Formal symptoms of relevance usually concern the propositional variables shared between the antecedent and the consequent of provable conditionals. Among the most famous results about such symptoms are Belnap’s early results showing that for sublogics of the strong relevant logic R, provable conditionals share a signed variable between antecedent and consequent. For logics weaker than R stronger variable sharing results are available. In 1984, Ross Brady gave one well-known example of such a result. As a corollary to the main result (...) of the paper, we give a very simple proof of a related but strictly stronger result. (shrink)

In this paper we introduce a novel way of building arithmetics whose background logic is R. The purpose of doing this is to point in the direction of a novel family of systems that could be candidates for being the infamous R#1/2 that Meyer suggested we look for.

Weak enough relevant logics are often closed under depth substitutions. To determine the breadth of logics with this feature, we show there is a largest sublogic of R closed under depth substitutions and that this logic can be recursively axiomatized.

Does the visual system adapt to number? For more than fifteen years, most have assumed that the answer is an unambiguous “yes”. Against this prevailing orthodoxy, we recently took a critical look at the phenomenon, questioning its existence on both empirical and theoretical grounds, and providing an alternative explanation for extant results (the old news hypothesis). We subsequently received two critical responses. Burr, Anobile, and Arrighi rejected our critiques wholesale, arguing that the evidence for number adaptation remains overwhelming. Durgin questioned (...) our old news hypothesis — preferring instead a theory about density adaptation he has championed for decades — but also highlighted several ways in which our arguments do pose serious challenges for proponents of number adaptation. Here, we reply to both. We first clarify our position regarding number adaptation. Then, we respond to our critics’ concerns, highlighting seven reasons why we remain skeptical about number adaptation. We conclude with some thoughts about where the debate may head from here. (shrink)

Relevant logics infamously have the property that they only validate a conditional when some propositional variable is shared between its antecedent and consequent. This property has been strengthened in a variety of ways over the last half-century. Two of the more famous of these strengthenings are the strong variable sharing property and the depth relevance property. In this paper I demonstrate that an appropriate class of relevant logics has a property that might naturally be characterized as the supremum of these (...) two properties. I also show how to use this fact to demonstrate that these logics seem to be constructive in previously unknown ways. (shrink)

In 1988, Kit Fine published a semantic theory for quantified relevant logics. He referred to this theory as stratified semantics. While it has received some attention in the literature, 1–20, 1992; Mares & Goldblatt, Journal of Symbolic Logic 71, 163–187, 2006), stratified semantics has overall received much less attention than it deserves. There are two plausible reasons for this. First, the only two dedicated treatments of stratified semantics available are, 27–59, 1988; Mares, Studia Logica 51, 1–20, 1992), both of which (...) are quite dense and technically challenging. Second, there are a number of prima facie reasons to be worried about stratified semantics. The purpose of this paper is to revitalize research on stratified semantics. I will do so by giving a ‘user friendly’ presentation of the semantics, and by giving reasons to think that the prima facie reasons to be worried about it are too simplistic. (shrink)

Consider the set of inferences that are acceptable to use in all our theory building endeavors. Call this set of inferences the universal theory building toolkit, or just ’the toolkit’ for short. It is clear that the toolkit is tightly connected to logic in a variety of ways. Beall, for example, has argued that logic just is the toolkit. This paper avoids making a stand on that issue and instead investigates reasons for thinking that, logic or not, the toolkit is (...) substructural. It is presented as a dialogue for the simple reason that it summarizes a range of dialogues on this subject that the author has had with various folks over the past few years. The method I use to investigate the toolkit is inspired in both philosophical and technical details by Alasdair Urquhart’s work on semantics for relevance logics from the early 1970s. (shrink)

For some years now, Michael Bergmann has urged a dilemma against internalist theories of epistemic justification. For reasons I explain below, some epistemologists have thought that Michael Huemer’s principle of Phenomenal Conservatism can split the horns of Bergmann’s dilemma. Bergmann has recently argued, however, that PC must inevitably, like all other internalist views, fall prey to his dilemma. In this paper, I explain the nature of Bergmann’s dilemma and his reasons for thinking that PC cannot escape it before arguing that (...) he is mistaken: PC can indeed split its horns. (shrink)

Nietzsche (1844–1900) struggles with complexity and many-sidedness throughout his life. He is a nuanced thinker who offers fragments instead of a rigid philosophical system, yet he admires the ‘virtuous energy’ with which systematic thinkers, especially the pre-Socratic philosophers, express themselves. His ability to write with comparable energy is hindered by university philosophy, which privileges restraint and consistency. Therefore, he adopts a practice of spontaneous life writing in order to become simple and honest in thought and life. Inspired by figures such (...) as Emerson, Diogenes, and Sterne, he grasps the ‘nearest shoddy words’ and continually produces new insights in disjointed monologues and aphorisms. Nietzsche's vague metaphors, loose language, inconsistency, and hyperbole stem from this practice, and his autobiography, Ecce Homo (1888), is the closest that he ever comes to rekindling the energy of the pre-Socratics. (shrink)

Abstractionism in the philosophy of mathematics aims at deriving large fragments of mathematics by combining abstraction principles (i.e. the abstract objects $\S e_1, \S e_2$, are identical if, and only if, an equivalence relation $Eq_\S$ holds between the entities $e_1, e_2$) with logic. Still, as highlighted in work on the semantics for relevant logics, there are different ways theories might be combined. In exactly what ways must logic and abstraction be combined in order to get interesting mathematics? In this paper, (...) we investigate the matter by deriving the axioms of second-order Peano Arithmetic from Frege's Basic Law V (the extension of $F$ is identical with the extension of $G$ if, and only if, $F$ and $G$ are extensionally equivalent) in the presence of a relevant higher-order logic. The results are interesting. Not only must we take on logic as true, and not only must we apply our logic to abstraction principles, but also we have to apply our theory of abstraction back to the logic in order to arrive at arithmetic. Thus, what Abstractionism gives us is not simply what we get from abstraction via logic, but also what we get from logic via abstraction. (shrink)

What is the role of affect in moral epistemology? Sentimentalists assert that moral knowledge is rooted in knowledge of specific situational moral truths, which affect is a necessary means for attaining. Rationalists claim moral knowledge is rooted in moral principles, knowledge of which is acquired a priori through reason alone; affect is unnecessary. Note that in this way of framing the debate, the issue concerns solely moral knowledge. Recent epistemology, however, has also highlighted the importance of understanding as an epistemic (...) good separate from knowledge. As such, moral understanding might have value over and above mere moral knowledge. Some philosophers have pointed to the importance moral understanding possesses for reliably doing the right thing, justifying yourself to others, developing virtue, and performing morally worthy action. In this paper, I argue that the sentimentalist account of understanding both specific moral truths and moral principles has significant advantages over, and can ground, the rationalist alternative. (shrink)

It is still a live question in epistemology and philosophy of science as to what exactly evidence is. In my view, evidence consists in experiences called “seemings.” This view is a version of the phenomenal conception of evidence, the position that evidence consists in nonfactive mental states with propositional content. This conception is opposed by sense-data theorists, disjunctivists, and those who think evidence consists in physical objects or publicly observable states of affairs—call it the courtroom conception of evidence. Thomas Kelly (...) has recently argued that the phenomenal conception cannot play all the roles evidence plays and is thus inadequate. Having first explained the nature of seemings, in this essay I utilize Kelly’s own understanding of the four major roles of evidence and argue that the phenomenal conception can play each one. Experience is a good candidate for evidence. (shrink)

In this paper, we provide a semantics for a range of positive substructural logics, including both logics with and logics without modal connectives. The semantics is novel insofar as it is meant to explicitly capture the computational flavor of these logics, and to do so in a way that builds in both nondeterministic and nonconcurrent computational processes.

We criticize the classical evidentialist approach to religious epistemology as articulated by John DePoe from the perspective of phenomenal conservatism.

Truthmaker monism is the view that the one and only truthmaker is the world. Despite its unpopularity, this view has recently received an admirable defence by Schaffer :307–324, 2010b). Its main defect, I argue, is that it omits partial truthmakers. If we omit partial truthmakers, we lose the intimate connection between a truth and its truthmaker. I further argue that the notion of a minimal truthmaker should be the key notion that plays the role of constraining ontology and that truthmaker (...) monism is not necessary for an appropriate solution to the problem of finding truthmakers for negative truths. I conclude that we should reject truthmaker monism once and for all. (shrink)

This paper presents a new semantics for the weak relevant logic DW that makes the role of the infamous Routley star more explicable. Central to this rewriting is combining aspects of both the American and Australian plan for understanding negations in relevance logics.

A brief introduction to a diverse and interesting group of papers in contemporary epistemology.

In this chapter, Logan Paul Gage examines the only real attempt to disprove God’s existence by a New Atheist: Richard Dawkins’s “Ultimate 747 Gambit.” Central to Dawkins’s argument is the claim that God is more complex than what he is invoked to explain. Gage evaluates this claim using the main extant notions of simplicity in the literature. Gage concludes that on no reading does this claim survive scrutiny. Along the way, Dawkins claims that there are no good positive arguments (...) for God’s existence. Gage attempts to show that Dawkins’s argument depends upon distinctively philosophical assumptions that do not appear to withstand scrutiny. (shrink)

I present a version of Kit Fine's stratified semantics for the logic RWQ and define a natural family of related structures called RW hyperdoctrines. After proving that RWQ is sound with respect to RW hyperdoctrines, we show how to construct, for each stratified model, a hyperdoctrine that verifies precisely the same sentences. Completeness of RWQ for hyperdoctrinal semantics then follows from completeness for stratified semantics, which is proved in an appendix. By examining the base category of RW hyperdoctrines, we find (...) reason to be worried about the ontology of stratified models. (shrink)

This work offers an analysis of all the legal and moral issues surrounding humanitarian intervention: the deaths of innocent persons and the Doctrine of Double Effect Governmental legitimacy - The Doctrine of Effective Political Control; UN Charter and evaluation of the Nicaragua ruling; The Morality of not intervening; US-led invasion of Iraq; Humanitarian intervention authorised by the UN Security Council - Iraq, Somalia, Haiti, Rwanda, and Bosnia among others highlight NATO's intervention in Kosovo; The Nicaragua Decision; and The precedents of (...) Panama, Liberia and Sierra Leone. The book's features include: a new framework based on the doctrine of double effect; basic principles of international ethics; outline of the moral argument for humanitarian intervention; explores the morality and legality of military action to end tyranny or anarchy; arguments in a much more detailed and complete fashion than in previous editions; in-depth examination of philosophy of international law; the relationship between custom and moral theory; new discussion of the question of right authority; and a full analysis of recent interventions in Kosovo and Iraq. book addresses a broad interdisciplinary audience of international lawyers, philosophers, and political scientists. In this new edition, the author responds to critics while updating the discussion in the light of the momentous events that took place at the beginning of the new millennium. (shrink)

Linnebo and Pettigrew present some objections to category theory as an autonomous foundation. They do a commendable job making clear several distinct senses of ‘autonomous’ as it occurs in the phrase ‘autonomous foundation’. Unfortunately, their paper seems to treat the ‘categorist’ perspective rather unfairly. Several infelicities of this sort were addressed by McLarty. In this note I address yet another apparent infelicity.

This paper explores personal identity and persistence through time in the Many Worlds Interpretation (MWI) of quantum mechanics (QM). First, I will motivate the MWI’s relevance in the domain of metaphysics. Second, I will define endurantism. Third, I will explain the foundational physics underlying the MWI which entails branching worlds. Finally, I will argue that the privileged branch view best captures endurantist judgments about personal identity and persistence through time in the many-worlds framework. (Note that this work is in its (...) early draft stages - later versions will be updated and revised). (shrink)

In a time when conservatives believe that the traditional family is under increasing fire, some think an appeal to Darwinian science may be the answer. I argue that these conservatives are wrong to maintain that Darwinian theory can serve as the intellectual foundation for the traditional conception of the family. Contra Larry Arnhart and James Q. Wilson, a Darwinian philosophy of nature simply lacks the stability the traditional family requires; it cannot support the traditional conception of human nature and the (...) normativity it was thought to contain. If conservatives are to maintain these traditional ideas, the theoretical foundation must lie elsewhere. (shrink)

Categorial logic, as its name suggests, applies the techniques and machinery of category theory to topics traditionally classified as part of logic. We claim that these tools deserve attention from a greater range of philosophers than just the mathematical logicians. We support this claim with an example. In this paper we show how one particular tool from categorial logic---hyperdoctrines---suggests interesting metaphysics. Hyperdoctrines can provide semantics for quantified languages, but this account of quantification suggests a metaphysical picture quite different from the (...) one suggested by standard model-theoretic semantics. (shrink)

This paper attempts to explain the conceptual connections between happiness and well-being. It first distinguishes episodic happiness from happiness in the personal attribute sense. It then evaluates two recent proposals about the connection between happiness and well-being: (1) the idea that episodic happiness and well-being both have the same fundamental determinants, so that a person is well-off to a particular degree in virtue of the fact that they are happy to that degree, and (2) the idea that happiness in the (...) personal attribute sense can serve as a ‘‘proxy’’ for well-being, i.e., that a person’s degree of deep or robust happiness approximates their degree of well-being. It is argued that happiness in both these senses is conceptually, metaphysically, and empirically distinct from well- being. A new analysis of welfare, well-being as agential flourishing, can explain welfare’s real connection to happiness in both the episodic and personal attribute senses. It predicts that such happiness is only directly beneficial when it is valued, when it is a form of valuing, or when it underwrites (i.e., serves as the causal basis for) the disposition to realize one’s values. It is therefore a necessary—but not sufficient—condition for especially high levels of well-being. This analysis of welfare integrates many insights from the eudaimonic tradition of welfare and happiness research in psychology, and also addresses common criticisms of these eudaimonic models. (shrink)

Among the factors necessary for the occurrence of some event, which of these are selectively highlighted in its explanation and labeled as causes — and which are explanatorily omitted, or relegated to the status of background conditions? Following J. S. Mill, most have thought that only a pragmatic answer to this question was possible. In this paper I suggest we understand this ‘causal selection problem’ in causal-explanatory terms, and propose that explanatory trade-offs between abstraction and stability can provide a principled (...) solution to it. After sketching that solution, it is applied to a few biological examples, including to a debate concerning the ‘causal democracy’ of organismal development, with an anti-democratic (though not a gene-centric) moral. (shrink)

The role of certitude in our mental lives is, to put it mildly, controversial. Many current epistemologists (including epistemologists of religion) eschew certitude altogether. Given his emphasis on certitude, some have maintained that John Henry Newman was an infallibilist about knowledge. In this paper, we argue that a careful examination of his thought (especially as seen in the Grammar of Assent) reveals that he was an epistemic fallibilist. We first clarify what we mean by fallibilism and infallibilism. Second, we explain (...) why some have read Newman as an infallibilist. Third, we offer two arguments that Newman is at least a fallibilist in a weak sense. In particular, the paradox he seeks to resolve in the Grammar and his dispute with John Locke both indicate that he is at least a weak fallibilist. We close with a consideration of whether Newman is a fallibilist in a much stronger sense as well. (shrink)

Exploitation and Economic Justice in the Liberal Capitalist State offers the first new, liberal theory of economic justice to appear in more than 30 years. The theory presented is designed to offer an alternative to the most popular liberal egalitarian theories of today and aims to be acceptable to both right and left libertarians too.

In this chapter, we argue for a phenomenal conservative perspective on religious epistemology and attempt to answer some common criticisms of this perspective.

In this paper, we examine a number of relevant logics’ variable sharing properties from the perspective of theories of topic or subject-matter. We take cues from Franz Berto’s recent work on topic to show an alignment between families of variable sharing properties and responses to the topic transparency of relevant implication and negation. We then introduce and defend novel variable sharing properties stronger than strong depth relevance—which we call cn-relevance and lossless cn-relevance—showing that the properties are satisfied by the weak (...) relevant logics and , respectively. We argue that such properties address a sort of semantic lossiness of strong depth relevance. (shrink)

Adam Smith is respected as the father of contemporary economics for his work on systemizing classical economics as an independent field of study in The Wealth of Nations. But he was also a significant moral philosopher of the Scottish Enlightenment, with its characteristic concern for integrating sentiments and rationality. This article considers Adam Smith as a key moral philosopher of commercial society whose critical reflection upon the particular ethical challenges posed by the new pressures and possibilities of commercial society remains (...) relevant today. The discussion has three parts. First I address the artificial separation between self-interest and morality often attributed to Smith, in which his work on economics is stripped of its ethical context. Second I outline Smith’s ethical approach to economics, focusing on his vigorous but qualified defence of commercial society for its contributions to prosperity, justice, and freedom. Third I outline Smith’s moral philosophy proper as combining a naturalistic account of moral psychology with a virtue ethics based on propriety in commercial society. (shrink)

David Lewis objected to theories that posit necessary connections between distinct entities and to theories that involve a magical grasping of their primitives. In On the Plurality of Worlds, Lewis objected to nondescript ersatzism on these grounds. The literature contains several reconstructions of Lewis’ critique of nondescript ersatzism but none of these interpretations adequately address his main argument because they fail to see that Lewis’ critique is based on broader methodological considerations. I argue that a closer look at his methodology (...) reveals the broader objection he presented against nondescript ersatzism. This objection, I further argue, remains a challenge for the ersatzer who posits structure-less entities as possible worlds. (shrink)

A discussion of several tensions between Thomistic philosophy and modern Darwinian theory as well as several recent Thomistic criticisms of intelligent design.

Recent authors, emphasizing Newman’s distaste for natural theology—especially William Paley’s design argument—have urged us to follow Newman’s lead and reject design arguments. But I argue that Newman’s own argument for God’s existence (his argument from conscience) fails without a supplementary design argument or similar reason to think our faculties are truth-oriented. In other words, Newman appears to need the kind of argument he explicitly rejects. Finding Newman’s rejection of natural theology to stem primarily from factors other than worries about cogency, (...) however, I further argue that there is little reason not to pursue design arguments in order to save the argument from conscience. (shrink)

Artificial intelligence (AI) and machine learning (ML) models have undoubtedly become useful tools in science. In general, scientists and ML developers are optimistic – perhaps rightfully so – about the potential that these models have in facilitating scientific progress. The philosophy of AI literature carries a different mood. The attention of philosophers remains on potential epistemological issues that stem from the so-called “black box” features of ML models. For instance, Eamon Duede (2023) argues that opacity in deep learning models (DLMs) (...) is epistemically problematic in the context of justification, though not in the context of discovery. -/- In this paper, I aim to show that a similar epistemological concern is echoed in the epistemology of imagination literature. It is traditionally held that, given its black box features, reliance on the imagination is epistemically problematic in the context of justification, though not in the context of discovery. The constraints-based approach to the imagination answers the epistemological concern by providing an account of how we can rely on the imagination in the context of justification by way of constraints. I argue by analogy that a similar approach can be applied to the opaque DLM case. Ultimately, my goal is to explore just how far this analogy extends, and whether a constraints-based approach to opaque DLMs can answer the epistemological concern surrounding their black box features in the context of justification. -/- (Note that this paper is IN PROGRESS and UNPUBLISHED). (shrink)

This essay shows how John Henry Newman reconciled the certitude of faith with a fallibilist epistemology. While Newman holds that many of our beliefs are held with certitude, he does not conceive of all certitude as Cartesian, apodictic certitude. In this way, he walks a middle road between rationalism and fideism.

In this essay, I describe my journey to Catholicism and explain one of the many reasons I became Catholic--namely, an argument from the canon of Scripture.

Contextualism (the view that ‘knowledge’ and its variants are context-sensitive) has been supported in large part through appeal to intuitions about Keith DeRose’s Bank Cases. Recently, however, the contextualist construal of these cases has come under fire from Kent Bach and Jennifer Nagel who question whether the Bank Case subject’s confidence can remain constant in both low- and high-stakes cases. Having explained the Bank Cases and this challenge to them, I argue that DeRose has given a reasonable reply to this (...) initial challenge. However, I proceed to argue that the current stalemate can be broken. Seeking to extend the Bach-Nagel critique, I offer a novel interpretation of the Bank Cases according to which the subject’s evidence changes between low- and high-stakes cases. If I am correct, then, given the amount of support the Bank Cases have been thought to lend contextualism, the case for contextualism is seriously weakened. (shrink)

We criticize the approach of covenantal epistemology to religious epistemology as articulated by Scott Oliphint from the perspective of phenomenal conservatism.

A brief introduction to the life and key work of Rudolf Carnap with special attention to his work on inductive logic.

A brief introduction to the life and work of William Paley, including a discussion of the structure of his famous design argument.

We criticize the proper functionalist approach to religious epistemology as articulated by Tyler McNabb from the perspective of phenomenal conservatism.

We critique MacIntyre's traditions-based perspectivalist approach to religious epistemology as articulated by Erik Baldwin from the perspective of phenomenal conservatism.

In this chapter, Gage and McAllister respond to various objections to the phenomenal conservative position in religious epistemology. In particular, they respond to the objections that seemings are the ultimate source of justification, that PC makes epistemic justification too easy, that PC involves conceptual circularity, and that PC lacks an objective connection to truth.