If the total state of the universe is encodable by a real number, Hardin and Taylor have proved that there is a solution to one version of the problem of induction, or at least a solution to a closely related epistemological problem. Is this philosophical application of the Hardin-Taylor result modest enough? The paper advances grounds for doubt. [A longer and more detailed sequel to this paper, 'Proving Induction', was published in the Australasian Journal of Logic in 2011.].

In ‘Induction and Natural Kinds’, I proposed a solution to the problem of induction according to which our use of inductive inference is reliable because it is grounded in the natural kind structure of the world. When we infer that unobserved members of a kind will have the same properties as observed members of the kind, we are right because all members of the kind possess the same essential properties. The claim that the existence of natural kinds is (...) what grounds reliable use of induction is based on an inference to the best explanation of the success of our inductive practices. As such, the argument for the existence of natural kinds employs a form of ampliative inference. But induction is likewise a form of ampliative inference. Given both of these facts, my account of the reliability of induction is subject to the objection that it provides a circular justification of induction, since it employs an ampliative inference to justify an ampliative inference. In this paper, I respond to the objection of circularity by arguing that what justifies induction is not the inference to the best explanation of its reliability. The ground of induction is the natural kinds themselves. (shrink)

My first goal is to motivate a distinctively metaphysical approach to the problem of induction. I argue that there is a precise sense in which the only way that orthodox Humean and non-Humean views can justify induction is by appealing to extremely strong and unmotivated probabilistic biases. My second goal is to sketch what such a metaphysical approach could possibly look like. After sketching such an approach, I consider a toy case that illustrates the way in which such (...) a metaphysics can help us make progress on the problem of induction. (shrink)

When an empirical prediction E of hypothesis H is observed to be true, such observation is said to confirm, i.e., support (although not prove) the truth of the hypothesis. But why? What justifies the claim that such evidence supports the hypothesis? The widely accepted answer is that it is justified by induction. More specifically, it is commonly held that the following argument, (1) If H then E; (2) E; (3) Therefore, (probably) H (here referred to as ‘hypothetico-deductive confirmation argument’), (...) is inductively strong. Yet this argument looks nothing like an inductive generalization, i.e., it does not seem inductive in the term’s traditional, enumerative sense. If anything, it has the form of the fallacy of affirming the consequent. This paper aims to solve this puzzle. True, in recent decades, ‘induction’ has been sometimes used more broadly to encompass any non-deductive, i.e., ampliative, argument. Applying Bayesian confirmation theory has famously demonstrated that hypothetico-deductive confirmation is indeed inductive in this broader, ampliative sense. Nonetheless, it will be argued here that, despite appearance, hypothetico-deductive confirmation can also be recast as enumerative induction. Hence, by being enumeratively inductive, the scientific method of hypothetico-deductive confirmation is justified through this traditional, more restrictive type of induction rather than merely by ampliative induction. (shrink)

While the traditional conception of inductive logic is Carnapian, I develop a Peircean alternative and use it to unify formal learning theory, statistics, and a significant part of machine learning: supervised learning. Some crucial standards for evaluating non-deductive inferences have been assumed separately in those areas, but can actually be justified by a unifying principle.

As our epistemic ambitions grow, the common and scientific endeavours are becoming increasingly dependent on Machine Learning (ML). The field rests on a single experimental paradigm, which consists of splitting the available data into a training and testing set and using the latter to measure how well the trained ML model generalises to unseen samples. If the model reaches acceptable accuracy, an a posteriori contract comes into effect between humans and the model, supposedly allowing its deployment to target environments. Yet (...) the latter part of the contract depends on human inductive predictions or generalisations, which infer a uniformity between the trained ML model and the targets. The paper asks how we justify the contract between human and machine learning. It is argued that the justification becomes a pressing issue when we use ML to reach ‘elsewheres’ in space and time or deploy ML models in non-benign environments. The paper argues that the only viable version of the contract can be based on optimality (instead of on reliability which cannot be justified without circularity) and aligns this position with Schurz’s optimality justification. It is shown that when dealing with inaccessible/unstable ground-truths (‘elsewheres’ and non-benign targets), the optimality justification undergoes a slight change, which should reflect critically on our epistemic ambitions. Therefore, the study of ML robustness should involve not only heuristics that lead to acceptable accuracies on testing sets. The justification of human inductive predictions or generalisations about the uniformity between ML models and targets should be included as well. Without it, the assumptions about inductive risk minimisation in ML are not addressed in full. (shrink)

We are often justified in acting on the basis of evidential confirmation. I argue that such evidence supports belief in non-quantificational generic generalizations, rather than universally quantified generalizations. I show how this account supports, rather than undermines, a Bayesian account of confirmation. Induction from confirming instances of a generalization to belief in the corresponding generic is part of a reasoning instinct that is typically (but not always) correct, and allows us to approximate the predictions that formal epistemology would make.

I would like to assume that Reichenbach's distinction of Justification and Discovery lives on, and to seek arguments in his texts that would justify their relevance in this field. The persuasive force of these arguments transcends the contingent circumstances apart from which their genesis and local transmission cannot be made understandable. I shall begin by characterizing the context distinction as employed by Reichenbach in "Experience and Prediction" to differentiate between epistemology and science (1). Following Thomas Nickles and Kevin T. Kelly, (...) one can distinguish two meanings of the context distinction in Reichenbach's work. One meaning, which is primarily to be found in the earlier writings, conceives of scientific discoveries as potential objects of epistemological justification. The other meaning, typical for the later writings, removes scientific discoveries from the possible domain of epistemology. The genesis of both meanings, which demonstrates the complexity of the relationships obtaining between epistemology and science, can be made understandable by appealing to the historical context (2). Both meanings present Reichenbach with the task of establishing the autonomy of epistemology through the justification of induction. Finally, I shall expound this justification and address some of its elements of rationality characterizing philosophy of science(3). (shrink)

The thesis of this paper is that we can justify induction deductively relative to one end, and deduction inductively relative to a different end. I will begin by presenting a contemporary variant of Hume ’s argument for the thesis that we cannot justify the principle of induction. Then I will criticize the responses the resulting problem of induction has received by Carnap and Goodman, as well as praise Reichenbach ’s approach. Some of these authors compare induction (...) to deduction. Haack compares deduction to induction, and I will critically discuss her argument for the thesis that we cannot justify the principles of deduction next. In concluding I will defend the thesis that we can justify induction deductively relative to one end, and deduction inductively relative to a different end, and that we can do so in a non-circular way. Along the way I will show how we can understand deductive and inductive logic as normative theories, and I will briefly sketch an argument to the effect that there are only hypothetical, but no categorical imperatives. (shrink)

John D. Norton is responsible for a number of influential views in contemporary philosophy of science. This paper will discuss two of them. The material theory of induction claims that inductive arguments are ultimately justified by their material features, not their formal features. Thus, while a deductive argument can be valid irrespective of the content of the propositions that make up the argument, an inductive argument about, say, apples, will be justified (or not) depending on facts about apples. The (...) argument view of thought experiments claims that thought experiments are arguments, and that they function epistemically however arguments do. These two views have generated a great deal of discussion, although there hasn’t been much written about their combination. I argue that despite some interesting harmonies, there is a serious tension between them. I consider several options for easing this tension, before suggesting a set of changes to the argument view that I take to be consistent with Norton’s fundamental philosophical commitments, and which retain what seems intuitively correct about the argument view. These changes require that we move away from a unitary epistemology of thought experiments and towards a more pluralist position. (shrink)

Many realists argue that present scientific theories will not follow the fate of past scientific theories because the former are more successful than the latter. Critics object that realists need to show that present theories have reached the level of success that warrants their truth. I reply that the special theory of relativity has been repeatedly reinforced by unconceived scientific methods, so it will be reinforced by infinitely many unconceived scientific methods. This argument for the special theory of relativity overcomes (...) the critics’ objection, and has advantages over the no-miracle argument and the selective induction for it. (shrink)

Interpreters of Hume on causation consider that an advantage of the ‘quasi-realist’ reading is that it does not commit him to scepticism or to an error theory about causal reasoning. It is unique to quasi-realism that it maintains this positive epistemic result together with a rejection of metaphysical realism about causation: the quasi-realist supplies an appropriate semantic theory in order to justify the practice of talking ‘as if’ there were causal powers in the world. In this paper, I problematise the (...) quasi-realist reading of Hume on causation by showing how quasi-realism does not speak to inductive scepticism. I also offer evidence that Hume takes inductive scepticism to result from his theory of causation, and that his scepticism is tied to his rejection of metaphysical causal realism. (shrink)

This paper argues that a view of science, expounded and defended elsewhere, solves the problem of induction. The view holds that we need to see science as accepting a hierarchy of metaphysical theses concerning the comprehensibility and knowability of the universe, these theses asserting less and less as we go up the hierarchy. It may seem that this view must suffer from vicious circularity, in so far as accepting physical theories is justified by an appeal to metaphysical theses in (...) turn justified by the success of science. But this is rebutted. A thesis high up in the hierarchy asserts that the universe is such that the element of circularity, just indicated, is legitimate and justified, and not vicious. Acceptance of the thesis is in turn justified without appeal to the success of science. It may seem that the practical problem of induction can only be solved along these lines if there is a justification of the truth of the metaphysical theses in question. It is argued that this demand must be rejected as it stems from an irrational conception of science. (shrink)

Evaluative studies of inductive inferences have been pursued extensively with mathematical rigor in many disciplines, such as statistics, econometrics, computer science, and formal epistemology. Attempts have been made in those disciplines to justify many different kinds of inductive inferences, to varying extents. But somehow those disciplines have said almost nothing to justify a most familiar kind of induction, an example of which is this: “We’ve seen this many ravens and they all are black, so all ravens are black.” This (...) is enumerative induction in itsfullstrength. For it does not settle with a weaker conclusion (such as “the ravens observed in the future will all be black”); nor does it proceed with any additional premise (such as the statistical IID assumption). The goal of this paper is to take some initial steps toward a justification for the full version of enumerative induction, against counterinduction, and against the skeptical policy. The idea is to explore various epistemic ideals, mathematically defined as different modes of convergence to the truth, and look for one that is weak enough to be achievable and strong enough to justify a norm that governs both the long run and the short run. So the proposal is learning-theoretic in essence, but a Bayesian version is developed as well. (shrink)

The pessimistic induction holds that successful past scientific theories are completely false, so successful current ones are completely false too. I object that past science did not perform as poorly as the pessimistic induction depicts. A close study of the history of science entitles us to construct an optimistic induction that would neutralize the pessimistic induction. Also, even if past theories were completely false, it does not even inductively follow that the current theories will also turn (...) out to be completely false because the current theories are more successful and have better birth qualities than the past theories. Finally, the extra success and better birth qualities justify an anti-induction in favor of the present theories. (shrink)

I examine the views of Thomas Reid with respect to a certain version of the problem of induction: Why are inductions using natural kinds successful, and what justifies them? I argue that while both Reid holds a kind of conventionalist view about natural kinds, this conventionalism has a realistic component which allows him to answer both questions.

This paper responds to recent work in the philosophy of Homotopy Type Theory by James Ladyman and Stuart Presnell. They consider one of the rules for identity, path induction, and justify it along ‘pre-mathematical’ lines. I give an alternate justification based on the philosophical framework of inferentialism. Accordingly, I construct a notion of harmony that allows the inferentialist to say when a connective or concept is meaning-bearing and this conception unifies most of the prominent conceptions of harmony through category (...) theory. This categorical harmony is stated in terms of adjoints and says that any concept definable by iterated adjoints from general categorical operations is harmonious. Moreover, it has been shown that identity in a categorical setting is determined by an adjoint in the relevant way. Furthermore, path induction as a rule comes from this definition. Thus we arrive at an account of how path induction, as a rule of inference governing identity, can be justified on mathematically motivated grounds. (shrink)

Confronted with the problem of induction, Hans Reichenbach accepts that we cannot justify that induction is reliable. He tries to solve the problem by proving a weaker proposition: that induction is an optimal method of prediction, because it is guaranteed not to be worse and may be better than any alternative. Regarding the most serious objection to his approach, Reichenbach himself hints at an answer without spelling it out. In this paper, I will argue that there are (...) two workable strategies to rehabilitate Reichenbach’s account. The first leads to the widely discussed method of meta-induction, as proposed by Gerhard Schurz. The second strategy has not been suggested thus far. I will develop the second strategy and argue for it being, in some respects, superior to the first and closer to Reichenbach’s own position. (shrink)

At its strongest, Hume's problem of induction denies the existence of any well justified assumptionless inductive inference rule. At the weakest, it challenges our ability to articulate and apply good inductive inference rules. This paper examines an analysis that is closer to the latter camp. It reviews one answer to this problem drawn from the VC theorem in statistical learning theory and argues for its inadequacy. In particular, I show that it cannot be computed, in general, whether we are (...) in a situation where the VC theorem can be applied for the purpose we want it to. (shrink)

The paper offers a three-premise argument that a person with first-hand experience of possession and exorcism, such as an exorcist, can have a justified belief in the existence of demons. (1) “Exorcism involves a process by which the exorcist comes to believe that testimony is offered by a demon.” Cited for (1) are the Gospels, the Roman Ritual, some modern cases of exorcism, and exorcism practices in non-Christian contexts. (2) “If defeaters are absent, the exorcist may treat as reliable the (...) process by which he comes to believe that testimony is offered by a demon.” For (2) a case is offered that we have a reliable ability to identify when testimony is being offered and when it is being offered by particular types of agents, what is termed testifier-identification. (3) “In many cases of exorcism, defeaters are absent.” An inductive case is given for (3) by responding to possible defeaters, including several suggested recently by David Kyle Johnson. Therefore, in many cases of exorcism the exorcist may treat as reliable the processes by which he comes to believe that testimony is offered by a demon, and so can have a justified belief in the existence of demons. (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)

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)

On the basis of the distinction between logical and factual probability, epistemic justification is distinguished from logical justification of induction. It is argued that, contrary to the accepted interpretation of Hume, Hume believes that inductive inferences are epistemically legitimate and justifiable. Hence the beliefs arrived at via (correct) inductive inferences are rational beliefs. According to this interpretation, Hume is not a radical skeptic about induction.

This paper discusses ethical issues surrounding Integrated Assessment Models (IAMs) of the economic effects of climate change, and how climate economists acting as policy advisors ought to represent the uncertain possibility of catastrophe. Some climate economists, especially Martin Weitzman, have argued for a precautionary approach where avoiding catastrophe should structure climate economists’ welfare analysis. This paper details ethical arguments that justify this approach, showing how Weitzman’s “fat tail” probabilities of climate catastrophe pose ethical problems for widely used IAMs. The main (...) claim is that economists who ignore or downplay catastrophic risks in their representations of uncertainty likely fall afoul of ethical constraints on scientists acting as policy advisors. Such scientists have duties to honestly articulate uncertainties and manage (some) inductive risks, or the risks of being wrong in different ways. (shrink)

Where does the necessity that seems to accompany causal inferences come from? “Why [do] we conclude that … particular causes must necessarily have such particular effects?” In 1.3.6 of the Treatise, Hume entertains the possibility that this necessity is a function of reason. However, he eventually dismisses this possibility, where this dismissal consists of Hume’s “negative” argument concerning induction. This argument has received, and continues to receive, a tremendous amount of attention. How could causal inferences be justified if they (...) are not justified by reason? If we believe that p causes q, isn’t it reason that allows us to conclude q when we see p with some assurance, i.e. with some necessity? (shrink)

This article develops a constructive criticism of methodological conventionalism. Methodological conventionalism asserts that standards of inductive risk ought to be justified in virtue of their ability to facilitate coordination in a research community. On that view, industry bias occurs when conventional methodological standards are violated to foster industry preferences. The underlying account of scientific conventionality, however, is problematically incomplete. Conventions may be justified in virtue of their coordinative functions, but often qualify for posterior empirical criticism as research advances. Accordingly, industry (...) bias does not only threaten existing conventions but may impede their empirically warranted improvement if they align with industry preferences. My empiricist account of standards of inductive risk avoids such a problem by asserting that conventional justification can be pragmatically warranted but has, in principle, only a provisional status. Methodological conventions, therefore, should not only be defended from preference-based infringements on their coordinative function but ought to be subjected to empirical criticism. (shrink)

Le problème de l’induction (humien) a récemment été abordé par Steel dans son article de 2010. Celui-ci soutient que les théories d’apprentissage formelles permettent de justifier logiquement le principe de l’induction, ce dernier assurant la fiabilité logique des méthodes. Cette proposition a été critiquée par Howson en 2011, ce dernier mettant en doute la possibilité même qu’une méthode puisse être logiquement fiable. Bien que Steel ait offert une réponse à cette critique, il n’y répond pas directement. Dans le (...) présent article, une réponse frontale à celle-ci est offerte en s’inspirant des pratiques de tests d’hypothèses en sciences biologiques. Pour ce faire, une règle de construction des ensembles d’hypothèses est proposée, règle offrant une justification logique au fait qu’une méthode convergera nécessairement vers la vérité. Cet amendement étant cohérent avec l’ensemble de la proposition de Steel, il est ainsi possible d’affirmer que sa thèse est renforcée par cette proposition. (shrink)

Nelson Goodman observed that we use only certain ‘good’ (viz. projectible) predicates during reasoning, with no obvious demarcation criterion in sight to distinguish them from the bad and gruesome ones. This apparent arbitrariness undermines the justifiability of our reasoning practices. Inspired by Quine’s 1969 paper on Natural Kinds, Peter Gärdenfors proposes a cognitive criterion based on his theory of Conceptual Spaces (CS). He argues the good predicates are those referring to natural concepts, and that we can capture naturalness in terms (...) of similarity. In contrast to Quine, he does not primarily rely on logic, but geometry. He frames his account as a descriptive project, however, and it is not obvious how it addresses the normative dimension of Goodman’s Riddle. This paper develops a charitable reconstruction of his argument, based on the idea that the instrumental success of our projectible concepts is grounded in their cognitive-pragmatic naturalness. It then explores three lines of reasoning against the argument: Evolutionarily motivated skepticism, the miracles argument, and the relation between instrumental and pragmatic success. I conclude that in its current form, the CS account fails to provide any justification of reasoning beyond appealing to its instrumental success, and that a metaphysically robust notion of naturalness helps to achieve the desired goal. (shrink)

In this paper, we develop an account of the justification thinkers have for employing certain basic belief-forming methods. The guiding idea is inspired by Reichenbach's work on induction. There are certain projects in which thinkers are rationally required to engage. Thinkers are epistemically justified in employing any belief-forming method such that "if it doesn't work, nothing will" for successfully engaging in such a project. We present a detailed account based on this intuitive thought and address objections to it. We (...) conclude by commenting on the implications that our account may have for other important epistemological issues and debates. (shrink)

The idea of the uniformity of nature, as a solution to the problem of induction, has at least two contemporary versions: natural kinds and natural necessity. Then there are at least three alternative ontological ideas addressing the problem of induction. In this paper, I articulate how these ideas are used to justify the practice of inductive inference, and compare them, in terms of their applicability, to see whether each of them is preferred in addressing the problem of (...) class='Hi'>induction. Given the variety of contexts in which inductive inferences are made, from natural science to social science and to everyday thinking, I suggest that no singular idea is absolutely preferred, and a proper strategy is probably to welcome the plurality of ideas helpful to induction, and to take pragmatic considerations into account, in order to judge in every single case. (shrink)

According to John D. Norton's Material Theory of Induction, all inductive inferences are justified by local facts, rather than their formal features or some grand principles of nature's uniformity. Recently, Richard Dawid (Found Phys 45(9):1101–1109, 2015) has offered a challenge to this theory: in an adaptation of Norton's own celebrated "Dome" thought experiment, it seems that there are certain inductions that are intuitively reasonable, but which do not have any local facts that could serve to justify them in accordance (...) with Norton's requirements. Dawid's suggestion is that “raw induction” might have a limited but important role for such inferences. I argue that the Material Theory can accommodate such inductions, because there are local facts concerning the combinatoric features of the induction’s target populations that can licence the inferences in an analogous way to existing examples of material induction. Since my arguments are largely independent of the details of the Dome, Norton's theory emerges as surprisingly robust against criticisms of excessive narrowness. (shrink)

To justify inductive inference and vanquish classical skepticisms about human memory, external world realism, etc., Richard Fumerton proposes his “inferential internalism,” an epistemology whereby humans ‘see’ by Russellian acquaintance Keynesian probable relations (PRs) between propositions. PRs are a priori necessary relations of logical probability, akin to but not reducible to logical entailments, such that perceiving a PR between one’s evidence E and proposition P of unknown truth value justifies rational belief in P to an objective degree. A recent critic of (...) inferential internalism is Alan Rhoda, who questions its psychological plausibility. Rhoda argues that in order to see necessary relations between propositions E and P, one would need acquaintance with too many propositions at once, since our evidence E is often complex. In this paper, I criticize Rhoda’s implausibility objection as too quick. Referencing the causal status effect (CSE) from psychology, I argue that some of the complex features of evidence E contribute to our type-categorizing it as E-type, and thus we do not need to ‘see’ all of the complex features when we see the PR between E and P. My argument leaves unchanged Fumerton’s justificatory role for the PR, but enhances its psychological plausibility. (shrink)

In Fact, Fiction and Forecast, Nelson Goodman claims that the problem of justifying induction is not something over and above the problem of describing valid induction. Such claim, besides suggesting his commitment to the collapse of the distinction between the context of description and the context of justification, seems to open the possibility that the new riddle of induction could be addressed empirically. Discoveries about psychological preferences for projecting certain classes of objects could function as a (...) criterion for determining which predicates are after all projectible. In this paper, I argue that Goodman's claim must be construed within his project for constructional definitions, which is methodologically oriented by reflective equilibrium. The description of inductive practice is committed to the articulation of the extension of the class selected by the predicate ‘valid induction’. The mutual adjustment between theoretical considerations and inductive practice involved in the proposal of a definition of ‘valid induction’ must preserve that practice as much as possible, there is no way to get rid of entrenchment. Empirical discoveries about the psychological mechanism that underlies projections may help that adjustment but they cannot substitute the role played by the entrenchment of predicates. (shrink)

Why should one think Frege's definition of the ancestral correct? It can be proven to be extensionally correct, but the argument uses arithmetical induction, and that seems to undermine Frege's claim to have justified induction in purely logical terms. I discuss such circularity objections and then offer a new definition of the ancestral intended to be intensionally correct; its extensional correctness then follows without proof. This new definition can be proven equivalent to Frege's without any use of arithmetical (...) induction. This proves, without any use of arithmetical induction, that Frege's definition is extensionally correct and so answers the circularity objections. (shrink)

The main purpose of this paper is to refute the metaphysicians ‘methodological continuation’ argument supporting epistemic realism in metaphysics. This argument aims to show that scientific realists have to accept that metaphysics is as rationally justified as science given that they both employ inference to the best explanation, i.e. that metaphysics and science are methodologically continuous. I argue that the reasons given by scientific realists as to why inference to the best explanation is reliable in science do not constitute a (...) reason to believe that it is reliable in metaphysics. The justification of IBE in science and the justification of IBE in metaphysics are two distinct issues with only superficial similarities, and one cannot rely on one for the other. This becomes especially clear when one analyses the debate about the legitimacy of IBE that has taken place between realists and empiricists. The metaphysician seeking to piggyback on the realist defense of IBE in science by the methodological continuation argument presupposes that the defense is straightforwardly applicable to metaphysics. I will argue that it is, in fact, not. The favoured defenses of IBE in scientific realism make extensive use of empirical considerations, predictive power and inductive evidence, all of which are paradigmatically absent in the metaphysical context. Furthermore, I argue that the metaphysician, even if the realist would concede to the methodological continuation argument, fails to offer any agreed upon conclusions resulting from its application in metaphysics. As a result, the scientific realist is not committed to believing that there is metaphysical knowledge. (shrink)

In this dissertation, I address the question of how to construct scientific theories of emotions that are both conceptually sound and empirically fruitful. To do this, I offer an analysis of the main challenges scientific theories of emotions face, and I propose a meta-theoretical framework to construct scientific concepts of emotions as explications of folk emotion concepts. Part I discusses the main challenges theories of emotions in psychology and neuroscience encounter. The first states that a proper scientific theory of emotions (...) must explain all and only the phenomena under the vernacular term ‘emotion’ with a common set of conceptual resources and under an overarching generic concept of emotion. The second demands that each emotion category corresponds to well-coordinated sets of neural, physiological, and behavioral patterns of responses. I argue that none of the best contemporary theories of emotions in psychology and neuroscience overcomes these challenges. As a result, a new theory of emotions is required. In Part II, I develop the meta-theoretical framework to construct a theory of emotions that overcomes the challenges above. First, I propose a pluralistic account of scientific kinds based on different patterns of projection that various disciplines may take to justify inductive inferences. These are essentialist, historical, and social patterns. Each of these patterns provides a framework to construct different types of scientific concepts. I argue that among the frameworks for scientific kinds available, the one that is best suited to explicate emotion concepts is a functional framework. Consequently, I conclude by recommending scientists pursue functionalist theories of emotions over essentialist, historical, or social theories. (shrink)

The inductive argument from evil to the non-existence of God contains the premise that, probably, there is gratuitous evil. Some skeptical theists object: one's justification for the premise that, probably, there is gratuitous evil involves an inference from the proposition that we don't see a good reason for some evil to the proposition that it appears that there is no good reason for that evil, and they use a principle, "CORNEA," to block that inference. The common sense problem of evil (...) threatens the CORNEA move, because the common sense problem of evil does not involve any inference to justify the belief that there is gratuitous evil. In this paper, I argue that the common sense problem of evil doesn't avoid CORNEA. CORNEA, or a reformulated version of it, can still prevent one from having justification for the belief that there is gratuitous evil. (shrink)

Inductively defined structures are ubiquitous in mathematics; their specification is unambiguous and their properties are powerful. All fields of mathematical logic feature these structures prominently: the formula of a language, the set of theorems, the natural numbers, the primitive recursive functions, the constructive number classes and segments of the cumulative hierarchy of sets. -/- This dissertation gives a mathematical characterization of a species of inductively defined structures, called accessible domains, which include all of the above examples except the set of (...) theorems. The concept of an accessible domain comes from Wilfried Sieg's analysis of proof-theoretic practices, starting with his dissertation. In particular, he noticed the special epistemological character of elements of an accessible domain: they can always be uniquely identified with their build-up. Generally, the unique build-up of elements justifies the principles of induction and recursion. -/- I use category theory to give an abstract characterization of accessible domains. I claim that accessible domains are all instances of initial algebras for endofunctors. Grounded in the historical roots of Sieg's discussions, this dissertation shows how the properties of initial algebras for endofunctors and accessible domains coincide in a satisfying and natural way. -/- Filling out this characterization, I show how important examples of accessible domains fit into this broad characterization. I first characterize some accessible domains by relatively simple functors (e.g. finite, polynomial, those that preserve certain colimits) where we can see how iterating the functor can produce the accessible domain. Then I describe accessible domains that result from more involved specifications (e.g. ordinals and segments of the cumulative hierarchies associated with CZF, IZF, and ZF) by relying heavily on algebraic set theory. I end with a discussion of some of the methodological features of category theory in particular that helped characterize accessible domains. (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 the Riemann hypothesis, have had to be considered in terms of the evidence for and against them. In recent decades, massive increases in computer power have permitted the gathering of huge amounts of numerical evidence, both for conjectures in pure mathematics and (...) for the behavior of complex applied mathematical models and statistical algorithms. Mathematics has therefore become (among other things) an experimental science (though that has not diminished the importance of proof in the traditional style). We examine how the evaluation of evidence for conjectures works in mathematical practice. We explain the (objective) Bayesian view of probability, which gives a theoretical framework for unifying evidence evaluation in science and law as well as in mathematics. Numerical evidence in mathematics is related to the problem of induction; the occurrence of straightforward inductive reasoning in the purely logical material of pure mathematics casts light on the nature of induction as well as of mathematical reasoning. (shrink)

How the mind works have always been one of the most important and fascinating puzzles. For a long time, countless scholars have devoted themselves to this research, but there has no decisive progress been made yet. We believe that the fundamental reason for this situation is that the research paradigm learned from the study of objective sciences such as physics is not applicable to the study of the mind. In this paper, we suggest that the proper way to study the (...) mind is to think of it as a computational system that can program itself. In this self-programming system, there are two key components: storage structure and bootstrap program. In this paper, we only focus on analyzing the principle of the storage structure. Although this paper does not give a full mechanism of the self-programming system, the mere study of the storage structure can generate some important findings. Specifically, by using the storage structure, the problem of induction can be solved; And the mechanism of deduction and causality can easily be explained. Some of our findings sharply contrast with the existing theories. For example, we argue that the validity of induction is attributed to the intention of self-programming systems, not because it can be justified as mainstream inductivists try to prove. (shrink)

Inductive logic would be the logic of arguments that are not valid, but nevertheless justify belief in something like the way in which valid arguments would. Maybe we could describe it as the logic of “almost valid” arguments. There is a sort of transitivity to valid arguments. Valid arguments can be chained together to form arguments and such arguments are themselves valid. One wants to distinguish the “almost valid” arguments by noting that chains of “almost valid” arguments are weaker than (...) the links that form them. But it is not clear that this is so. I have an apparent counterexample the claim. Though: as is typical in these sorts of situations, it is hard to tell where the problem lies. (shrink)

This is a commentary on Adrian Heathcote’s interesting paper ‘Hume’s Master Argument’. Heathcote contends that No-Ought-From-Is is primarily a logical thesis, a ban on Is/Ought inferences which Hume derives from the logic of Ockham. NOFI is thus a variation on what Heathcote calls ‘Hume’s Master Argument’, which he also deploys to prove that conclusions about the future (and therefore a-temporal generalizations) cannot be derived by reason from premises about the past, and that conclusions about external objects or other minds cannot (...) be derived by reason from premises about impressions. Heathcote raises an important question. Having (apparently) argued that our inductive inferences are not justified by reason, Hume puts them down to Custom, and seems to suggest that we OUGHT to indulge this propensity but NOt the superstitious propensities that lead to religious belief. (Query: Why is it right to indulge one non-rational propensity but not the others?) Finally Heathcote argues that just as there are valid, but not formally valid, arguments taking us from claims about inferential relations to claims about what we ought to believe, so there may be valid, but not formally valid, arguments taking us from factual claims about some situation to claims about what we ought to do. -/- I reply that Hume does indeed have a Master Argument and that it does rely on logical principles but not on the logic of Ockham which had been largely forgotten by Hume’s day. Instead Hume relies on the idea widely believed in the 18th Century and taught to Hume at Edinburgh by his logic Professor Colin Drummond, that in a logically valid argument the conclusion is contained in the premises. I reconstruct Hume’s Master Argument using this principle. I draw a careful distinction between two theses: 1) that we cannot get from non-moral premises to moral conclusions with the aid of logic alone and 2) that we cannot get from non-moral premises to moral conclusions with aid of analytic bridge principles. Hume believed the first but not the second. What then is the role of NOFI in the larger argument of the Treatise? To show that the truths of ethics cannot be derived via logic from self-evident truths of some other kind and thus that they are not demonstrable. How can we make sense of Hume’s apparent belief that it is sometimes right to transcend reason and sometimes not? In the case of Custom, we live in a world governed by causal regularities, and, in such a world, induction is in fact a fairly reliable belief-forming mechanism. Thus a suitably qualified spectator (one aware of the kind of world we live in) would tend to approve of indulging it, even if it cannot be justified by reason. However, our superstitious propensities are (and can be known to be) unreliable, since they produce different and inconsistent results in different people. Thus it is it is wrong (something a suitably qualified spectator would disapprove of) to indulge the faculty of Superstition. I also take issue with Heathcote’s penchant for valid, but not formally valid, inferences. I supply the missing premises for Heathcote’s Is/Ought inferences and argue that they are either not true or not necessary. (shrink)

State of the art paper on the problem of induction: how to justify the conclusion that ‘all Fs are Gs’ from the premise that ‘all observed Fs are Gs’. The most prominent theories of contemporary philosophical literature are discussed and analysed, such as: inductivism, reliabilism, perspective of laws of nature, rationalism, falsificationism, the material theory of induction and probabilistic approaches, according to Carnap, Reichenbach and Bayesianism. In the end, we discuss the new problem of induction of Goodman, (...) raised by the grue predicate. (shrink)

The Kripke/Wittgenstein paradox and Goodman’s riddle of induction can be construed as problems of multiple redescription, where the relevant sceptical challenge is to provide factual grounds justifying the description we favour. A choice of description or predicate, in turn, is tantamount to the choice of a curve over a set of data, a choice apparently governed by implicitly operating constraints on the relevant space of possibilities. Armed with this analysis of the two paradoxes, several realist solutions of Kripke’s (...) paradox are examined that appeal to dispositions or other non-occurrent properties. It is found that all neglect crucial epistemological issues: the entities typically appealed to are not observational and must be inferred on the basis of observed entities or events; yet, the relevant sceptical challenge concerns precisely the factual basis on which this inference is made and the constraints operating on it. All disposition ascriptions, the thesis goes on to argue, contain elements of idealization. To ward off the danger of vacuity resulting from the fact that any disposition ascription is true under just the right ideal conditions, dispositional theories need to specify limits on legitimate forms of idealization. This is best done by construing disposition ascriptions as forms of (implicit) curve-fitting, I argue, where the “data” is not necessarily numeric, and the “curve” fitted not necessarily graphic. This brings us full circle: Goodman’s and Kripke’s problems are problems concerning curve-fitting, and the solutions for it appeal to entities the postulation of which is the result of curve-fitting. The way to break the circle must come from a methodology governing the idealizations, or inferences to the best idealization, that are a part of curve-fitting. The thesis closes with an argument for why natural science cannot be expected to be of much help in this domain, given the ubiquity of idealization. (shrink)

In the first part of this investigation we highlight two, seemingly irreconcilable, beliefs that suggest an impending crisis in the teaching, research, and practice of—primarily state-supported—mathematics: (a) the belief, with increasing, essentially faith-based, conviction and authority amongst academics that first-order Set Theory can be treated as the lingua franca of mathematics, since its theorems—even if unfalsifiable—can be treated as ‘knowledge’ because they are finite proof sequences which are entailed finitarily by self-evidently Justified True Beliefs; and (b) the slowly emerging, but (...) powerfully rooted in economic imperatives, belief that only those Justified True Beliefs can be treated as ‘knowledge’ which are, further, categorically communicable as Factually Grounded Beliefs—hence as comprehensible pre-formal ‘mathematical truths’—by any intelligence that lays claims to a mathematical lingua franca. We argue that this seeming irreconcilability merely reflects a widening chasm between an increasing under-estimation of the value to society of ‘semantic arithmetical truth’, and an increasing over-estimation of the value to society of ‘syntactic set-theoretical provability’; a chasm which must be narrowed and bridged explicitly. We thus proffer a Complementarity Thesis which seeks to recognize that mathematical ‘provability’ and mathematical ‘truth’ need to be interdependent and complementary, ‘evidence-based’, assignments-by-convention to the formulas of a formal mathematical language; where (a) the goal of mathematical ‘proofs’ may be viewed as seeking to ensure that any mathematical language intended to formally represent our pre-formal conceptual metaphors and their inter-relatedness is unambiguous, and free from contradiction; whilst (b) the goal of mathematical ‘truths’ must be viewed as seeking to ensure that any such representation does, indeed, uniquely identify and adequately represent such metaphors and their inter-relatedness. Our thesis is that, by universally ignoring the need to introduce goal (b) in our curriculum, the teaching of, and research in, mathematics at the post-graduate level cannnot justify its value to society beyond the mere intellectual stimulation of individual minds. In the second part we appeal to some recent—and hitherto unsuspected—unarguably constructive Tarskian interpretations, of the first-order Peano Arithmetic PA, which establish PA as both finitarily consistent, and categorical. Since we also show that the second order subsystem ACA0 of Peano Arithmetic and PA cannot both be assumed provably consistent, we conclude that there can be no mathematical, or meta-mathematical, proof of consistency for Set Theory. Hence the theorems of any Set Theory are not sufficient for distinguishing between (i) what we can believe to be a ‘mathematical truth’; (ii) what we can evidence as a ‘mathematical truth’; and (iii) what we ought not to believe is a ‘mathematical truth’; whilst the theorems of the first-order Peano Arithmetic PA are sufficient for distinguishing between (i), (ii) and (iii). We conclude from this that the holy grail of mathematics ought to be ‘arithmetical truth’, not ‘set-theoretical proof’. (shrink)

The “demarcation problem,” the issue of how to separate science from pseu- doscience, has been around since fall 1919—at least according to Karl Pop- per’s (1957) recollection of when he first started thinking about it. In Popper’s mind, the demarcation problem was intimately linked with one of the most vexing issues in philosophy of science, David Hume’s problem of induction (Vickers 2010) and, in particular, Hume’s contention that induction cannot be logically justified by appealing to the fact that (...) “it works,” as that in itself is an inductive argument, thereby potentially plunging the philosopher straight into the abyss of a viciously circular argument. (shrink)

The article critically discusses Walton’s (and co-authors’) argument scheme approach to good argumentation. Four characteristics of Walton’s approach are presented: 1. Argument schemes provide normative requirements. 2. These schemata are enthymematic. 3. There are associated critical questions. 4. The method is inductive, abstracting schemata from groups of similar arguments. Four adequacy conditions are applied to these characteristics: AC1: effectiveness in achieving the epistemic goal of obtaining and communicating justified acceptable opinions; AC2: completeness in capturing the good argument types; AC3: efficiency (...) in achieving the goals; AC4: justification of the argument schemes. The discussion reveals weaknesses in Walton’s account, including they are neither effective nor truly justified. A better alternative is an epistemological approach based on epistemological principles. (shrink)

Introduction: Clinical practice guidelines (CPGs) are an important source of justification for clinical decisions in modern evidence-based practice. Yet, we have given little attention to how they argue their evidence. In particular, how do CPGs argue for treatment with long-term medications that are increasingly prescribed to older patients? Approach and rationale: I selected six disease-specific guidelines recommending treatment with five of the medication classes most commonly prescribed for seniors in Ontario, Canada. I considered the stated aims of these CPGs and (...) the techniques employed towards those aims. Finally, I reconstructed and logically analysed the arguments supporting recommendations for pharmacotherapy. Analysis: The primary function of CPGs is rhetorical, or persuasive, and their means of persuasion include both a display of their credibility and their argumentation. Arguments supporting pharmacotherapy recommendations for the target population follow a common inductive pattern: statistical generalization from randomized controlled trial (RCT) and meta-analysis evidence. Two of the CPGs also argue their treatment recommendations for older patients in this style, while three fail to justify pharmacotherapy specifically for the older population. Discussion: The arguments analysed lack the auxiliary assumptions that would warrant making a generalization about the clinical effectiveness of medications for the older population. Guidelines reason using simple induction, while ignoring important inferential gaps. Future guidelines should aspire to be well-reasoned rather than simply evidence-based; argue from a plurality of evidence; be wary of hasty inductions; appropriately limit the scope of their recommendations; and avoid making law-like, prescriptive generalizations. (shrink)

The “problem of memory” in epistemology is concerned with whether and how we could have knowledge, or at least justification, for trusting our apparent memories. I defend an inductive solution—more precisely, an abductive solution—to the problem. A natural worry is that any such solution would be circular, for it would have to depend on memory. I argue that belief in the reliability of memory can be justified from the armchair, without relying on memory. The justification is, roughly, that my having (...) the sort of experience that my apparent memory should lead me to expect is best explained by the hypothesis that my memories are reliable. My solution is inspired by Harrod’s (1942) inductive solution. Coburn (1960) argued that Harrod’s solution contains a fatal flaw. I show that my solution is not vulnerable to Coburn’s objection, and respond to a number of other, recent and likely objections. (shrink)

Several philosophers have recently tried to define natural kinds in epistemic terms only. Given the persistent problems with finding a successful metaphysical theory, these philosophers argue that we would do better to describe natural kinds solely in terms of their epistemic usefulness, such as their role in supporting inductive inferences. In this paper, I argue against these epistemology-only theories of natural kinds and in favor of, at least partly, metaphysical theories. I do so in three steps. In the first section (...) of the paper, I propose two desiderata for a theory of natural kinds. In the second section, I discuss one example of a ‘general’ epistemology-only theory, proposed by Marc Ereshefsky and Thomas Reydon, and argue that theories like theirs fail to provide adequate criteria of natural kinds. In the third section, I focus on one example of a ‘specific’ epistemology-only theory, proposed by P. D. Magnus, and use it to show why such theories cannot justify the claim that the proposed epistemic criteria account for the naturalness of kinds. (shrink)