Traditional epistemic and doxastic logics cannot deal with inconsistent beliefs nor do they represent the evidence an agent possesses. So-called ‘evidence logics’ have been introduced to deal with both of those issues. The semantics of these logics are based on neighbourhood or hypergraph frames. The neighbourhoods of a world represent the basic evidence available to an agent. On one view, beliefs supported by evidence are propositions derived from all maximally consistent collections evidence. An alternative concept of beliefs takes them to (...) be propositions derivable from consistent partitions of one’s inconsistent evidence; this is known as Schotch-Jennings Forcing. This paper develops a modal logic based on the hypergraph semantics to represent Schotch-Jennings Forcing. The modal language includes an operator U(φ1,…,φn;ψ)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$U(\varphi _1, \ldots, \varphi _n;\psi )$$\end{document} which is similar to one introduced in Instantial Neighbourhood Logic. It is of variable arity and the input formulas enjoy distinct roles. The U operator expresses that all evidence at a particular world that supports ψ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\psi $$\end{document} can be supported by at least one of the φi\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varphi _i$$\end{document}s. U can then be used to express that all the evidence available can be unified by the finite set of formulas φ1,…,φn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varphi _1,\ldots, \varphi _n$$\end{document} if ψ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\psi $$\end{document} is taken to be ⊤\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\top $$\end{document}. Future developments will then use that semantics as the basis for a doxastic logic akin to evidence logics. (shrink)

We argue that artificial networks are explainable and offer a novel theory of interpretability. Two sets of conceptual questions are prominent in theoretical engagements with artificial neural networks, especially in the context of medical artificial intelligence: Are networks explainable, and if so, what does it mean to explain the output of a network? And what does it mean for a network to be interpretable? We argue that accounts of “explanation” tailored specifically to neural networks have ineffectively reinvented the wheel. In (...) response to, we show how four familiar accounts of explanation apply to neural networks as they would to any scientific phenomenon. We diagnose the confusion about explaining neural networks within the machine learning literature as an equivocation on “explainability,” “understandability” and “interpretability.” To remedy this, we distinguish between these notions, and answer by offering a theory and typology of interpretation in machine learning. Interpretation is something one does to an explanation with the aim of producing another, more understandable, explanation. As with explanation, there are various concepts and methods involved in interpretation: Total or Partial, Global or Local, and Approximative or Isomorphic. Our account of “interpretability” is consistent with uses in the machine learning literature, in keeping with the philosophy of explanation and understanding, and pays special attention to medical artificial intelligence systems. (shrink)

The counterfactual and regularity theories are universal accounts of causation. I argue that these should be generalized to produce local accounts of causation. A hallmark of universal accounts of causation is the assumption that apparent variation in causation between locations must be explained by differences in background causal conditions, by features of the causal-nexus or causing-complex. The local account of causation presented here rejects this assumption, allowing for genuine variation in causation to be explained by differences in location. I argue (...) that local accounts of causation are plausible, and have pragmatic, empirical and theoretical advantages over universal accounts. I then report on the use of presheaves as models of local causation. The use of presheaves as models of local variation has precedents in algebraic geometry, category theory and physics; they are here used as models of local causal variation. The paper presents this idea as stemming from an approach using presheaves as models of local truth. Finally, I argue that a proper balance between universal and local causation can be assuaged by moving from presheaves to fully-fledged sheaf models. (shrink)

The current conception of the plurality of worlds is founded on a set theoretic understanding of possibilia. This paper provides an alternative category theoretic conception and argues that it is at least as serviceable for our understanding of possibilia. In addition to or instead of the notion of possibilia conceived as possible objects or possible individuals, this alternative to set theoretic modal realism requires the notion of possible morphisms, conceived as possible changes, processes or transformations. To support this alternative conception (...) of the plurality of worlds, I provide two examples where a category theoretic account can do work traditionally done by the set theoretic account: one on modal logic and another on paradoxes of size. I argue that the categorial account works at least as well as the set theoretic account, and moreover suggest that it has something to add in each case: it makes apparent avenues of inquiry that were obscured, if not invisible, on the set theoretic account. I conclude with a plea for epistemological humility about our acceptance of either a category-like or set-like realist ontology of modality. (shrink)

In a recent reply to our article, “What is Interpretability?,” Prasetya argues against our position that artificial neural networks are explainable. It is claimed that our indefeasibility thesis—that adding complexity to an explanation of a phenomenon does not make the phenomenon any less explainable—is false. More precisely, Prasetya argues that unificationist explanations are defeasible to increasing complexity, and thus, we may not be able to provide such explanations of highly complex AI models. The reply highlights an important lacuna in our (...) original paper, the omission of the unificationist account of explanation, and affords us the opportunity to respond. Here, we argue that artificial neural networks are explainable in a way that should satisfy unificationists and that interpretability methods present ways in which ML theories can achieve unification. (shrink)

In the 1970s, R.D. MacElroy coined the term ‘extremophile’ to describe microorganisms that thrive under extreme conditions (MacElroy 1974). This hybrid word transliterates to ‘love of extremes’ and has been studied as a straightforward concept for the past 40 years. In this paper, we discuss several ways the term has been understood in the scientific literature, each of which has different consequences for the distribution and importance of extremophiles. They are, briefly, Human-Centric, at the Edge of life’s habitation of Morphospace, (...) by appeal to Statistical Rarity, described by Objective Limits, and at the Limits of Impossibility for metabolic processes. Importantly, these concepts have co-existed, unacknowledged and conflated, for decades. Confusion and equivocation threaten to follow from the wildly varied inclusion or exclusion of organisms as extremophiles depending on the concept used. Under some conceptions, entire kinds of extremophiles become meaningless. Since our understanding of how life works is shaped by what we take to be its extremes, clarifying extremophily is key for many large-scale projects in biology, ecology, biotechnology and astrobiology. In what follows, we proceed as if a noncontroversial account of life is possible and that it is possible to find complex chemistry in the Universe that is similar enough to Life on Earth such that both may be considered instances of ‘life’ (but see Mariscal & Doolittle 2018). We raise, but do not address, the questions of whether the distribution of Life on Earth is representative of what we may find elsewhere in the Universe, whether the same kinds of extremophiles would exist given a replay of the tape of life. Additionally, each of these concepts assumes life based on some sort of biochemistry in this universe, effectively setting aside claims made by some artificial life proponents that their digital organisms are genuine examples of life (Langton 1989, Ray 1995). On the distinction between extremophilic and extremotolerant, we note that all accounts accept the latter as a broader category than the former, since ‘phily’ means love and tolerance is a prerequisite for love under any conception. Indeed, there will be many extremely impoverished environments where tolerance is the only option and thriving is precluded, e.g. Bacillus marismortui was extracted and grown from 250-million-year-old salt crystals in the Permian Salado Formation in an inactive yet persistent state (Vreeland et al., 2000). We also note that extremophily, as a functional category, is potentially applicable at many levels of the biological hierarchy. Extremophily at one level does not necessarily extend to higher and lower levels. For instance, a microorganism in isolation might be quite intolerant to certain environmental conditions yet flourish when subjected to the same conditions as a community or natural biofilm. Alternatively, a protein molecule might be quite stable or active under certain conditions even if the optimal environment for the organism containing it is far more mesophilic. There is an industry of artificially selecting organisms and proteins to adapt to extreme environments (see van den Burg & Eijsink 2002), providing some justification to consider ‘functioning at extremes’ as a worthwhile category of investigation. Finally, we also note certain physico-chemical ranges are rarely considered with respect to extremophily – timespan, size, nutrient availability (Hoehler & Jørgensen 2013), etc. – as well as some biological parameters – abundance, isolation, competition, etc. Perhaps scientific interest must also come into play as to the reason these criteria are not considered relevant. We return to this issue later. In the next section, we give five definitions of extremophily, show their benefits, drawbacks, and unintended yet unavoidable consequences. These arguments are summarized in Table 1 and represented visually in Figures 1 and 2. Given research on polyextremophiles, it seems Figure 2 is a more plausible representation of the state of current knowledge than Figure 1 (Harrison et al. 2013). Life is patchily distributed across various dimensions, which may reflect its contingent history, poor sampling, or (perhaps) fundamental limits. Figure 3 shows the conceptual flowchart for all of these views. In the following section, we take a step back to ask whether we should choose between these definitions and how such a judgment could be made. We argue for a limited pluralism, in which some, but not all, of the concepts are acceptable relative to certain practical and theoretical aims. (shrink)

Constructive Neutral Evolution is an evolutionary mechanism that can explain much molecular inter-dependence and organismal complexity without assuming positive selection favoring such dependency or complexity, either directly or as a byproduct of adaptation. It differs from but complements other non-selective explanations for complexity, such as genetic drift and the Zero Force Evolutionary Law, by being ratchet-like in character. With CNE, purifying selection maintains dependencies or complexities that were neutrally evolved. Preliminary treatments use it to explain specific genetic and molecular structures (...) or processes, such as retained gene duplications, the spliceosome, and RNA editing. Here we aim to expand the scope of such explanation beyond the molecular level, integrating CNE with Multi-Level Selection theory, and arguing that several popular higher-level selection scenarios are in fact instances of CNE. Suitably contextualized, CNE occurs at any level in the biological hierarchy at which natural selection as normally construed occurs. As examples, we focus on modularity in protein–protein interaction networks or “interactomes,” the origin of eukaryotic cells and the evolution of co-dependence in microbial communities—a variant of the “Black Queen Hypothesis” which we call the “Gray Queen Hypothesis”. (shrink)

Microbiologists are transitioning from the study and characterization of individual strains or species to the profiling of whole microbiomes and microbial ecology. Equipped with high-throughput methods for studying the taxonomic and functional characteristics of diverse samples, they are just beginning to encounter the conceptual, theoretical, and experimental problems of comparing taxonomy to function, and extracting useful measures from such comparisons. Although still unresolved, these problems are well studied in macro-ecology and are reiterated here as an historical precautionary for microbial ecologists. (...) Beyond expected and unresolved terminological vagueness, we argue that assessments and comparisons of taxonomic and functional profiles in micro-ecology suffer from theoretically unresolvable arbitrariness and ambiguities. We divide these into problems of scale, individuation, and commensurability. We argue that there is no technically/theoretically “correct” scale, individuation, or comparison of taxonomy and function, but there are nonetheless better and worse methodologies for profiling. (shrink)

Recent debates about the biological and evolutionary conditions for sentience have generated a renewed interest in fine-grained functionalism. According to one such account advanced by Peter Godfrey-Smith, sentience depends on the fine-grained activities characteristic of living organisms. Specifically, the scale, context and stochasticity of these fine-grained activities. One implication of this view is that contemporary artificial intelligence is a poor candidate for sentience. Insofar as current AI lacks the ability to engage in such living activities it will lack sentience, no (...) matter what its coarse-grained functions. In this paper, we review the case for fine-grained functionalism and show that there are contemporary machines that fulfil the fine-grained functional criteria identified by Godfrey-Smith, and thus are candidates for sentience. Molecular machines such as Brownian computers are analogous to metabolic activity in their scale, context and stochasticity, and can serve as the basis of AI. Molecular computation is a promising candidate for artificial sentience according to contemporary philosophical accounts of sentience. (shrink)

Constructive Neutral Evolution theory provides selectively neutral explanations of the origin and maintenance of biological complexity. This essay provides an analysis of CNE as an explanatory strategy defined by a tripartite set of conditions, and shows how this applies to cases of the evolution of complexity at higher-levels of the biological hierarchy. CNE was initially deployed to help explain a variety of complex molecular structures and processes, including spliceosomal splicing, trypansomal pan-editing, scrambled genes in ciliates, duplicate gene retention and fungal (...) ATP synthetase structure. CNE has also been generalized to apply to phenomena at the cellular level, including protein-protein interaction network modularity, obligate microbial symbioses, eukaryogenesis and microbial unculturability. This essay further extends CNE to cases of complexity at levels of organization higher than the molecular and cellular. These are multicellular phenotypic complexity, multicellular ecological complexity and, some cases of cultural complexity. (shrink)

We begin with the idea that lines of reasoning are continuous mental processes and develop a notion of continuity in proof. This requires abstracting the notion of a proof as a set of sentences ordered by provability. We can then distinguish between discrete steps of a proof and possibly continuous stages, defining indexing functions to pick these out. Proof stages can be associated with the application of continuously variable rules, connecting continuity in lines of reasoning with continuously variable reasons. Some (...) examples of continuous proofs are provided. We conclude by presenting some fundamental facts about continuous proofs, analogous to continuous structural rules and composition. We take this to be a development on its own, as well as lending support to non-finitistic constructionism. (shrink)

1 Since commentary on the M ideas t is s o fraugh t with controversy, let me state s ome of my s tarting p oints up front. I am a strong believer in a market economy, and in W estern civilization. My foreign p olicy instincts tend to be dovish, in recognition of the imperfections in governments, but I am not, like some libertarians , in principle oppo sed to A merican intervention abroad. I am not religious , and (...) the M iddle East holds no s pecial theological s ignificance fo r me. I h ave fo llowe d events in the region, and read wid ely on its h isto ry, but have no literacy in either Hebrew or Arabic. (shrink)

Recent research in computational neuroscience has demonstrated that we now possess the ability to simulate neural systems in significant detail and on a large scale. Simulations on the scale of a human brain have recently been reported. The ability to simulate entire brains (or significant portions thereof) would be a revolutionary scientific advance, with substantial benefits for brain science. However, the prospect of whole-brain simulation comes with a set of new and unique ethical questions. In the present paper, we briefly (...) outline certain of those problems and emphasize the need to begin considering the ethical aspects of computational neuroscience. (shrink)

Many medical ethicists accept the thesis that there is no moral difference between withholding and withdrawing life-sustaining therapy. In this paper, we offer an interesting counterexample which shows that this thesis is not always true. Withholding is distinguished from withdrawing by the simple fact that therapy must have already been initiated in order to speak coherently about withdrawal. Provided that there is a genuine need and that therapy is biomedically effective, the historical fact that therapy has been initiated entails a (...) claim to continue therapy that cannot be attributed to patients who have not yet received therapy. This intrinsic difference between withholding and withdrawing therapy is of moral importance. In many instances, patients will waive this claim. But when one considers withdrawing therapy from one patient to help another in a setting of scarce resources, this intrinsic moral difference comes into sharp focus. In an era of shrinking medical resources, this difference cannot be ignored. (shrink)

Recent studies in semantics of modal and superintuitionistic predicate logics provided many examples of incompleteness, especially for Kripke semantics. So there is a problem: to find an appropriate possible- world semantics which is equivalent to Kripke semantics at the propositional level and which is strong enough to prove general completeness results. The present paper introduces a new semantics of Kripke metaframes' generalizing some earlier notions. The main innovation is in considering "n"-tuples of individuals as abstract "n"-dimensional vectors', together with some (...) transformations of these vectors. Soundness of the semantics is proved to be equivalent to some non- logical properties of metaframes; and thus we describe the maximal semantics of Kripke- type. (shrink)

OBJECTIVE: To examine the long-term effects of an innovative curriculum on medical house officers' (HOs') knowledge, confidence, and attitudes regarding medical ethics. DESIGN: Long term cohort study. The two-year curriculum, implemented by a single physician ethicist with assistance from other faculty, was fully integrated into the programme. It consisted of monthly sessions: ethics morning report alternating with didactic conferences. The content included topics such as ethics vocabulary and principles, withdrawing life support, informed consent, and justice. Identical content was offered simultaneously (...) at the largest affiliated community hospital. SETTING: A multi-hospital university training programme from July, 1992 to June, 1994. PARTICIPANTS: Thirty-nine HOs responded in 92. Thirty HOs from the same cohort responded in 94 (response rates = 83% v 71%; P = 0.19). RESULTS: The curriculum was well received, with 96% of HOs finding the sessions stimulating. Previously validated scales of knowledge and confidence were administered at baseline and at follow-up. The average knowledge score improved 14% (P < 0.001). Confidence also improved, rising from 3.3 to 3.8 on a 5-point Likert scale (P < 0.001). These findings were independent of age, gender, religion, and prior education. The only attitudinal change was an increase in the proportion of residents who thought that ethics should be a required part of residency training (57% v 80%, P = 0.05). CONCLUSION: This curriculum appears practical, popular, and effective. It should be readily transferable to other institutions. (shrink)

We report the results of a randomized trial to assess the impact of an innovative ethics curriculum on the knowledge and confidence of 85 medical house officers in a university hospital programme, as well as their responses to a simulated clinical case. Twenty-five per cent of the house officers received a lecture series, 25 per cent received lectures and case conferences, with an ethicist in attendance, and 50 per cent served as controls. A post-intervention questionnaire was administered. Knowledge scores did (...) not differ among the groups. Confidence regarding ethical issues was significantly greater in the aggregate intervention group compared to the control group. Confidence regarding procedural issues related to ethics was significantly higher for the EI group than for the controls. Responses to a simulated case showed that significantly fewer house officers in the EI group would intubate a patient for whom such therapy would be futile. We conclude that ethics education can have an impact on house officers' confidence and their responses to a simulated case, and that the EI was more effective than the LI. Such results have implications regarding the implementation of ethics education during residency. (shrink)

This new, second edition of the popular college textbook offers the beginning philosophy student a comprehensive introduction to several aspects of one of the most influential schools of thought in the twentieth century. Professor Klemke begins by pointing out the distinctions among the various types of analytic and linguistic philosophies, while emphasising that they all arose as a response to the formerly predominant school of absolute idealism. After a prologue section containing a representative exposition of idealism by Josiah Royce, the (...) following sections show the radically new philosophical approach of the analytic school in its various guises: realism and common sense (G. E. Moore); logical atomism (Bertrand Russell); logical positivism (A. J. Ayer); conceptual analysis (Gilbert Ryle, G. E. Moore, John Wisdom); logico-metaphysical analysis (Gustav Bergman, W. V. Quine); linguistic analysis (J. L. Austin, P. F. Strawson, J. R. Searle); and the recent development of new realism (Saul Kripke, Hilary Putnam, Tyler Burge, Richard N. Boyd). (shrink)