Christopher Belanger

In this article I examine two mathematical definitions of observational equivalence, one proposed by Charlotte Werndl and based on manifest isomorphism, and the other based on Ornstein and Weiss’s ε-congruence. I argue, for two related reasons, that neither can function as a purely mathematical definition of observational equivalence. First, each definition permits of counterexamples; second, overcoming these counterexamples will introduce non-mathematical premises about the systems in question. Accordingly, the prospects for a broadly applicable and purely mathematical definition of observational equivalence are unpromising. Despite this critique, I suggest that Werndl’s proposals are valuable because they clarify the distinction between provable and unprovable elements in arguments for observational equivalence.

In Laws and Lawmakers: Science, Metaphysics, and the Laws of Nature, Marc Lange has presented an engagingly written, tightly argued, and novel philosophical account of the laws of nature. One of the intuitions behind the notion of a law of nature is, roughly, that of the many regularities we observe in the world there are some which appear to be due to mere happen-stance (“accidental” regularities, in the philosopher’s jargon), while others, which we call “laws,” seem to be possessed of a degree of necessity. For example, if the only music ever to come out of my stereo system during the entirety of its existence were that of James Brown, we would term this an accidental regularity: it seems that it could have been otherwise had the world been different, perhaps by the stereo having a different owner or my having different tastes. On the other hand, the various relations and properties that determine the electrical functioning of my stereo seem more necessary and lawlike: presumably Ohm’s law would have held even had my stereo never been built.1 But even if Ohm’s law is somehow necessary, it seems less necessary than other “broadly logical” truths. Certainly Ohm’s law could have been different, perhaps by a factor of two, yet it seems unreasonable to say that the number 6 could have been prime. Although many philosophers, and certainly most scientists, will readily agree that there is a difference between logical, law-like, and accidental regularities, spelling out the nature of this difference has proved a remarkably difficult task. It is precisely this puzzle which Lange intends Laws and Lawmakers to address. In this review I shall first give a quick and broad outline of Lange’s account of natural laws as I understand it, followed by a brief summary of the contents of the book, and then close with a few critical comments

Scientific models are often said to be more or less general depending on how many cases they cover. In this paper we argue that the cardinality of cases is insufficient as a metric of generality, and we present a novel account based on measure theory. This account overcomes several problems with the cardinality approach, and additionally provides some insight into the nature of assessments of generality. Specifically, measure theory affords a natural and quantitative way of describing local spaces of possibility. The generality of models can be understood as the measure of possibilities to which the models apply. In order to illustrate our view, we consider the example of structural genomics, the ongoing project of building three-dimensional models of biological macromolecules like proteins. Using measure theory, we interpret the practice of homology modeling, where such models are understood to apply widely but imperfectly to the space of possible proteins

In this paper I examine two mathematical definitions of observational equivalence, one proposed by Charlotte Werndl and based on manifest isomorphism, and the other based on Ornstein and Weiss's ε-congruenceε-congruence. I argue, for two related reasons, that neither can function as a purely mathematical definition of observational equivalence. First, each definition permits of counterexamples; second, overcoming these counterexamples will introduce non-mathematical premises about the systems in question. Accordingly, the prospects for a broadly applicable and purely mathematical definition of observational equivalence are unpromising. Despite this critique, I suggest that Werndl's proposals are valuable because they clarify the distinction between provable and unprovable elements in arguments for observational equivalence

Research suggests that the experience of meaningless work is prevalent in various occupations, and that it is destructive for organizations and individuals, making this an issue of major ethical importance. In this paper, we present the results of a qualitative study based on interviews with Canadian public servants who self-identified as experiencing meaninglessness at work. Our main goal is to better understand participants' responses to the experience of meaningless work and the broader implications their experiences had on the rest of their lives. We surface and explore the harms inflicted on participants through their experiences with meaningless work and suggest that these harms may have been made worse by structural features of our study's public-sector setting. We contribute to organization studies literature by showing the intersection of meaningless work with three related concepts: bullshit jobs, empty labour, and functional stupidity and argue that our empirical findings complement and complicate these frameworks by presenting the complex but hidden emotional experiences that can accompany outwardly observable workplace behaviours.