The usual conception of transcendence is as the success of a process or practice of mediation, meditation, transmutation, salvation, supplication, application or implication. Blanchot's unusual transcendence escapes the inevitable ruin of such achievements by arriving in the form of the failure of immanence. Although it is impossible to describe that failure explicitly, it can be approached apophatically. Following an impossible imperative to see the whole, immanence generates inadvertent transcendence “thus exposing the essential ambiguity of transcendence and the impossibility (...) that this ambiguity be measured according to truth or legitimacy.” ( Writing of the Disaster p.65). The demanding process of bringing enough ambiguity into play in order to elucidate the failure of immanence and demonstrate a glimpse of an unavowable transcendence shall be undertaken through an assemblage of fragments from The Writing of the Disaster , interpreted as instructions for constructing and interrogating a temporary singularity. (shrink)

Impossible worlds are representations of impossible things and impossible happenings. They earn their keep in a semantic or metaphysical theory if they do the right theoretical work for us. As it happens, a worlds-based account provides the best philosophical story about semantic content, knowledge and belief states, cognitive significance and cognitive information, and informative deductive reasoning. A worlds-based story may also provide the best semantics for counterfactuals. But to function well, all these accounts need use of (...) class='Hi'>impossible and as well as possible worlds. So what are impossible worlds? Graham Priest claims that any of the usual stories about possible worlds can be told about impossible worlds, too. But far from it. I'll argue that impossible worlds cannot be genuine worlds, of the kind proposed by Lewis, McDaniel or Yagisawa. Nor can they be ersatz worlds on the model proposed by Melia or Sider. Constructing impossible worlds, it turns out, requires novel metaphysical resources. (shrink)

Impossible fictions are valuable evidence both for a theory of fiction and for theories of meaning, mind and epistemology. This article focuses on what we can learn about fiction from reflecting on impossible fictions. First, different kinds of impossible fiction are considered, and the question of how much fiction is impossible is addressed. What impossible fiction contributes to our understanding of "truth in fiction" and the logic of fiction will be examined. Finally, our understanding of (...) unreliable narrators and unreliable narration in fiction needs to accommodate stories that, on the face of it, cannot possibly be true. (shrink)

Impossible Worlds focuses on an exciting new theory in philosophy, with applications in metaphysics, logic, and the theory of meaning. Its central topic is: how do we meaningfully talk and reason about situations which, unbeknownst to us, are impossible? This issue emerges as a central problem in contemporary philosophical accounts of meaning, information, knowledge, belief, fiction, conditionality, and counterfactual supposition. The book is written bytwo of the leading philosophers in the area and contains original research of relevance to (...) professional philosophers and logicians working in metaphysics, philosophy of language, formal logic, and adjacentareas. (shrink)

Mark Jago presents an original philosophical account of meaningful thought: in particular, how it is meaningful to think about things that are impossible. We think about impossible things all the time. We can think about alchemists trying to turn base metal to gold, and about unfortunate mathematicians trying to square the circle. We may ponder whether God exists; and philosophers frequently debate whether properties, numbers, sets, moral and aesthetic qualities, and qualia exist. In many philosophical or mathematical debates, (...) when one side of the argument gets things wrong, it necessarily gets them wrong. As we consider both sides of one of these philosophical arguments, we will at some point think about something that’s impossible. Yet most philosophical accounts of meaning and content hold that we can’t meaningfully think or reason about the impossible. -/- In The Impossible, Jago argues that we often gain new information, new beliefs, and, sometimes, fresh knowledge through logic, mathematics, and philosophy. That is why logic, mathematics, and philosophy are useful. We therefore require accounts of knowledge and belief, of information and content, and of meaning which allow space for the impossible. Jago’s aim in this book is to provide such accounts. He gives a detailed analysis of the concept of hyperintensionality, whereby logically equivalent contents may be distinct, and develops a theory in terms of possible and impossible worlds. Along the way, he provides a theory of what those worlds are and how they feature in our analysis of normative epistemic concepts: knowledge, belief, information, and content. (shrink)

Arrhenius’s impossibility theorems purport to demonstrate that no population axiology can satisfy each of a small number of intuitively compelling adequacy conditions. However, it has recently been pointed out that each theorem depends on a dubious assumption: Finite Fine-Grainedness. This assumption states that there exists a finite sequence of slight welfare differences between any two welfare levels. Denying Finite Fine-Grainedness makes room for a lexical population axiology which satisfies all of the compelling adequacy conditions in each theorem. Therefore, Arrhenius’s theorems (...) fail to prove that there is no satisfactory population axiology. In this paper, I argue that Arrhenius’s theorems can be repurposed. Since all of our population-affecting actions have a non-zero probability of bringing about more than one distinct population, it is population prospect axiologies that are of practical relevance, and amended versions of Arrhenius’s theorems demonstrate that there is no satisfactory population prospect axiology. These impossibility theorems do not depend on Finite Fine-Grainedness, so lexical views do not escape them. (shrink)

I want to model a finite, fallible cognitive agent who imagines that p in the sense of mentally representing a scenario—a configuration of objects and properties—correctly described by p. I propose to capture imagination, so understood, via variably strict world quantifiers, in a modal framework including both possible and so-called impossible worlds. The latter secure lack of classical logical closure for the relevant mental states, while the variability of strictness captures how the agent imports information from actuality in the (...) imagined non-actual scenarios. Imagination turns out to be highly hyperintensional, but not logically anarchic. Section 1 sets the stage and impossible worlds are quickly introduced in Sect. 2. Section 3 proposes to model imagination via variably strict world quantifiers. Section 4 introduces the formal semantics. Section 5 argues that imagination has a minimal mereological structure validating some logical inferences. Section 6 deals with how imagination under-determines the represented contents. Section 7 proposes additional constraints on the semantics, validating further inferences. Section 8 describes some welcome invalidities. Section 9 examines the effects of importing false beliefs into the imagined scenarios. Finally, Sect. 10 hints at possible developments of the theory in the direction of two-dimensional semantics. (shrink)

Accounts of propositions as sets of possible worlds have been criticized for conflating distinct impossible propositions. In response to this problem, some have proposed to introduce impossible worlds to represent distinct impossibilities, endorsing the thesis that impossible worlds must be of the same kind; this has been called the parity thesis. I show that this thesis faces problems, and propose a hybrid account which rejects it: possible worlds are taken as concrete Lewisian worlds, and impossibilities are represented (...) as set-theoretic constructions out of them. This hybrid account (1) distinguishes many intuitively distinct impossible propositions; (2) identifies impossible propositions with extensional constructions; (3) avoids resorting to primitive modality, at least so far as Lewisian modal realism does. (shrink)

This paper gives a framework for understanding causal counterpossibles, counterfactuals imbued with causal content whose antecedents appeal to metaphysically impossible worlds. Such statements are generated by omissive causal claims that appeal to metaphysically impossible events, such as “If the mathematician had not failed to prove that 2+2=5, the math textbooks would not have remained intact.” After providing an account of impossible omissions, the paper argues for three claims: (i) impossible omissions play a causal role in the (...) actual world, (ii) causal counterpossibles have broad applications in philosophy, and (iii) the truth of causal counterpossibles provides evidence for the nonvacuity of counterpossibles more generally. (shrink)

In this paper, I investigate whether we can use a world-involving framework to model the epistemic states of non-ideal agents. The standard possible-world framework falters in this respect because of a commitment to logical omniscience. A familiar attempt to overcome this problem centers around the use of impossible worlds where the truths of logic can be false. As we shall see, if we admit impossible worlds where “anything goes” in modal space, it is easy to model extremely non-ideal (...) agents that are incapable of performing even the most elementary logical deductions. A much harder, and considerably less investigated challenge is to ensure that the resulting modal space can also be used to model moderately ideal agents that are not logically omniscient but nevertheless logically competent. Intuitively, while such agents may fail to rule out subtly impossible worlds that verify complex logical falsehoods, they are nevertheless able to rule out blatantly impossible worlds that verify obvious logical falsehoods. To model moderately ideal agents, I argue, the job is to construct a modal space that contains only possible and non-trivially impossible worlds where it is not the case that “anything goes”. But I prove that it is impossible to develop an impossible-world framework that can do this job and that satisfies certain standard conditions. Effectively, I show that attempts to model moderately ideal agents in a world-involving framework collapse to modeling either logical omniscient agents, or extremely non-ideal agents. (shrink)

Abstract Impossible fictions have lessons to teach us about linguistic representation, about mental content and concepts, and about uses of conceivability in epistemology. An adequate theory of impossible fictions may require theories of meaning that can distinguish between different impossibilities; a theory of conceptual truth that allows us to make useful sense of a variety of conceptual falsehoods; and a theory of our understanding of necessity and possibility that permits impossibilities to be conceived. After discussing these questions, strategies (...) for resisting the picture of impossible fictions presented here and in Part I are discussed. Perhaps apparently impossible fictions describe possibilities after all; or perhaps impossible fictions are all trivial; or perhaps some apparently intelligible impossible fictions are unintelligible after all. (shrink)

What does it mean for the laws of logic to fail? My task in this paper is to answer this question. I use the resources that Routley/Sylvan developed with his collaborators for the semantics of relevant logics to explain a world where the laws of logic fail. I claim that the non-normal worlds that Routley/Sylvan introduced are exactly such worlds. To disambiguate different kinds of impossible worlds, I call such worlds logically impossible worlds. At a logically impossible (...) world, the laws of logic fail. In this paper, I provide a definition of logically impossible worlds. I then show that there is nothing strange about admitting such worlds. (shrink)

Lewisian Genuine Realism about possible worlds is often deemed unable to accommodate impossible worlds and reap the benefits that these bestow to rival theories. This thesis explores two alternative extensions of GR into the terrain of impossible worlds. It is divided in six chapters. Chapter I outlines Lewis’ theory, the motivations for impossible worlds, and the central problem that such worlds present for GR: How can GR even understand the notion of an impossible world, given Lewis’ (...) reductive theoretical framework? Since the desideratum is to incorporate impossible worlds into GR without compromising Lewis’ reductive analysis of modality, Chapter II defends that analysis against objections. The rest of the thesis is devoted to incorporating impossible worlds into GR. Chapter III explores GR-friendly impossible worlds in the form of set-theoretic constructions out of genuine possibilia. Then, Chapters IV-VI venture into concrete impossible worlds. Chapter IV addresses Lewis’ objection against such worlds, to the effect that contradictions true at impossible worlds amount to true contradictions tout court. I argue that even if so, the relevant contradictions are only ever about the non-actual, and that Lewis’ argument relies on a premise that cannot be nonquestion- beggingly upheld in the face of genuine impossible worlds in any case. Chapter V proposes that Lewis’ reductive analysis can be preserved, even in the face of genuine impossibilia, if we differentiate the impossible from the possible by means of accessibility relations, understood non-modally in terms of similarity. Finally, Chapter VI counters objections to the effect that there are certain impossibilities, formulated in Lewis’ theoretical language, which genuine impossibilia should, but cannot, represent. I conclude that Genuine Realism is still very much in the running when the discussion turns to impossible worlds. (shrink)

In this critical notice of Kment's _Modality and Explanatory Reasoning_, we focus on Kment’s arguments for impossible worlds and on a key part of his discussion of the interactions between modality and explanation – the analogy that he draws between scientific and metaphysical explanation.

Are there dispositions which not only do not manifest, but which could not manifest? We argue that there are dispositions to Ф in circumstances C where C is impossible, and some where Ф is impossible. Furthermore, postulating these dispositions does useful theoretical work. This paper describes a number of cases of dispositions had by objects even though those dispositions are not possibly manifest, and argues for the importance of these dispositions.

Possible worlds have found many applications in contemporary philosophy: from theories of possibility and necessity, to accounts of conditionals, to theories of mental and linguistic content, to understanding supervenience relationships, to theories of properties and propositions, among many other applications. Almost as soon as possible worlds started to be used in formal theories in logic, philosophy of language, philosophy of mind, metaphysics, and elsewhere, theorists started to wonder whether impossible worlds should be postulated as well. In many applications, possible (...) worlds face limitations that can be dealt with through postulating impossible worlds as well. This chapter examines some of the uses of impossible worlds, and philosophical challenges theories of impossible worlds face. (shrink)

In this paper, I will argue for two interrelated theses. First, if we take phenomenological psychopathology seriously, and want to understand what it is like to undergo various psychopathological experiences, we cannot treat madpeople’s testimony as mere data for sane clinicians, philosophers, and other scholars to analyze and interpret. Madpeople must be involved with analysis an interpretation too. Second, sane clinicians and scholars must open their minds to the possibility that there may be experiences that other people have, which they (...) nevertheless cannot conceive of. I look at influential texts in which philosophers attempt to analyze and understand depersonalization and thought insertion. They go astray because they keep using their own powers of conceivability as a guide to what is or is not humanly possible to experience. Several experiences labeled inconceivable and therefore impossible by these philosophers, are experiences I have had myself. Philosophers and others would be less likely to make this mistake if they would converse and collaborate more with the madpeople concerned. When this is not feasible, they should nevertheless strive to keep an open mind. Fantastical fiction may have a role to play here, by showing how bizarre experiences may nevertheless be prima facie conceivable. (shrink)

Standard impossibility theorems on judgment aggregation over logically connected propositions either use a controversial systematicity condition or apply only to agen- das of propositions with rich logical connections. Are there any serious impossibilities without these restrictions? We prove an impossibility theorem without systematicity that applies to most standard agendas: Every judgment aggregation function (with rational inputs and outputs) satisfying a condition called unbiasedness is dictatorial (or e¤ectively dictatorial if we remove one of the agenda conditions). Our agenda conditions are tight. (...) Applied illustratively to (strict) preference aggregation repres- ented in our model, the result implies that every unbiased social welfare function with universal domain is e¤ectively dictatorial. (shrink)

One response to the problem of logical omniscience in standard possible worlds models of belief is to extend the space of worlds so as to include impossible worlds. It is natural to think that essentially the same strategy can be applied to probabilistic models of partial belief, for which parallel problems also arise. In this paper, I note a difficulty with the inclusion of impossible worlds into probabilistic models. Under weak assumptions about the space of worlds, most of (...) the propositions which can be constructed from possible and impossible worlds are in an important sense inexpressible; leaving the probabilistic model committed to saying that agents in general have at least as many attitudes towards inexpressible propositions as they do towards expressible propositions. If it is reasonable to think that our attitudes are generally expressible, then a model with such commitments looks problematic. (shrink)

There has been a sharp increase in the use of impossible worlds as theoretical tools for solving difficult philosophical problems. Some philosophers, however, warn against their use. For example, Timothy Williamson argues that impossible worlds should not be used in an analysis of conditionals because they do not provide a compositional semantics. In this paper, we set out to resolve some of the potential problems associated with impossible worlds, thereby providing justification for their uses in a variety (...) of contexts and applications. Graham Priest provides two directives for an account of impossible worlds. We argue that Priest’s directives, and, thus, the traditional view on impossibility, overextend the class of impossible worlds. We argue that all worlds, possible or impossible, are describable and that nonsense cannot play a role in a proper description. So, putative worlds that include nonsense are not worlds at all, possible or impossible. The exclusion of nonsense sentences from worlds undermines Priest’s two directives, but by separating nonsense from impossibility, we can resolve many of the worries about the use of impossible worlds. (shrink)

Provides an overview and examples of what impossible figures are, and explains their interest to many different disciplines including philosophy, psychology, art and mathematics.

Reasoning about situations we take to be impossible is useful for a variety of theoretical purposes. Furthermore, using a device of impossible worlds when reasoning about the impossible is useful in the same sorts of ways that the device of possible worlds is useful when reasoning about the possible. This paper discusses some of the uses of impossible worlds and argues that commitment to them can and should be had without great metaphysical or logical cost. The (...) paper then provides an account of reasoning with impossible worlds, by treating such reasoning as reasoning employing counterpossible conditionals, and provides a semantics for the proposed treatment. (shrink)

Why does something exist rather than nothing—could there ever have been literally nothing at all? This paper argues that absolute nothingness—a state with no things, no properties, no laws, not even modal facts—is metaphysically impossible. Three converging lines of reasoning challenge the coherence of an empty world: a logical puzzle, a language-based paradox, and a modal thought-experiment. Together they yield a concise argument that something must exist in every possible scenario. Along the way I chart five grades of ‘nothing’, (...) address nine familiar objections, and sketch what this result means for metaphysics, cosmology, and theology. (shrink)

Saul Kripke’s work on the semantics of non-normal modal logics introduced the idea of non-normal worlds, worlds where certain connectives behave differently from the way in which they behave in the worlds of normal modal logics. Such worlds may be thought of as impossible worlds, though Kripke did not, himself, talk of them in this way. Since Kripke’s invention, the notion of an impossible world has undergone much fruitful development and application. Impossible worlds may be of different (...) kinds—or maybe different degrees of impossibility; and these worlds have found application in many areas where hyperintensionality appears to play a significant role: intentional mental states, counterfactuals, meaning, property theory, to name but a few areas. But what, exactly, is an impossible world? How is it best to characterise the notion? To date, the notion is used more by example than by definition. In this paper I will investigate the question, and propose a general characterisation, suitable for all standard purposes and tastes. (shrink)

Philosophers are divided on whether it is possible to intend believed-impossible outcomes. Several thought experiments in the action theory literature suggest that this is conceptually possible, though they have not been tested in ordinary social cognition. We conducted three experiments to determine whether, on the ordinary view, it is conceptually possible to intend believed-impossible outcomes. Our findings indicate that participants firmly countenance the possibility of intending believed-impossible outcomes, suggesting that it is conceptually possible to intend to do (...) something that one believes is impossible. (shrink)

Circumstantialists already have a logical semantics for impossibilities. They expand their logical space of possible worlds by adding impossible worlds. These are impossible circumstances serving as indices of evaluation, at which impossibilities are true. A variant of circumstantialism, namely modal Meinongianism (noneism), adds impossible objects as well. These are so-called incomplete objects that are necessarily non-existent. The opposite of circumstantialism, namely structuralism, has some catching-up to do. What might a structuralist logical semantics for impossibilities without impossibilia look (...) like? This paper makes a structuralist counterproposal. We present a semantics based on a procedural interpretation of the typed λ-calculus. The fundamental idea is that talk about impossibilities should be construed in terms of procedures: some yield as their product a condition that could not possibly have a satisfier, while the rest fail to yield a product altogether. Dispensing with a ‘bottom’ of impossibilia requires instead a ‘top’ consisting of structured hyperintensions, intensions, intensions defining other intensions, a typed universe, and dual (de dicto and de re) predication. We explain how the theory works by going through several examples. (shrink)

In social choice theory with ordinal preferences, a voting method satisfies the axiom of positive involvement if adding to a preference profile a voter who ranks an alternative uniquely first cannot cause that alternative to go from winning to losing. In this note, we prove a new impossibility theorem concerning this axiom: there is no ordinal voting method satisfying positive involvement that also satisfies the Condorcet winner and loser criteria, resolvability, and a common invariance property for Condorcet methods, namely that (...) the choice of winners depends only on the ordering of majority margins by size. (shrink)

The Impossible Arises is an art history and philosophy of impossible pictures, focused especially on the contributions of Oscar Reutersvärd. The book draws on an archive of Reutersvärd’s letters an...

Philosophers have found postulating possible worlds to be very useful in a number of areas, including philosophy of language and mind, logic, and metaphysics. Impossible worlds are a natural extension to this use of possible worlds, and can help resolve a number of difficulties thrown up by possible‐worlds frameworks.

This is an exploration of some problems of nonexistence, with special attention paid to Nathan Salmón’s account of merely possible and impossible objects (or entities or things). According to this account, we can refer to such objects and attribute properties to them. The terms ‘possible’ and ‘impossible’ should be understood in the familiar metaphysical sense, so that a merely possible object is one that does not exist at the actual world but exists at some metaphysically possible world (it (...) could exist even though it does not) and an impossible object is one that does not exist at any metaphysically possible world (it could not exist at all). Other nonexistents, such as objects that once existed at the actual world but no longer do, will also be discussed, but mainly by way of comparison to merely possible and impossible objects. Salmón subscribes to both the direct reference theory of names and the Millian theory of names. Section I is a preliminary discussion of these theories, contrasting them with the formerly orthodox views of Frege and Russell. Section II presents Salmón’s account of merely possible and impossible objects. Sections III and IV are an evaluation and defense of a modified version of the account. Among other things, it is argued that Salmón’s account does not slip into any problematic form of Meinongianism. However, section V questions why Salmón’s account of impossible objects would not extend to Meinong’s notorious round square. (shrink)

There is a theorem that shows that it is impossible for an algorithm to jointly satisfy the statistical fairness criteria of Calibration and Equalized Odds non-trivially. But what about the recently advocated alternative to Calibration, Base Rate Tracking? Here we show that Base Rate Tracking is strictly weaker than Calibration, and then take up the question of whether it is possible to jointly satisfy Base Rate Tracking and Equalized Odds in non-trivial scenarios. We show that it is not, thereby (...) establishing an even more general impossibility theorem. (shrink)

Ulrike Heuer argues that there can be a reason for a person to perform an action that this person cannot perform, as long as this person can take efficient steps towards performing this action. In this reply, I first argue that Heuer's examples fail to undermine my claim that there cannot be a reason for a person to perform an action if it is impossible that this person will perform this action. I then argue that, on a plausible interpretation (...) of what 'efficient steps' are, Heuer's claim is consistent with my claim. I end by showing that Heuer fails to undermine the arguments I gave for my claim. (shrink)

A search is under way for a theory that can accommodate our intuitions in population axiology. The object of this search has proved elusive. This is not surprising since, as we shall see, any welfarist axiology that satisfies three reasonable conditions implies at least one of three counter-intuitive conclusions. I shall start by pointing out the failures in three recent attempts to construct an acceptable population axiology. I shall then present an impossibility theorem and conclude with a short discussion of (...) how it might be extended to pluralist axiologies, that is, axiologies that take more values than welfare into account. (shrink)

Epistemological accounts that make use of a safety condition on knowledge, historically, face serious problems regarding beliefs that are necessarily true. This is because necessary truths are true in all possible worlds, and so such beliefs can be safe even when the bases for the beliefs are epistemically problematic. The existence of such problematically safe beliefs would undermine a major motivation for the condition itself: the ability to evaluate how well a belief tracks the truth. This paper argues that incorporating (...) impossible worlds into the evaluation of beliefs solves this problem, but only if the relevant account of impossible worlds entails that many impossible worlds are incredibly similar to the actual world. Further, the paper argues that, as a result of including impossible worlds, some philosophical beliefs are unsafe, and many more are potentially unsafe. But, it argues, even if this is the case, we can still make philosophical progress. (shrink)

In this paper, we argue that a distinction ought to be drawn between two ways in which a given world might be logically impossible. First, a world w might be impossible because the laws that hold at w are different from those that hold at some other world (say the actual world). Second, a world w might be impossible because the laws of logic that hold in some world (say the actual world) are violated at w. We (...) develop a novel way of modelling logical possibility that makes room for both kinds of logical impossibility. Doing so has interesting implications for the relationship between logical possibility and other kinds of possibility (for example, metaphysical possibility) and implications for the necessity or contingency of the laws of logic. (shrink)

Ulrike Heuer argues that there can be a reason for a person to perform an action that this person cannot perform, as long as this person can take efficient steps towards performing this action. In this reply, I first argue that Heuer’s examples fail to undermine my claim that there cannot be a reason for a person to perform an action if it is impossible that this person will perform this action. I then argue that, on a plausible interpretation (...) of what ‘efficient steps’ are, Heuer’s claim is consistent with my claim. I end by showing that Heuer fails to undermine the arguments I gave for my claim. (shrink)

Theories of content are at the centre of philosophical semantics. The most successful general theory of content takes contents to be sets of possible worlds. But such contents are very coarse-grained, for they cannot distinguish between logically equivalent contents. They draw intensional but not hyperintensional distinctions. This is often remedied by including impossible as well as possible worlds in the theory of content. Yet it is often claimed that impossible worlds are metaphysically obscure; and it is sometimes claimed (...) that their use results in a trivial theory of content. In this paper, I set out the need for impossible worlds in a theory of content; I briefly sketch a metaphysical account of their nature; I argue that worlds in general must be very fine-grained entities; and, finally, I argue that the resulting conception of impossible worlds is not a trivial one. (shrink)

John Barrow is increasingly recognized as one of our most elegant and accomplished science writers, a brilliant commentator on cosmology, mathematics, and modern physics. Barrow now tackles the heady topic of impossibility, in perhaps his strongest book yet. Writing with grace and insight, Barrow argues convincingly that there are limits to human discovery, that there are things that are ultimately unknowable, undoable, or unreachable. He first examines the limits on scientific inquiry imposed by the deficiencies of the human mind: our (...) brain evolved to meet the demands of our immediate environment, Barrow notes, and much that lies outside this small circle may also lie outside our understanding. Barrow investigates practical impossibilities, such as those imposed by complexity, uncomputability, or the finiteness of time, space, and resources. Is the universe finite or infinite? Can information be transmitted faster than the speed of light? The book also examines the deeper theoretical restrictions on our ability to know, including Godel's theorem--which proved that there were things that could not be proved--and Arrow's Impossibility theorem about democratic voting systems. Finally, having explored the limits imposed on us from without, Barrow considers whether there are limits we should impose upon ourselves. For instance, if the secrets of the atom are to be found only by recreating extreme environments at great financial cost, just how much should we devote to that quest? Weaving together this intriguing tapestry, he illuminates some of the most profound questions of science, from the possibility of time travel to the very structure of the universe. (shrink)

Distinguishing “business” concerns from “ethical” values is not only an unfruitful and meaningless task, it is also an impossible endeavor. Nevertheless, fruitless attempts to separate facts from values produce detrimental second-order effects, both for theory and practice, and should therefore be abandoned. We highlight examples of exemplary research that integrate economic and moral considerations, and point the way to a business ethics discipline that breaks new groundby putting ideas and narratives about business together with ideas and narratives about ethics.

The article looks at the structure of impossible worlds, and their deployment in the analysis of some intentional notions. In particular, it is argued that one can, in fact, conceive anything, whether or not it is impossible. Thus a semantics of conceivability requires impossible worlds.

I address objections to impossible worlds (IWs) by Timothy Williamson and Kit Fine. Two species of IWs Mark Jago and I had in our Impossible Worlds book were FDE worlds (worlds used in the semantics of the nonclassical logic of First Degree Entailment) and open worlds (worlds not closed under any non-trivial logical consequence relation). Williamson attacks the idea that propositional contents are sets of open worlds; but we explicitly disavowed that very idea. He endorses uses of IWs (...) we developed, except he calls these ‘pseudo-worlds’. In Angellic Content (AC), Fine champions a truthmaker semantics and in Constructing the Impossible advocates its superiority over IWs. But his semantics also includes states that are IWs, as characterized in the literature: representations of absolute impossibilities. They are like Barwise and Perry’s situations – which is how FDE worlds have been interpreted for decades. A key difference between AC and FDE is that only the latter validates ‘absorption principles’ one may find unwelcome in a characterization of propositional content. But a more topic-sensitive FDE can make them fail. Williamson has also objected to the idea of giving truth(making) and falsity(making) conditions separately, as in both AC and FDE. But FDE can work with truth conditions only and the compatibility semantics for negation. AC can work the same way. (shrink)

“There is no use in trying,” said Alice; “one can’t believe impossible things.” “I dare say you haven’t had much practice,” said the Queen. “When I was your age, I always did it for half an hour a day. Why, sometimes I’ve believed as many as six impossible things before breakfast”. Lewis Carroll, Through the Looking Glass. -/- It is a rather common view among philosophers that one cannot, properly speaking, be said to believe, conceive, imagine, hope for, (...) or seek what is impossible. -/- Some philosophers, for instance George Berkeley and the early Wittgenstein, thought that logically contradictory propositions lack cognitive meaning (informational content) and cannot, therefore, be thought or believed. Philosophers who do not go as far as Berkeley and Wittgenstein in denying that impossible propositions or states of affairs are thinkable, may still claim that it is impossible to rationally believe an impossible proposition. On a classical “Cartesian” view of belief, belief is a purely mental state of the agent holding true a proposition p that she “grasps” and is directly acquainted with. But if the agent is directly acquainted with an impossible proposition, then, presumably, she must know that it is impossible. But surely no rational agent can hold true a proposition that she knows is impossible. Hence, no rational agent can believe an impossible proposition. Thus it seems that on the Cartesian view of propositional attitudes as inner mental states in which proposition are immediately apprehended by the mind, it is impossible for a rational agent to believe, imagine or conceive an impossible proposition. -/- Ruth Barcan Marcus (1983) has suggested that a belief attribution is defeated once it is discovered that the proposition, or state of affairs that is believed is impossible. According to her intuition, just as knowledge implies truth, belief implies possibility. -/- It is commonplace that people claim to believe propositions that later turn out to be impossible. According to Barcan Marcus, the correct thing to say in such a situation is not: I once believed that A but I don’t believe it any longer since I have come to realize that it is impossible that A. What one should say is instead: It once appeared to me that I believed that A, but I did not, since it is impossible that A. Thus, Barcan Marcus defends what we might call Alice’s thesis: Necessarily, for any proposition p and any subject x, if x believes p, then p is possible. -/- Alice’s thesis that it is impossible to hold impossible beliefs, seems to come into conflict with our ordinary practices of attributing beliefs. Consider a mathematical example. Some mathematicians believe that CH (the continuum hypothesis) is true and others believe that it is false. But if CH is true, then it is necessarily true; and if it is false, then it is necessarily false. Regardless of whether CH is true or false, the conclusion seems to be that there are mathematicians who believe impossible propositions. -/- Examples of apparent beliefs in impossible propositions outside of mathematics are also easy to come by. Consider, for example, Kripke’s (1999) story of the Frenchman Pierre who without realizing it has two different names ‘London’ and ‘Londres’ for the same city, London. After having arrived in London, Pierre may assent to ‘Londres is beautiful and London is not beautiful’ without being in any way irrational. It seems reasonably to infer from this that Pierre believes that Londres is beautiful and London is not beautiful. But since ‘Londres’ and ‘London’ are rigid designators for the same city, it seems to follow from this that Pierre believes the inconsistent proposition that we may express as ‘London is both beautiful and not beautiful’. (shrink)

!Author’s Note (Update - June 18, 2025) -/- Subsequent to the completion of this paper, a widely discussed study by Shojaee et al. at Apple (The Illusion of Thinking, 2025) presented empirical evidence that several advanced reasoning models (e.g., Claude 3.7 Sonnet, DeepSeek-R1) exhibit a collapse in reasoning effort and accuracy as task complexity increases — despite sufficient inference budget. Notably, the observations they report closely mirror the predictions derived in Chapters 6 and 7 of this paper, particularly regarding entropy (...) divergence in heavy-tailed decision spaces and the increased instability introduced by deeper model architectures. While developed independently and prior to these results, the framework presented here may be seen as a theoretical explanation for the empirical phenomena documented in their study. -/- Abstract -/- This paper presents a second, independent proof that Artificial General Intelligence (AGI) is mathematically impossible. -/- While Part 1 established the Infinite Choice Barrier (ICB) through computability theory, this paper presents an information-theoretic proof that general algorithmic reasoning faces a fundamental structural limit — the Infinite Choice Barrier (ICB). In decision spaces governed by heavy-tailed distributions with tail exponent \alpha \leq 1, entropy does not converge, and additional information increases uncertainty rather than reducing it. We define this phenomenon as Information Opens, Entropy Rises (IOpenER) and show that such spaces are undecidable by algorithmic systems, regardless of compute scale or architectural depth. We also introduce the Layer Hypothesis, which predicts that deeper models produce more semantic divergence under structural instability. Taken together, these results offer a formal limit on the reasoning capacity of current AI systems. Notably, key predictions derived here have since been empirically confirmed in Shojaee et al. (Apple, 2025), which documents collapse behaviors in frontier reasoning models consistent with this framework. (Note: Sections 2.-4. are identical to those in the first paper "AGI is Impossible - Here is The Proof") -/- . (shrink)

In this paper, I discuss two different metaethical challenges based on population ethical impossibility results. According to the anti‐realist challenge, the results pose a serious threat to the existence of objective moral facts. According to the skeptical challenge, the results pose a serious threat to the reliability of our moral intuitions. My aim is to systematically explore and evaluate these challenges. In addition to clarifying the issues, I argue that population ethical impossibility results do not in fact support any anti‐realist (...) or skeptical conclusions. (shrink)

I offer a framework for impossibility in the legal domain. I argue for two main points: the use of ‘impossibility’ and ‘impossible’ in the legal domain is often incoherent; in the law we often different concepts of impossibility as well as concepts that differ from impossibility that are nonetheless called ‘impossibility’.

The moral philosophy of Levinas offers a stark prospectus of impossibility for corporate ethics. It differs from most traditional ethical theories in that, for Levinas, the ethical develops in a personal meeting of one with the Other, rather than residing in some internal deliberation of the moral subject. Levinasian ethics emphasises an infinite personal responsibility arising for each of us in the face of the Other and in the presence of the Third. It stresses the imperious demand we experience to (...) be open to, prepared for and impassioned with that which we may not know, or recognise, about ourselves or about the Other. Such a demand transcends our intellectual and/or rational potential; it involves us in a carnal and somatic bodily experience of otherness. If we are to speak of Levinasian ethics in a business context, it cannot be a matter of corporate ethics but only a matter of individual managerial ethics. What such an ethics would be like is yet to be outlined. This paper proposes a series of questions and suggestions that will explicate some key terms of a practice organised around a Levinasian vocabulary of otherness, responsibility, proximity, diachrony and justice. (shrink)

Can natural language represent logically impossible circumstances? Can there be logically impossible contents? The received view on semantic content allows for logically impossible contents. Much recent work in the philosophy of language and logic meant to account for hyperintensional phenomena also assumes that the answer to both of these questions is “yes.” I want to argue that this widespread assumption is indefensible. Representing the logically impossible in language, contrary to the dominant view in semantics, is not (...) truly possible. The main argument for this position appeals to a highly plausible and minimal condition for the possession of semantic content. I call this the negative coherence condition. Any candidate's meaningful sentence S possesses semantic content only if the content of S is logically compossible with the content of the meaning-constituting sentences associated with each of the descriptive constituent terms of S. However, the sentences of L thought to express logically impossible contents that cannot meet the negative coherence condition on semantic content. In an intuitive sense, sentences with logically impossible contents are incoherent with the conditions of their own meaningfulness. (shrink)