Where E is the proposition that [If H and O were true, H would explain O], William Roche and Elliot Sober have argued that P(H|O&E) = P(H|O). In this paper I argue that not only is this equality not generally true, it is false in the very kinds of cases that Roche and Sober focus on, involving frequency data. In fact, in such cases O raises the probability of H only given that there is an explanatory connection between them.

Defenders of Inference to the Best Explanation claim that explanatory factors should play an important role in empirical inference. They disagree, however, about how exactly to formulate this role. In particular, they disagree about whether to formulate IBE as an inference rule for full beliefs or for degrees of belief, as well as how a rule for degrees of belief should relate to Bayesianism. In this essay I advance a new argument against non-Bayesian versions of IBE. My argument focuses on (...) cases in which we are concerned with multiple levels of explanation of some phenomenon. I show that in many such cases, following IBE as an inference rule for full beliefs leads to deductively inconsistent beliefs, and following IBE as a non-Bayesian updating rule for degrees of belief leads to probabilistically incoherent degrees of belief. (shrink)

I argue that when we use ‘probability’ language in epistemic contexts—e.g., when we ask how probable some hypothesis is, given the evidence available to us—we are talking about degrees of support, rather than degrees of belief. The epistemic probability of A given B is the mind-independent degree to which B supports A, not the degree to which someone with B as their evidence believes A, or the degree to which someone would or should believe A if they had B as (...) their evidence. My central argument is that the degree-of-support interpretation lets us better model good reasoning in certain cases involving old evidence. Degree-of-belief interpretations make the wrong predictions not only about whether old evidence confirms new hypotheses, but about the values of the probabilities that enter into Bayes’ Theorem when we calculate the probability of hypotheses conditional on old evidence and new background information. (shrink)

I advance a novel argument for an infallibilist theory of knowledge, according to which we know all and only those propositions that are certain for us. I argue that this theory lets us reconcile major extant theories of knowledge, in the following sense: for any of these theories, if we require that its central condition (evidential support, reliability, safety, etc.) obtains to a maximal degree, we get a theory of knowledge extensionally equivalent to infallibilism. As such, the infallibilist can affirm (...) that, when their conditions are suitably interpreted, most post-Gettier theories of knowledge offer necessary and sufficient conditions for knowledge. The infallibilist can thus reconcile major theories of knowledge, and is in a better position to explain the intuitive appeal of these theories than the fallibilist who only accepts one of them, and rejects the rest. (shrink)

A common argument for atheism runs as follows: God would not create a world worse than other worlds he could have created instead. However, if God exists, he could have created a better world than this one. Therefore, God does not exist. In this paper I challenge the second premise of this argument. I argue that if God exists, our world will continue without end, with God continuing to create value-bearers, and sustaining and perfecting the value-bearers he has already created. (...) Given this, if God exists, our world—considered on the whole—is infinitely valuable. I further contend that this theistic picture makes our world's value unsurpassable. In support of this contention, I consider proposals for how infinitely valuable worlds might be improved upon, focusing on two main ways—adding value-bearers and increasing the value in present value-bearers. I argue that neither of these can improve our world. Depending on how each method is understood, either it would not improve our world, or our world is unsurpassable with respect to it. I conclude by considering the implications of my argument for the problem of evil more generally conceived. (shrink)

According to a simple Bayesian argument from evil, the evil we observe is less likely given theism than given atheism, and therefore lowers the probability of theism. I consider the most common skeptical theist response to this argument, according to which our cognitive limitations make the probability of evil given theism inscrutable. I argue that if skeptical theists are right about this, then the probability of theism given evil is itself largely inscrutable, and that if this is so, we ought (...) to be agnostic about whether God exists. (shrink)

The epistemic probability of A given B is the degree to which B evidentially supports A, or makes A plausible. This paper is a first step in answering the question of what determines the values of epistemic probabilities. I break this question into two parts: the structural question and the substantive question. Just as an object’s weight is determined by its mass and gravitational acceleration, some probabilities are determined by other, more basic ones. The structural question asks what probabilities are (...) not determined in this way—these are the basic probabilities which determine values for all other probabilities. The substantive question asks how the values of these basic probabilities are determined. I defend an answer to the structural question on which basic probabilities are the probabilities of atomic propositions conditional on potential direct explanations. I defend this against the view, implicit in orthodox mathematical treatments of probability, that basic probabilities are the unconditional probabilities of complete worlds. I then apply my answer to the structural question to clear up common confusions in expositions of Bayesianism and shed light on the “problem of the priors.”. (shrink)

I present a cumulative case for the thesis that we only know propositions that are certain for us. I argue that this thesis can easily explain the truth of eight plausible claims about knowledge: -/- (1) There is a qualitative difference between knowledge and non-knowledge. (2) Knowledge is valuable in a way that non-knowledge is not. (3) Subjects in Gettier cases do not have knowledge. (4) If S knows that P, P is part of S’s evidence. (5) If S knows (...) that P, ~P is epistemically impossible for S. (6) If S knows that P, S can rationally act as if P. (7) If S knows that P, S can rationally stop inquiring whether P. (8) If S knows each of {P1, P2, … Pn}, and competently deduces Q from these propositions, S knows that Q. -/- I then argue that the skeptical costs of this thesis are outweighed by its explanatory power. (shrink)

Molinists hold that there are contingently true counterfactuals about what agents would do if put in specific circumstances, that God knows these prior to creation, and that God uses this knowledge in choosing how to create. In this essay we critique Molinism, arguing that if these theses were true, agents would not be free. Consider Eve’s sinning upon being tempted by a serpent. We argue that if Molinism is true, then there is some set of facts that fully explains both (...) Eve’s action and everything else Eve does that influences that action; and that if this is the case, Eve does not act freely. The first premise of this argument follows from the explanatory relations the Molinist is committed to, and the second premise follows from libertarian intuitions about free will. (shrink)

This chapter presents a typology of the different kinds of inductive inferences we can draw from our evidence, based on the explanatory relationship between evidence and conclusion. Drawing on the literature on graphical models of explanation, I divide inductive inferences into (a) downwards inferences, which proceed from cause to effect, (b) upwards inferences, which proceed from effect to cause, and (c) sideways inferences, which proceed first from effect to cause and then from that cause to an additional effect. I further (...) distinguish between direct and indirect forms of downwards and upwards inferences. I then show how we can subsume canonical forms of inductive inference mentioned in the literature, such as inference to the best explanation, enumerative induction, and analogical inference, under this typology. Along the way, I explore connections with probability and confirmation, epistemic defeat, the relation between abduction and enumerative induction, the compatibility of IBE and Bayesianism, and theories of epistemic justification. (shrink)

Among Bayesian confirmation theorists, several quantitative measures of the degree to which an evidential proposition E confirms a hypothesis H have been proposed. According to one popular recent measure, s, the degree to which E confirms H is a function of the equation P(H|E) − P(H|~E). A consequence of s is that when we have two evidential propositions, E1 and E2, such that P(H|E1) = P(H|E2), and P(H|~E1) ≠ P(H|~E2), the confirmation afforded to H by E1 does not equal the (...) confirmation afforded to H by E2. I present several examples that demonstrate the unacceptability of this result, and conclude that we should reject s (and other measures that share this feature) as a measure of confirmation. (shrink)

"Correlation is not causation" is one of the mantras of the sciences—a cautionary warning especially to fields like epidemiology and pharmacology where the seduction of compelling correlations naturally leads to causal hypotheses. The standard view from the epistemology of causation is that to tell whether one correlated variable is causing the other, one needs to intervene on the system—the best sort of intervention being a trial that is both randomized and controlled. In this paper, we argue that some purely correlational (...) data contains information that allows us to draw causal inferences: statistical noise. Methods for extracting causal knowledge from noise provide us with an alternative to randomized controlled trials that allows us to reach causal conclusions from purely correlational data. (shrink)

Several scholars, including Martin Hengel, R. Alan Culpepper, and Richard Bauckham, have argued that Papias had knowledge of the Gospel of John on the grounds that Papias’s prologue lists six of Jesus’s disciples in the same order that they are named in the Gospel of John: Andrew, Peter, Philip, Thomas, James, and John. In “A Note on Papias’s Knowledge of the Fourth Gospel” (JBL 129 [2010]: 793–794), Jake H. O’Connell presents a statistical analysis of this argument, according to which the (...) probability of this correspondence occurring by chance is lower than 1%. O’Connell concludes that it is more than 99% probable that this correspondence is the result of Papias copying John, rather than chance. I show that O’Connell’s analysis contains multiple mistakes, both substantive and mathematical: it ignores relevant evidence, overstates the correspondence between John and Papias, wrongly assumes that if Papias did not know John he ordered the disciples randomly, and conflates the probability of A given B with the probability of B given A. In discussing these errors, I aim to inform both Johannine scholarship and the use of probabilistic methods in historical reasoning. (shrink)

This chapter explores the role that non-textual narrations of biblical stories can play in Christian life and practice. Our case study is the Shrine of Divine Mercy in Kabuga, Rwanda. The stations at the shrine tell the story of Jesus’s life and passion, incorporating images from the Catholic devotional tradition of Divine Mercy and elements evoking the Rwandan genocide. While many philosophical accounts of narratives presuppose that narratives are textual, material and visual art like the Kabuga shrine can also be (...) narrative, in that, like text, material and visual art can selectively represent multiple events and connections between them. We argue that material-visual narratives like the shrine can be effective in achieving commonly identified functions of narratives, such as focusing attention, immersing in a story, engaging the emotions, and fostering a common perspective on the world. We further argue that material-visual art is well-suited to narrating the Gospel in particular, for it can present the Gospel story alongside other stories (in this case, the story of the Rwandan genocide) and in so doing reframe these other stories in light of the Gospel. (shrink)

In this paper, I examine whether John Stuart Mill’s account of free speech can survive three main challenges posed by social media. First, I consider the problem of social media failing to distinguish between emotive and factual language. Second, I look at the problem of algorithms creating moralism. I then turn to a potential objection to my first two challenges. The objection elucidates the benefits of social media’s emotional and algorithmic character, amplifying arguments and increasing public engagement. However, I take (...) issue with this objection on consequentialist terms. I finally return to the third challenge, where I focus on how anonymity removes the consequences to our words; I contend that this final failure is the ultimate reason why Mill’s account cannot persist in the modern age. In conclusion, I argue that Mill’s account cannot withstand the problems posed by social media. (shrink)

The initiation of bipedal gait is a willed action that causes a body at rest to move. Newton's first principle of motion is applied to experimental footprint data. leading to the premise that the big toe is the source of the body action force that initiates and controls bipedal gait.

The moral justification of intellectual property is often called into question when placed in the context of pharmaceutical patents and global health concerns. The theoretical accounts of both John Rawls and Robert Nozick provide an excellent ethical framework from which such questions can be clarified. While Nozick upholds an individuals right to intellectual property, based upon its conformation with Lockean notions of property and Nozicks ideas of just acquisition and transfer, Rawls emphasizes the importance of basic liberties, such as an (...) individuals right to health, superceding such secondary rights as intellectual property rights. From a policy perspective, patent protection for pharmaceutical products necessarily entails the balancing of corporate intellectual property interests and public interests in healthcare. The moral dilemma that occurs when these two interests clash is not easily resolved. Aside from corporate and public interests, the state maintains an interest in creating and preserving policies that regulate the moral dilemma itself. This paper analyzes the economic and ethical factors surrounding the production and distribution of the anti-HIV medication, AZT. Potential policy implications and recommendations are also discussed. (shrink)

Recent work in the philosophy of religion has resurrected Leibniz’s idea that there is a best possible world, perhaps ours. In particular, Klaas Kraay’s [2010] construction of a theistic multiverse and Nevin Climenhaga’s [2018] argument from infinite value theory are novel defenses of a best possible world. I do not think that there is a best world, and show how both Kraay and Climenhaga may be resisted. First, I argue that Kraay’s construction of a theistic multiverse can be resisted (...) from plausible assumptions about set theory. Next, I argue against the value-theoretic assumptions that underlie Climenhaga’s argument and show how to give an infinite value theory where there is no best world. (shrink)

Report submitted by Gregory B. Sadler, Pilot Project Coordinator to Sonya Brown, WAC Activity Director, Fayetteville State University, June 28 2011. -/- A Pilot program focused on improving student performance in carrying out Close Readings in humanities-based discipline courses was developed and implemented under the auspices of Writing Across the Curriculum and Title III at Fayetteville State University in Winter and Spring 2011. Five faculty were involved in the Pilot, myself as the coordinator, and four other faculty from four (...) different disciplines as participants. -/- The central idea behind the Pilot was that by focusing on the lower-order skills which are scaffolded as components into the higher-order activity of Close Reading of texts, and redesigning courses to emphasize development of these lower-order skills, student performances in Close Readings would also be improved. This did turn out to be the case. Most of the supporting data is qualitative rather than quantitative. -/- It is recommended that similar activities be continued, but that participating faculty be required to provide much more prescriptively structured and detailed assessment data and information about their course design. (shrink)

This is a critical notice of Christos Kyriacou and Kevin Wallbridge (eds.), Skeptical Invariantism Reconsidered. New York and London: Routledge, 2021. Pp. x + 324. ISBN 978-0-367-37018-3. It discusses in some detail contributions by Nevin Climenhaga, Christos Kyriacou, Michael Hannon, Kevin Wallbridge, Annalisa Coliva, and Genia Schönbaumsfeld.