This paper contends that some of the recent critical appraisals of universals theories of natural laws, namely, van Fraassen's analysis of Armstrong's probabilistic laws, are largely ineffective since they fail to disclose the incompatibility of universals and any realistic natural law setting. Rather, a more profitable line of criticism is developed that contests the universalists' claim to have resolved the induction problem (i.e., the separation of natural laws from mere accidental regularities), and thereby reveals the universals' philosophically inadequate concept (...) of a physical property. (shrink)

Robert Aumann argues that common knowledge of rationality implies backward induction in finite games of perfect information. I have argued that it does not. A literature now exists in which various formal arguments are offered in support of both positions. This paper argues that Aumann's claim can be justified if knowledge is suitably reinterpreted.

The problem of induction is sometimes motivated via a comparison between rules of induction and rules of deduction. Valid deductive rules are necessarily truth preserving, while inductive rules are not.

It is common to assume that the problem of induction arises only because of small sample sizes or unreliable data. In this paper, I argue that the piecemeal collection of data can also lead to underdetermination of theories by evidence, even if arbitrarily large amounts of completely reliable experimental and observational data are collected. Specifically, I focus on the construction of causal theories from the results of many studies (perhaps hundreds), including randomized controlled trials and observational studies, where the (...) studies focus on overlapping, but not identical, sets of variables. Two theorems reveal that, for any collection of variables V, there exist fundamentally different causal theories over V that cannot be distinguished unless all variables are simultaneously measured. Underdetermination can result from piecemeal measurement, regardless of the quantity and quality of the data. Moreover, I generalize these results to show that, a priori, it is impossible to choose a series of small (in terms of number of variables) observational studies that will be most informative with respect to the causal theory describing the variables under investigation. This final result suggests that scientific institutions may need to play a larger role in coordinating differing research programs during inquiry. (shrink)

In this three-part paper, my concern is to expound and defend a conception of science, close to Einstein's, which I call aim-oriented empiricism. I argue that aim-oriented empiricsim has the following virtues. (i) It solve the problem of induction; (ii) it provides decisive reasons for rejecting van Fraassen's brilliantly defended but intuitively implausible constructive empiricism; (iii) it solves the problem of verisimilitude, the problem of explicating what it can mean to speak of scientific progress given that science (...) advances from one false theory to another; (iv) it enables us to hold that appropriate scientific theories, even though false, can nevertheless legitimately be interpreted realistically, as providing us with genuine , even if only approximate, knowledge of unobservable physical entities; (v) it provies science with a rational, even though fallible and non-mechanical, method for the discovery of fundamental new theories in physics. In the third part of the paper I show that Einstein made essential use of aim-oriented empiricism in scientific practice in developing special and general relativity. I conclude by considering to what extent Einstein came explicitly to advocate aim-oriented empiricism in his later years. (shrink)

A new approach to Hume's problem of induction that justifies the optimality of induction at the level of meta-induction. Hume's problem of justifying induction has been among epistemology's greatest challenges for centuries. In this book, Gerhard Schurz proposes a new approach to Hume's problem. Acknowledging the force of Hume's arguments against the possibility of a noncircular justification of the reliability of induction, Schurz demonstrates instead the possibility of a noncircular justification of the optimality of induction, or, more (...) precisely, of meta-induction (the application of induction to competing prediction models). Drawing on discoveries in computational learning theory, Schurz demonstrates that a regret-based learning strategy, attractivity-weighted meta-induction, is predictively optimal in all possible worlds among all prediction methods accessible to the epistemic agent. Moreover, the a priori justification of meta-induction generates a noncircular a posteriori justification of object induction. Taken together, these two results provide a noncircular solution to Hume's problem. Schurz discusses the philosophical debate on the problem of induction, addressing all major attempts at a solution to Hume's problem and describing their shortcomings; presents a series of theorems, accompanied by a description of computer simulations illustrating the content of these theorems (with proofs presented in a mathematical appendix); and defends, refines, and applies core insights regarding the optimality of meta-induction, explaining applications in neighboring disciplines including forecasting sciences, cognitive science, social epistemology, and generalized evolution theory. Finally, Schurz generalizes the method of optimality-based justification to a new strategy of justification in epistemology, arguing that optimality justifications can avoid the problems of justificatory circularity and regress. (shrink)

In the mid-eighteenth century David Hume argued that successful prediction tells us nothing about the truth of the predicting theory. But physical theory routinely predicts the values of observable magnitudes within very small ranges of error. The chance of this sort of predictive success without a true theory suggests that Hume's argument is flawed. However, Colin Howson argues that there is no flaw and examines the implications of this disturbing conclusion; he also offers a solution to one of the central (...) problems of Western philosophy, the problem of induction. (shrink)

The Problem of Old Evidence is a perennial issue for Bayesian confirmation theory. Garber (Test Sci Theor 10:99–131, 1983) famously argues that the problem can be solved by conditionalizing on the proposition that a hypothesis deductively implies the existence of the old evidence. In recent work, Hartmann and Fitelson (Philos Sci 82(4):712–717, 2015) and Sprenger (Philos Sci 82(3):383–401, 2015) aim for similar, but more general, solutions to the Problem of Old Evidence. These solutions are more general because (...) they allow the explanatory relationship between a new hypothesis and old evidence to be inductive, rather than deductive. In this paper, I argue that these solutions are either unsound or under-motivated, depending on the case of inductive explanation that we have in mind. This lends support to the broader claim that Garber–Style Bayesian confirmation cannot capture the sense in which new hypotheses that do not deductively imply old evidence nevertheless seem to be confirmed via old evidence. (shrink)

This essay presents a point of view for looking at `free will', with the purpose of interpreting where exactly the freedom lies. For, freedom is what we mean by it. It compares the exercise of free will with the making of inferences, which usually is predominantly inductive in nature. The making of inference and the exercise of free will, both draw upon psychological resources that define our ‘selves’. I examine the constitution of the self of an individual, especially the (...) involvement of personal beliefs, personal memories, affects, emotions, and the hugely important psychological value-system, all of which distinguish the self of one individual from that of another. The foundational position that adopted in this essay is that all psychological processes are correlated with corresponding ones involving large scale neural aggregates in the brain, communicating with one another through wavelike modes of excitation and de-excitation. Of central relevance is the value-network around which the affect system is organized, the latter, in turn, being the axis around which is assembled the self, with all its emotional correlates. The self is a complex system. I include a brief outline of what complexity consists of. In reality all systems are complex, for complexity is ubiquitous, and certain parts of nature appear to us to be ‘simple’ only in certain specific contexts. It is in this background that the issue of determinism is viewed in this essay. Instead of looking at determinism as a grand principle entrenched in nature independent of our interpretation of it, I look at our ability to explain and to predict events and phenomena around us, which is made possible by the existence of causal links running in a complex course that set up correlations between diverse parts of nature, in this way putting the stamp of necessity on these events. However, the complexity of systems limits our ability to explain and to predict to within certain horizons defined by contexts. Our ability to explain and predict in matters relating to acts of free will is similarly limited by the operations of the self that remain hidden from our own awareness. The aspects of necessity and determinism appear to us in the form of reason and rationality that explain and predict only within a limited horizon, while the rest depends on the complex operation of self-linked psychological resources, where the latter appear as contingent in the context of the exercise of free will. The hallmark of complex systems is the existence of amplifying factors that operate as destabilizing ones, along with inhibiting or stabilizing factors as well that generally limit the destabilizing influences to local occurrences, while preserving the global integrity of a system. This complex interplay of destabilizing and stabilizing influences lead to the possibility of an enormous number of distinct modes of behavior that appear as emergent phenomena in complex systems. Looking at the particular case of the self of an individual that guide her actions and thoughts, it is the operation of our emotions, built around the psychological value-system, that provide for the amplifying and inhibiting factors mentioned above. The operation of these self-linked factors stamps our actions and thoughts as contingent ones that do not fit with our concepts of reason and rationality. And this is what provides the basis of our idea of free will. Free will is not ‘free’ in virtue of exemption from causal links running through all our self-based processes - ones that remain hidden from our awareness, but is free of what is perceived to be ‘reason and rationality’ based on knowledge and the common pool of beliefs and principles associated with a shared world-view. When we speak of the choice involved in an act of exercise of free will what we actually refer to is the commonly observed fact that various different individuals of a similar disposition respond differently when placed under similar circumstances. In other words, free will is ‘free’ precisely because it is not subject to constraints of a commonly accepted and shared set of principles, beliefs, and values. While it is possible that, in an exercise of free will, the self-linked psychological resources are brought into action when a number of alternatives are presented to the self by the operation of the ingredients of a commonly shared world-view, it seems likely that, that set of alternatives is not of primary relevance in the final response that the mind produces, since the latter is primarily a product of the operation of the self-based psychological resources. What is of greater relevance here is the operation of emotion-driven processes, guided by the psychological value-system based on the activity of the so-called reward-punishment network in the brain. These processes lead the individual to a response that appears to be free from the shackles of determinism precisely because their mechanisms, which are hidden from us, do not conform to commonly accepted and shared rules and principles. In contrast, inductive inference is a process that is based on the ‘cognitive face’ of self, where the self-based psychological resources play a supportive role to the commonly shared world-view of an individual. There is never any freedom from the all-pervading causal links representing correlations among all objects, entities, and events in nature. In the midst of all this, the closest thing to freedom that we can have in our life comes with self-examination and self-improvement. The possibility of self-examination appears in the form of specific conjunctions between our complex self-processes and the ceaseless changes of scenario in our external world. This actually makes the emergent phenomenon of self-examination a matter of chance, but one that keeps on appearing again and again in our life. Once realized, self examination creates possibilities that would not be there in the absence of it, and these possibilities include the enhancement of further self-enrichment and further diversity in the exercise of our free will. (shrink)

Vaidya & Wallner [2021] have recently formulated the Problem of Modal Epistemic Friction (PMEF) for three of the most discussed accounts in the epistemology of modality: conceivability-based, counterfactual-based and deduction-based accounts. They propose essentialist solutions in all three cases, arguing that all three discussed accounts should be supplemented by a suitable epistemology of essence. In this paper I argue that the PMEF also applies to Roca-Royes’ similarity-based account in the epistemology of modality. I also discuss if or to what (...) extent the version of the PMEF that applies to Roca-Royes can be given an essentialist solution. With regard to this question, I argue that besides the inductivist variant of the similarity-based account that Roca-Royes favors, there might also be an essentialist variant that would be successful in at least some cases. As for Roca-Royes’ inductivist variant I argue that the PMEF ultimately boils down to the notorious Problem of Induction. I shall discuss a popular solution to the Problem of Induction and the role essences might play in it. (shrink)

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

To solve the problem of induction we had first better know what it is. Some ways of formulating the worry about induction are underwhelming as they depend on assumptions that don’t survive much scrutiny. Perhaps the most disturbing argument for inductive skepticism appeals to the claim that we could not possibly be justified in taking our inductive methods to be reliable independently of our use of those methods. And the use of inductive methods cannot give us (...) justification to suppose that they are reliable. I argue for a new way to escape the first horn of this dilemma. (shrink)

Some patients, following brain injury, do not outwardly respond to spoken commands, yet show patterns of brain activity that indicate responsiveness. This is 'cognitive-motor dissociation' (CMD). Recent research has used machine learning to diagnose CMD from electroencephalogram recordings. These techniques have high false discovery rates, raising a serious problem of inductive risk. It is no solution to communicate the false discovery rates directly to the patient's family, because this information may confuse, alarm and mislead. Instead, we need a (...) procedure for generating case-specific probabilistic assessments that can be communicated clearly. This article constructs a possible procedure with three key elements: (1) A shift from categorical 'responding or not' assessments to degrees of evidence; (2) The use of patient-centred priors to convert degrees of evidence to probabilistic assessments; and (3) The use of standardised probability yardsticks to convey those assessments as clearly as possible. (shrink)

The Problem of Induction This article discusses the problem of induction, including its conceptual and historical perspectives from Hume to Reichenbach. Given the prominence of induction in everyday life as well as in science, we should be able to tell whether inductive inference amounts to sound reasoning or not, or at least we should be … Continue reading Induction, The Problem of →.

Inductive methods can be used to estimate the accuracies of inductive methods. Call a method immodest if it estimates that it is at least as accurate as any of its rivals. It would be unreasonable to adopt any but an immodest method. Under certain assumptions, exactly one of Carnap's lambda-methods is immodest. This may seem to solve the problem of choosing among the lambda-methods; but sometimes the immodest lambda-method is λ =0, which it would not be reasonable (...) to adopt. We should therefore reconsider the assumptions that led to this conclusion: for instance, the measure of accuracy. (shrink)

This book offers new insights into Hume&s problem of induction. In addition to that, it argues against the coherentist justification of induction, refuting Hume's initial problem of induction and develops counter-inductions to defend scientific realism from pessimists and advocates a realist theory of scientific development. In doing so, this book enriches the moral realism debate with the scientific realism debate and is of great value to researchers and advanced students in philosophy of science.

This essay defends the view that inductive reasoning involves following inductive rules against objections that inductive rules are undesirable because they ignore background knowledge and unnecessary because Bayesianism is not an inductive rule. I propose that inductive rules be understood as sets of functions from data to hypotheses that are intended as solutions to inductive problems. According to this proposal, background knowledge is important in the application of inductive rules and Bayesianism qualifies as (...) an inductive rule. Finally, I consider a Bayesian formulation of inductive skepticism suggested by Lange. I argue that while there is no good Bayesian reason for judging this inductive skeptic irrational, the approach I advocate indicates a straightforward reason not to be an inductive skeptic. (shrink)

Marc Lange has criticized my assertion that relative to a Bayesian conception of inductive reasoning, Hume's argument for inductive scepticism cannot be run. I reply that the way in which Lange suggests one should run the Humean argument in a Bayesian framework ignores the fact that in Bayesian models of learning from experience, the domain of an agent's probability measure is exogenously determined. I also show that Lange is incorrect to equate probability distributions which 'support inductive inferences' (...) with probability distributions which assign probability to contingent propositions/events. (shrink)

A cornerstone of game theory is backward induction, whereby players reason backward from the end of a game in extensive form to the beginning in order to determine what choices are rational at each stage of play. Truels, or three-person duels, are used to illustrate how the outcome can depend on (1) the evenness/oddness of the number of rounds (the parity problem) and (2) uncertainty about the endpoint of the game (the uncertainty problem). Since there is no known (...) endpoint in the latter case, an extension of the idea of backward induction is used to determine the possible outcomes. The parity problem highlights the lack of robustness of backward induction, but it poses no conflict between foundational principles. On the other hand, two conflicting views of the future underlie the uncertainty problem, depending on whether the number of rounds is bounded (the players invariably shoot from the start) or unbounded (they may all cooperate and never shoot, despite the fact that the truel will end with certainty and therefore be effectively bounded). Some real-life examples, in which destructive behavior sometimes occurred and sometimes did not, are used to illustrate these differences, and some ethical implications of the analysis are discussed. (shrink)

We present six significant open problems in Pure Inductive Logic, together with their background and current status, with the intention of raising awareness and leading ultimately to their resolution.

In this paper Beebee argues that the problem of induction, which she describes as a genuine sceptical problem, is the same for Humeans than for Necessitarians. Neither scientific essentialists nor Armstrong can solve the problem of induction by appealing to IBE, for both arguments take an illicit inductive step.

This paper examines a twofold tension in Gerhard Schurz’s (2019) recent proposal to solve Hume’s problem of induction. Schurz concedes to the skeptic that there is no non-circular epistemic justification of the reliability of induction, but then argues for the optimality of meta-induction so that if any prediction method is reliable, then meta-induction is. There is a tension in this proposal between meta-induction and our inductive practice: Are we supposed to abandon our inductive practice in favor of (...) meta-induction? Schurz claims that given the actual way the world has been, the meta-inductive method supports the standard inductive method. There then arises a second tension: The challenges Schurz cites against the reliability of induction—such as the anti-inductive hypothesis and the state-uniform probability distribution—cast doubt on Schurz’s claim that meta-induction supports induction. The reasoning in this paper moves in the opposite direction: There are ways of answering these challenges in defense of Schurz’s claim that meta-induction supports induction, but these ways also point to ways of defending induction directly without the mediation of meta-induction. (shrink)

The Problem of Old Evidence is a perennial issue for Bayesian confirmation theory. Garber (Test Sci Theor 10:99–131, 1983) famously argues that the problem can be solved by conditionalizing on the proposition that a hypothesis deductively implies the existence of the old evidence. In recent work, Hartmann and Fitelson (Philos Sci 82(4):712–717, 2015) and Sprenger (Philos Sci 82(3):383–401, 2015) aim for similar, but more general, solutions to the Problem of Old Evidence. These solutions are more general because (...) they allow the explanatory relationship between a new hypothesis and old evidence to be inductive, rather than deductive. In this paper, I argue that these solutions are either unsound or under-motivated, depending on the case of inductive explanation that we have in mind. This lends support to the broader claim that Garber–Style Bayesian confirmation cannot capture the sense in which new hypotheses that do not deductively imply old evidence nevertheless seem to be confirmed via old evidence. (shrink)

According to Hume, the paradigm type of inductive reasoning involves a constant conjunction. But, as Price points out, Hume misrepresents ordinary induction: we experience very few constant conjunctions. In this paper, I examine several ways of defending Hume’s (psychological) account of our practice against Price’s objection, and conclude that the theory cannot be upheld.

Just as Hume constructs an argument against factual inductions, so I construct a Humean argument against moral inductions. Just as Hume’s argument against factual inductions creates the problem of factual induction, so the Humean argument against moral inductions creates the problem of moral induction. The problem of factual induction spells trouble for the evolutionary debunking argument for moral skepticism. The problem of moral induction spells trouble for moral realism and cultural emotivism, but not for emotivism, prescriptivism, (...) error theory, quasi-realism, and moral functionalism. The problem of moral induction can trigger new meta-normative debates. (shrink)

The problem of induction is formulated as a set of three questions, namely: ‘What is the nature of the attitude of acceptance that we adopt in relation to certain theories?’ ‘What are the rules according to which we select those theories which we accept?’ and, ‘What is the justification for the adoption of those rules?’. An original answer is proposed for each question in turn, with the help of the new concepts of sub-theory, established sub-theory, aberrant, arbitrary and degenerate (...) theories. The answer to the third question follows the lines of Reichenbach's pragmatic strategy. (shrink)

The Problem of Old Evidence is a perennial issue for Bayesian confirmation theory. Garber (Test Sci Theor 10:99–131, 1983) famously argues that the problem can be solved by conditionalizing on the proposition that a hypothesis deductively implies the existence of the old evidence. In recent work, Hartmann and Fitelson (Philos Sci 82(4):712–717, 2015) and Sprenger (Philos Sci 82(3):383–401, 2015) aim for similar, but more general, solutions to the Problem of Old Evidence. These solutions are more general because (...) they allow the explanatory relationship between a new hypothesis and old evidence to be inductive, rather than deductive. In this paper, I argue that these solutions are either unsound or under-motivated, depending on the case of inductive explanation that we have in mind. This lends support to the broader claim that Garber–Style Bayesian confirmation cannot capture the sense in which new hypotheses that do not deductively imply old evidence nevertheless seem to be confirmed via old evidence. (shrink)

Inductive thinking is a universal human habit; we generalise from our experiences the best we can. The induction problem is to identify which observed regularities provide reasonable justification for inductive conclusions. In the natural sciences, we can often use strict laws in making successful inferences about unobserved states of affairs. In the social sciences, by contrast, we have no strict laws, only regularities which most often are conditioned on ceteris paribus clauses. This makes it much more difficult (...) to make reliable inferences in the social sciences. In particular, we want knowledge about general causal relations in order to be able to determine what to do in order to achieve a certain state of affairs. Knowledge about causal relations that are also valid in the future requires experiments or so called ‘natural experiments’. Only knowledge derived from such experiences enable us to draw reasonably reliable inferences about how to act in order to achieve our goals. (shrink)

This chapter contains sections titled: Hume's Problem of Induction Hume's Negative Argument concerning Induction.

Large language models (LLMs) often appear to vindicate a radical empiricist picture: train on vast corpora of experience-like text, and capacities emerge without explicit symbolic rules. Yet contemporary machine learning research repeatedly emphasizes that what is learned, how quickly it is learned, and how well it generalizes depend crucially on prior constraints: architectural structure, training objectives, optimization dynamics, and representational bottlenecks. These constraints constitute inductive biases in a precise, technical sense. This paper develops a philosophical argument that uses LLMs (...) as a case study to reassess the classical tabula rasa thesis associated with Locke and its descendants. I defend two claims. First, even the most ``data-driven'' generative models are saturated with structural priors that make learning possible at scale; thus, their success cannot be straightforwardly read as a triumph of unstructured empiricism. Second, once this is appreciated, the rhetorical appeal of a ``blank slate'' conception of the infant mind weakens further: if artificial systems trained on orders of magnitude more linguistic input than any child still require rich inductive biases, it is implausible that human cognition begins wholly unstructured. I then show how contemporary debates about whether LLMs ``understand'' language recapitulate the older dispute about whether experience alone can generate semantics and conceptual structure. The upshot is a more balanced, non-caricatured empiricism: experience matters, but explanation must explicitly account for the learning system's prior structure. (shrink)

I explain how Karl Popper resolved the problem of induction but not the pragmatic problem of induction. I show that Popper’s solution to the pragmatic problem of induction is inconsistent with his solution to the problem of induction. I explain how Popper’s falsificationist epistemology can solve the pragmatic problem of induction in the same negative way that it solves the problem of induction.

In this paper I adduce a new argument in support of the claim that IBE is an autonomous form of inference, based on a familiar, yet surprisingly, under-discussed, problem for Hume’s theory of induction. I then use some insights thereby gleaned to argue for the claim that induction is really IBE, and draw some normative conclusions.

Inductive logic generalizes the idea of logical entailment and provides standards for the evaluation of non-conclusive arguments. A main application of inductive logic is the generalization of observational data to theoretical models. In the empirical sciences, the mathematical theory of statistics addresses the same problem. This paper argues that there is no separable purely logical aspect of statistical inference in a variety of complex problems. Instead, statistical practice is often motivated by decision-theoretic considerations and resembles empirical science.

I want to examine a possible solution to the problem of induction-one which, as far as I know, has not been discussed elsewhere. The solution makes crucial use of the notion of objective natural necessity. For the purposes of this discussion, I shall assume that this notion is coherent. I am aware that this assumption is controversial, but I do not have space to examine the issue here.

In this paper, two different theoretical problems of induction are delineated. The first problem is addressed; the second problem is deferred to the sequel to this paper. The first problem of induction is taken to be the seemingly unformalizable nature of traditional inductive arguments. It is shown that the problem does not arise out of some particularly dubious argument form (all inductive argument forms being interderivable), but rather from the presupposition that inductive "logic" (...) is, like deductive logic, assertorie. Rather (it is urged), inductive logic is dialectical in nature. (shrink)

In this article, I argue that arguments from the history of science against scientific realism, like the arguments advanced by P. Kyle Stanford and Peter Vickers, are fallacious. The so-called Old Induction, like Vickers's, and New Induction, like Stanford's, are both guilty of confirmation bias—specifically, of cherry-picking evidence that allegedly challenges scientific realism while ignoring evidence to the contrary. I also show that the historical episodes that Stanford adduces in support of his New Induction are indeterminate between a pessimistic and (...) an optimistic interpretation. For these reasons, these arguments are fallacious, and thus do not pose a serious challenge to scientific realism. (shrink)

Even though evidence underdetermines theory, often in science one theory only is regarded as acceptable in the light of the evidence. This suggests there are additional unacknowledged assumptions which constrain what theories are to be accepted. In the case of physics, these additional assumptions are metaphysical theses concerning the comprehensibility and knowability of the universe. Rigour demands that these implicit assumptions be made explicit within science, so that they can be critically assessed and, we may hope improved. This leads to (...) a new conception of science, one which we need to adopt in order to solve the problem of induction. (shrink)

Inductive generalization asserts that what obtains in known instances can be generalized to all. Its original form is enumerative induction, the earliest form of inductive inference, and it has been elaborated in various ways, largely with the goal of extending its reach. Its principal problem is that it supplies no intrinsic notion of strength of support so that one cannot tell if the generalization has weak or strong support.

My dissertation explores the ways in which Rudolf Carnap sought to make philosophy scientific by further developing recent interpretive efforts to explain Carnap’s mature philosophical work as a form of engineering. It does this by looking in detail at his philosophical practice in his most sustained mature project, his work on pure and applied inductive logic. I, first, specify the sort of engineering Carnap is engaged in as involving an engineering design problem and then draw out the complications (...) of design problems from current work in history of engineering and technology studies. I then model Carnap’s practice based on those lessons and uncover ways in which Carnap’s technical work in inductive logic takes some of these lessons on board. This shows ways in which Carnap’s philosophical project subtly changes right through his late work on induction, providing an important corrective to interpretations that ignore the work on inductive logic. Specifically, I show that paying attention to the historical details of Carnap’s attempt to apply his work in inductive logic to decision theory and theoretical statistics in the 1950s and 1960s helps us understand how Carnap develops and rearticulates the philosophical point of the practical/theoretical distinction in his late work, offering thus a new interpretation of Carnap’s technical work within the broader context of philosophy of science and analytical philosophy in general. (shrink)

In my 2007 paper, “Is There a Problem of Induction for Mathematics?” I rejected the idea that enumerative induction has force for mathematical claims. My core argument was based on the fact that we are restricted to examining relatively small numbers, so our samples are always biased, and hence they carry no inductive weight. In recent years, I have come to believe that this argument is flawed. In particular, while arithmetical samples are indeed biased, my new view is (...) that this bias actually strengthens the inductive support that accrues from them. The reason is that small numbers typically provide a more severe test of general arithmetical claims due to the greater frequency of significant properties and boundary cases among such numbers. In this paper, I describe and defend this new view, which a call Positive Bias Pro-Inductivism. (shrink)