsing inferential reliabilism. (shrink)

This paper develops a stronger version of ‘inference-to-the-best explanation’ scientific realism. I argue against three standard assumptions of current realists: realism is confirmed if it provides the best explanation of theories’ predictive success ; the realist claim that successful theories are always approximately true provides the best explanation of their success ; and realists are committed to giving the same sort of truth-based explanation of superseded theories’ success that they give to explain our best current theories’ success. On the positive (...) side, I argue that the confirmation of realism requires explaining theories’ explanatory success, not just their predictive success ; in turn this task requires a richer realist model of explanation that brings into the explanans both successful theories’ epistemic virtues and the standards governing these virtues, as well as truth; this richer realist model is further confirmed because it can better explain the success of theories in gaining wide acceptance among scientists; and the model is further supported because it is superior to ‘preservative realism ’ in providing a plausible rebuttal of the pessimistic meta-induction from the many past successful-but-false theories to the like- lihood that our best current theories are likewise false. (shrink)

At the risk of being ostracized (if not annihilated) by the community of Popperians present, I wish to remark that Professor Lakatos is - and, I think - cannot help being, a second-level inductivist. If Professor Kuhn has pointed out (most eruditely) that science quite frequently is in a rut, and occasionally gets out of it (and into a new one), then Professor Lakatos appraises problem and theory shifts, and methodological innova- tions in the sciences, in the light of his (...) criteria of 'progress' or 'degenera- tion'. There can be little doubt that he wishes to serve (at least) in a critical and/or advisory capacity to scientists. But he can do that only if he 'places his bets', i.e., conjectures as to the fruitfulness of a method, and along with it of a theory engendered or supported by such a method along the lines of success or failure, whichever may be plausibly indicated. I find Professor Lakatos's refutations of simple inductivism (here he agrees with Popper), as well as of simple falsificationism (here he disagrees with a caricature of the early Popper), completely convincing. But if he is to fulfill the critical and/or advisory functions, what else can he do but watch the course of the 'shifts' and extrapolate?! (shrink)

Alice encounters at least three distinct problems in her struggles to understand and navigate Wonderland. The first arises when she attempts to predict what will happen in Wonderland based on what she has experienced outside of Wonderland. In many cases, this proves difficult -- she fails to predict that babies might turn into pigs, that a grin could survive without a cat or that playing cards could hold criminal trials. Alice's second problem involves her efforts to figure out the basic (...) nature of Wonderland. So, for example, there is nothing Alice could observe that would allow her to prove whether Wonderland is simply a dream. The final problem is manifested by Alice's attempts to understand what the various residents of Wonderland mean when they speak to her. In Wonderland, "mock turtles" are real creatures and people go places with a "porpoise" (and not a purpose). All three of these problems concern Alice's attempts to infer information about unobserved events or objects from those she has observed. In philosophical terms, they all involve *induction*. -/- In this essay, I will show how Alice's experiences can be used to clarify the relation between three more general problems related to induction. The first problem, which concerns our justification for beliefs about the future, is an instance of David Hume's classic *problem of induction*. Most of us believe that rabbits will not start talking tomorrow -- the problem of induction challenges us to justify this belief. Even if we manage to solve Hume's puzzle, however, we are left with what W.V.O. Quine calls the problems of *underdetermination *and *indeterminacy.* The former problem asks us to explain how we can determine *what the world is really like *based on *everything that could be observed about the world. *So, for example, it seems plausible that nothing that Alice could observe would allow her to determine whether eating mushrooms causes her to grow or the rest of the world to shrink. The latter problem, which might remain even if resolve the first two, casts doubt on our capacity to determine *what a certain person means *based on *which words that person uses.* This problem is epitomized in the Queen's interpretation of the Knave's letter. The obstacles that Alice faces in getting around Wonderland are thus, in an important sense, the same types of obstacles we face in our own attempts to understand the world. Her successes and failures should therefore be of real interest. (shrink)

Probability theory, epistemically interpreted, provides an excellent, if not the best available account of inductive reasoning. This is so because there are general and definite rules for the change of subjective probabilities through information or experience; induction and belief change are one and same topic, after all. The most basic of these rules is simply to conditionalize with respect to the information received; and there are similar and more general rules. 1 Hence, a fundamental reason for the epistemological success (...) of probability theory is that there at all exists a well-behaved concept of conditional probability. Still, people have, and have reasons for, various concerns over probability theory. One of these is my starting point: Intuitively, we have the notion of plain belief; we believe propositions2 to be true (or to be false or neither). Probability theory, however, offers no formal counterpart to this notion. Believing A is not the same as having probability 1 for A, because probability 1 is incorrigible3; but plain belief is clearly corrigible. And believing A is not the same as giving A a probability larger than some 1 - c, because believing A and believing B is usually taken to be equivalent to believing A & B.4 Thus, it seems that the formal representation of plain belief has to take a non-probabilistic route. Indeed, representing plain belief seems easy enough: simply represent an epistemic state by the set of all propositions believed true in it or, since I make the common assumption that plain belief is deductively closed, by the conjunction of all propositions believed true in it. But this does not yet provide a theory of induction, i.e. an answer to the question how epistemic states so represented are changed tbrough information or experience. There is a convincing partial answer: if the new information is compatible with the old epistemic state, then the new epistemic state is simply represented by the conjunction of the new information and the old beliefs. This answer is partial because it does not cover the quite common case where the new information is incompatible with the old beliefs. It is, however, important to complete the answer and to cover this case, too; otherwise, we would not represent plain belief as conigible. The crucial problem is that there is no good completion. When epistemic states are represented simply by the conjunction of all propositions believed true in it, the answer cannot be completed; and though there is a lot of fruitful work, no other representation of epistemic states has been proposed, as far as I know, which provides a complete solution to this problem. In this paper, I want to suggest such a solution. In [4], I have more fully argued that this is the only solution, if certain plausible desiderata are to be satisfied. Here, in section 2, I will be content with formally defining and intuitively explaining my proposal. I will compare my proposal with probability theory in section 3. It will turn out that the theory I am proposing is structurally homomorphic to probability theory in important respects and that it is thus equally easily implementable, but moreover computationally simpler. Section 4 contains a very brief comparison with various kinds of logics, in particular conditional logic, with Shackle's functions of potential surprise and related theories, and with the Dempster - Shafer theory of belief functions. (shrink)

Medical diagnosis has been traditionally recognized as a privileged field of application for so called probabilistic induction. Consequently, the Bayesian theorem, which mathematically formalizes this form of inference, has been seen as the most adequate tool for quantifying the uncertainty surrounding the diagnosis by providing probabilities of different diagnostic hypotheses, given symptomatic or laboratory data. On the other side, it has also been remarked that differential diagnosis rather works by exclusion, e.g. by modus tollens, i.e. deductively. By drawing on a (...) case history, this paper aims at clarifying some points on the issue. Namely: 1) Medical diagnosis does not represent, strictly speaking, a form of induction, but a type, of what in Peircean terms should be called ‘abduction’ (identifying a case as the token of a specific type); 2) in performing the single diagnostic steps, however, different inferential methods are used for both inductive and deductive nature: modus tollens, hypothetical-deductive method, abduction; 3) Bayes’ theorem is a probabilized form of abduction which uses mathematics in order to justify the degree of confidence which can be entertained on a hypothesis given the available evidence; 4) although theoretically irreconcilable, in practice, both the hypothetical- deductive method and the Bayesian one, are used in the same diagnosis with no serious compromise for its correctness; 5) Medical diagnosis, especially differential diagnosis, also uses a kind of “probabilistic modus tollens”, in that, signs (symptoms or laboratory data) are taken as strong evidence for a given hypothesis not to be true: the focus is not on hypothesis confirmation, but instead on its refutation [Pr (¬ H/E1, E2, …, En)]. Especially at the beginning of a complicated case, odds are between the hypothesis that is potentially being excluded and a vague “other”. This procedure has the advantage of providing a clue of what evidence to look for and to eventually reduce the set of candidate hypotheses if conclusive negative evidence is found. 6) Bayes’ theorem in the hypothesis-confirmation form can more faithfully, although idealistically, represent the medical diagnosis when the diagnostic itinerary has come to a reduced set of plausible hypotheses after a process of progressive elimination of candidate hypotheses; 7) Bayes’ theorem is however indispensable in the case of litigation in order to assess doctor’s responsibility for medical error by taking into account the weight of the evidence at his disposal. (shrink)

The historical debate of scientific realism portrays a monumental sign of science-a way of critiquing philosophy. At first sight, this centrepiece of scientific realism could line up against the no-miracles argument and the pessimistic meta-induction because, by means of the no-miracles assumption, fundamental theories in science would be the fine manifestation of reality as well as are most likely to be the truth. Nonetheless, a means to an end of the pessimistic meta-induction arguably states the anti-realistic position-since scientific speculations are (...) not always plausible to be the ultimate truth vis-à-vis mature hypotheses of science in history. By and large, I have herein put forward a systemic meaning for realism: an inspection of unseen objects in the world, which are broken free from the human mind. However, I will demonstrate the no-miracles argument in the vicinity of realism, whilst the pessimistic meta-induction lies towards anti-realism. In the bargain, I will examine structural realism in response to this scientific dichotomy. Briefly, this research article is, apparently, bound-up with a very limited account of relevancies; ergo, it would be recommended to further research on this controversy. (shrink)

The question of how we apply knowledge from biomedical science to medical and public health practice has been the subject of heated debates about generalizability and related concepts, such as applicability and inductive inference. In this essay, I interpret the term from the perspective of two causal models: determinism and indeterminism. I suggest that theories of generalizability can be formulated on the basis of both models and take the form of testable but unverifiable hypotheses, an attribute that is common (...) to all scientific theories. Nonetheless, there is one noteworthy difference between the two models: determinism allows one to rationalize a decision to treat a certain kind of patient but only indirectly a decision to treat any particular patient, whereas indeterminism accommodates both types of decisions. (shrink)

Pure causal theories of reference cannot account for cases of theoretical term reference failure and do not capture the scientific point of introducing new theoretical terminology. In order to account for paradigm cases of reference failure and the point of new theoretical terminology, a descriptive element must play a role in fixing the reference of theoretical terms. Richard Boyd's concept of theory constituitive metaphors provides the necessary descriptive element in reference fixing. In addition to providing a plausible account of reference (...) failure and success, a metaphor approach to reference fixing provides the basis for a plausible realist account of the progress of science. Indeed, the metaphor approach undermines the sceptical force of the meta-induction and Laudan's objections to scientific realism. (shrink)

We formalise a notion of dynamic rationality in terms of a logic of conditional beliefs on plausibility models. Similarly to other epistemic statements, dynamic rationality changes its meaning after every act of learning, and it may become true after players learn it is false. Applying this to extensive games, we "simulate" the play of a game as a succession of dynamic updates of the original plausibility model: the epistemic situation when a given node is reached can be thought (...) of as the result of a joint act of learning that the node is reached. We then use the notion of "stable belief, i.e. belief that is preserved during the play of the game, in order to give an epistemic condition for backward induction: rationality and common knowledge of stable belief in rationality. This condition is weaker than Aumann's and compatible with the implicit assumptions underlying Stalnaker's criticism of Aumann's proof. The "dynamic" nature of our concept of rationality explains why our condition avoids the apparent circularity of the "backward induction paradox": it is consistent to believe in a player's rationality after updating with his irrationality. (shrink)

Belief revision theory concerns methods for reformulating an agent's epistemic state when the agent's beliefs are refuted by new information. The usual guiding principle in the design of such methods is to preserve as much of the agent's epistemic state as possible when the state is revised. Learning theoretic research focuses, instead, on a learning method's reliability or ability to converge to true, informative beliefs over a wide range of possible environments. This paper bridges the two perspectives by assessing the (...) reliability of several proposed belief revision operators. Stringent conceptions of minimal change are shown to occasion a limitation called inductive amnesia: they can predict the future only if they cannot remember the past. Avoidance of inductive amnesia can therefore function as a plausible and hitherto unrecognized constraint on the design of belief revision operators. (shrink)

Four experiments investigated how people judge the plausibility of category-based arguments, focusing on the diversity effect, in which arguments with diverse premise categories are considered particularly strong. In Experiment 1 we show that priming people as to the nature of the blank property determines whether sensitivity to diversity is observed. In Experiment 2 we find that people's hypotheses about the nature of the blank property predict judgements of argument strength. In Experiment 3 we examine the effect of our priming (...) methodology on people's tendency to bring knowledge about causality or similarity to bear when evaluating arguments, and in Experiment 4 we show that whether people's hypotheses about the nature of the blank property were causal predicted ratings of argument strength. Together these results suggest that diversity effects occur because diverse premises lead people to bring general features of the premise categories to mind. Although our findings are broadly consistent with Bayesian and Relevance-based approaches to category-based inductive reasoning, neither approach captures all of our findings. (shrink)

Simpson’s book provides a provocative and interesting reading of several important sections of the Phenomenology of Spirit. It treats this text as a whole as a study in the logic of induction, the logic of what it is to learn from experience. Simpson does not, therefore, consider Hegel’s work as “inductive” in the modern sense of adding facts upon facts in order to arrive at general conclusions. Rather, linking his employment of the term “induction” back to Aristotelian epistemology, he (...) argues that Hegel’s text develops as we learn from experience what is involved in learning from experience. In other words, he aims to read the Phenomenology in such a way that the concept of induction itself can be seen to develop inductively. The author presents his study as an elucidation of the sense in which the Phenomenology is rightly described by Hegel as presenting the “process of origination” of science as such or of knowledge. At the conclusion of his book, Simpson indicates briefly the way in which the “inductive” argument traced throughout Hegel’s “science of the experience of consciousness” both supports and coincides with the “deductive” side of Hegel’s argument that appears more often to be the focus of commentaries. Simpson’s thesis—that Hegel’s text traces a pathway whereby the capacity for conscious experiencing is shown to develop in response to progressively more sophisticated attempts to articulate and unify experience—seems quite plausible, and receives a capable and insightful defense here. (shrink)

Three experiments examined the influence of argument length on plausibility judgements, in a category-based induction task. The general results were that when arguments were logically invalid they were considered stronger when they were longer, but for logically valid arguments longer arguments were considered weaker. In Experiments 1a and 1b when participants were forewarned to avoid using length as a cue to judging plausibility, they still did so. Indeed, participants given the opposite instructions did not follow those instructions either. (...) In Experiment 2 arguments came from a reliable or unreliable speaker. This manipulation affected accuracy as well as response bias, but the effects of argument length for both reliable and unreliable speakers replicated Experiments 1a and 1b. The results were analysed using receiver operating characteristic (ROC) curves and modelled using multidimensional signal detection theory (SDT). Implications for models of category-based inductive reasoning, and theories of reasoning more generally, are discussed. (shrink)

This recent addition to the well-known "Studies in Logic" series is sure to be of first importance to serious students of inductive logic, confirmation theory, and related issues. The book is an anthology of fourteen papers, which are classified under five different headings: "Extensions of Inductive Logic," "Induction and Information," "Prospects of Confirmation Theory," "The Paradoxes of Confirmation," and "Probability and Foundational Problems." Needless to say, all of the papers are of uniformly high quality. Especially worthy of mention (...) are two papers by Hintikka and Hilpinen which deal with an interesting generalization of Carnap's continuum of inductive methods, and which lead to a somewhat more plausible treatment of non-logically-true closed sentences. Suppes contributes two papers dealing with the recently revived Bayesian methods and their significance for concept formation in psychology and confirmation theory in the philosophy of science. Also under the heading of confirmation theory, one might mention Max Black's paper, "Notes on the Paradoxes of Confirmation," a lucid and rather novel approach to this problem. There is also an important paper by Dana Scott and Peter Krauss entitled "Assigning Probabilities to Logical Formulas." This piece of work presents a set-theoretical method for bridging the gap between the standard treatment of probability by means of axioms defining a real measure over a Boolean algebra and the usual logical inquiries into "degree of confirmation" and the like. The reference value of the book is enhanced by a subject index of terms and concepts dealt with in the various papers.—H. P. K. (shrink)

According to the standard interpretation, Aristotle has two accounts of induction (epagoge): intuitive induction (which is not an inference) and complete induction (which is not a kind of non-demonstrative inference). Hintikka has challenged the usual interpretation of Aristotle's "official account" in Analytica Priora II, 23. In this paper, Hintikka's view is compared with a similar, but in some respects perhaps even more plausible, interpretation that William Whewell gave already in 1850. Both Hintikka and Whewell argue convincingly that Aristotelean induction is (...) connected to concept formation. According to Whewell, the key to Aristotle's account is not the exhaustiveness or completeness of the sample of special cases, but rather its representativeness for the purpose of generalization. (shrink)