Hypothetico-deductive (H-D) confirmation builds on the idea that confirming evidence consists of successful predictions that deductively follow from the hypothesis under test. This article reviews scope, history and recent development of the venerable H-D account: First, we motivate the approach and clarify its relationship to Bayesian confirmation theory. Second, we explain and discuss the tacking paradoxes which exploit the fact that H-D confirmation gives no account of evidential relevance. Third, we review several recent proposals that aim (...) at a sounder and more comprehensive formulation of H-D confirmation. Finally, we conclude that the reputation of hypothetico-deductive confirmation as outdated and hopeless is undeserved: not only can the technical problems be addressed satisfactorily, the hypothetico-deductive method is also highly relevant for scientific practice. (shrink)

This paper synthesizes confirmation by instances and confirmation by successful predictions, and thereby the Hempelian and the hypothetico-deductive traditions in confirmation theory. The merger of these two approaches is subsequently extended to the piecemeal confirmation of entire theories. It is then argued that this synthetic account makes a useful contribution from both a historical and a systematic perspective.

To undermine much of what we ordinarily claim to know, sceptics have often appealed to a principle (known as the principle of closure) according to which knowledge (justification) is closed under known entailment. In this paper after expounding the views of Stein, Klein and others, I shall argue that they all fail to take note of different contexts in which the principle of closure is applied. The relevance of the principle of closure for scepticism is then analyzed in the light (...) of, what I call, the infectious' character of epistemic contexts. I shall also highlight the similarities in the behavior of the concepts of justification and confirmation and appeal to certain solutions to the paradoxes of confirmation to provide a comprehensive account of the different instances of the principle of closure. (shrink)

Mathematicians often speak of conjectures as being confirmed by evidence that falls short of proof. For their own conjectures, evidence justifies further work in looking for a proof. Those conjectures of mathematics that have long resisted proof, such as Fermat's Last Theorem and the Riemann Hypothesis, have had to be considered in terms of the evidence for and against them. It is argued here that it is not adequate to describe the relation of evidence to hypothesis as `subjective', `heuristic' or (...) `pragmatic', but that there must be an element of what it is rational to believe on the evidence, that is, of non-deductive logic. (shrink)

Existing accounts of hypothetico-deductive confirmation are able to circumvent the classical objections, but the confirmation of conjunctions of hypotheses brings them into trouble. Therefore this paper develops a new, falsificationist account of qualitative confirmation by means of Ken Gemes ' theory of content parts. The new approach combines the hypothetico-deductive view with falsificationist and instance confirmation principles. It is considerably simpler than the previous suggestions and gives a better treatment of conjunctive hypotheses while solving (...) the tacking problems equally well. (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)

This work is in two parts. The main aim of part 1 is a systematic examination of deductive, probabilistic, inductive and purely inductive dependence relations within the framework of Kolmogorov probability semantics. The main aim of part 2 is a systematic comparison of (in all) 20 different relations of probabilistic (in)dependence within the framework of Popper probability semantics (for Kolmogorov probability semantics does not allow such a comparison). Added to this comparison is an examination of (in all) 15 purely (...) inductive dependence relations. ————Part 1 leads in an axiomatic step-by-step development from the elementary classical truth value semantics of a sentential-logical language, called ‘L’, (chapter 1) to the elementary Kolmogorov probability semantics of L (chapter 2), which is then extended to four axiomatic semantical theories of dependence relations between the formulae of L. First the elementary Kolmogorov probability semantics of L is extended to a theory, called ‘Kdd’, of the relations of deductive dependence and deductive independence between formulae of L (chapter 3). Then Kdd is extended to a theory, called ‘Kpd1’, of the degree to which formulae of L probabilistically depend on each other in regard to a given probability distribution on the set of all formulae of L (chapter 4). Kpd1, in its turn, gets extended to a theory, called ‘Kpd2’, of the relations of probabilistic dependence and independence, relativized to unary Kolmogorov probability functions defined on L (chapter 5). Then Kpd2 is extended to a theory, called ‘Kid’, of the relations of inductive dependence and inductive independence, again relativized to unary Kolmogorov probability functions defined on L (chapter 6). Finally, Kid is extended to a theory, called ‘Kpid’, of the relations of purely inductive positive and negative dependence, relativized to unary Kolmogorov probability functions defined on L (chapter 7). ——Chapter 1, which deals with the familiar notions of truth value functions, tautologies, consequence relations and relations of logical opposition, is naturally the shortest chapter of part 1.——In chapter 2, the elementary classical semantics of L is extended to the elementary Kolmogorov probability semantics of L, i.e. to an axiomatic theory of unary and of binary Kolmogorov probability functions defined on the set of formulae of L. Because of the elementary character of this theory, chapter 2 is also rather short.——Chapter 3 introduces the first theory on dependence relations, to wit: Kdd, the theory of deductive (in)dependence between formulae of L. I follow here the well-known idea of Popper and Miller, who have used it in a famous discussion on the nature of probabilistic support for their arguments that probabilistic support is deductive, not inductive. I develop Kdd in the form of about 100 theorems, making ample use of the fact that deductive independence is nothing but subcontrary opposition, and close with a remark on the fundamental difference between deductive and logical dependence—two relations the ideas of which are all too easily mixed up.——Chapters 4 and 5 deal extensively with the traditional ideas of probabilistic (in)dependence, applied to formulae rather than to events. As always, I proceed axiomatically in a step-by-step process under systematic viewpoints and obtain about 300 theorems in this way. In the formulation of the theorems, I took special care to state clearly and expressly so-called tacit assumptions, especially those concerning the probability values of the formulae said to be dependent on each other. These assumptions are usually missing in the literature, due either to economy of writing or to sloppiness of thinking. Presumably, both chapters contain little that is new, their value lying more in the systematic grouping and organic development of the theorems than in the newness of these.——In chapter 6, I extend the axiomatic theory about probabilistic (in)dependence which has been elaborated in chapter 5, to an axiomatic theory of inductive (in)dependence by requiring of the relation of inductive (in)dependence that it be probabilistic (in)dependence, but not also logical implication or logical opposition. I point out the differences between probabilistic and inductive (in)dependence by means of some 60 theorems and close my examination of inductive (in)dependence by considering its relationship to the notion of support in the philosophy of science.——Finally, in chapter 7, the last of part 1, I take the step from inductive dependence to what I call ‘purely inductive dependence’ by combining the idea of inductive dependence with that of deductive independence in a way which is suggested by writings of Popper and Miller. I arrive at two noteworthy theorems. Firstly, there is indeed no purely inductive support. But secondly, and perhaps amazingly, countersupport is purely inductive.————Whereas the probabilistic framework of part 1 of the present work is Kolmogorov probability semantics, the framework of part 2 is Popper probability semantics, which is not only worth examining as a fascinating alternative to orthodox Kolmogorov probability semantics, but also allows us to examine dependence relations more deeply, than Kolmogorov probability semantics does. Part 2 leads—again in an axiomatic step-by-step development—from the basic Popper probability semantics of L, called ‘Pb’, (chapter 8) via a probabilistic theory of logical attributes, called ‘Ps’, (chapter 9) to four axiomatic semantical theories of dependence relations between the formulae of L. First, Ps is extended to a theory, called ‘Pdd’, of the relations of deductive dependence and deductive independence between formulae of L (chapter 10). Then Pdd is extended to a theory, called ‘Ppd’, of (in all) 20 relations of probabilistic (in)dependence, relativized to binary Popper probability functions defined on L (chapter 11). Ppd, in its turn, is extended to a theory, called ‘Pid’, of (in all) 10 relations of inductive dependence, again relativized to binary Popper probability functions defined on L (first part of chapter 12). Finally, Pid is extended to a theory, called ‘Ppid’, of (in all) 15 relations of purely inductive positive and negative dependence, relativized to binary Popper probability functions defined on L (second part of chapter 12).——Chapter 8, the first chapter of part 2 of the present work, is entirely preparatory. It introduces the axioms and about 180 theorems (150 of them together with their proofs) of basic Popper probability semantics in order to set this kind of semantics under way.——Then, in chapter 9, basic Popper probability semantics is extended to a probabilistic theory of logical properties of and relations between the formulae of L. Although I think that the way I did this extension is of some interest in itself, the main task of chapter 9 is again a preparatory one: to yield the indispensable lemmata (about 90 in number) for the theorems concerning probabilistic dependence relations in chapter 11 and concerning inductive dependence relations in chapter 12.——Chapter 10 brings the extension of Ps to the theory Pdd of deductive (in)dependence. Only half a dozen theorems are noted here for later use in the Pdd-extensions Ppd and Ppid. In view of the over 100 theorems already gained on this topic in the Kolmogorovian framework (cf. chapter 3), a similar extensive elaboration of Pdd would have been superfluous.——Chapter 11 is the most important one of part 2. It consists of a systematic comparison of 20 probabilistic (in)dependence concepts by means of about 230 theorems, obtained within the axiomatic theory Ppd, which is built up as an extension of Pdd. The main points of comparison were: differences in logical strength; reflexivity and symmetry; behaviour under the condition that the probability values of the formulae in question are extreme. It turned out that each of the examined concepts violates a strong and straightforward version of the intuitive requirement that probabilistic dependence should go with logical dependence. Whereas the corresponding chapter 5 in part 1 of the present work may not have led to new theorems, chapter 11 yields dozens of them in the process of comparison of concepts of dependence and independence which had—as far as I know—never before been treated in a single theoretical framework. With Popper probability semantics, this framework has become available, and here I have simply made full use of it.——In chapter 12, I extend the theory Ppd of probabilistic (in)dependence to the theories Pid and Ppid of inductive and purely inductive dependence, in a way very similar to that in which I have extended the theory Kpd2 to the theories Kid and Kpid in chapters 6 and 7. The first main result of Kpid (roughly: there is no purely inductive support) could be repeated for four of the five purely inductive positive dependence relations considered in chapter 12, whereas the second main result of Kpid (roughly: there is purely inductive countersupport ) could be repeated for each of the five examined purely inductive negative dependence relations. Chapter 12 closes with a brief recapitulation and critical discussion of the main results. (shrink)

The analysis of theory-confirmation generally takes the deductive form: show that a theory in conjunction with physical data and auxiliary hypotheses yield a prediction about phenomena; verify the prediction; provide a quantitative measure of the degree of theory-confirmation this yields. The issue of confirmation for an entire framework either does not arise, or is dismissed in so far as frameworks are thought not to be the kind of thing that admits scientific confirmation. I argue that (...) there is another form of scientific reasoning that has not received philosophical attention, what I call Newtonian abduction, that does provide confirmation for frameworks as a whole, and does so in two novel ways. I further argue that Newtonian abduction is at least as important a form of reasoning in science as standard deductive and inductive forms. The form is beautifully summed up by Maxwell : “The true method of physical reasoning is to begin with the phenomena and to deduce the forces from them by a direct application of the equations of motion.”. (shrink)

The analysis of theory-confirmation generally takes the deductive form: show that a theory in conjunction with physical data and auxiliary hypotheses yield a prediction about phenomena; verify the prediction; provide a quantitative measure of the degree of theory-confirmation this yields. The issue of confirmation for an entire framework (e.g., Newtonian mechanics en bloc, as opposed, say, to Newton’s theory of gravitation) either does not arise, or is dismissed in so far as frameworks are thought not to (...) be the kind of thing that admits scientific confirmation. I argue that there is another form of scientific reasoning that has not received philosophical attention, what I call Newtonian abduction, that does provide confirmation for frameworks as a whole, and does so in two novel ways. (In particular, Newtonian abduction is not inference to the best explanation, but rather is closer to Peirce’s original idea of abduction.) I further argue that Newtonian abduction is at least as important a form of reasoning in science as standard deductive and inductive forms. The form is beautifully summed up by Maxwell (Proc Camb Philos Soc II:292–294, 1876): “The true method of physical reasoning is to begin with the phenomena and to deduce the forces from them by a direct application of the equations of motion.”. (shrink)

One of the most debated questions in psychology and cognitive science is the nature and the functioning of the mental processes involved in deductive reasoning. However, all existing theories refer to a specific deductive domain, like syllogistic, propositional or relational reasoning.Our goal is to unify the main types of deductive reasoning into a single set of basic procedures. In particular, we bring together the microtheories developed from a mental models perspective in a single theory, for which we (...) provide a formal foundation. We validate the theory through a computational model (UNICORE) which allows fine‐grained predictions of subjects' performance in different reasoning domains.The performance of the model is tested against the performance of experimental subjects—as reported in the relevant literature—in the three areas of syllogistic, relational and propositional reasoning. The computational model proves to be a satisfactory artificial subject, reproducing both correct and erroneous performance of the human subjects. Moreover, we introduce a developmental trend in the program, in order to simulate the performance of subjects of different ages, ranging from children (3–6) to adolescents (8–12) to adults (>21). The simulation model performs similarly to the subjects of different ages.Our conclusion is that the validity of the mental model approach is confirmed for the deductive reasoning domain, and that it is possible to devise a unique mechanism able to deal with the specific subareas. The proposed computational model (UNICORE) represents such a unifying structure. (shrink)

We investigate how the perceived uncertainty of a conditional affects a person's choice of conclusion. We use a novel procedure to introduce uncertainty by manipulating the conditional probability of the consequent given the antecedent. In Experiment 1, we show first that subjects reduce their choice of valid conclusions when a conditional is followed by an additional premise that makes the major premise uncertain. In this we replicate Byrne. These subjects choose, instead, a qualified conclusion expressing uncertainty. If subjects are given (...) a third statement that qualifies the likelihood of the additional premise, then the uncertainty of the conclusions they choose is systematically related to the suggested uncertainty. Experiment 2 confirms these observations in problems that omit the additional premise and qualify the first premise directly. Experiment 3 shows that the qualifying statement also affects the perceived probability of the consequent given the antecedent of the conditional. Experiment 4 investigates the effect of suggested uncertainty on the fallacies and shows that increases in uncertainty reduce the number of certain conclusions that are chosen while affirming the consequent but have no effect on denying the antecedent. We discuss our results in terms of rule theories and mental models and conclude that the latter give the most natural account of our results. (shrink)

A broad class of inductive logics that includes the probability calculus is defined by the conditions that the inductive strengths [A|B] are defined fully in terms of deductive relations in preferred partitions and that they are asymptotically stable. Inductive independence is shown to be generic for propositions in such logics; a notion of a scale-free inductive logic is identified; and a limit theorem is derived. If the presence of preferred partitions is not presumed, no inductive logic is definable. This (...) no-go result precludes many possible inductive logics, including versions of hypothetico-deductivism. (shrink)

In spite of several attempts to explicate the relationship between a scientific hypothesis and evidence, the issue still cries for a satisfactory solution. Logical approaches to confirmation, such as the hypothetico-deductive method and the positive instance account of confirmation, are problematic because of their neglect of the semantic dimension of hypothesis confirmation. Probabilistic accounts of confirmation are no better than logical approaches in this regard. An outstanding probabilistic account of confirmation, the Bayesian approach, for (...) instance, is found to be defective in that it treats evidence as a formal entity and this creates the problem of relevance of evidence to the hypothesis at issue, in addition to the difficulties arising from the subjective interpretation of probabilities. This essay purports to satisfy the need for a successful account of hypothesis confirmation by offering an original formulation based on the notion of instantiation of the relation urged by an hypothesis. (shrink)

How do people make deductions? The orthodox view in psychology is that they use formal rules of inference like those of a “natural deduction” system.Deductionargues that their logical competence depends, not on formal rules, but on mental models. They construct models of the situation described by the premises, using their linguistic knowledge and their general knowledge. They try to formulate a conclusion based on these models that maintains semantic information, that expresses it parsimoniously, and that makes explicit something not directly (...) stated by any premise. They then test the validity of the conclusion by searching for alternative models that might refute the conclusion. The theory also resolves long-standing puzzles about reasoning, including how nonmonotonic reasoning occurs in daily life. The book reports experiments on all the main domains of deduction, including inferences based on prepositional connectives such as “if” and “or,” inferences based on relations such as “in the same place as,” inferences based on quantifiers such as “none,” “any,” and “only,” and metalogical inferences based on assertions about the true and the false. Where the two theories make opposite predictions, the results confirm the model theory and run counter to the formal rule theories. Without exception, all of the experiments corroborate the two main predictions of the model theory: inferences requiring only one model are easier than those requiring multiple models, and erroneous conclusions are usually the result of constructing only one of the possible models of the premises. (shrink)

Mathematicians often speak of conjectures, yet unproved, as probable or well-confirmed by evidence. The Riemann Hypothesis, for example, is widely believed to be almost certainly true. There seems no initial reason to distinguish such probability from the same notion in empirical science. Yet it is hard to see how there could be probabilistic relations between the necessary truths of pure mathematics. The existence of such logical relations, short of certainty, is defended using the theory of logical probability (or objective Bayesianism (...) or non-deductive logic), and some detailed examples of its use in mathematics surveyed. Examples of inductive reasoning in experimental mathematics are given and it is argued that the problem of induction is best appreciated in the mathematical case. (shrink)

Using the matching bias example, the aim of the present studies was to show that adults' reasoning biases are due to faulty executive inhibition programming. In the first study, the subjects were trained on Wason's classical card selection task; half were given training in how to inhibit the perceptual matching bias (experimental group) and half in logic without the inhibition component (control group). On the pre- and post-tests, their performance was assessed on the Evans conditional rule falsification task (with a (...) negation in the antecedent of the rule), a task that also involves matching bias. In addition, subjects were tested for perceptual field dependence/independence using the Embedded Figures Test. The results brought out a specific inhibition training effect, as well as a clear-cut relationship in the experimental group between receptiveness to training and perceptual field independence. In the second study, the training paradigm was the same except that on the pre- and post-tests, the negation was in the consequent of the conditional rule (in this case, the perceptual matching response corresponds to the logical response). The subjects succeeded on the pre-test, and the matching-bias inhibition training had a negative effect on post-test performance. This specific negative priming effect confirms the inhibitory impact of our experimental training and outlines the dissociation of inhibition and logical components. (shrink)

The use of idealizations and approximations in scientific explanations poses a problem for traditional philosophical theories of confirmation since, strictly speaking, these sorts of statements are false. Furthermore, in several central cases in the history of science, theoretical predictions seen as confirmatory are not, in any usual sense, even approximately true. As a means of eliminating the puzzling nature of these cases, two theses are proposed. First, explanations consist of idealized deductive-nomological sketches plus what are called modal auxiliaries, (...) i.e., arguments showing that if the idealizations used in the initial conditions are improved, then there will be an improvement in the prediction. Second, a theory is confirmed if it can be shown that its idealized sketches can be improved; similarly, a theory is disconfirmed if its idealized sketches cannot be improved. Several examples are given to illustrate both confirmation and disconfirmation achieved by means of the modal auxiliary. These cases are compared with Scriven's bridge example. (shrink)

In spite of several attempts to explicate the relationship between a scientific hypothesis and evidence, the issue still cries for a satisfactory solution. Logical approaches to confirmation, such as the hypothetico-deductive method and the positive instance account of confirmation, are problematic because of their neglect of the semantic dimension of hypothesis confirmation. Probabilistic accounts of confirmation are no better than logical approaches in this regard. An outstanding probabilistic account of confirmation, the Bayesian approach, for (...) instance, is found to be defective in that it treats evidence as a formal entity and this creates the problem of relevance of evidence to the hypothesis at issue, in addition to the difficulties arising from the subjective interpretation of probabilities. This essay purports to satisfy the need for a successful account of hypothesis confirmation by offering an original formulation based on the notion of instantiation of the relation urged by an hypothesis. (shrink)

The paper aims at the rehabilitation of deductive reasoning. As a paradigm of reliable reasoning, it should be applicable in every confirmation context. In particular, it should transmit inductive justification, so that if D justifies a hypothesis H, then D also justifies all deductive conclusions from H. Nevertheless, most current philosophers of science reject such a transmission principle as false. They argue against it by providing apparent counter-examples and also by showing that it is incompatible with common (...) confirmation theories such as HD-confirmation and Bayesianism. I argue in the opposite direction that we should stick to the transmission principle and revise instead our justification theories towards more cautious justification procedures that respect the transmission principle. This will avoid further paradoxes of these theories and, in particular, will enable us to apply our confirmed hypotheses to new situations in a well-founded way. (shrink)

According to the traditional requirement, formulated by William Whewell in his account of the “consilience of inductions” in 1840, a scientific hypothesis should have unifying power in the sense that it explains and predicts several mutually independent phenomena. Variants of this notion of consilience or unification include deductive, inductive, and approximate systematization. Inference from surprising phenomena to their theoretical explanations was called abduction by Charles Peirce. As a unifying theory is independently testable by new kinds of phenomena, it should (...) also receive confirmation from its empirical success. The study of the prospects of probabilistic Bayesianism to motivate this kind of criterion for abductive confirmation is shown to lead to two quite distinct conceptions of unification. (shrink)

It is commonly acknowledged that, in order to test a theoretical hypothesis, one must, in Duhem' s phrase, rely on a "theoretical scaffolding" to connect the hypothesis with something measurable. Hypothesis-confirmation, on this view, becomes a three-place relation: evidence E will confirm hypothesis H only relative to some such scaffolding B. Thus the two leading logical approaches to qualitative confirmation--the hypothetico-deductive (H-D) account and Clark Glymour' s bootstrap account--analyze confirmation in relative terms. But this raises questions (...) about the philosophical interpretation of the technical conditions these accounts describe. What does it mean to say that E confirms H "relative to B"? How should we interpret the relation we are trying to analyze? (shrink)

Recent work on the logical theory of confirmation has centered on accounts of the confirmation of hypotheses relative to auxiliary assumptions or background theory. Whether such relative confirmation actually increases the credibility of the (relatively) confirmed hypothesis will depend in various ways on the epistemic status of the auxiliaries involved. Most obviously, if the auxiliaries are not themselves credible, confirmation relative to them will not increase the credibility of the hypothesis thus confirmed. A complete theory of (...) confirmation must thus combine an account of relative confirmation with an account of the route from relative confirmation to real confirmation. Some recent criticisms of hypothetico-deductive and bootstrapping accounts of relative confirmation are undermined by failure to appreciate the limitations of relative confirmation. (shrink)

Glymour has developed an account of the confirmation of scientific hypotheses which he advocates as an alternative to the hypothetico-deductive and Bayesian accounts. This account is subject to a counter-example which may be accomodated by a slight modification. So modified it describes an important dimension of confirmation. If the modification of Glymour's account is slightly extended, both the resulting account and the hypothetico-deductive account may be seen as special cases of a Bayesian theory which is immune (...) to Glymour's criticisms. (shrink)

Whereas an inference (deductive as well as inductive) is usually viewed as being valid in virtue of its argument form, the present paper argues that scientific reasoning is material inference, i.e., justified in virtue of its content. A material inference is licensed by the empirical content embodied in the concepts contained in the premises and conclusion. Understanding scientific reasoning as material inference has the advantage of combining different aspects of scientific reasoning, such as confirmation, discovery, and explanation. This (...) approach explains why these different aspects (including discovery) can be rational without conforming to formal schemes, and why scientific reasoning is local, i.e., justified only in certain domains and contingent on particular empirical facts. The notion of material inference also fruitfully interacts with accounts of conceptual change and psychological theories of concepts. (shrink)

We use recently developed approaches in argumentation theory in order to revamp the hypothetico-deductive model of confirmation, thus alleviating the well-known paradoxes the H-D account faces. More specifically, we introduce the concept of dialectic confirmation on the background of the so-called theory of dialectical structures (Betz 2010, 2012b). Dialectic confirmation generalises hypothetico-deductive confirmation and mitigates the raven paradox, the grue paradox, the tacking paradox, the paradox from conceptual difference, and the problem of surprising evidence.

This thesis is about how deduction is analytic and, at the same time, informative. In the first two chapters I am after the question of the justification of deduction. This justification is circular in the sense that to explain how deduction works we use some basic deductive rules. However, this circularity is not trivial as not every rule can be justified circularly. Moreover, deductive rules may not need suasive justification because they are not ampliative. Deduction preserves meaning, that (...) is, the meaning of non-logical vocabulary of any theory which is developed by deductive reasoning remains unchanged. It means that deduction adds no information to what we already had in our premises. This is why deduction is analytic. -/- However, there are many ways deduction can be informative. In the next three chapters, I will pick a specific kind of deductive reasoning, namely arithmetical reasoning, and will attempt to understand the nature of information we obtain by this kind of reasoning. There is a difference between simple deductive moves such as inferring `Socrates is mortal' from `All human are mortal' and `Socrates is human', and inferring that a relation is reflexive given that it is directed, symmetric and transitive. The latter is more complicated and not as easy to prove as the former. Therefore it is informative and the proof we construct to prove it puts us in an epistemic position that we were not in before having the proof. To be more specific, I show that concepts we need to confirm the conclusion are made in the process of proving the conclusion. (shrink)

SummaryScientists regard their inductive hypotheses as confirmed when consistence exists between two or more results obtained by differing methods. Three hierarchical levels of confirmation are applied. Certainty is obtained by the deductive element of the third level. The question of uniformity o i nature is less decisive than the question whether or not the complexity of the processes observed or the limited scope of our senses and instruments permits to see through the causal connections involved.

We provide a new link between deductive and probabilistic reasoning fallacies. Illusory inferences from disjunction are a broad class of deductive fallacies traditionally explained by recourse to a matching procedure that looks for content overlap between premises. In two behavioral experiments, we show that this phenomenon is instead sensitive to real-world causal dependencies and not to exact content overlap. A group of participants rated the strength of the causal dependence between pairs of sentences. This measure is a near (...) perfect predictor of fallacious reasoning by an independent group of participants in illusory inference tasks with the same materials. In light of these results, we argue that all extant accounts of these deductive fallacies require non-trivial adjustments. Crucially, these novel _indirect_ illusory inferences from disjunction bear a structural similarity to seemingly unrelated _probabilistic reasoning_ problems, in particular the conjunction fallacy from the heuristics and biases literature. This structural connection was entirely obscure in previous work on these deductive problems, due to the theoretical and empirical focus on content overlap. We argue that this structural parallelism provides arguments against the need for rich descriptions and individuating information in the conjunction fallacy, and we outline a unified theory of deductive illusory inferences from disjunction and the conjunction fallacy, in terms of Bayesian confirmation theory. (shrink)

Many believe that Goodman’s new riddle of induction proves the impossibility of a purely syntactical theory of confirmation. After discussing and rejecting Jackson’s solution to Goodman’s paradox, I formulate the “new riddle of deduction,” in analogy to the new riddle of induction. Since it is generally agreed that deductive validity can be defined syntactically, the new riddle of induction equally does not show that inductive validity cannot be defined syntactically. I further rely on the analogy between induction and (...) deduction in order to explain why some predicates, such as “grue,” are unprojectible. (shrink)

This paper is an effort to realize and explore the connections that exist between nonmonotonic logic and confirmation theory. We pick up one of the most wide-spread nonmonotonic formalisms – default logic – and analyze to what extent and under what adjustments it could work as a logic of induction in the philosophical sense. By making use of this analysis, we extend default logic so as to make it able to minimally perform the task of a logic of induction, (...) having as a result a system which we believe has interesting properties from the standpoint of theory of confirmation. It is for instance able to represent chains of inductive rules as well as to reason paraconsistently on the conclusions obtained from them. We then use this logic to represent some traditional ideas concerning confirmation theory, in particular the ones proposed by Carl Hempel in his classical paper "Studies in the Logic of Confirmation" of 1945 and the ones incorporated in the so-called abductive and hy-pothetico-deductive models. (shrink)

Franz Huber’s (2008a) attempt to unify inductivist and hypothetico-deductivist intuitions on confirmation by means of a single measure are examined and compared with previous work on the theory of verisimilitude or truthlikeness. The idea of connecting ‘the logic of confirmation’ with ‘the logic of acceptability’ is also critically discussed, and it is argued that ‘acceptability’ takes necessarily into account some pragmatic criteria, and that at least two normative senses of ‘acceptability’ must be distinguished: ‘acceptable’ in the sense of (...) ‘being allowed to accept’, and ‘acceptable’ in the sense of ‘being obliged to accept’. Lastly, some connections of confirmation theory with naturalism, intertheoretic reduction, and explanation vs. understanding are explored. (shrink)

This chapter contains section titled: Aristotelian Prelude Cartesian Ambition From Le Monde to the Discourse Discourse, Part Six The Principles of Philosophy Summing‐Up References and Further Reading.

Having been neglected or maligned for most of this century, Newton's method of 'deduction from the phenomena' has recently attracted renewed attention and support. John Norton, for example, has argued that this method has been applied with notable success in a variety of cases in the history of physics and that this explains why the massive underdetermination of theory by evidence, seemingly entailed by hypothetico-deductive methods, is invisible to working physicists. This paper, through a detailed analysis of Newton's deduction (...) of one particular 'proposition' in optics 'from the phenomena', gives a clearer account than hitherto of the method - highlighting the fact that it is really one of deduction from the phenomena plus 'background knowledge'. It argues, that, although the method has certain heuristic virtues, examination of its putative accreditational strengths reveals a range of important problems that its defenders have yet adequately to address. (shrink)

I contrast our own evidence for the hypothesis of organic fossil origins with that available in previous centuries, suggesting that the most powerful contemporary evidence consists in a form of projective support whose distinctive features are not well captured by familiar hypothetico-deductive, abductive, or even more recent and more technically sophisticated accounts of scientific confirmation. I suggest that such accounts either misrepresent or ignore something important about the heterogeneous ways in which scientific hypotheses can be supported by evidence, (...) and I go on to suggest that the search for any single such account may be misguided in any case. (shrink)

The Transcendental Deduction in the second edition of Kant’s Critique of Pure Reason is divided in two parts. Nevertheless, the role of the second half is not immediately clear. This article intends to examine the argument presented in the second half after clarifying its purpose. Based on this approach, we sustain an interpretation according to which Kant tries to establish the validity of categories for all intuition given through sensibility. This interpretation seeks to confirm a conceptual articulation among sensible intuitions (...) that is not regarded as a result of objective judgment. (shrink)

Yehezkel presents an interesting argument to resolve Goodman’s New Riddle of Induction, and in effect to claim that a purely syntactical theory of confirmation is possible. In this paper I suggest that Yehezkel’s argument relies on two premises not proven in his paper. The first premise is that if “a New Riddle of Deduction” can be formulated then there is no New Riddle of Induction. This premise seems to be wrong as I claim in part 2 of this paper. (...) The second premise is that a New Riddle of Deduction can be formulated. Despite Yehezkel’s efforts to prove this claim, it seems to me false, or at least, unproven. I therefore conclude that there is no New Riddle of Deduction, and therefore, no actual resolution to the New Riddle of Induction. (shrink)

in this paper i assess Pierre Duhem’s criticism of crucial experiments, and argue that we have reasons to vindicate their existence. i then analize the experiments carried out by Fizeau and Foucault in 1850, and criticize Duhem’s interpretation of their results. i contend that the results of crucial experiences can be described in terms that are neutral with respect to the competing theories. For that reason an experimental result is relatively stable and open to different interpretations in the light of (...) new theories. i conclude by distinguishing successful crucial experiments from decisive experiments. The former are meant to provide evidence that confirms one theory and disconfirms its rivals, but not necessarily to provide sufficient reasons for accepting or rejecting one of those theories. (shrink)

It is generally accepted among philosophers of science that hypothesis testing is a key methodological feature of science. As far as philosophical theories of confirmation are con...

En este trabajo hago una comparación sistemática entre las dos teorías de la confirmación más populares en la actualidad: el método hipotético-deductivo y el bayesianismo. En primer lugar, enumero los cinco problemas fundamentales de la teoría hipotético-deductivista. Estos son el problema de las hipótesis estadísticas, el del grado de confirmación, el de la conjunción irrelevante, el del holismo epistemológico y el de las hipótesis alternativas. Luego, hago una presentación general de la epistemología bayesiana y muestro de qué manera estos problemas (...) resultan tratables en el marco bayesiano. Finalmente, concluyo que los tres primeros admiten una solución satisfactoria, sobre la base de algunos supuestos razonables. Los dos últimos, en cambio, todavía son problemas abiertos para la teoría bayesiana de la confirmación. Bayesians often affirm they have produced the best available theory of confirmation. In particular, they claim to have superseded the venerable hypothetico-deductive method. In this paper I intend to assess that claim by making a systematic comparison between both theories of confirmation. I begin by listing the main problems of hypothetico-deductive confirmation. I then show that this conception is incompatible with Hempel's conditions of adequacy for qualitative confirmation. I expound the Bayesian theory of confirmation with some detail in order to show that this theory is able to solve three out of the five fundamental problems of hypothetico-deductive confirmation. largue that the remaining two problems are still open questions for the Bayesians. (shrink)