Paul Bartha

Green nudges (GNs) are increasingly popular behavioral interventions aimed at mitigating environmentally mediated harm, particularly in the context of climate change. The justification of GNs traditionally relies on cost-benefit analysis (CBA), which quantifies the total costs and benefits, factoring in probabilities to maximize expected utility. However, the application of CBA faces significant challenges when GNs involve potential catastrophic outcomes associated with climate change and climate nudging. We argue that the qualitative distinction between catastrophic and non-catastrophic outcomes poses a challenge for traditional CBA. While CBA is adept at assessing ordinary costs and benefits, it struggles to accommodate the putative catastrophic outcomes linked to climate change and climate nudging. To address this challenge, this article considers the lexical precautionary principle (LPP) as a viable decision-making framework for climate nudging. Unlike CBA's decision rule, maximize expected utility, LPP maximizes lexical utility, thereby prioritizing the avoidance of catastrophic outcomes.

This concluding chapter outlines how my theory of analogical arguments can be extended to analogies in scientific revolutions and, more generally, outside science. As an example, Hacking's analogical argument for entity realism is presented and evaluated. The chapter also argues that a solid understanding of analogical arguments sheds light on thought experiments. Finally, it is argued that a good normative theory of analogical arguments has specific implications for current empirical and computational work on analogical reasoning.

This chapter has two purposes. First, it explores the connection between analogical reasoning and symmetry to provide a second justification for the argument form, independent of the one offered in chapter 7. The chapter proposes that good analogical arguments are sanctioned by norms of symmetry and Reflection, as expounded by van Fraassen. This idea is elaborated first in a nonprobabilistic setting and then in a probabilistic framework. It is argued that a psychological construal of the relationship between symmetry and probability, as championed by de Finetti and others, is inadequate. The second objective of the chapter is to integrate analogical arguments into a Bayesian model of theoretical confirmation by refining Salmon's idea that analogical arguments contribute to establishing non‐negligible prior probability for hypotheses.

This chapter provides a defense of analogical reasoning by linking it to standard pragmatic virtues that guide us in the choice of scientific theories. The idea is based on a high‐level analogy between science and the law. In case law, the basic justification for _stare decisis_ (following precedent) is that it promotes consistency and predictability while still permitting the evolution of the legal system. We seek an analogous balance when we turn to plausibility arguments in science. It is argued that analogical arguments that satisfy the general principles of the articulation model strike an excellent balance between conservative epistemic values (such as simplicity and coherence with existing theory) and progressive epistemic values (such as fruitfulness and theoretical unification).

This chapter develops the thesis that the goal of an analogical argument is to generalize a particular logical, causal or explanatory relationship. Three separate types of similarity prominent in scientific analogies are characterized: feature matching, formal similarity, and parametric similarity (or continuity). These types are linked to prominent forms of generalization: common kinds, common mathematical formalisms and invariant relations. Notably, the chapter considers—and rejects—Steiner's thesis that an inscrutable class of “Pythagorean” analogies played a fundamental role in advancing nineteenth‐ and twentieth‐century physics.

This chapter is devoted to the special class of mathematical analogies. Following Poincaré, it is argued that analogical arguments in mathematics provide clear support for a link between good analogies and fruitful generalization. At the same time, a consideration of mathematical examples serves to refine and deepen the theory of chapter 4. Specifically, the chapter addresses the role of similarity in mathematical analogies, the philosophical basis of analogical arguments, and the use of analogy in extended mathematical research programs.

This chapter proposes the _articulation model_ for evaluating analogical arguments. The core of the model consists of two principles. First, there must be a _prior association_, a clear relationship in the source domain between the known similarities and the further similarity projected to hold in the target domain. Second, there must be _potential for generalization_, reason to believe that the same type of relationship could hold in the target domain. Rather than assessing an analogical argument in terms of overall similarity between two domains, the central idea is that similarity must be assessed relative to a model of the source. The chapter proposes a simple classification of analogical arguments corresponding to different types of prior association, together with evaluation criteria tailored to each type. The theory is extended to handle reasoning with multiple analogies.

This chapter selectively reviews computational theories of analogical reasoning from Evans, Gentner, Holyoak and Thagard, Ashley, Carbonell, and Hofstadter. While these theories provide insight into the processes involved in analogical reasoning, many of them operate with a perceptual model of analogical reasoning and appear to neglect normative questions. It is argued that most of the computational theories do, at least implicitly, incorporate normative principles and that those principles need to be examined critically. In particular, the chapter takes a close look at Gentner's _systematicity principle_. It is alleged that systematicity per se neither produces nor explains the plausibility of analogical arguments.

This chapter discusses attempts by Aristotle, Hesse, Mill and others to deal with two problems: (1) finding criteria for evaluating analogical arguments, and (2) providing some form of philosophical justification. As regards the first problem, we can identify a valuable “commonsense” model in Hesse's work, though one that is capable of refinement. As regards the second problem, it is argued that most analyses to date have unsuccessfully cast the analogical argument as an incomplete form of deductive argument, as some type of sampling argument, or as induction by enumeration. Agassi's skeptical rejection of all analogical reasoning is criticized because it too misrepresents the logical structure of the argument form.

This introductory chapter motivates the importance of a normative theory of analogical _arguments_ as part of the broader project of understanding analogical reasoning. The chapter further recommends that we start with analogical arguments in science and mathematics, where we find clear and intuitively persuasive examples. Analogical arguments in science aim, in varying degrees, to establish the plausibility of a hypothesis. A distinction is made between a probabilistic notion of plausibility as reasonable credence, and a nonprobabilistic notion of prima facie plausibility, roughly the idea that a hypothesis is worthy of serious investigation. A basic characterization of analogical arguments is provided along with a preview of the theory to be developed in the book.

Lexical utilities have emerged as a promising way to model the precautionary principle in recent years. But some object that the lexical precautionary principle is hypersensitive because slight increases in risk of catastrophe can prompt it to recommend precautions regardless of cost. This article defends the lexical precautionary principle from the hypersensitivity objection by explaining why costs matter for what it recommends. In addition, we show how minimizing the probability of catastrophe tends to make the lexical precautionary principle insensitive to the precise dividing line between catastrophe and non-catastrophe. Finally, our discussion leads to a novel interpretation and justification of a de minimis condition for invoking the precautionary principle.

This article explores the consequences of falling costs of solar and wind power for the ethics of climate change mitigation. We suggest that price competitiveness of renewables reveals a divergence of interest between fossil fuel consumers and producers: cheap renewables strengthen precautionary arguments for aggressive mitigation for consumers but threaten the economic base of producers. As existing applications of the precautionary principle to climate change do not address this issue, we develop a novel approach based on lexical utilities. Given the premise that climate catastrophe entails economic catastrophe but not vice versa, we argue that both producers and consumers should favor mitigation.

We claim that a moral obligation to take climate leadership by means of unilateral mitigation depends on the existence of a plausible follow-the-leader mechanism whereby unilateral mitigation by some increases the probability of sufficient mitigation by others to avert catastrophic climate impacts. By understanding these mechanisms, we can better articulate the obligation for climate leadership across various sectors, from government to individual actors, in the fight against climate change. [Open access]

The many-gods objection is perhaps the most famous criticism levelled against Pascal’s wager. This chapter offers a response that combines two main ideas. The first is the development of the ‘many-wagers’ model, a dynamics of rational deliberation that allows the credences in a many-gods problem to evolve in a rationally permissible manner, even in the absence of relevant new evidence. The second idea is that stability of these credences, within this evolutionary model, is a necessary condition for viability. This stability condition provides the Pascalian with convincing responses to a wide range of many-gods problems. Thus, many versions of the many-gods objection contribute no difficulties for Pascal’s wager beyond those that already plague its classic formulation with just one deity.

Pascal’s Wager is based on the idea that “wagering for God” has infinite expected utility, assuming non-zero probability of an infinite reward (salvation). But infinite positive utility appears to trap us in puzzles and paradoxes. Similar difficulties arise for decisions where there is a risk of catastrophic outcomes (negative infinite utility). The precautionary principle (PP) has emerged as a tool for making such decisions, especially those involving environmental catastrophe. Commentators have noted the analogy between Pascal’s Wager and PP. They use it negatively: careless formulations of PP are vulnerable to analogues of wellknown objections to Pascal’s Wager. In this paper, I use the analogy positively: successful replies to objections against PP can be adapted to yield successful responses to prominent objections against Pascal’s Wager. Furthermore, these responses do not require that we give up the use of infinite utilities in either Pascal’s Wager or precautionary reasoning.

We examine a distinctive kind of problem for decision theory, involving what we call discontinuity at infinity. Roughly, it arises when an infinite sequence of choices, each apparently sanctioned by plausible principles, converges to a ‘limit choice’ whose utility is much lower than the limit approached by the utilities of the choices in the sequence. We give examples of this phenomenon, focusing on Arntzenius et al.’s Satan’s apple, and give a general characterization of it. In these examples, repeated dominance reasoning (a paradigm of rationality) apparently gives rise to a situation closely analogous to having intransitive preferences (a paradigm of irrationality). Indeed, the agents in these examples are vulnerable to a money pump set-up despite having preferences that exhibit no obvious defect of rationality. We explore several putative solutions to such problems, particularly those that appeal to binding and to deliberative dynamics. We consider the prospects for these solutions, concluding that if they fail, the examples show that money pump arguments are invalid.

The Principle of Indifference, which dictates that we ought to assign two outcomes equal probability in the absence of known reasons to do otherwise, is vulnerable to well-known objections. Nevertheless, the appeal of the principle, and of symmetry-based assignments of equal probability, persists. We show that, relative to a given class of symmetries satisfying certain properties, we are justified in calling certain outcomes equally probable, and more generally, in defining what we call relative probabilities. Relative probabilities are useful in providing a generalized approach to conditionalization. The technique is illustrated by application to simple examples.

In analogical reasoning, observations about one or more source domains provide varying degrees of support for a conjecture about a target domain. Norton (2021) challenges the usefulness of formal models of analogical inference. Other philosophers (Dardashti et al. 2019) develop just such formal models in order to show how analogue experiments can confirm a hypothesis, even when the target domain is inaccessible. This paper defends the value of quasi-formal models of analogical reasoning. Such models are broadly compatible with Norton’s position, but help to clarify the structure of analogical reasoning and to identify basic requirements for a good analogical inference.

Confronted with the possibility of severe environmental harms, such as catastrophic climate change, some researchers have suggested that we should abandon the principle at the heart of standard decision theory—the injunction to maximize expected utility—and embrace a different one: the Precautionary Principle. Arguably, the most sophisticated philosophical treatment of the Precautionary Principle is due to Steel. Steel interprets PP as a qualitative decision rule and appears to conclude that a quantitative decision-theoretic statement of PP is both impossible and unnecessary. In this article, we propose a decision-theoretic formulation of PP in terms of lexical utilities. We show that this lexical model is largely faithful to Steel’s approach, but also that it corrects three problems with Steel’s account and clarifies the relationship between PP and standard decision theory. Using a range of examples, we illustrate how the lexical model can be used to explore a variety of issues related to precautionary reasoning.

We provide a solution to the well-known “Shooting-Room” paradox, developed by John Leslie in connection with his Doomsday Argument. In the “Shooting-Room” paradox, the death of an individual is contingent upon an event that has a 1/36 chance of occurring, yet the relative frequency of death in the relevant population is 0.9. There are two intuitively plausible arguments, one concluding that the appropriate subjective probability of death is 1/36, the other that this probability is 0.9. How are these two values to be reconciled? We show that only the first argument is valid for a standard, countably additive probability distribution. However, both lines of reasoning are legitimate if probabilities are non-standard. The subjective probability of death rises from 1/36 to 0.9 by conditionalizing on an event that is not measurable, or whose probability is zero. Thus we can sometimes meaningfully ascribe conditional probabilities even when the event conditionalized upon is not of positive finite (or even infinitesimal) measure.

Some environmental ethicists and economists argue that attributing infinite value to the environment is a good way to represent an absolute obligation to protect it. Others argue against modelling the value of the environment in this way: the assignment of infinite value leads to immense technical and philosophical difficulties that undermine the environmentalist project. First, there is a problem of discrimination: saving a large region of habitat is better than saving a small region; yet if both outcomes have infinite value, then decision theory prescribes indifference. Second, there is a problem of swamping probabilities: an act with a small but positive probability of saving an endangered species appears to be on par with an act that has a high probability of achieving this outcome, since both have infinite expected value. Our paper shows that a relative concept of infinite value can be meaningfully defined, and provides a good model for securing the priority of the natural environment while avoiding the failures noted by sceptics about infinite value. Our claim is not that the relative infinity utility model gets every detail correct, but rather that it provides a rigorous philosophical framework for thinking about decisions affecting the environment.

Carter and Leslie (1996) have argued, using Bayes's theorem, that our being alive now supports the hypothesis of an early 'Doomsday'. Unlike some critics (Eckhardt 1997), we accept their argument in part: given that we exist, our existence now indeed favors 'Doom sooner' over 'Doom later'. The very fact of our existence, however, favors 'Doom later'. In simple cases, a hypothetical approach to the problem of 'old evidence' shows that these two effects cancel out: our existence now yields no information about the coming of Doom. More complex cases suggest a move from countably additive to non-standard probability measures.

In his famous Wager, Blaise Pascal offers the reader an argument that it is rational to strive to believe in God. Philosophical debates about this classic argument have continued until our own times. This volume provides a comprehensive examination of Pascal's Wager, including its theological framework, its place in the history of philosophy, and its importance to contemporary decision theory. The volume starts with a valuable primer on infinity and decision theory for students and non-specialists. A sequence of chapters then examines topics including the Wager's underlying theology, its influence on later philosophical figures, and contemporary analyses of the Wager including Alan Hájek's challenge to its validity, the many gods objection, and the ethics of belief. The final five chapters explore various ways in which the Wager has inspired contemporary decision theory, including questions related to infinite utility, imprecise probabilities, and infinitesimals.

Analogical reasoning plays a significant role in the evolution of scientific thought. Not only is analogy extensively used in the early stages of investigation to demonstrate the plausibility of hypotheses, but in some fields, such as archaeology and evolutionary biology, it is often the strongest possible form of theoretical confirmation. This widely used form of reasoning, however, has seldom been subjected to rigorous examination by philosophers of science. Not surprisingly, there is a notable absence of standards for distinguishing between 'good' and 'bad' analogies in scientific reasoning. This dissertation proposes such criteria. ;The starting point is Hesse's principle that for a legitimate analogical argument, causal relations must obtain between the known and projected similarities in one domain, and there must be "no compelling reasons" for denying that "causal relations of the same kind" may hold in the other domain. The dissertation goes beyond this principle by incorporating causal relations within a broader framework of logical, explanatory and statistical connections. It then articulates the nature of these connections on the basis of contemporary accounts of scientific explanation, mathematical proof and statistical correlation. In effect, it formulates a set of models of analogical reasoning corresponding to the most prominent types of connections that occur in such fields as mathematics, physics, biology and archaeology. The dissertation uses these models to define and test workable criteria for a 'good' scientific analogy. ;The dissertation also discusses computational approaches to analogy, such as case-based reasoning. While CBR programs successfully perform a species of analogical reasoning, they work only in specialized and well-defined situations where knowledge of relevant factors is already established. Consequently, their applicability to exploratory science appears to be limited. ;The dissertation contributes to confirmation theory by extending the Bayesian approach to evaluating scientific hypotheses. Within the Bayesian framework, a recognized problem has been to justify the assumption that a hypothesis has non-negligible prior probability. A number of writers have suggested that analogies might be relevant to this aspect of the confirmation process. The dissertation affirms this intuition, and develops a novel procedure for providing the required justification.