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)

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)

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)

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)

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)

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)

SummaryHeterozygous 4.1 hereditary elliptocytosis results from the absence of one haploid set of protein 4.1, a major component of the red cell skeleton. Two successive epidemiological investigations revealed fifteen probands in the French Northern Alps. The frequency of this disease seems to be very high in four small villages isolated in the Aravis mountains. The genealogical study shows that eleven probands share common ancestors who lived eight or ten generations ago in these villages. Thus there was probably a founder effect (...) from one pair of ancestors, strengthened by endogamy. In contrast, four probands originate from another area and are not genealogically related. Recent results in molecular genetics support the present data. (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)

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)

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)

The origin of the notochord is one of the key remaining mysteries of our evolutionary ancestry. Here, we present a multi‐level comparison of the chordate notochord to the axochord, a paired axial muscle spanning the ventral midline of annelid worms and other invertebrates. At the cellular level, comparative molecular profiling in the marine annelids P. dumerilii and C. teleta reveals expression of similar, specific gene sets in presumptive axochordal and notochordal cells. These cells also occupy corresponding positions in a conserved (...) anatomical topology and undergo similar morphogenetic movements. At the organ level, a detailed comparison of bilaterian musculatures reveals that most phyla form axochord‐like muscles, suggesting that such a muscle was already present in urbilaterian ancestors. Integrating comparative evidence at the cell and organ level, we propose that the notochord evolved by modification of a ventromedian muscle followed by the assembly of an axial complex supporting swimming in vertebrate ancestors. (shrink)

In ”Skepticism,” Peter Klein distinguishes between the “Academic Skeptic” who proposes that we cannot have knowledge of a certain set of propositions and the “Pyrrhonian Skeptic” who refrains from opining about whether we can have knowledge. Klein argues that Academic Skepticism is plausibly supported by a “Closure Principle‐style” argument based on the claim that if x entails y and S has justification for x, then S has justification for y. He turns to contextualism to see if it can contribute to (...) the discussion between one who claims that we can have knowledge about some epistemically interesting class of propositions and the Academic Skeptic. He outlines the background of Pyrrhonian Skepticism, pointing out that the Pyrrhonist withholds assent concerning our knowledge‐bearing status because reason cannot provide an adequate basis for assent. He assesses three possible patterns of reasoning, and concludes that the Pyrrhonist view, that reason cannot resolve matters concerning the nonevident, is vindicated. (shrink)

Bioethics needs an expanded moral vision. It is now time for bioethics to take full account of the problems of health disparities and structural injustice that are made newly urgent by the COVID-19 pandemic and the effects of climate change. Nancy M. P. King, Gail E. Henderson, and Larry R. Churchill make the case for a more social understanding and application of justice, a deeper humility in assessing expertise in bioethics consulting, a broader and more relevant research agenda, and greater (...) appreciation of the profound health implications of global warming. (shrink)

This book views Green's philosophical opus through his public life and political commitments. It demonstrates how his main ethical and political conceptions -- his idea of 'self realisation' and his theory of individuality within community -- were informed by evangelical theology, popular Protestantism and an idea of the English national consciousness as formed by religious conflict. While the significance of Kant and Hegel is acknowledged, it is argued that 'indigenous' qualities of Green's teachings resonated with Victorian Liberal values.

First published in 1987. Routledge is an imprint of Taylor & Francis, an informa company.

First published in 1982, this reissue contains a critical exposition of the views of Frege, Dedekind and Peano on the foundations of arithmetic. The last quarter of the 19th century witnessed a remarkable growth of interest in the foundations of arithmetic. This work analyses both the reasons for this growth of interest within both mathematics and philosophy and the ways in which this study of the foundations of arithmetic led to new insights in philosophy and striking advances in logic. This (...) historical-critical study provides an excellent introduction to the problems of the philosophy of mathematics - problems which have wide implications for philosophy as a whole. This reissue will appeal to students of both mathematics and philosophy who wish to improve their knowledge of logic. (shrink)