Arguments for the effectiveness, and even the indispensability, of mathematics in scientific explanation rely on the claim that mathematics is an effective or even a necessary component in successful scientific predictions and explanations. Well-known accounts of successful mathematical explanation in physical science appeals to scientists’ ability to solve equations directly in key domains. But there are spectacular physical theories, including general relativity and fluid dynamics, in which the equations of the theory cannot be solved directly in target domains, and yet (...) scientists and mathematicians do effective work there (McLarty 2023, Elder 2023). Building on extant accounts of structural scientific explanation (Bokulich 2011, Leng 2021), I argue that philosophical accounts of the role of equations in scientific explanation need not rely on scientists’ ability to solve equations independently of their understanding of the empirical or experimental context. For instance, the process of formulating solutions to equations can involve significant appeal to information about experimental contexts (Curiel 2010) or of physically similar systems (Sterrett 2023). Working from a close analysis of work in fluid mechanics by Martin Bazant and Keith Moffatt (2005), I propose an account of heuristic structural explanation in mathematics (Einstein 1921, Pincock 2021), which explains how physical explanations can be constructed even in domains where basic equations cannot be solved directly. (shrink)

This essay will first present a vignette of Luxemburg’s life and work, referring to classic and recent biographies. Following that, section 3 examines concepts of the state and nation in Hegel, Marx, Engels, and Lenin. The subject of section 4 is Luxemburg’s substantial work of political economy, The Accumulation of Capital. It is a most significant achievement, analyzing the contradictions of the capitalist state and its role in driving imperialist expansion and colonialism. Section 5 traces how Luxemburg’s political economy in (...) Accumulation underwrites her interventions in the heated debates over Polish independence. And section 6 concludes with remarks on Luxemburg’s significance for philosophy and political thought. (shrink)

This paper will focus on a famous nineteenth century debate over the physiology of perception between Ewald Hering and Hermann von Helmholtz. This debate is often explained as a contest between empiricism (Helmholtz) and nativism (Hering) about perception. I will argue that this is only part of the picture. Hering was a pioneer of Lamarckian explanations, arguing for an early version of the biogenetic law. Hering explains physical processes, including perception, in terms of ‘organic memory’ that is supported by ‘vital (...) forces’ located throughout the body. Helmholtz, on the other hand, argues that vital forces are in direct conflict with the results he and others proved in the 1840s and 50s on the conservation of force. The battleground of the debate was the interpretation of Johannes Müller’s ‘law of specific nerve energies’, which Hering interpreted in terms of vital forces, and Helmholtz interpreted using a naturalized neo-Kantian approach. In the end, the debate revealed deep fissures in nineteenth century accounts of scientific explanation, as well as in the conception of how physiology, psychology, physics, and philosophy are related. (shrink)

In this paper I discuss five meta-ethical challenges to Naturalistic Moral Realism, which includes secular moral codes such as Secular Humanism that, in my view, naturalists need to address to keep their commitment to moral realism from looking like special pleading. The five challenges are as follows: 1. The Ontological Problem (OP): How do such moral principles exist? 2. The Epistemic Problem (EP): How does our moral sense/intuition track such principles? 3. The Influence Problem (IP): What authority does the existence (...) of such principles have to supervene on our behavior? 4. The Axiological Problem (AP): What entities have moral value and deserve moral consideration? 5. Methodological Problem (MP): How do we go about arbitrating between moral claims when they conflict? (shrink)

I examine the role of inference from experiment in theory building. What are the options open to the scientific community when faced with an experimental result that appears to be in conflict with accepted theory? I distinguish, in Laudan's (1977), Nickels's (1981), and Franklin's (1993) sense, between the context of pursuit and the context of justification of a scientific theory. Making this distinction allows for a productive middle position between epistemic realism and constructivism. The decision to pursue a new or (...) a revised theory in response to the new evidence may not be fully rationally determined. Nonetheless, it is possible to distinguish the question of whether there is reason to pursue a theory from the question of whether that theory, once it has been pursued over time, solves a problem of interest to science. I argue that, in this context, there is a solid way to distinguish between the contexts of pursuit and of justification, on the basis of a theory's evidential support and problem-solving ability. (shrink)

In this article, I will discuss some of the arguments for and against the existence of God, in particular the monotheistic God believed in the Abramahamic religions (Judiasm, Islam, and Christianity) as well as Babism, the Bahai Faith, and Sikhism. Arguments for the existence of God try to argue that either God exists (based on other things people agree with) or that belief in God is reasonable. Arguments against the existence of God try to argue that the existence of God (...) leads to some contradiction or other absurdity. (shrink)

This work deals with problems involving infinities and infinitesimals. It explores the ideas behind zero, its relationship to ontological nothingness, finititude (such as finite numbers and quantities), and the infinite. The idea of infinity and zero are closely related, despite what many perceive as an intuitive inverse relationship. The symbol 0 generally refers to nothingness, whereas the symbol infinity refers to ``so much'' that it cannot be quantified or captured. The notion of finititude rests somewhere between complete nothingness and something (...) having no end. -/- My concern is that many of the philosophers arguing for or against the ontology (or possibility) of an actual infinite set are unaware or unfamiliar with the mathematical literature attempting to clearly and rigorously define these terms. I believe it is a mistake to leave mathematicians out of this conversation, as analysts in particular have defined (and used) infinity in a way that is relevant to the ongoing debate between philosophers. -/- For this paper, I have selected examples from Principles of Analysis by Walter Rudin, which has become a standard text for Real Analysis classes taken by pure mathematicians and engineers. I will also restrict the scope of examples to Euclidean spaces for simplicity. Finally, I will be using addition, + and multiplication * in their usual way. (shrink)

The problem of evil is one of the most significant challenges to theism and Christianity in particular, asking why there seems to be so much evil if an omnibenevolent (all good), loving God exists. The problem of evil, as posed by many atheists and agnostics today, (following Epicurus) often asserts that the following premises cannot all be true: 1. God exists, and is omnipotent (all-powerful) 2. God exists, and is omnibenevolent (all-good) 3. God exists, and is omniscient (all-knowing) 4. Evil (...) exists Christian thinkers over the past two thousand years have given various responses to the problem of evil in the form of various theodicies, or attempts to explain why evil exists (or appears to exist) given the existence of an Omniscient, Omnipotent, Omnibenevolent God. This document serves as a brief overview of different theodicies offered by Christian thinkers throughout history. (shrink)

German supporters of the Kantian philosophy in the late 19th century took one of two forks in the road: the fork leading to Baden, and the Southwest School of neo-Kantian philosophy, and the fork leading to Marburg, and the Marburg School, founded by Hermann Cohen. Between 1876, when Cohen came to Marburg, and 1918, the year of Cohen's death, Cohen, with his Marburg School, had a profound influence on German academia.

In my dissertation, I present Hermann Cohen's foundation for the history and philosophy of science. My investigation begins with Cohen's formulation of a neo-Kantian epistemology. I analyze Cohen's early work, especially his contributions to 19th century debates about the theory of knowledge. I conclude by examining Cohen's mature theory of science in two works, The Principle of the Infinitesimal Method and its History of 1883, and Cohen's extensive 1914 Introduction to Friedrich Lange's History of Materialism. In the former, Cohen gives (...) an historical and philosophical analysis of the foundations of the infinitesimal method in mathematics. In the latter, Cohen presents a detailed account of Heinrich Hertz's Principles of Mechanics of 1894. Hertz considers a series of possible foundations for mechanics, in the interest of finding a secure conceptual basis for mechanical theories. Cohen argues that Hertz's analysis can be completed, and his goal achieved, by means of a philosophical examination of the role of mathematical principles and fundamental concepts in scientific theories. (shrink)

In a famous debate between Thomas Kuhn and Karl Popper, Popper accused Kuhn and Quine of propagating the “Myth of the Framework”: that some broad set of specific background commitments are required for interlocutors to be able to have a fruitful conversation. The Myth of the Framework could be used to argue for a beneficial version of the canon: that training in these shared background commitments allows for the growth of a robust community of inquiry. Popper argues, however, that the (...) position that truth or inquiry can be framework-dependent is a pernicious form of relativism, and undermines the possibility of rational inquiry. I subject Popper’s view to criticism, showing that it can be used to undermine “orthodoxy” and the canon in some ways, but that it props up the canon in others. In closing, the paper examines the connections between Popper’s position on the community of inquiry and standpoint epistemology, and argues for the claim that Popper’s view, to be persuasive, requires a more robust account of how critical inquiry relies on the evaluative capacities of rational agents within a community. (shrink)

My paper will analyze Cassirer’s logic of the cultural sciences as it developed in close engagement with work on logic, psychology, biology, and linguistics in the nineteenth and early twentieth centuries. The paper focuses on Chajim Steinthal, who sees the “expressive form” of language as a natural function of human engagement with the environment, developing independently of logic. When read in the context of his engagement with Steinthal, the biologist Uexküll, and the neuroscientist Kurt Goldstein, The Philosophy of Symbolic Forms (...) reimagines the role of logic and language in the construction of the cultural world. This provides a reading of what Cassirer means by the logic of the cultural sciences, and what he means by culture itself. My reading highlights the tension, which I argue stems from Steinthal’s earlier work, between the assertion that phenomena including linguistic expression, living beings, and consciousness develop independently of a unifying logic, and Cassirer’s assertion that we live in a common, objective human world. (shrink)

Kant's account of space as an infinite given magnitude in the Critique of Pure Reason is paradoxical, since infinite magnitudes go beyond the limits of possible experience. Michael Friedman's and Charles Parsons's accounts make sense of geometrical construction, but I argue that they do not resolve the paradox. I argue that metaphysical space is based on the ability of the subject to generate distinctly oriented spatial magnitudes of invariant scalar quantity through translation or rotation. The set of determinately oriented, constructed (...) geometrical spaces is a proper subset of metaphysical space, thus, metaphysical space is infinite. Kant's paradoxical doctrine of metaphysical space is necessary to reconcile his empiricism with his transcendental idealism. (shrink)

In this essay, I will explain why Methodological Naturalism (MN) fails as a demarcating criteria for science. I will argue that MN is not precise enough to be useful for demarcation, unable to follow the evidence where it leads, not theologically neutral (despite its stated goals as such), and difficult to justify (and currently unjustified) as an ontological or epistemic principle.

This paper investigates the claim that artificial Intelligence Systems cannot be held morally responsible because they do not have an ability for agential self-awareness e.g. they cannot be aware that they are the agents of an action. The main suggestion is that if agential self-awareness and related first person representations presuppose an awareness of a self, the possibility of responsible artificial intelligence systems cannot be evaluated independently of research conducted on the nature of the self. Focusing on a specific account (...) of the self from the phenomenological tradition, this paper suggests that a minimal necessary condition that artificial intelligence systems must satisfy so that they have a capability for self-awareness, is having a minimal self defined as ‘a sense of ownership’. As this sense of ownership is usually associated with having a living body, one suggestion is that artificial intelligence systems must have similar living bodies so they can have a sense of self. Discussing cases of robotic animals as examples of the possibility of artificial intelligence systems having a sense of self, the paper concludes that the possibility of artificial intelligence systems having a ‘sense of ownership’ or a sense of self may be a necessary condition for having responsibility. (shrink)

In the nineteenth century, the separation of naturalist or psychological accounts of validity from normative validity came into question. In his 1877 Logical Studies (Logische Studien), Friedrich Albert Lange argues that the basis for necessary inference is demonstration, which takes place by spatially delimiting the extension of concepts using imagined or physical diagrams. These diagrams are signs or indications of concepts' extension, but do not represent their content. Only the inference as a whole captures the objective content of the proof. (...) Thus, Lange argues, the necessity of an inference is independent of psychological accounts of how we grasp the content of a proposition. (shrink)

For years, the European world saw millions of swans, and all of them without exception were white. If inductive reasoning is valid, one may conclude that all swans are white. However, this would be incorrect: in 1667 Dutch explorer Willem de Vlamingh observed black swans in Australia, falsifying the hypothesis that all swans are white. While often used as a cautionary tale for the use of induction, such as with Popper’s falsification principle, I want to explore a slightly different idea: (...) does the existence of fabricated or otherwise failed accounts of Black swans give me a reason to ignore future arguments or doubt their existence? I argue that while faulty or fabricated reports do not give us a logical reason to reject a claim, they can give us a practical one for refusing to consider future arguments. This practical vs logical distinction gives an inductive reason for believing that future arguments will be invalid, but keeps one from being able to necessarily deny the claim in question without further argumentation. (shrink)

In this article, I define a cultural epistemology as a set of socially reinforced assumptions about how knowledge and truth are produced. Unlike a philosophical epistemology, a cultural epistemology is largely the product of culture and largely invisible. As products of culture, cultural epistemology are relatively unquestioned and, in many cases, philosophically unsophisticated. There are three common types of cultural epistemologies, influenced by who holds power in a given society: an epistemological monarchy, an epistemological oligarchy and an epistemological democracy. A (...) given cultural epistemology subsequently influences the legitimacy of culture and government itself. I argue argue that Americans tend to hold an "epistemological democracy" with two distinct facets: a trust in consensus, linked to living in a democratic republic, and a trust in their own self-interest, linked to market economics and capitalism more generally. These two facets combine, interact, and even oppose each other to legitimize and challenge American culture and its political and economic systems. (shrink)

In this paper, I wish to criticize the notion that consensus is an epistemology. While I have never seen it explicitly claimed that “consensus is an epistemology,” I have nonetheless seen it implied in many scholarly (and layperson) articles. This occurs whenever articles cite, “a majority of scholars agree that…” or “most scientists/researchers think…” In our democratic, individualistic society, we put a value on high value votes and the quantification of majority viewpoints, whether it be in political polls (due to (...) living in a democracy), online on websites with ranking or voting systems such as Reddit, YouTube, or Instagram. The danger here is we may defer too much to the consensus view without appropriate justification. I will give several reasons why we should be skeptical of appeals to consensus (including a consensus of experts), which include its non-obvious link to ontology, the fact that consensus changes, and a lack of specificity of who counts as an ``expert,'' the lack of specificity on how to handle consensus (if it does occur), and epistemic undercutting defeaters from evolutionary epistemology. While an appeal to consensus may not tell us much about whether a theory is true, they can give us practical or pragmatic reasons for trusting a position. (shrink)

Scientists working within a paradigm must play by the rules of the game of that paradigm in solving problems, and that is why incommensurability arises when the rules of the game change. If we deny the thesis of the priority of paradigms, then there is no good argument for the incommensurability of theories and thus for taxonomic incommensurability, because there is no invariant way to determine the set of results provable, puzzles solvable, and propositions cogently formulable under a given paradigm.

In the early 1900s, Russell began to recognize that he, and many other mathematicians, had been using assertions like the Axiom of Choice implicitly, and without explicitly proving them. In working with the Axioms of Choice, Infinity, and Reducibility, and his and Whitehead’s Multiplicative Axiom, Russell came to take the position that some axioms are necessary to recovering certain results of mathematics, but may not be proven to be true absolutely. The essay traces historical roots of, and motivations for, Russell’s (...) method of analysis, which are intended to shed light on his view about the status of mathematical axioms. I describe the position Russell develops in consequence as “immanent logicism,” in contrast to what Irving (1989) describes as “epistemic logicism.” Immanent logicism allows Russell to avoid the logocentric predicament, and to propose a method for discovering structural relationships of dependence within mathematical theories. (shrink)

Psillos, Kitcher, and Leplin have defended convergent scientific realism against the pessimistic meta-induction by arguing for the divide et impera strategy. I argue that DEI faces a problem more serious than the pessimistic meta-induction: the problem of accretion. When empirically successful theories and principles are combined, they may no longer make successful predictions or allow for accurate calculations, or the combination otherwise may be an empirical failure. The shift from classical mechanics to the new quantum theory does not reflect the (...) discarding of “idle wheels.” Instead, scientists had to contend with new principles that made classical calculations difficult or impossible, and new results that were inconsistent with classical theorems, and that suggested a new way of conceiving of atomic dynamics. In this shift, reference to atoms and to electrons was preserved, but the underlying causal explanations and descriptions of atoms and electrons changed. I propose that the emphasis on accurate description of causal agents as a virtue of background theory be replaced with Ruetsche’s advocacy of pragmatic, modal resourcefulness. (shrink)

The Marburg neo-Kantians argue that Hermann von Helmholtz's empiricist account of the a priori does not account for certain knowledge, since it is based on a psychological phenomenon, trust in the regularities of nature. They argue that Helmholtz's account raises the 'problem of validity' (Gueltigkeitsproblem): how to establish a warranted claim that observed regularities are based on actual relations. I reconstruct Heinrich Hertz's and Ludwig Wittgenstein's Bild theoretic answer to the problem of validity: that scientists and philosophers can depict the (...) necessary a priori constraints on states of affairs in a given system, and can establish whether these relations are actual relations in nature. The analysis of necessity within a system is a lasting contribution of the Bild theory. However, Hertz and Wittgenstein argue that the logical and mathematical sentences of a Bild are rules, tools for constructing relations, and the rules themselves are meaningless outside the theory. Carnap revises the argument for validity by attempting to give semantic rules for translation between frameworks. Russell and Quine object that pragmatics better accounts for the role of a priori reasoning in translating between frameworks. The conclusion of the tale, then, is a partial vindication of Helmholtz's original account. (shrink)

Anti-intellectualism involves general mistrust of scholars, academics, and ex- perts, often as pretentious or power-motivated. While scholars have described currents of anti-intellectualism in American public life, evangelical Christianity, in responses to COVID, and rural identity, to my knowledge none have looked at how anti-intellectualism specifically manifests in the New Atheism movement. In this work, we explore the way anti-intellectualism is commonly found and expressed in New Atheism and the modern Skeptical Movement, including scientific skepticism more generally.

Western, secularized capitalism appraises the “worth” of a worker through a wage, a numerical value assumed to reflect the value of one’s time (in the case of hourly jobs) or contribution (in the case of salary or commision-based work). Computers and AI models are capable of matching and even exceeding human performance on a variety of tasks such as mathematical computation, handwritten digit recognition, and even complex tasks such as playing the game Go. Furthermore, they can work around the clock (...) with no need for sleep, healthcare, or even a salary. As a result, computers are more “valuable” than humans under capitalism because they are more productive (in terms of quantity and, in many cases, quality of work). Combined with an erosion of the religious idea of explicit human worth or dignity, other humans are seen as mere means to the ends of those powerful enough to exploit them. Any hope of reducing inequality or promoting justice must come from an explicit belief in the “value” of human life independent of his or her ability to produce. (shrink)

Ott (2009) identifies two kinds of philosophical theories about laws: top-down, and bottom-up. An influential top-down reading, exemplified by Ernst Cassirer, emphasized the ‘mere form of law’. Recent bottom-up accounts emphasize the mind-independent natures of objects as the basis of laws of nature. Stang and Pollok in turn focus on the transcendental idealist elements of Kant’s theory of matter, which leads to the question: is the essence of Kantian matter that it obeys the form of law? I argue that Kant (...) has an independent theory of matter in the Metaphysical Foundations of Natural Science, one that gives what Kant himself calls a ‘real definition’ of matter as a theory-independent (if not mind-independent) entity. I argue that this matter theory underpins physical arguments about inertia and impenetrability, which resemble Einstein’s arguments about the unification of fields in general relativity. (shrink)

Ernst Mach’s defense of relativist theories of motion in Die Mechanik involves a well-known criticism of Newton’s theory appealing to absolute space, and of Newton’s “bucket” experiment. Sympathetic readers (Norton 1995) and critics (Stein 1967, 1977) agree that there’s a tension in Mach’s view: he allows for some constructed scientific concepts, but not others, and some kinds of reasoning about unobserved phenomena, but not others. Following Banks (2003), I argue that this tension can be interpreted as a constructive one, springing (...) from Mach’s approach to scientific reasoning. Mach’s “economy of science” allows for a principled distinction to be made, between natural and artificial hypothetical reasoning, and Mach defends a division of labor between the sciences in a 1903 paper for The Monist, “Space and Geometry from the Point of View of Physical Inquiry”. That division supports counterfactual reasoning in Mach’s system, something that’s long been denied is possible for him. (shrink)

In the article ”Against Physicalism-plus-God: How Creation Accounts for Divine Action in the World’, I defined a framework which allows us to make some progress in our understanding of how God acts in the world. In the present article, I apply this framework to the specific question of chance events. I show that chance does not provide an explanation for special divine action. Nevertheless, chance does not hamper God’s ability to act in the world, and creation provides a framework for (...) the understanding of chance, which is akin to what we see in modern science. (shrink)

In his early and unpublished essay on Schiller’s trilogy Wallenstein, Hegel criticizes the plays’ denouement as “horrific” and “appalling” and for depicting the triumph of death over life. Why was the young Hegel’s response to Wallenstein so negative? To answer this question, I first offer an analysis of Wallenstein in terms of Hegel’s mature theory of modern tragedy. I argue that Schiller’s portrayal of Wallenstein’s character and death indeed render the play a particularly dark and unredemptive example of modern tragedy (...) as Hegel understands it. I suggest, however, that Hegel’s early objections are primarily motivated by his philosophy of history rather than by his theory of tragedy. Hegel accurately sensed the loss of faith in historical progress that Schiller experienced in the wake of the French Revolution; in essays written shortly before Wallenstein appeared, Schiller associates the tragic sublime with humans’ ability to act in the face of the meaninglessness of history. In his essay “The German Constitution,” composed during the same period as his Wallenstein review, Hegel instead formulates his familiar exhortation that we see history as meaningful. Hegel’s objection to Wallenstein’s darkness, then, is primarily an objection to the vision of history it portrays. Against the background of Peter Stein’s 2007 Berlin production of Wallenstein, I suggest that Wallenstein’s lasting appeal lies in its ability to allow audiences to experience the sublime as Schiller intended: as an assertion of our agency despite the cycles of history we so little control. (shrink)

Hermann von Helmholtz (1821-1894) established results both controversial and enduring: analysis of mixed colors and of combination tones, arguments against nativism, and the analysis of sensation and perception using the techniques of natural science. The paper focuses on Helmholtz’s account of sensation, perception, and representation via “physiological psychology”. Helmholtz emphasized that external stimuli of sensations are causes, and sensations are their effects, and he had a practical and naturalist orientation toward the analysis of phenomenal experience. However, he argued as well (...) that sensation must be interpreted to yield representation, and that representation is geared toward objective representation (the central thesis of contemporary intentionalism). The interpretation of sensation is based on “facts” revealed in experiment, but extends to the analysis of the quantitative, causal relationships between stimuli and responses. A key question for Helmholtz’s theory is the extent to which mental operations are to be ascribed a role in interpreting sensation. (shrink)

The way citizens regard and treat one another in everyday life, even when they are not engaged in straightforwardly “political” activities, matters for achieving democratic ideals. This claim provokes an underexamined unease in many. Here I articulate these concerns, which I argue are prompted by the approaches most often associated with these issues. Such theories, like democratic communitarianism, require problematic sorts of unity in everyday social life. To avoid these difficulties, I offer an alternative, called procedural democratic informal politics, which (...) allows democrats to evaluate everyday life without demanding questionable forms of unity within it. (shrink)

Hermann von Helmholtz allows for not only physiological facts and psychological inferences, but also perspectival reasoning, to influence perceptual experience and knowledge gained from perception. But Helmholtz also defends a version of the view according to which there can be a kind of “perspectival truth” revealed in scientific research and investigation. Helmholtz argues that the relationships between subjective and objective, real and actual, actual and illusory, must be analyzed scientifically, within experience. There is no standpoint outside experience from which we (...) can reason, no extra-sensory knowledge of the constitution of the “ideal subject” or of the properties of “real objects.” In the tradition of psychophysics inherited by Helmholtz, we can arrive at a kind of perspectival analysis of perceptual experience, which embeds an account of that experience within the context of the history and situation of the perceiving subject. That analysis is relative to the perceiving subject, but the perspectival explanations Helmholtz constructs are not thereby relativist: in fact, for Helmholtz, the more squarely the perceiving subject is placed in a scientific, perspectival context, the more facts we are able to learn about her experience and the objects with which she interacts. (shrink)

Philip Roth’s novel 'The Human Stain' recounts an instance of racial passing: its protagonist, Coleman Silk, is African-American but light-skinned enough to pass as white. Coleman’s decision to pass and his subsequent violent death, I argue, confront us with complex ethical questions regarding unjust social roles, loyalty, and moral luck. I also argue, building on Hegel’s definition of tragedy, that 'The Human Stain' is a particularly modern tragedy. The novel highlights conflicting role obligations, inadequate conceptions of freedom, and the tensions (...) of cultural paradigm shifts—all characteristics typical of modern tragedy. I claim that parsing 'The Human Stain' as a tragedy deepens our understanding of the novel as well as drawing our attention to its philosophical significance. (shrink)

Christine Korsgaard attempts to reinterpret Kantian ethics in a way that might alleviate Bernard Williams’ famous worry that a man cannot save his drowning wife without determining impartially that he may do so. She does this by dividing a reflective self that chooses the commitments that make up an agent’s practical identity from a self defined as a jumble of desires. An agent, she then argues, must act on the commitments chosen by the reflective self on pain of disintegration. Using (...) Harry Frankfurt’s emphasis on love as a final end, I argue that disintegration as motivation is not a more acceptable motivation than impartiality and so does not adequately address Williams’ criticism. I also argue that the idea of a divided self either leads to an infinite regress or to an implausible description of how our commitments evolve and change. To make this last claim, I discuss a case from John Updike’s novel 'In the Beauty of the Lilies.'. (shrink)

Immanuel Kant's description of humans' first encounter with each other depicts a peaceful recognition of mutual worth. G.W.F. Hegel's by contrast depicts a struggle to the death. I argue in this paper that Hegel's description of conflict results in an ethical theory that better preserves the distinctness of the other. I consider Christine Korsgaard's description of first encounters as a third alternative but conclude that Hegel's approach better accounts for the specific commitments we make--as family members, works, and citizens --in (...) ethical life. (shrink)

Towards the very end of his wide-ranging lectures on the philosophy of art, Hegel unexpectedly expresses a preference for comedy over tragedy. More surprisingly, given his systematic claims for his aesthetic theory, he suggests that this preference is arbitrary. This essay suggests that this arbitrariness is itself systematic, given Hegel’s broader claims about unity and necessity in art generally and his analysis of ancient as opposed to modern drama in particular. With the emergence of modern subjectivity, tragic plots lose their (...) necessity and so their redemptive conclusions; comic plots disintegrate into mockery and entertainment. In many cases, the dramas in question consequently fail to be art. This does not, however, mean that art ends: insofar as it inspires humans to a better understanding of their unity with the divine, it will continue to meet its mandate. But the lack of necessity in modern drama means we are free to prefer happy endings. Hegel’s seemingly arbitrary preference is, in the end, systematically justified. (shrink)

Detlefsen (1986) reads Hilbert's program as a sophisticated defense of instrumentalism, but Feferman (1998) has it that Hilbert's program leaves significant ontological questions unanswered. One such question is of the reference of individual number terms. Hilbert's use of admittedly "meaningless" signs for numbers and formulae appears to impair his ability to establish the reference of mathematical terms and the content of mathematical propositions (Weyl (1949); Kitcher (1976)). The paper traces the history and context of Hilbert's reasoning about signs, which illuminates (...) Hilbert's account of mathematical objectivity, axiomatics, idealization, and consistency. (shrink)

Moti Mizrahi has argued that Thomas Kuhn does not have a good argument for the incommensurability of successive scientific paradigms. With Rouse, Andersen, and others, I defend a view on which Kuhn primarily was trying to explain scientific practice in Structure. Kuhn, like Hilary Putnam, incorporated sociological and psychological methods into his history of science. On Kuhn’s account, the education and initiation of scientists into a research tradition is a key element in scientific training and in his explanation of incommensurability (...) between research paradigms. The first part of this paper will explain and defend my reading of Kuhn. The second part will probe the extent to which Kuhn’s account can be supported, and the extent to which it rests on shaky premises. That investigation will center on Moti Mizrahi’s project, which aims to transform the Kuhnian account of science and of its history. While I do defend a modified kind of incommensurability, I agree that the strongest version of Kuhn’s account is steadfastly local and focused on the practice of science. (shrink)

In the growing Prussian university system of the early nineteenth century, "Wissenschaft" (science) was seen as an endeavor common to university faculties, characterized by a rigorous methodology. On this view, history and jurisprudence are sciences, as much as is physics. Nineteenth century trends challenged this view: the increasing influence of materialist and positivist philosophies, profound changes in the relationships between university faculties, and the defense of Kant's classification of the sciences by neo-Kantians. Wilhelm Dilthey's defense of the independence of the (...) methodology of the human sciences (Geisteswissenschaften) from those of the natural sciences (Naturwissenschaften) is as much a return to the ideal of Wissenschaft as a cooperative endeavor as it is a defense of the autonomy of interpretive or hermeneutic methods. The debate between Dilthey and the neo-Kantian Wilhelm Windelband at the close of the century illuminates the development of this dialogue over the nineteenth century. (shrink)

It is argued that logic, and in particular mathematical logic, should play a key role in the undergraduate curriculum for students in the computing fields, which include electrical engineering (EE), computer engineering (CE), and computer science (CS). This is based on 1) the history of the field of computing and its close ties with logic, 2) empirical results showing that students with better logical thinking skills perform better in tasks such as programming and mathematics, and 3) the skills students are (...) expected to have in the job market. Further, we believe teaching logic to students explicitly will improve student retention, especially involving underrepresented minorities. Though this work focuses specifically on the computing fields, these results demonstrate the importance of logic education to STEM (science, technology, engineering, and mathematics) as a whole. (shrink)

Two questions should be considered when assessing the Kantian dimensions of Kuhn’s thought. First, was Kuhn himself a Kantian? Second, did Kuhn have an influence on later Kantians and neo-Kantians? Kuhn mentioned Kant as an inspiration, and his focus on explanatory frameworks and on the conditions of knowledge appear Kantian. But Kuhn’s emphasis on learning; on activities of symbolization; on paradigms as practical, not just theoretical; and on the social and community aspects of scientific research as constitutive of scientific reasoning, (...) are all outside the Kantian perspective. Kuhn’s admiration for Kant is tempered by his desire to understand the processes of learning, of initiation into a scientific community, of experimentation using instruments, and of persuasion, drawing on the work of familiar influences, including Piaget, Koyré, and Wittgenstein, and less familiar ones, including Langer, Demos, and Frank. Both Kuhn and Kant were interested in the question: what is the status of science, and what is the role of the scientist in its development and justification? But Kuhn presents science in a much more messy, historically contingent, and socially charged way than Kant does. The paper’s conclusion evaluates Kuhn’s reception among researchers including Richardson and Friedman, assessing the prospects for future work. (shrink)

The framework of the modern Western analysis of culture, in terms of the socio-historical situation of the subject and the reciprocal influence of one on the other, has its roots in nineteenth century discussions. This paper will examine two traditions: the hermeneutic approach of Wilhelm Dilthey, and the Völkerpsychologie of Moses Lazarus and Chajim Steinthal. The account will focus on two elements. First, Lazarus and Steinthal attempted to motivate an account based on collective structures, or forms, of rationality made manifest (...) by a people or Volk; the paper will explore their account of how collective structures can be employed in sociohistorical analysis. Second, Dilthey rejected Lazarus’s and Steinthal’s argument that it was possible to identify the norms of action governing social phenomena. Dilthey rejected any account of psychology that took it to be law-governed, even retrospectively, because he argued that the ‘nexus of life’ that is the ultimate basis of the human sciences cannot be reduced to any law-governed or explanatory relationship between the self, society, and nature. However, there is a deep tension in Dilthey’s position here, which is evident in the development of his work over time. The account below will explore this tension and its significance for the understanding of the subject and the role of psychology in the human sciences. (shrink)

In this paper, building on recent and longstanding work (Warren 2001, Friedman 2013, Glezer 2018), I investigate how the account of the essences or natures of material substances in the Metaphysical Foundations is related to Kant’s demand for the completeness of the system of nature. We must ascribe causal powers to material substances for the properties of those substances to be observable and knowable. But defining those causal powers requires admitting laws of nature, taken as axioms or principles of natural (...) science, which govern anything that can be constructed mathematically or “given as an object of experience” (MAN, 4:474–75). Presenting a complete system of nature requires adumbrating the properties of material substances that can be objects of experience. But it is not possible to show how those properties are involved in explanations of the phenomena without involving the laws that govern interactions between material substances. For Kant, or so I will argue, it is not possible to account for the natures of things, or for the features of laws of nature, independently of each other. The paper will substantiate the Finitist Account (FA) of Kant on laws. The Finitist Account has it that modal judgments about the possible proofs that can be made, or interactions that can be explained, are (1) based on concrete intuitive reasoning and motivated by the desire to avoid appeal to the actual infinite, (2) grounded in finite decision procedures, which are (3) based on reliable systems of axioms or rules of inference. (shrink)

George Boole emerged from the British tradition of the “New Analytic”, known for the view that the laws of logic are laws of thought. Logicians in the New Analytic tradition were influenced by the work of Immanuel Kant, and by the German logicians Wilhelm Traugott Krug and Wilhelm Esser, among others. In his 1854 work An Investigation of the Laws of Thought on Which are Founded the Mathematical Theories of Logic and Probabilities, Boole argues that the laws of thought acquire (...) normative force when constrained to mathematical reasoning. Boole’s motivation is, first, to address issues in the foundations of mathematics, including the relationship between arithmetic and algebra, and the study and application of differential equations (Durand-Richard, van Evra, Panteki). Second, Boole intended to derive the laws of logic from the laws of the operation of the human mind, and to show that these laws were valid of algebra and of logic both, when applied to a restricted domain. Boole’s thorough and flexible work in these areas influenced the development of model theory (see Hodges, forthcoming), and has much in common with contemporary inferentialist approaches to logic (found in, e.g., Peregrin and Resnik). (shrink)

Ernst Cassirer’s focus on the expressive function of language should be read, not in the context of Carnap’s debate with Heidegger, but in the context of the earlier work of Chajim (Heymann) Steinthal. Steinthal distinguishes the expressive form of language, when language is studied as a natural phenomenon, from language as a logical, inferential system. Steinthal argues that language always can be expressed in terms of logical inference. Thus, he would disagree with Heidegger, just as Carnap does. But, Steinthal insists, (...) that is not to say that language, as a natural phenomenon, is exhausted by logic or by the place of terms or relations in inferential structures. Steinthal’s “form” of linguistic “expression” is an early version of Cassirer’s “expressive function” for language. The expressive function, then, should not be seen to place a barrier between Carnap and Cassirer. Rather, Steinthal and Cassirer deal with a question that, as far as I know, Carnap does not address directly: how should philosophers analyze human language as a natural phenomenon, as a part of our expression as animals? And how does that expression determine the semantic categories, kind terms, and other structures that develop within, and characterize, human language itself? (shrink)

Christine Korsgaard attempts to reinterpret Kantian ethics in a way that might alleviate Bernard Williams’ famous worry that a man cannot save his drowning wife without determining impartially that he may do so. She does this by dividing a reflective self that chooses the commitments that make up an agent’s practical identity from a self defined as a jumble of desires. An agent, she then argues, must act on the commitments chosen by the reflective self on pain of disintegration. Using (...) Harry Frankfurt’s emphasis on love as a final end, I argue that disintegration as motivation is not a more acceptable motivation than impartiality and so does not adequately address Williams’ criticism. I also argue that the idea of a divided self either leads to an infinite regress or to an implausible description of how our commitments evolve and change. To make this last claim, I discuss a case from John Updike’s novel 'In the Beauty of the Lilies.'. (shrink)

Linear Algebra is an extremely important field that extends everyday concepts about geometry and algebra into higher spaces. This text serves as a gentle motivating introduction to the principles (and philosophy) behind linear algebra. This is aimed at undergraduate students taking a linear algebra class - in particular engineering students who are expected to understand and use linear algebra to build and design things, however it may also prove helpful for philosophy majors and anyone else interested in the ideas behind (...) linear algebra. Linear algebra is used extensively in statistics, mechanical engineering, circuit theory, signal processing, economics and data science/machine learning. I have found in my teaching career that students tend to struggle the most with motivating the "why" behind the abstract concepts discussed in linear algebra. This can be difficult for professors to understand because we are so used to using the language of linear algebra we take for granted why these questions are important in the first place. In other words, we may understand the “why” (after years of using these tools), but our students may not. This text seeks to explain this “why” in an accessible, engaging way. (shrink)

The conception of a ‘law of nature’ is a human product. It was created to play a role in natural philosophy, in the Cartesian tradition. In light of this, philosophers and scientists must sort out what they mean by a law of nature before evaluating rival theories and approaches. If one’s conception of the laws of nature is yoked to metaphysical notions of truth and explanation, that connection must be made explicit and defended. If, on the other hand, one’s aim (...) is to disentangle laws from truth or from explanation, that must be stated and defended as well. If philosophers do not make such assumptions, intuitions, and methodological commitments clear, then it will be impossible to identify the source of disagreement in debates about the laws of nature. Are the conflicts rooted in disagreement about the conclusions reached, or do the background commitments of the combatants block any resolution to the dispute in principle or in practice? (shrink)

The goal of achieving Universal Health Coverage (UHC) can generally be realized only in stages. Moreover, resource, capacity and political constraints mean governments often face difficult trade-offs on the path to UHC. In a 2014 report, Making fair choices on the path to UHC, the WHO Consultative Group on Equity and Universal Health Coverage articulated principles for making such trade-offs in an equitable manner. We present three case studies which illustrate how these principles can guide practical decision-making. These case studies (...) show how progressive realization of the right to health can be effectively guided by priority-setting principles, including generating the greatest total health gain, priority for the worse off, and financial risk protection. They also demonstrate the value of a fair and accountable process of priority setting. (shrink)

In this paper, I give a brief overview of ideas from Reformed Epistemology, and the relationship between faith, evidence, and belief. I discuss what makes belief in God rationally warranted, and how reformed epistemology strikes a middle ground between fideism and evidentialism. In effect, reformed epistemology avoids the fideist idea that belief in God must be taken on "blind faith," but also avoids some of the epistemic issues present in evidentialism, such as its self-referential incoherence. The reformed epistemologist says belief (...) in God is rational, but not for the reasons demanded by evidentialists. (shrink)