We investigate the notion of definability with respect to a full satisfaction class σ for a model M of Peano arithmetic. It is shown that the σ-definable subsets of M always include a class which provides a satisfaction definition for standard formulas. Such a class is necessarily proper, therefore there exist recursively saturated models with no full satisfaction classes. Nonstandard extensions of overspill and recursive saturation are utilized in developing a criterion for nonstandard definability. Finally, these techniques yield some information (...) concerning the extendibility of full satisfaction classes from one model to another. (shrink)

We prove results about nonstandard formulas in models of Peano arithmetic which complement those of Kotlarski, Krajewski, and Lachlan in [KKL] and [L]. This enables us to characterize both recursive saturation and resplendency in terms of statements about nonstandard sentences. Specifically, a model M of PA is recursively saturated iff M is nonstandard and M-logic is consistent.M is resplendent iff M is nonstandard, M-logic is consistent, and every sentence φ which is consistent in M-logic is contained in a full satisfaction (...) class for M. Thus, for models of PA, recursive saturation can be expressed by a (standard) Σ 1 1 -sentence and resplendency by a ▵ 1 2 -sentence. (shrink)

We show that IE1 proves that every element greater than 1 has a unique factorization into prime powers, although we have no way of recovering the exponents from the prime powers which appear. The situation is radically different in Bézout models of open induction. To facilitate the construction of counterexamples, we describe a method of changing irreducibles into powers of irreducibles, and we define the notion of a frugal homomorphism into Ẑ = ΠpZp, the product of the p-adic integers for (...) each prime p. (shrink)

We show that $\mathrm{IE}_1$ proves that every element greater than 1 has a unique factorization into prime powers, although we have no way of recovering the exponents from the prime powers which appear. The situation is radically different in Bezout models of open induction. To facilitate the construction of counterexamples, we describe a method of changing irreducibles into powers of irreducibles, and we define the notion of a frugal homomorphism into $\hat\mathbb{Z} = \Pi_p\mathbb{Z}_p$, the product of the $p$-adic integers for (...) each prime $p$. (shrink)

While philosophers hold that it is patently absurd to blame robots or hold them morally responsible [1], a series of recent empirical studies suggest that people do ascribe blame to AI systems and robots in certain contexts [2]. This is disconcerting: Blame might be shifted from the owners, users or designers of AI systems to the systems themselves, leading to the diminished accountability of the responsible human agents [3]. In this paper, we explore one of the potential underlying reasons for (...) robot blame, namely the folk's willingness to ascribe inculpating mental states or "mens rea" to robots. In a vignette-based experiment (N=513), we presented participants with a situation in which an agent knowingly runs the risk of bringing about substantial harm. We manipulated agent type (human v. group agent v. AI-driven robot) and outcome (neutral v. bad), and measured both moral judgment (wrongness of the action and blameworthiness of the agent) and mental states attributed to the agent (recklessness and the desire to inflict harm). We found that (i) judgments of wrongness and blame were relatively similar across agent types, possibly because (ii) attributions of mental states were, as suspected, similar across agent types. This raised the question - also explored in the experiment - whether people attribute knowledge and desire to robots in a merely metaphorical way (e.g., the robot "knew" rather than really knew). However, (iii), according to our data people were unwilling to downgrade to mens rea in a merely metaphorical sense when given the chance. Finally, (iv), we report a surprising and novel finding, which we call the inverse outcome effect on robot blame: People were less willing to blame artificial agents for bad outcomes than for neutral outcomes. This suggests that they are implicitly aware of the dangers of overattributing blame to robots when harm comes to pass, such as inappropriately letting the responsible human agent off the moral hook. (shrink)

We propose Rhythmic Relating for autism: a system of supports for friends, therapists, parents, and educators; a system which aims to augment bidirectional communication and complement existing therapeutic approaches. We begin by summarizing the developmental significance of social timing and the social-motor-synchrony challenges observed in early autism. Meta-analyses conclude the early primacy of such challenges, yet cite the lack of focused therapies. We identify core relational parameters in support of social-motor-synchrony and systematize these using the communicative musicality constructs: pulse; quality; (...) and narrative. Rhythmic Relating aims to augment the clarity, contiguity, and pulse-beat of spontaneous behavior by recruiting rhythmic supports and relatable vitality; facilitating the predictive flow and just-ahead-in-time planning needed for good-enough social timing. From here, we describe possibilities for playful therapeutic interaction, small-step co-regulation, and layered sensorimotor integration. Lastly, we include several clinical case examples demonstrating the use of Rhythmic Relating within four different therapeutic approaches. These clinical case examples are introduced here and several more are included in the Supplementary Material. A suite of pilot intervention studies is proposed to assess the efficacy of combining Rhythmic Relating with different therapeutic approaches in playful work with individuals with autism. Further experimental hypotheses are outlined, designed to clarify the significance of certain key features of the Rhythmic Relating approach. (shrink)

We might think that thought experiments are at their most powerful or most interesting when they produce new knowledge. This would be a mistake; thought experiments that seek understanding are just as powerful and interesting, and perhaps even more so. A growing number of epistemologists are emphasizing the importance of understanding for epistemology, arguing that it should supplant knowledge as the central notion. In this chapter, I bring the literature on understanding in epistemology to bear on explicating the different ways (...) that thought experiments increase three important kinds of understanding: explanatory, objectual and practical. (shrink)

Sometimes we learn through the use of imagination. The epistemology of imagination asks how this is possible. One barrier to progress on this question has been a lack of agreement on how to characterize imagination; for example, is imagination a mental state, ability, character trait, or cognitive process? This paper argues that we should characterize imagination as a cognitive ability, exercises of which are cognitive processes. Following dual process theories of cognition developed in cognitive science, the set of imaginative processes (...) is then divided into two kinds: one that is unconscious, uncontrolled, and effortless, and another that is conscious, controlled, and effortful. This paper outlines the different epistemological strengths and weaknesses of the two kinds of imaginative process, and argues that a dual process model of imagination helpfully resolves or clarifies issues in the epistemology of imagination and the closely related epistemology of thought experiments. (shrink)

Imagination is important for many things in science: solving problems, interpreting data, designing studies, etc. Philosophers of imagination typically account for the productive role played by imagination in science by focusing on how imagination is constrained, e.g., by using self-imposed rules to infer logically, or model events accurately. But the constraints offered by these philosophers either constrain too much, or not enough, and they can never account for uses of imagination that are needed to break today’s constraints in order to (...) make progress tomorrow. Thus, epistemology of imagination needs to make room for an element of epistemological anarchy. (shrink)

What role does the imagination play in scientific progress? After examining several studies in cognitive science, I argue that one thing the imagination does is help to increase scientific understanding, which is itself indispensable for scientific progress. Then, I sketch a transcendental justification of the role of imagination in this process.

Scientists imagine for epistemic reasons, and these imaginings can be better or worse. But what does it mean for an imagining to be epistemically better or worse? There are at least three metaepistemological frameworks that present different answers to this question: epistemological consequentialism, deontic epistemology, and virtue epistemology. This paper presents empirical evidence that scientists adopt each of these different epistemic frameworks with respect to imagination, but argues that the way they do this is best explained if scientists are fundamentally (...) epistemic consequentialists about imagination. (shrink)

This is the introduction to the Routledge Companion to Thought Experiments.

In this article, we analyse the evidential value of the corpus of experimental philosophy. While experimental philosophers claim that their studies provide insight into philosophical problems, some philosophers and psychologists have expressed concerns that the findings from these studies lack evidential value. Barriers to evidential value include selection bias and p-hacking. To find out whether the significant findings in x-phi papers result from selection bias or p-hacking, we applied a p-curve analysis to a corpus of 365 x-phi chapters and articles. (...) Our results suggest that this corpus has evidential value, although there are hints of p-hacking in a few parts of the x-phi corpus. (shrink)

I claim that one way thought experiments contribute to scientific progress is by increasing scientific understanding. Understanding does not have a currently accepted characterization in the philosophical literature, but I argue that we already have ways to test for it. For instance, current pedagogical practice often requires that students demonstrate being in either or both of the following two states: 1) Having grasped the meaning of some relevant theory, concept, law or model, 2) Being able to apply that theory, concept, (...) law or model fruitfully to new instances. Three thought experiments are presented which have been important historically in helping us pass these tests, and two others that cause us to fail. Then I use this operationalization of understanding to clarify the relationships between scientific thought experiments, the understanding they produce, and the progress they enable. I conclude that while no specific instance of understanding (thus conceived) is necessary for scientific progress, understanding in general is. (shrink)

Thought experiments are a means of imaginative reasoning that lie at the heart of philosophy, from the pre-Socratics to the modern era, and they also play central roles in a range of fields, from physics to politics. The Routledge Companion to Thought Experiments is an invaluable guide and reference source to this multifaceted subject. Comprising over 30 chapters by a team of international contributors, the Companion covers the following important areas: -/- · the history of thought experiments, from antiquity to (...) the trolley problem and quantum non-locality; -/- · thought experiments in the humanities, arts, and sciences, including ethics, physics, theology, biology, mathematics, economics, and politics; -/- · theories about the nature of thought experiments; -/- · new discussions concerning the impact of experimental philosophy, cross-cultural comparison studies, metaphilosophy, computer simulations, idealization, dialectics, cognitive science, the artistic nature of thought experiments, and metaphysical issues. -/- This broad ranging Companion goes backwards through history and sideways across disciplines. It also engages with philosophical perspectives from empiricism, rationalism, naturalism, skepticism, pluralism, contextualism, and neo-Kantianism to phenomenology. This volume will be valuable for anyone studying the methods of philosophy or any discipline that employs thought experiments, as well as anyone interested in the power and limits of the mind. (shrink)

Computational systems biologists create and manipulate computational models of biological systems, but they do not always have straightforward epistemic access to the content and behavioural profile of such models because of their length, coding idiosyncrasies, and formal complexity. This creates difficulties both for modellers in their research groups and for their bioscience collaborators who rely on these models. In this paper we introduce a new kind of visualization that was developed to address just this sort of epistemic opacity. The visualization (...) is unusual in that it depicts the dynamics and structure of a computer model instead of that model’s target system, and because it is generated algorithmically. Using considerations from epistemology and aesthetics, we explore how this new kind of visualization increases scientific understanding of the content and function of computer models in systems biology to reduce epistemic opacity. (shrink)

John D. Norton defends an empiricist epistemology of thought experiments, the central thesis of which is that thought experiments are nothing more than arguments. Philosophers have attempted to provide counterexamples to this claim, but they haven’t convinced Norton. I will point out a more fundamental reason for reformulation that criticizes Norton’s claim that a thought experiment is a good one when its underlying logical form possesses certain desirable properties. I argue that by Norton’s empiricist standards, no thought experiment is ever (...) justified in any deep sense due to the properties of its logical form. Instead, empiricists should consider again the merits of evaluating thought experiments more like laboratory experiments, and less like arguments. (shrink)

Jaswal & Akhtar provide several quotes ostensibly from people with autism but obtained via the discredited techniques of Facilitated Communication and the Rapid Prompting Method, and they do not acknowledge the use of these techniques. As a result, their argument is substantially less convincing than they assert, and the article lacks transparency.

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)

Can an ugly experiment be a good experiment? Philosophers have identified many beautiful experiments and explored ways in which their beauty might be connected to their epistemic value. In contrast, the present chapter seeks out (and celebrates) ugly experiments. Among the ugliest are those being designed by AI algorithms. Interestingly, in the contexts where such experiments tend to be deployed, low aesthetic value correlates with high epistemic value. In other words, ugly experiments can be good. Given this, we should conclude (...) that beauty is not generally necessary or sufficient for epistemic value, and increasing beauty will not generally tend to increase epistemic value. (shrink)

Scientists imagine constantly. They do this when generating research problems, designing experiments, interpreting data, troubleshooting, drafting papers and presentations, and giving feedback. But when and how do scientists learn how to use imagination? Across 6 years of ethnographic research, it has been found that advanced career scientists feel comfortable using and discussing imagination, while graduate and undergraduate students of science often do not. In addition, members of marginalized and vulnerable groups tend to express negative views about the strength of their (...) imaginations and the general usefulness of imagination in science. After introducing these findings and discussing the typical relationship between a scientist and their imagination across a career, we argue that reducing the number or power of active imaginations in science is epistemically counterproductive. We suggest several ways to bring imagination back into science in a more inclusive way, especially through courses on imagination for scientists, good role models, and exemplar-based learning. (shrink)

The history of the philosophy of thought experiments has touched on the work of Kuhn, Popper, Duhem, Mach, Lakatos, and other big names of the 20th century, but so far, almost nothing has been written about Paul Feyerabend. His most influential work was Against Method, 8 chapters of which concern a case study of Galileo with a specific focus on Galileo’s thought experiments. In addition, the later Feyerabend was very interested in what might be called the epistemology of drama, including (...) stories and myths. This paper brings these different aspects of Feyerabend’s work together in an attempt to present what might have been his considered views on scientific thought experiments. I conclude by contrasting Feyerabend’s ideas with two modern currents in the debate surrounding thought experiments: 1) the claim that the epistemology of thought experiments is just the epistemology of deductive or inductive arguments, and 2) the claim that the specifically narrative quality of thought experiments must be taken into account if we want a complete epistemology of thought experiments. (shrink)

Thought experiments, models, diagrams, computer simulations, and metaphors can all be understood as tools of the imagination. While these devices are usually treated separately in philosophy of science, this paper provides a unified account according to which tools of the imagination are epistemically good insofar as they improve scientific imaginings. Improving scientific imagining is characterized in terms of epistemological consequences: more improvement means better consequences. A distinction is then drawn between tools being good in retrospect, at the time, and in (...) general. In retrospect, tools are evaluated straightforwardly in terms of the quality of their consequences. At the cutting edge, tools are evaluated positively insofar as there is reason to believe that using them will have good consequences. Lastly, tools can be generally good, insofar as their use encourages the development of epistemic virtues, which are good because they have good epistemic consequences. (shrink)

Philosophical conceptual analysis is an experimental method. Focusing on this helps to justify it from the skepticism of experimental philosophers who follow Weinberg, Nichols & Stich. To explore the experimental aspect of philosophical conceptual analysis, I consider a simpler instance of the same activity: everyday linguistic interpretation. I argue that this, too, is experimental in nature. And in both conceptual analysis and linguistic interpretation, the intuitions considered problematic by experimental philosophers are necessary but epistemically irrelevant. They are like variables introduced (...) into mathematical proofs which drop out before the solution. Or better, they are like the hypotheses that drive science, which do not themselves need to be true. In other words, it does not matter whether or not intuitions are accurate as descriptions of the natural kinds that undergird philosophical concepts; the aims of conceptual analysis can still be met. (shrink)

Paul Thagard has recently argued that thought experiments are dangerous and misleading when we try to use them as evidence for claims. This paper refutes his skepticism. Building on Thagard’s own work in cognitive science, I suggest that Thagard has much that is positive to say about how thought experiments work. My last section presents some new directions for research on the intersection between thought experiments and cognitive science.

Scientists recognize the necessity of imagination for solving tough problems. But how does the cognitive faculty responsible for daydreaming help in solving scientific problems? Philosophers claim that imagination is informative only when it is constrained to be maximally realistic. However, using a case study from space science, we show that scientists use imagination intentionally to break reality-oriented constraints. To do this well, they first target low-confidence constraints, and then higher-confidence constraints, until a plausible solution is found. This paper exemplifies a (...) new approach to epistemology of imagination that focuses on sets of imaginings (rather than individual imaginings), and responsible (rather than reliable) imaginings. (shrink)

Imagination is extremely important for science, yet very little is known about how scientists actually use it. Are scientists taught to imagine? What do they value imagination for? How do social and disciplinary factors shape it? How is the labor of imagining distributed? These questions should be high priority for anyone who studies or practices science, and this paper argues that the best methods for addressing them are qualitative. I summarize a few preliminary findings derived from recent interview-based and observational (...) qualitative studies that I have performed. These finding include: (i) imagination is only valued for use in addressing maximally specific problems, and only when all else fails; (ii) younger scientists and scientists who are members of underrepresented groups express less positive views about imagination in general, and have less confidence in their own imaginations; (iii) while scientists seem to employ various epistemological frameworks to evaluate imaginings, overall they appear to be epistemic consequentialists about imagination, and this holds also for their evaluations of the tools they use to extend the power of their imaginations. I close by discussing the epistemic and ethical consequences of these findings, and then suggesting a few research avenues that could be explored next as we move forward in the study of scientific imagination. (shrink)

An observation of Hume’s has received a lot of attention over the last decade and a half: Although we can standardly imagine the most implausible scenarios, we encounter resistance when imagining propositions at odds with established moral (or perhaps more generally evaluative) convictions. The literature is ripe with ‘solutions’ to this so-called ‘Puzzle of Imaginative Resistance’. Few, however, question the plausibility of the empirical assumption at the heart of the puzzle. In this paper, we explore empirically whether the difficulty we (...) witness in imagining certain propositions is indeed due to claim type (evaluative v. non-evaluative) or whether it is much rather driven by mundane features of content. Our findings suggest that claim type plays but a marginal role, and that there might hence not be much of a ‘puzzle’ to be solved. (shrink)

As Nelson Goodman highlighted, there are two main senses of “abstract” that can be found in discussions about abstract art. On the one hand, a representation is abstract if it leaves out certain features of its target. On the other hand, something can be abstract to the extent that it does not represent a concrete subject. The first sense of “abstract” is well-known in philosophy of science. For example, philosophers discuss mathematical models of physical, biological, and economic systems as being (...) abstract in this sense. However, it is the second sense that dominates discussions of abstract art in aesthetics. For example, abstract art was (and is) considered revolutionary precisely for being non-figurative. Through an analysis of artists including Kandinsky, Malevich, and Mondrian, we develop a reading of this second sense, which we call “generative abstraction,” as opposed to “subtractive” abstraction. Generative abstraction is a process in which a new artifact is created which does not represent the initial concrete target system that inspired it (if there was one), where the artifact’s features are explored for their own sake, and where the “language” of the new artifact is in some way more “universal.” Focusing on this sense of abstraction is helpful in revealing the complexity of the process of crafting an abstract artifact, in problematizing the notion that abstraction can always be un-done (or concretized), as well as revealing new ways for abstractions to be epistemically (un)successful. (shrink)

Recent research shows – somewhat astonishingly – that people are willing to ascribe moral blame to AI-driven systems when they cause harm [1]–[4]. In this paper, we explore the moral- psychological underpinnings of these findings. Our hypothesis was that the reason why people ascribe moral blame to AI systems is that they consider them capable of entertaining inculpating mental states (what is called mens rea in the law). To explore this hypothesis, we created a scenario in which an AI system (...) runs a risk of poisoning people by using a novel type of fertilizer. Manipulating the computational (or quasi-cognitive) abilities of the AI system in a between-subjects design, we tested whether people’s willingness to ascribe knowledge of a substantial risk of harm (i.e., recklessness) and blame to the AI system. Furthermore, we investigated whether the ascription of recklessness and blame to the AI system would influence the perceived blameworthiness of the system’s user (or owner). In an experiment with 347 participants, we found (i) that people are willing to ascribe blame to AI systems in contexts of recklessness, (ii) that blame ascriptions depend strongly on the willingness to attribute recklessness and (iii) that the latter, in turn, depends on the perceived “cognitive” capacities of the system. Furthermore, our results suggest (iv) that the higher the computational sophistication of the AI system, the more blame is shifted from the human user to the AI system. (shrink)

Originally published in 1957, this book collects together large sections of important tracts from a variety of political documents, particularly those concerned with democracy, communism, Protestantism or Catholicism. The extracts come from a wide range of authors including Bertrand Russell, Karl Marx, John Locke and Pope Pius XII. This book will be of value to anyone seeking an overview of the key political divisions in the late 20th century or who is interested in political theory generally.

Metaphors are found all throughout science: in published papers, working hypotheses, policy documents, lecture slides, grant proposals, and press releases. They serve different functions, but perhaps most striking is the way they enable understanding, of a theory, phenomenon, or idea. In this paper, we leverage recent advances on the nature of metaphor and the nature of understanding to explore how they accomplish this feat. We attempt to shift the focus away from the epistemic value of the content of metaphors, to (...) the epistemic value of the metaphor’s consequences. Many famous scientific metaphors are epistemically good, not primarily because of what they say about the world, but because of how they cause us to think. Specifically, metaphors increase understanding either by improving our sets of representations, or by making it easier for us to encode and process data about complex subjects by changing how we are disposed to conceptualize those subjects. This view hints towards new positions concerning testimonial understanding, factivity, abilities, discovery via metaphor, and the relation between metaphors and models. (shrink)

This is the introduction to a special issue of HOPOS on the history of the philosophy of thought experiments.

In Rethinking the Enlightenment, Dr. Stuart demonstrates that the three primary strategies employed during the Enlightenment -- conflict, engagement, and retreat -- are time-tested methods that should be employed in our own anti-Christian age"--The publisher.