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.

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)

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.

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)

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.

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)

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)

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)

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.

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)

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)

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)

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)

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)

Amie Thomasson’s work provides numerous ways to rethink and improve our approach to metaphysics. This chapter is my attempt to begin to sketch why I still think the easy approach leaves room for substantive metaphysical work, and why I do not think that metaphysics need rely on any ‘epistemically metaphysical’ knowledge. After distinguishing two possible forms of deflationism, I argue that the easy ontologist needs to accept (implicitly or explicitly) that there are worldly constraints on what sorts of entities could (...) exist, and could co-exist. I argue this leaves room for a substantive role for metaphysics if (following the work of E.J. Lowe) we take metaphysics to be concerned with the possible ways that reality could be. I explain how this conception does not need to appeal to any ‘epistemically metaphysical’ knowledge, and need only make use of conceptual and/or empirical means to arrive at views on what could exist (and co-exist). Thus, the answer I propose to the question posed in the title, at least in my view, is no-one. Or, at least, no-one should be afraid of conceptual analysis. Not even metaphysicians. (shrink)

We are immersed within an odorous sea of chemical currents that we parse into individual odors with complex structures. Odors have been posited as determined by the structural relation between the molecules that compose the chemical compounds and their interactions with the receptor site. But, naturally occurring smells are parsed from gaseous odor plumes. To give a comprehensive account of the nature of odors the chemosciences must account for these large distributed entities as well. We offer a focused review of (...) what is known about the perception of odor plumes for olfactory navigation and tracking, which we then connect to what is known about the role odorants play as properties of the plume in determining odor identity with respect to odor quality. We end by motivating our central claim that more research needs to be conducted on the role that odorants play within the odor plume in determining odor identity. (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)

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)

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.

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

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)

In this chapter I argue that writers on metaphor have misunderstood Aristotle on metaphor. Aristotle is not an elitist about metaphor and does not consider metaphors to be merely ornamental. Rather, Aristotle believes that metaphors are ubiquitous and believes that people can express themselves in a clearer and more attractive way through the use of metaphors and that people learn and understand things better through metaphor. He also distinguishes between the use of metaphor and the coinage of metaphor, and believes (...) that the ability to coin marvelous new metaphors is a form of literary genius, and he provided an entirely natural origin of metaphor coinage. (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)

It is a reasonable worry that God would not truly love us and want our salvation if He fixed a definite point after which He will no longer offer us the graces to repent of our sins. I propose that Thomas Aquinas succeeds in showing us that God would not be cruel or arbitrary in setting up a world where embodied agents end up after death in a state where they will inevitably fail to repent of their sins. Aquinas proposes (...) that being disembodied is to be in a state where a person cannot be mistaken about what they want, given that they know themselves perfectly. If the disembodied state were like this, it would not be surprising that being in that state makes repentance impossible, since a soul would become fully integrated around whatever one desired, without any conflicting desires that could prompt repentance. Thus, humans would persist in whatever desires they had at the moment of death and disembodiment. I conclude by arguing that, while this scenario stands in need of fuller theodicy, Aquinas’ scenario is helpful in defending a view that God is not cruel or arbitrary for creating a world in which post-mortem repentance is impossible. (shrink)

In How We Get Along, philosopher David Velleman compares our social interactions to the interactions among improvisational actors on stage. He argues that we play ourselves - not artificially but authentically, by doing what would make sense coming from us as we really are. And, like improvisational actors, we deal with one another in dual capacities: both as characters within the social drama and as players contributing to the shared performance. In this conception of social intercourse, Velleman finds rational grounds (...) for morality, though not a rational guarantee. He maps a middle course between skepticism and rationalism, arguing that practical reasoning is 'pro-moral' without requiring moral action. The result is what he calls a 'Kinda Kantian metaethics'. How We Get Along is the summation of Velleman's thinking to date, incorporating and unifying previous work on agency, the self, the emotions, narrative and Kantian moral theory. (shrink)

In this essay I argue that Shelley's "A Defense of Poetry" is best understood as a defense of poetic language, which is in turn best understood as a defense of metaphorical language. According to Shelley, the metaphors of the poets reveal (extra-linguistic) reality, and have a truth value – they are true insofar as they capture reality. The literal language of "mere reasoners" of science and philosophy, by contrast, only reveals relations between ideas already known, and their statements are true (...) in virtue of the meanings of the words. Shelley's essays has been misunderstood because writers on metaphor such as David Cooper and Richard Rorty have assumed that metaphors are neither true nor false, and that defenders of metaphorical language such as Shelley are defending non-truth-apt language. Even those writers on metaphor who believe that metaphors are truth-apt, such as Raymond Gibbs, fail to understand that Shelley should be included in their number. (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)

In this chapter I argue that Richard Rorty and others are wrong to contrast the Romantic poets with Plato and other philosophers in virtue of a lack of concern for the truth. Percy Bysshe Shelley, in particular, believed that the metaphors in poetry revealed the fundamental truth about the world.

This project has been supported by the Australian Government through the Australian Research Council (project number CS170100008); the Department of Industry, Innovation and Science; and the Department of Prime Minister and Cabinet. ACOLA collaborates with the Australian Academy of Health and Medical Sciences and the New Zealand Royal Society Te Apārangi to deliver the interdisciplinary Horizon Scanning reports to government. The aims of the project which produced this report are: 1. Examine the transformative role that artificial intelligence may play in (...) different sectors of the economy, including the opportunities, risks and challenges that advancement presents. 2. Examine the ethical, legal and social considerations and frameworks required to enable and support broad development and uptake of artificial intelligence. 3. Assess the future education, skills and infrastructure requirements to manage workforce transition and support thriving and internationally competitive artificial intelligence industries. (shrink)

In this thesis, I examine how "truth" is never adequately defined yet still used as a foundation for meaning and purpose. The elephant which is ignored is the paradoxical nature of truth and how it relates to the infinite, which is something we have not yet come to understand well enough. I propose that it is still possible if we are open-minded enough to accept the unexpected.

Naïve realism, often overlooked among philosophical theories of perception, has in recent years attracted a surge of interest. Broadly speaking, the central commitment of naïve realism is that mind-independent objects are essential to the fundamental analysis of perceptual experience. Since the claims of naïve realism concern the essential metaphysical structure of conscious perception, its truth or falsity is of central importance to a wide range of topics, including the explanation of semantic reference and representational content, the nature of phenomenal consciousness, (...) and the basis of perceptual justification and knowledge. One of the greatest difficulties surrounding discussions of naïve realism, however, has been lack of clarity concerning exactly what affirming or denying it entails. In particular, it is sometimes unclear how naïve realism is related to the claim that perceptual experience is in some sense direct or unmediated, and also to what extent the view is compatible with another widely discussed thesis in the philosophy of perception, the claim that perceptual experiences are states with representational content. In this essay, I discuss how recent work on these issues helps to clarify both the central commitments of naïve realism, as well as its relation to representationalist theories of perception. Along the way, I will attempt to shed light on the different ways in which each approach tries to address the various theoretical challenges facing a philosophical theory of perception, and also to assess the prospects for views that attempts to combine features of each approach. (shrink)

An Aristotelian Philosophy of Mathematics breaks the impasse between Platonist and nominalist views of mathematics. Neither a study of abstract objects nor a mere language or logic, mathematics is a science of real aspects of the world as much as biology is. For the first time, a philosophy of mathematics puts applied mathematics at the centre. Quantitative aspects of the world such as ratios of heights, and structural ones such as symmetry and continuity, are parts of the physical world and (...) are objects of mathematics. Though some mathematical structures such as infinities may be too big to be realized in fact, all of them are capable of being realized. Informed by the author's background in both philosophy and mathematics, but keeping to simple examples, the book shows how infant perception of patterns is extended by visualization and proof to the vast edifice of modern pure and applied mathematical knowledge. (shrink)

Integrated Information Theory (IIT) identifies consciousness with having a maximum amount of integrated information. But a thing’s having the maximum amount of anything cannot be intrinsic to it, for that depends on how that thing compares to certain other things. IIT’s consciousness, then, is not intrinsic. A mereological argument elaborates this consequence: IIT implies that one physical system can be conscious while a physical duplicate of it is not conscious. Thus, by a common and reasonable conception of intrinsicality, IIT’s consciousness (...) is not intrinsic. It is then argued that to avoid the implication that consciousness is not intrinsic, IIT must abandon its Exclusion Postulate, which prohibits overlapping conscious systems. Indeed, theories of consciousness that attribute consciousness to physical systems, should embrace the view that some conscious systems overlap. A discussion of the admittedly counterintuitive nature of this solution, along with some medical and neuroscientific realities that would seem to support it, is included. (shrink)

Most agree that, in some special scenarios, prudence can speak against feeling a fitting emotion. Some go further, arguing that the tension between fittingness and prudence afflicts some emotions in a fairly general way. This paper goes even further: it argues that, when it comes to anxiety, the tension between fittingness and prudence is nearly inescapable. On any plausible theory, an enormous array of possible outcomes are both bad and epistemically uncertain in the right way to ground fitting anxiety. What’s (...) more, the fittingness of an emotion is a demanding, not a permissive, normative status. So the norms of fitting emotion demand a great deal of anxiety. For almost any realistic agent, it would be deeply imprudent to feel anxiety in a way that meets the demands set by norms of fitting emotion. (shrink)