I EXPLORE ONE WAY IN WHICH THE THEORY OF RELATIVE IDENTITY (DEVELOPED ALONG LINES SUGGESTED BY GEACH’S WRITINGS) CAN BE USED TO UNDERSTAND THE WAY LANGUAGE FUNCTIONS IN TRINITARIAN DOCTRINE. THIS INCLUDES A DISCUSSION OF REDUPLICATIVE PROPOSITIONS.

Suppose we wish to decide which of a pair of actions has better consequences in a case in which both actions result in infinite utility. Peter Vallentyne and others have proposed that one action has better consequences than a second if there is a time after which the cumulative utility of the first action always outstrips the cumulative utility of the second. I argue against this principle, in particular I show how cases may arise in which up to any point (...) of time action a1 produces more utility than action a2, yet for each individual involved a2 produces more utility. (shrink)

Frankfurt examples are frequently used in arguments designed to show that agents lacking alternatives, or lacking ‘regulative control’ over their actions, can be morally responsible for what they do. I will maintain that Frankfurt examples can be constructed that undermine those very arguments when applied to actions for which the agent bears fundamental responsibility.

Many philosophers accept with certainty that we are morally responsible but take it to be an open question whether determinism holds. They treat determinism as epistemically compatible with responsibility. Should one who accepts this form of epistemic compatibilism also hold that determinism is metaphysically compatible with responsibility—that it is metaphysically possible for determinism and responsibility to coexist? John Martin Fischer gives two arguments that appear to favor an affirmative answer to this question. He argues that accounts of responsibility, such as (...) his, that are neutral with respect to whether responsible actions are determined have a "resiliency" that counts in their favor. Furthermore, he criticizes libertarians who argue on a priori grounds that determinism cannot coexist with responsibility and who admit that they would retract their argument if determinism were shown to hold; this "metaphysical flip-flopping" is said to render their positions implausible. I assess the merits of these arguments. (shrink)

I will argue that the Kane-Widerker objection to Frankfurt examples is much weaker than is generally recognized. The Kane-Widerker objection holds that proponents of Frankfurt examples beg the question against incompatibilist accounts of free and responsible action by constructing examples that tacitly assume a compatibilist account of moral responsibility; that is, they assume that one can have non-derivative responsibility for choices that were not undetermined prior to their occurrence. The notion of an event, E, being ‘undetermined prior to its occurrence’ (...) is ambiguous. It can mean either (1) with respect to each time t prior to E’s occurrence, it is not the case that at t E’s occurrence is determined to take place, or it can mean (2) with respect to the whole collection of times prior to E’s occurrence, E’s occurrence is not determined to take place. Kane’s argument shows that (under certain constraints) if a choice is to be undetermined (in the second sense) prior to its occurrence, then a prior-sign Frankfurt example cannot be successful. But he fails to show that prior-sign Frankfurt examples cannot be constructed in which the choice is undetermined (in the first sense) prior to its occurrence, and he would need to do so in order to sustain his charge that those using Frankfurt examples beg the question against traditional incompatibilist accounts of responsibility. Widerker’s argument avoids the above problem, but at the cost of only applying to a rather restricted set of Frankfurt examples. (shrink)

There is a conception of hell that holds that God punishes some people in a way that brings about endless suffering and unhappiness. An objection to this view holds that such punishment could not be just since it punishes finite sins with infinite suffering. In answer to this objection, it is shown that endless suffering, even intense suffering, is consistent with the suffering being finite. Another objection holds that such punishment is contrary to God's love. A possible response to this (...) objection is developed. (shrink)

It is well known that the following features hold of AR + T under the strong Kleene scheme, regardless of the way the language is Gödel numbered: 1. There exist sentences that are neither paradoxical nor grounded. 2. There are 2ℵ0 fixed points. 3. In the minimal fixed point the weakly definable sets (i.e., sets definable as {n∣ A(n) is true in the minimal fixed point where A(x) is a formula of AR + T) are precisely the Π1 1 sets. (...) 4. In the minimal fixed point the totally defined sets (sets weakly defined by formulae all of whose instances are true or false) are precisely the ▵1 1 sets. 5. The closure ordinal for Kripke's construction of the minimal fixed point is ωCK 1. In contrast, we show that under the weak Kleene scheme, depending on the way the Gödel numbering is chosen: 1. There may or may not exist nonparadoxical, ungrounded sentences. 2. The number of fixed points may be any positive finite number, ℵ0, or 2ℵ0 . 3. In the minimal fixed point, the sets that are weakly definable may range from a subclass of the sets 1-1 reducible to the truth set of AR to the Π1 1 sets, including intermediate cases. 4. Similarly, the totally definable sets in the minimal fixed point range from precisely the arithmetical sets up to precisely the ▵1 1 sets. 5. The closure ordinal for the construction of the minimal fixed point may be ω, ωCK 1, or any successor limit ordinal in between. In addition we suggest how one may supplement AR + T with a function symbol interpreted by a certain primitive recursive function so that, irrespective of the choice of the Godel numbering, the resulting language based on the weak Kleene scheme has the five features noted above for the strong Kleene language. (shrink)

According to the free-will defence, the exercise of free will by creatures is of such value that God is willing to allow the existence of evil which comes from the misuse of free will. A well-known objection holds that the exercise of free will is compatible with determinism and thus, if God exists, God could have predetermined exactly how the will would be exercised; God could even have predetermined that free will would be exercised sinlessly. Thus, it is held, the (...) free-will defence cannot be used as a partial account of why God should have allowed evil to exist. I investigate this objection using Kripke's apparatus for treating modalities and natural kinds to explore the nature of the incompatibilism required by the free-will defence. I show why the objection fails even if the standard arguments for compatibilism are acceptable. This is because the modality involved in the incompatibilism needed by the free-will defence differs from the modality involved in the compatibilism that is supported by standard compatibilist arguments. Finally, an argument is sketched for a variety of incompatibilism of the kind needed by the free-will defence. (shrink)

Contemporary accounts of the Trinity and Incarnation sometimes employ aspects of Peter Geach's theory of relative identity. Geach's theory provides an account not merely of identity predicates, but also proper names and restricted quantification. In a previous work I developed an account of the doctrines of the Trinity and Incarnation incorporating these three aspects of Geach's theory and tried to show how each might contribute to our understanding of the doctrines. Joseph Jedwab has recently argued that my account—or any that (...) employs Geach's treatment of restricted quantifiers—leads to serious doctrinal errors. I reply to his criticisms. (shrink)

Frankfurt style examples (FSEs) have played an important role in the development of metaphysical accounts of moral agency. The legitimacy of this approach often requires that FSEs be metaphysically possible. I argue that, given our current knowledge of the nature of decision-making, we have no grounds to accept the metaphysical possibility of many standard FSEs involving a device that can be triggered to bring about a predetermined decision.

A language in which we can express arithmetic and which contains its own satisfaction predicate (in the style of Kripke's theory of truth) can be formulated using just two nonlogical primitives: (the successor function) and Sat (a satisfaction predicate).

The notion of computability is developed through the study of the behavior of a set of languages interpreted over the natural numbers which contain their own fully defined satisfaction predicate and whose only other vocabulary is limited to "0", individual variables, the successor function, the identity relation and operators for disjunction, conjunction, and existential quantification.

Classical utilitarianism attempts to reduce the moral significance of the individual to something more basic: the value of the individual is seen as fully grounded in considerations of utility maximization. This paper criticizes this aspect of utilitarianism and tries to do so through an appeal to considerations that would be acceptable to one who embraces utilitarianism. First, an example is developed in which (1) a pair of mutually exclusive actions each yield infinite utility; (2) neither action can be said to (...) yield more utility than the other, and (3) one of the actions is clearly preferable. This provides a case in which the moral significance of the individual cannot be fully reduced to considerations of utility maximizing features of the action. A second example, developed along the lines of the first example, involves only finite utilities. (shrink)

This essay reframes salient issues in discussions of free will using conceptual apparatus developed in the works of Saul Kripke, with particular attention paid to his little-discussed technical notion of a prejudice. I begin by focusing on how various forms of modality (metaphysical, epistemic, and conceptual) underlie alternate forms of compatibilism and discuss why it is important to avoid conflating these forms of compatibilism. The concept of a prejudice is then introduced. We consider the semantic role of prejudices, in particular (...) conditions in which prejudices turn out to express metaphysically necessary truths. With that as background, I discuss a set of prejudices involving the notion of choice. We consider the role these prejudices might play, should they turn out to be true, in determining the answer to various compatibility questions concerning the nature of moral responsibility and choice. (shrink)

P. T. Geach has argued that it is impossible to demonstrate that the doctrine of the Trinity is consistent. I try to show why -- on a common understanding of the notion of consistency -- his reasoning is flawed and why, on Geach’s own principles, one should expect that if the doctrine of the Trinity is true then it will be possible to prove that the doctrine is consistent, and it will be possible to do this in a way that (...) makes no appeal to the truth of any religious doctrine. (shrink)

Hubert Dreyfus has argued that cases of absorbed bodily coping show that there is no room for self-awareness in flow experiences of experts. In this paper, I argue against Dreyfus’ maxim of vanishing self-awareness by suggesting that awareness of agency is present in expert bodily action. First, I discuss the phenomenon of absorbed bodily coping by discussing flow experiences involved in expert bodily action: merging into the flow; immersion in the flow; emergence out of flow. I argue against the claim (...) that flow experience does not involve an awareness of agency for each of these features, while conceding that fluent agency does not involve self-awareness in the thetic sense. I challenge the assumption that the awareness of fluent agency must be understood in terms of a thetic awareness of agency. Instead, I develop an Anscombean account of the awareness of fluent agency in terms of the phenomenal character of knowing one’s aims. I respond to the challenge that if an Anscombean account of the awareness of agency is to succeed, then agents must be able to answer Anscombean questions. I consider the objection that awareness of agency is not a form of self-awareness by outlining an account of self-awareness as self-synthesis that is distinct from self-perception and self-ascription, but which makes room for self-awareness in expert bodily action. (shrink)

In this article, I offer an account of what one of the short-term political aims of proponents of greater equality ought to be. I claim that the strengthening of reflective capacity—citizens’ ability to impose a temporary level of distance from their commitments, to consider alternatives to them, and to evaluate their origins and validity—ought to be one key aim of egalitarian politics under present political conditions. I then propose activist-led education programs as one desirable means to deliver this end of (...) strengthened reflective capacity. Where activist-led education provides plentiful informational resources and opportunities to practice deploying one’s reflective capacity, and also emphasizes and encourages intellectual humility, it seems well placed to help bring about this aim. Activist-led education programs are commonly subject to what I term the indoctrination worry, but I try to show that there are not good grounds for concluding in advance of further study that the delicate balancing of ends that permissible activist-led education requires is either categorically unachievable, or avoidable in the way these objectors often press. The argument thus provides presumptive grounds for considering the proliferation of suitably organized activist-led education programs an important component of a broader strategy of egalitarian social change. (shrink)

Recent debates about the most appropriate political agents for realising social justice have largely focused on the potential value of national political parties on the one hand, and trade unions on the other. Drawing on the thought of Murray Bookchin, this article suggests that democratic municipalist agents – democratic associations of local residents that build and empower neighbourhood assemblies and improve the municipal provision of basic goods and services – can often also make valuable contributions to projects of just social (...) change. I identify a long-term and a more short-term argument for the value of democratic municipalist agency in Bookchin's thought and claim that the latter provides a compelling case for the valuable contributions this form of action can make to the achievement of a wide variety of visions of social justice. This provides a useful partial corrective to recent political theorising about the nature of the partisanship and trade unionism necessary to secure social justice. (shrink)

The Monad’s components are as follows: 1: Monism as the state of eternal undifferentiation 2: Dualism as the state of infinite differentiations -/- MONAD = ET = INF ET Ψ INF.

Scepticism about ought simpliciter is the view that there is no such thing as what one ought simpliciter to do. Instead, practical deliberation is governed by a plurality of normative standpoints, each authoritative from their own perspective but none authoritative simpliciter. This paper aims to resist such scepticism. After setting out the challenge in general terms, I argue that scepticism can be resisted by rejecting a key assumption in the sceptic’s argument. This is the assumption that standpoint-relative ought judgments bring (...) with them a commitment to act in accordance with those judgments. Instead, I propose an alternative account of our normative concepts according to which only ought simpliciter judgments commit one to acting in accordance with those judgments. In addition to answering the sceptical challenge, the proposal offers an independently motivated account of what makes a concept normatively authoritative. (shrink)

This paper addresses the so-called paradox of fiction, the problem of explaining how we can have emotional responses towards fiction. I claim that no account has yet provided an adequate explanation of how we can respond with genuine emotions when we know that the objects of our responses are fictional. I argue that we should understand the role played by the imagination in our engagement with fiction as functionally equivalent to that which it plays under the guise of acceptance in (...) practical reasoning, suggesting that the same underlying cognitive-affective mechanisms are involved in both activities. As such, our imaginative engagement with fiction un-problematically arouses emotions, but only to the extent that we are not occurrently attending to our epistemic relation to the fiction i.e. fully attending to the fact that the object of our response is merely fictional. In order to illuminate this idea I examine a recent proposal that the phenomenology of attention is partially non-attributive, and I argue that emotional phenomenology too shares this characteristic. (shrink)

A lineage of prominent philosophers who have discussed the second-person relation can be regarded as advancing structural accounts. They posit that the second-person relation effects one transformative change to the structure of practical reasoning. In this paper, I criticise this orthodoxy and offer an alternative, substantive account. That is, I argue that entering into second-personal relations with others does indeed affect one's practical reasoning, but it does this not by altering the structure of one's agential thought, but by changing what (...) reasons can become available. The importance of second-personal thought for action is heterogenous. Second-person relations make possible the emergence of a wide variety of different kinds of practical reasons: creating some, revealing others. Recognising this diminishes the appeal of the traditional, structural accounts of the practical significance of such second-personal relations. Moving away from structural accounts facilitates a more thorough understanding of the intersubjective form of action. (shrink)

This paper is about the similarity between the appreciation of a piece of art, such as a cherished music album, and the loving appreciation of a person whom one knows well. In philosophical discussion about the rationality of love, the Qualities View (QV) says that love can be justified by reference to the qualities of the beloved. I argue that the oft-rehearsed trading-up objection fails to undermine the QV. The problems typically identified by the objection arise from the idea that (...) love-worthy qualities could be coarse-grained, when in fact they must be fine-grained. The analogy with appreciation of aesthetic qualities helps to draw out this point. Once the fine-grained nature of love-worthy qualities is properly understood, it is clear that critics of the QV cannot rely on the trading-up objection to motivate its rejection. Moreover, the paper’s core argument helps to illuminate the persistently aesthetic nature of interpersonal affections. (shrink)

ABSTRACT This paper explores the role of aesthetic judgements in mathematics by focussing on the relationship between the epistemic and aesthetic criteria employed in such judgements, and on the nature of the psychological experiences underpinning them. I claim that aesthetic judgements in mathematics are plausibly understood as expressions of what I will call ‘aesthetic-epistemic feelings’ that serve a genuine cognitive and epistemic function. I will then propose a naturalistic account of these feelings in terms of sub-personal processes of representing and (...) assessing the relation between cognitive processes and certain properties of the stimuli at which they are directed. (shrink)

Software application ontologies have the potential to become the keystone in state-of-the-art information management techniques. It is expected that these ontologies will support the sort of reasoning power required to navigate large and complex terminologies correctly and efficiently. Yet, there is one problem in particular that continues to stand in our way. As these terminological structures increase in size and complexity, and the drive to integrate them inevitably swells, it is clear that the level of consistency required for such navigation (...) will become correspondingly difficult to maintain. While descriptive semantic representations are certainly a necessary component to any adequate ontology-based system, so long as ontology engineers rely solely on semantic information, without a sound ontological theory informing their modeling decisions, this goal will surely remain out of reach. In this paper we describe how Language and Computing nv (L&C), along with The Institute for Formal Ontology and Medical Information Sciences (IFOMIS), are working towards developing and implementing just such a theory, combining the open software architecture of L&C’s LinkSuiteTM with the philosophical rigor of IFOMIS’s Basic Formal Ontology. In this way we aim to move beyond the more or less simple controlled vocabularies that have dominated the industry to date. (shrink)

Why are natural theories pre-well-ordered by consistency strength? In previous work, an approach to this question was proposed. This approach was inspired by Martin's Conjecture, one of the most prominent conjectures in recursion theory. Fixing a reasonable subsystem $T$ of arithmetic, the goal was to classify the recursive functions that are monotone with respect to the Lindenbaum algebra of $T$. According to an optimistic conjecture, roughly, every such function must be equivalent to an iterate $\mathsf{Con}_T^\alpha$ of the consistency operator ``in (...) the limit'' within the ultrafilter of sentences that are true in the standard model. In previous work the author established the first case of this optimistic conjecture; roughly, every recursive monotone function is either as weak as the identity operator in the limit or as strong as $\mathsf{Con}_T$ in the limit. Yet in this note we prove that this optimistic conjecture fails already at the next step; there are recursive monotone functions that are neither as weak as $\mathsf{Con}_T$ in the limit nor as strong as $\mathsf{Con}_T^2$ in the limit. In fact, for every $\alpha$, we produce a function that is cofinally equivalent to $\mathsf{Con}^\alpha_T$ yet cofinally equivalent to $\mathsf{Con}_T$. (shrink)

This Ideas and Opinions article revisits an argument from Judith Jarvis Thomson in her essay “A Defense of Abortion” that abortion can be an ethical choice even if we assume that fetuses have full moral personhood and moral rights. The authors examine the implications of laws that require a pregnant person to care for another with their body and what other impositions states may also require of citizens to care for others.

Goetz outlined legal models of identical entities that include natural persons who are identical to a coregency and natural persons who are identical to a general partnership. Those entities cohere with the formula logic of relative identity. This essay outlines the coexistence of relative identity and numerical identity in the models of identical legal entities, which is impure relative identity. These models support the synthesis of Relative Trinitarianism and Social Trinitarianism, which I call Relative-Social Trinitarianism.

Mathematicians often speak of conjectures as being confirmed by evidence that falls short of proof. For their own conjectures, evidence justifies further work in looking for a proof. Those conjectures of mathematics that have long resisted proof, such as the Riemann hypothesis, have had to be considered in terms of the evidence for and against them. In recent decades, massive increases in computer power have permitted the gathering of huge amounts of numerical evidence, both for conjectures in pure mathematics and (...) for the behavior of complex applied mathematical models and statistical algorithms. Mathematics has therefore become (among other things) an experimental science (though that has not diminished the importance of proof in the traditional style). We examine how the evaluation of evidence for conjectures works in mathematical practice. We explain the (objective) Bayesian view of probability, which gives a theoretical framework for unifying evidence evaluation in science and law as well as in mathematics. Numerical evidence in mathematics is related to the problem of induction; the occurrence of straightforward inductive reasoning in the purely logical material of pure mathematics casts light on the nature of induction as well as of mathematical reasoning. (shrink)

A model of metaphysics associated with EJ Lowe and Tuomas Tahko sees metaphysics as involving a priori knowledge of possible essences, or at least modal facts, and delimiting the actual ‘ontological categories,’ the ultimate and essential divisions of what exists, based on the results of a posteriori scientific investigation. Their approach to metaphysics has been criticized by those who argue that such metaphysics is unsuitably a priori, disconnected with empirical research in natural science, and ends up failing to provide meaningful (...) constraints on metaphysical theorization. I present different epistemological and semantic worries about these accounts to motivate an alternative perspective on which metaphysics centers on form, rather than possibility. This scholastic perspective is shown to incorporate the skeptical insights as constitutive of its approach to existence, by way of the position that ‘being’ is not a genus. Rather, ‘being’ is a determinable. The scholastic approach can thus provide responses to the skeptics, since it denies that ontological categories – in the Lowe/Tahko sense – are what metaphysicians investigate and proposes a different view of ontological categories as classes of forms. (shrink)

In this paper I wish to defend a particular form of the traditional, and now almost wholly unfashionable, notion of an aesthetic attitude.

Many of us think human extinction would be a very bad thing, and that we have moral reasons to prevent it. But there is disagreement over what would make extinction so bad, and thus over what grounds these moral reasons. Recently, several theorists have argued that our reasons to prevent extinction stem not just from the value of the welfare of future lives, but also from certain additional values relating to the existence of humanity itself (for example, humanity's “final” value, (...) or the value of humanity in itself). In this paper, I argue against these “additional value” views. Despite their initial appeal, these views will inevitably face conflicts between the additional values to which they appeal, and the value of the welfare of future lives. And, I argue, the views cannot plausibly resolve these conflicts. In contrast, these conflicts do not arise for a rival view, on which our reasons to prevent extinction stem just from the value of the welfare of future lives. I conclude that this gives us reason to prefer the latter view, despite the greater initial plausibility of additional value views. (shrink)

Abstract: In the Philebus, Socrates constructs a dialectical argument in which he purports to explain to Protarchus why the pleasure that spectators feel when watching comedy is a mixture of pleasure and pain. To do this he brings in phthonos (malice or envy) as his prime example (47d-50e). I examine the argument and claim that Socrates implicitly challenges Protarchus’ beliefs about himself as moderate and self-knowing. I discuss two reasons to think that more is at stake in the argument than (...) the mixed pleasure and pain of comic malice. (shrink)

This schedule, provided as a companion to my “Teaching Firefly” article, was used for a sophomore level philosophy course that was populated mostly by non-majors. The original idea for the course was to develop a popular culture philosophy course that would attract students from all over campus, which was meant to both introduce them to multiple philosophical ideas and theories and hopefully convince some of them to major or minor in philosophy. The course was quite successful at drawing Whedon fans (...) from across the university (after a certain amount of advertising through posters and social media). Students were very engaged with both discussions of episodes and the readings. (shrink)

Experimental philosophy brings empirical methods to philosophy. These methods are used to probe how people think about philosophically interesting things such as knowledge, morality, and freedom. This paper explores the contribution that qualitative methods have to make in this enterprise. I argue that qualitative methods have the potential to make a much greater contribution than they have so far. Along the way, I acknowledge a few types of resistance that proponents of qualitative methods in experimental philosophy might encounter, and provide (...) reasons to think they are ill-founded. (shrink)

This paper examines the general prospects for conceptual role expressivism, expressivist theories that embrace conceptual role semantics. It has two main aims. The first aim is to provide a general characterisation of the view. The second aim is to raise a challenge for the general view. The challenge is to explain why normative concepts are not a species of defective concepts, where defective concepts are those that cannot meaningfully embed and participate in genuine inference. After rejecting existing attempts to answer (...) the challenge, I propose an alternative solution. However, the solution leaves conceptual role expressivism a far less distinctive and interesting position than its proponents claim. I conclude that we should be sceptical about how much expressivists gain by appealing to conceptual role semantics. (shrink)

The world provides us with an ocean of opportunities for fitting emotion. But we are beings with limited emotional resources, so missed opportunities are common. This chapter argues that these failures to take up fitting emotions are very frequently unfitting in their own right—so frequently, in fact, that most of us lead lives replete with unfitting absences of emotion. It begins by showing that, whenever an emotion can be unfitting in virtue of being too weak, the absence of that emotion (...) can also be unfitting, and for just the same reason. But emotional responses to a host of everyday objects—a funny joke, a nasty insult, and so on—can be unfittingly weak. This means that failures to respond emotionally to an enormous host of everyday objects are similarly unfitting. (shrink)

It is a plausible and compelling theoretical assumption that epistemic rationality is just a matter of having doxastic attitudes that are the correct responses to one’s epistemic reasons, or that all requirements of epistemic rationality reduce to requirements on doxastic attitudes. According to this idea, all instances of epistemic rationality are instances of rational belief. Call this assumption, and any theory working under it, _belief-centered_. In what follows, I argue that we should not accept belief-centered theories of epistemic rationality. This (...) is an argument in three acts. In the first, I present counterexamples that problematize the belief-centered assumption: cases whose protagonists (i) fail to meet any plausible requirements on belief but (ii) nevertheless appear epistemically rational. In the second act, I consider alternative explanations of the counterexamples, friendly to the belief-centered theorist, and find them wanting. In the third and final act, I show that there are significant theoretical benefits to acknowledging a distinct agent-centered dimension of epistemic rationality and sketch a candidate agent-centered approach: a view that grounds an agent’s epistemic rationality in the possession of _good epistemic policies_. In the end, we see that a complete theory of epistemic rationality is as much of a theory of rational _agents_ as it is of rational _belief_. (shrink)