The phenomenon of inverse linking, where a noun phrase embedded within another behaves with respect to binding as though it were structurally independent, has proven challenging for theories of the syntax–semantics interface. In this paper I show that, using an LF-movement style approach to the syntax–semantics interface, we can derive all and only the appropriate meanings for such constructions using no semantic operations other than function application and composition. The solution relies neither on a proliferation of lexical ambiguity nor on (...) abandoning the idea that pronouns denote variables, but rather on a straightforward (and standard) reification of assignment functions, which allows us to define abstraction operators within our models. (shrink)

This paper formulates a bilateral account of harmony that is an alternative to one proposed by Francez. It builds on an account of harmony for unilateral logic proposed by Kürbis and the observation that reading the rules for the connectives of bilateral logic bottom up gives the grounds and consequences of formulas with the opposite speech act. I formulate a process I call 'inversion' which allows the determination of assertive elimination rules from assertive introduction rules, and rejective elimination rules (...) from rejective introduction rules, and conversely. It corresponds to Francez's notion of vertical harmony. I also formulate a process I call 'conversion', which allows the determination of rejective introduction rules from assertive elimination rules and conversely, and the determination of assertive introduction rules from rejective elimination rules and conversely. It corresponds to Francez's notion of horizontal harmony. The account has a number of features that distinguish it from Francez's. (shrink)

Inverted sensation arguments such as the inverted spectrum thought experiment are often criticized for relying on an unconstrained notion of 'qualia'. In reply to this criticism, 'qualia-free' arguments for inversion have been proposed, in which only physical changes happen: inversions in the world, such as the replacement of surface colors by their complements, and a rewiring of peripheral input cables to more central areas in the nervous system. I show why such constrained inversion arguments won't work. The first (...) problem is that the world lacks the symmetry required to invert physical properties in the way required. The second problem concerns 'rewiring'. Empirical evidence indicates that the rewirings are either impossible, or would not result in an inversion of sensation. I propose the deeper reason for the failure of constrained inversion arguments lies in the fact that sensations are not properties of brain states, but spread into the world and the body. (shrink)

In this paper I examine whether representationalism can account for various thought experiments about colour inversions. Representationalism is, at minimum, the view that, necessarily, if two experiences have the same representational content then they have the same phenomenal character. I argue that representationalism ought to be rejected if one holds externalist views about experiential content and one holds traditional exter- nalist views about the nature of the content of propositional attitudes. Thus, colour inver- sion scenarios are more damaging to externalist (...) representationalist views than have been previously thought. More specifically, I argue that representationalists who endorse externalism about experiential content either have to become internalists about the content of propositional attitudes or they have to adopt a novel variety of externalism about the content of propositional attitudes. This novel type of propositional attitude externalism is investigated. It can be seen that adopting it forces one to reject Putnam. (shrink)

Even if spectrum inversion of various sorts is possible, spectrum inversion without a difference in representation is not. So spectrum inversion does not pose a challenge for the intentionalist thesis that, necessarily, within a given sense modality, if two experiences are alike with respect to content, they are also alike with respect to their phenomenal character. On the contrary, reflection on variants of standard cases of spectrum inversion provides a strong argument for intentionalism. Depending on one’s (...) views about the possibility of spectrum inversion, the impossibility of spectrum inversion without a difference in representation can also be used as an argument against a variety of reductive theories of mental representation. (shrink)

In the pure powers ontology (PPO), basic physical properties have wholly dispositional essences. PPO has clear advantages over categoricalist ontologies, which suffer from familiar epistemological and metaphysical problems. However, opponents argue that because it contains no qualitative properties, PPO lacks the resources to individuate powers, and generates a regress. The challenge for those who take such arguments seriously is to introduce qualitative properties without reintroducing the problems that PPO was meant to solve. In this paper, I distinguish the core claim (...) of PPO: (i) basic physical properties have dispositional essences, from a hitherto unnoticed assumption: (ii) the dispositional essences of basic physical properties exclusively involve type-causal relations to other basic physical properties. I reject (ii), making room for a structuralist ontology in which all basic physical properties are pure powers, individuated by their places in a causal structure that includes not only other powers, but also physically realized qualitative properties such as shapes, patterns and structures. Such qualities individuate pure powers in the way that non-mental input and output properties individuate realized mental properties in functionalist theories of mind, except that here it is basic physical powers that are individuated by relations to realized non-powers. I distinguish one Platonic and two Aristotelian version of this theory, and argue that the Aristotelian versions require that grounding is not always a relative fundamentality relation, because the powers ground the qualities that individuate them. By considering ontic structural realism, I argue that symmetric grounding is the best way to make sense of relational individuation in structuralist ontologies, and is therefore no additional commitment of the one proposed here. (shrink)

We investigate, for several modal logics but concentrating on KT, KD45, S4 and S5, the set of formulas B for which ${\square B}$ is provably equivalent to ${\square A}$ for a selected formula A (such as p, a sentence letter). In the exceptional case in which a modal logic is closed under the (‘cancellation’) rule taking us from ${\square C \leftrightarrow \square D}$ to ${C \leftrightarrow D}$ , there is only one formula B, to within equivalence, in this inverse image, (...) as we shall call it, of ${\square A}$ (relative to the logic concerned); for logics for which the intended reading of “ ${\square}$ ” is epistemic or doxastic, failure to be closed under this rule indicates that from the proposition expressed by a knowledge- or belief-attribution, the propositional object of the attitude in question cannot be recovered: arguably, a somewhat disconcerting situation. More generally, the inverse image of ${\square A}$ may comprise a range of non-equivalent formulas, all those provably implied by one fixed formula and provably implying another—though we shall see that for several choices of logic and of the formula A, there is not even such an ‘interval characterization’ of the inverse image (of ${\square A}$ ) to be found. (shrink)

In this paper, we will consider a phenomenon known as inverse linking, a term coined by May (1977) to describe the most salient readings of sentences such as “Someone from every city despises it.”.

Given a 1-ary sentence operator , we describe L - another 1-ary operator - as as a left inverse of in a given logic if in that logic every formula is provably equivalent to L. Similarly R is a right inverse of if is always provably equivalent to R. We investigate the behaviour of left and right inverses for taken as the operator of various normal modal logics, paying particular attention to the conditions under which these logics are conservatively extended (...) by the addition of such inverses, as well as to the question of when, in such extensions, the inverses behave as normal modal operators in their own right. (shrink)

The possibility that what looks red to me may look green to you has traditionally been known as "spectrum inversion." This possibility is thought to create difficulties for any attempt to define mental states in terms of behavioral dispositions or functional roles. If spectrum inversion is possible, then it seems that two perceptual states may have identical functional antecedents and effects yet differ in their qualitative content. In that case the qualitative character of the states could not be (...) functionally defined. (shrink)

The idea of an ?inversion principle?, and the name itself, originated in the work of Paul Lorenzen in the 1950s, as a method to generate new admissible rules within a certain syntactic context. Some fifteen years later, the idea was taken up by Dag Prawitz to devise a strategy of normalization for natural deduction calculi (this being an analogue of Gentzen's cut-elimination theorem for sequent calculi). Later, Prawitz used the inversion principle again, attributing it with a semantic role. (...) Still working in natural deduction calculi, he formulated a general type of schematic introduction rules to be matched ? thanks to the idea supporting the inversion principle ? by a corresponding general schematic Elimination rule. This was an attempt to provide a solution to the problem suggested by the often quoted note of Gentzen. According to Gentzen ?it should be possible to display the elimination rules as unique functions of the corresponding introduction rules on the basis of certain requirements?. Many people have since worked on this topic, which can be appropriately seen as the birthplace of what are now referred to as ?general elimination rules?, recently studied thoroughly by Sara Negri and Jan von Plato. In this study, we retrace the main threads of this chapter of proof-theoretical investigation, using Lorenzen's original framework as a general guide. (shrink)

If people believe that some property is true of all members of a class such as sofas, then they should also believe that the same property is true of all members of a conjunctively defined subset of that class such as uncomfortable handmade sofas. A series of experiments demonstrated a failure to observe this constraint, leading to what is termed the inverse conjunction fallacy. Not only did people often express a belief in the more general statement but not in the (...) more specific, but also when they accepted both beliefs, they were inclined to give greater confidence to the more general. It is argued that this effect underlies a number of other demonstrations of fallacious reasoning, particularly in category-based induction. Alternative accounts of the phenomenon are evaluated, and it is concluded that the effect is best interpreted in terms of intensional reasoning [Tversky, A., & Kahneman, D.. Extensional versus intuitive reasoning: the conjunction fallacy in probability judgment. Psychological Review, 90, 293-315.]. (shrink)

The standard account of weakness of will identifies it with akrasia, that is, with action against one's best judgment. Elsewhere I have argued that weakness of will is better understood as over-readily giving up on one's resolutions. Many cases of weak willed action will not be akratic: in over-readily abandoning a resolution an agent may well do something that they judge at the time to be best. Indeed, in so far as temptation typically gives rise to judgment shift -- to (...) a tendency to change one's judgment so that one values the tempting option as the best -- weak willed action will typically be akratic. But conversely, strong willed action now looks as though it will be akratic. I argue though that it need not be, once we distinguish between actual judgment, and dispositions to judge. Within this framework, the issue of inverse akrasia looks rather different. I argue that whilst Huckleberry Finn plausibly does show weakness of will in abandoning his resolve to turn Jim in, it is far from clear that he is akratic: a point brought out well in Twain's later additions to the text. Whilst cases of inverse akrasia are clearly theoretically possible, I suggest that, given cognitive dissonance mechanisms, they are unlikely to be very common. (shrink)

The inversion principle for logical rules expresses a relationship between introduction and elimination rules for logical constants. Hallnäs & Schroeder-Heister proposed the principle of definitional reflection, which embodies basic ideas of inversion in the more general context of clausal definitions. For the context of admissibility statements, this has been further elaborated by Schroeder-Heister. Using the framework of definitional reflection and its admissibility interpretation, we show that, in the sequent calculus of minimal propositional logic, the left introduction rules are (...) admissible when the right introduction rules are taken as the definitions of the logical constants and vice versa. This generalizes the well-known relationship between introduction and elimination rules in natural deduction to the framework of the sequent calculus. (shrink)

Strange inversions occur when things work in ways that turn received wisdom upside down. Hume offered a strangely inverted story about causation, and Darwin, about apparent design. Dennett suggests that a strange inversion also occurs when we project our own reactive complexes outward, painting our world with elusive properties like cuteness, sweetness, blueness, sexiness, funniness, and more. Such properties strike us as experiential causes, but they are really effects—a kind of shorthand for whole sets of reactive dispositions rooted in (...) the nuts and bolts of human information processing. Understanding the nature and origins of that strange inversion, Dennett believes, is thus key to understanding the nature and origins of human experience itself. This paper examines this claim, paying special attention to recent formulations that link that strange inversion to the emerging vision of the brain as a Bayesian estimator, constantly seeking to predict the unfolding sensory barrage. (shrink)

This article1 deals with a well-known but still ill-explained fact about German, namely scope inversion under a particular accent contour, as illustrated with the following examples, where “/” and “\” stand for rising and falling accent: (a) Mindestens ein Stu- dent hat jeden Roman gelesen, lit. ‘at least one student has every novel read’, with the reading “For at least one student x: x read every book”, and (b) Mindestens /EIN Student hat \JEDen Roman gelesen, with the additional reading (...) “For every novel y: at least one student read y”. I will derive the scope inversion in this reading from general principles of scope assignment and focus marking in German. In particular, I will argue that focus is assigned to constituents that precede the verbal predicate, which leads to syntactic configurations that in turn result in ambiguous interpretations. This explanation must be couched in a framework of derivational economy that favors shorter derivations. It is argued that the relevant comparison class is defined with respect to phonological form, not, as has been suggested for English, with respect t o identity of semantic interpretation, and that this may be a general property of “free” word order languages. (shrink)

The inversion principle for logical rules expresses a relationship between introduction and elimination rules for logical constants. Hallnäs & Schroeder-Heister proposed the principle of definitional reflection, which embodies basic ideas of inversion in the more general context of clausal definitions. For the context of admissibility statements, this has been further elaborated by Schroeder-Heister . Using the framework of definitional reflection and its admissibility interpretation, we show that, in the sequent calculus of minimal propositional logic, the left introduction rules (...) are admissible when the right introduction rules are taken as the definitions of the logical constants and vice versa. This generalizes the well-known relationship between introduction and elimination rules in natural deduction to the framework of the sequent calculus. (shrink)

The present paper introduces "ontomimetic simulation" and argues that this class of models has enabled the investigation of hypotheses about complex systems in new ways that have epistemological relevance. Ontomimetic simulation can be differentiated from other types of modeling by its reliance on causal similarity in addition to representation. Phenomena are modeled not directly but via mimesis of the ontology (i.e. the "underlying physics", microlevel etc.) of systems and a subsequent animation of the resulting model ontology as a dynamical system. (...) While the ontology is clearly used for computing system states, what is epistemologically important is that it is viewed as a hypothesis about the makeup of the studied system. This type of simulation, where model ontologies are used as hypotheses, is here called inverse ontomimetic simulation since it reverses the typical informational path from the target to the model system. It links experimental and analytical techniques in being explicitly dynamical while at the same time capable of abstraction. Inverse ontomimetic simulation is argued to have a great impact on science and to be the tool for hypothesis-testing that has made systematic theory development for complex systems possible. (shrink)

The modern study of versification is based on the hypothesis that language is rhythmically organized, that metrical patterns are defined by simple rhythmic schemata, and that the two are related by correspondence constraints. Some analyses of the phenomenon of “inversion” in iambic verse reject a central aspect of this hypothesis in positing more complex metrical schemata containing both trochaic and iambic feet. I present evidence against such “trochaic substitution” analyses and demonstrate the iambic character of inverted feet with statistical (...) data from the metrical practice of thirtysix Finnish poets. As a latecomer to the use of statistical evidence in theoretical linguistics I gratefully dedicate this article to one of the pioneers of this method. (shrink)

According to the Contingency Theory of Laws, if there are possible worlds in which it is a law that all Fs are G, there are also possible F-containing worlds in which it is not. I argue here that the theory is forced to accept the possibility of nomic inversion: i.e. pairs of properties that have their actual nomic roles swapped in some possible world. Such inversions cannot be ruled out on grounds of logical or metaphysical inconsistency, and therefore – (...) since nomic inversion is counterintuitive – the Contingency Theory is undermined. (shrink)

Spectrum inversion is a thought experiment, and I would wager that there is no better diagnostic test to the disciplinary affiliation of a randomly selected member of the audience than your reaction to a thought experiment. It is a litmus test. If you find that you are paying close attention, subvocalizing objections, and that your heart-rate and metabolism go up, you have turned pink: you are a philosopher. If on the other hand the thought experiment leaves you cold, and (...) you wonder why otherwise sensible people would worry about such things, you have turned blue and you are a psychologist. (shrink)

Philosophical (p-) zombies are constructs that possess all of the behavioral features and responses of a sentient human being, yet are not conscious. P-zombies are intimately linked to the hard problem of consciousness and have been invoked as arguments against physicalist approaches. But what if we were to invert the characteristics of p-zombies? Such an inverse (i-) zombie would possess all of the behavioral features and responses of an insensate being yet would nonetheless be conscious. While p-zombies are logically possible (...) but naturally improbable, an approximation of i-zombies actually exists: individuals experiencing what is referred to as “anesthesia awareness.” Patients under general anesthesia may be intubated (preventing speech), paralyzed (preventing movement), and narcotized (minimizing response to nociceptive stimuli). Thus, they appear—and typically are—unconscious. In 1-2 cases/1000, however, patients may be aware of intraoperative events, sometimes without any objective indices. Furthermore, a much higher percentage of patients (22% in a recent study) may have the subjective experience of dreaming during general anesthesia. P-zombies confront us with the hard problem of consciousness—how do we explain the presence of qualia? I-zombies present a more practical problem—how do we detect the presence of qualia? The current investigation compares p-zombies to i-zombies and explores the “hard problem” of unconsciousness with a focus on anesthesia awareness. (shrink)

Dans « Games and the Art of Agency » puis dans Games : Agency as Art, Thi Nguyen introduit l’inversion motivationnelle, un état motivationnel adopté par certain·e·s agent·e·s qui ne visent la victoire que pour éprouver les défis qui se présentent dans le cadre du jeu. Celleux-ci sont amené·e·s à considérer les objectifs largables du jeu comme des fins, bien qu’iels sachent ne désirer les rencontrer que dans une perspective instrumentale. Il s’agit ici de préciser la description de ce (...) phénomène et de la comparer aux perspectives prévalentes de la duperie de soi. Si j’insiste sur les ressemblances entre ces dernières et l’état d’inversion motivationnelle, je ne tente pas de le réduire à un cas d’irrationalité. Il semble cependant que la nécessité de préciser davantage le concept d’agentivité chez Thi Nguyen se dessine pour éviter de traiter l’inversion motivationnelle comme un simple cas de duperie de soi ainsi que certaines conséquences curieuses se dégageant de leurs ressemblances. (shrink)

In civil libertarian discourse, the inverse relationship between government secrecy and privacy is well recognized and widely acknowledged - so widely, in fact, that it can come to seem as though we might regain sufficient privacy simply by cabining official secrecy. But regimes of secrecy that insulate private-sector data processing practices also contribute materially to the decline of privacy, and indeed play a vital role in facilitating government efforts to make citizens' lives transparent. In addition, there is an inverse relationship (...) between openness and privacy that we are inclined to resist discussing. When, for example, a government agency posts on its website documents containing private information about individual citizens, or when a social networking service establishes default rules for transmitting information from member pages to commercial partners, openness contributes materially to the exposure that people experience. Our public discourse about information policy reinforces the devaluation of privacy in two opposite but mutually-reinforcing ways, by valorizing political economies organized around secrecy and by elevating openness as an ultimate good. The shelter that privacy affords for self-development is essential to a healthy democracy. It is therefore important to interrogate both our regimes of secrecy and our discourses about openness. (shrink)

This paper examines an important issue facing academia-pay inversion. It discusses how inversion is accompanied by ethical issues including secrecy, moral dilemmas for faculty, honesty, and keeping promises. It then examines this issue from five ethical viewpoints: a legalistic perspective, ethical egoism, utilitarianism, distributive justice, and Kants deontological approach. As part of the discussion, the effect of the moral philosophy on the universitys corporate culture is examined, with attention given to morale and productivity. Finally, alternatives to pay (...) class='Hi'>inversion that universities may want to consider are discussed. (shrink)

At the end of the 19th century, the vocabulary of sexuality - perversion - became one of the primary means by which people began to articulate and think about their individuality, their sense of self. Joining authors like Ian Hacking and Arnold Davidson, I suggest the importance of a ‘style of reasoning’ to the creation of sexual kinds at the end of the 19th century, a kind of reasoning that might be styled as historical. For the invert to become possible (...) as a human kind, the conceptual space for an understanding of inverts as specific kinds needed to be cleared. In France, this was accomplished by conceiving individuals as elaborated historically, as the product of prior generations, and by differentiating them from other kinds of people via notions of heredity and degeneration. The invert was plotted within the meta-récit of French progress (and national degeneration). This logic of ‘historicization’ also entailed the scrutiny of the patient’s past in order to reveal his or her ‘nature’ as pathological. Understanding the conceptualization of inversion as including, in part, a ‘pursuit of memory’ provides a window onto the vexing question of how people come to take up their classifications; that is, how discourses interact with the subjects they purport to describe. Through the ‘pursuit of memory’, persons were encouraged to (re)describe their pasts in terms of the present diagnosis. An essential attribute of the literature on ‘inversion’ was precisely such an historically formed understanding of pathological individuals; an understanding that ushered in the transformation from acts to natures, from individuals to kinds, from sodomites to homosexuals. (shrink)

Suppose $\lambda$ is a singular cardinal of uncountable cofinality $\kappa$. For a model $\mathscr{M}$ of cardinality $\lambda$, let No ($\mathscr{M}$) denote the number of isomorphism types of models $\mathscr{N}$ of cardinality $\lambda$ which are L$_{\infty\lambda}$- equivalent to $\mathscr{M}$. In [7] Shelah considered inverse $\kappa$- systems $\mathscr{A}$ of abelian groups and their certain kind of quotient limits Gr($\mathscr{A}$)/ Fact($\mathscr{A}$). In particular Shelah proved in [7, Fact 3.10] that for every cardinal $\mu$ there exists an inverse $\kappa$-system $\mathscr{A}$ such that $\mathscr{A}$ consists (...) of abelian groups having cardinality at most $\mu^\kappa$ and card(Gr($\mathscr{A}$)/Fact($\mathscr{A}$)) = $\mu$. Later in [8, Theorem 3.3] Shelah showed a strict connection between inverse $\kappa$-systems and possible values of No (under the assumption that $\theta^\kappa < \lambda$ for every $\theta < \lambda$): if $\mathscr{A}$ is an inverse $\kappa$- system of abelian groups having cardinality < $\lambda$, then there is a model $\mathscr{M}$ such that card $(\mathscr{M}) = \lambda$ and No($\mathscr{M}$) = card(Gr($\mathscr{A}$)/Fact($\mathscr{A}$)). The following was an immediate consequence (when $\theta^\kappa < \lambda$ for every $\theta < \lambda$): for every nonzero $\mu < \lambda$ or $\mu = \lambda^\kappa$ there is a model $\mathscr{M}_\mu$ of cardinality $\lambda$ with No$(\mathscr{M}_\mu) = \mu$. In this paper we show: for every nonzero $\mu \leq \lambda^\kappa$ there is an inverse $\kappa$-system $\mathscr{A}$ of abelian groups having cardinality < $\lambda$ such that card(Gr($\mathscr{A}$)/Fact($\mathscr{A}$)) = $\mu$ (under the assumptions $2^\kappa < \lambda$ and $\theta^{<\kappa} < \lambda$ for all $\theta < \lambda$ when $\mu > \lambda$), with the obvious new consequence concerning the possible value of No. Specifically, the case No($\mathscr{M}$) = $\lambda$ is possible when $\theta^\kappa < \lambda$ for every $\theta < \lambda$. (shrink)

The paper points out that Adam Smith’s famous argument about the “invisible hand” (IH) of markets can be inverted. While the IH argument suggests that the baker and butcher do what is in their costumers’ interests not because they care for their costumers, but out of their own self-interest, one can also defend the converse claim: if one cares for other people and finds a way to satisfy their needs, one can expect that those others will be willing to pay (...) for the satisfaction of their needs. The paper argues that the IH argument has a strong link to the view that the ultimate goal of management should be “profit maximization” and to neo-liberalism’s tenet that in a market economy where companies attempt to maximize profits, a “socially optimal” allocation will be achieved. It is argued, however, that profit maximization is well-defined only within a mathematical model, while real-world decision-making requires one to choose the “relevant set” of options before any assessment of associated profits can be attempted. “Profit maximization” is therefore characterized as a heuristic for managerial decision-making, and it is pointed out that it is by no means essential for management to be successful and sustainable. The inverse IH argument supports natural alternatives, such as Prahalad and Hart’s “bottom-of-the-pyramid” and Yunus’s “social entrepreneurship” approach. Both require the manager to focus on people’s needs first, and regard the “money-making” aspect as secondary. (shrink)

Resumen Propongo interpretar la inversión de Deleuze del platonismo como la creación de conceptos nuevos a partir de elementos teóricos tomados de la filosofía del propio Platón. En primer lugar, consideraré el origen nietzscheano de la inversión y su interpretación heideggeriana, de la cual, creo, Deleuze se vale para ciertos argumentos. En segundo lugar, me basaré en la hipótesis de Francis Wolff e Isabelle Ginoux de que la filosofía platónica tiene un carácter ambiguo en la obra deleuziana para analizar esa (...) ambigüedad en términos de la pregunta por los elementos positivos que Deleuze rescata para la creación de una nueva imagen del pensamiento.I propose to interpret the deleuzian reversal of Platonism as the creation of new concepts from the same elements the French philosopher extracts from Plato’s thought. To justify this I will first examine the nietzschean origins of the reversal as well as Heidegger’s interpretation of it, which I think inspires Deleuze. Then, based on the works of Francis Wolff and Isabelle Ginoux, I will explore the ambiguity of Plato’s role in Deleuze’s philosophy, especially in those elements he recovers and exploits to build a new image of thought. (shrink)

We extend the results of Laver on using inverse limits to reflect large cardinals of the form, there exists an elementary embedding Lα → Lα. Using these inverse limit reflection embeddings directly and by broadening the collection of U-representable sets, we prove structural results of L under the assumption that there exists an elementary embedding j : L → L. As a consequence we show the impossibility of a generalized inverse limit X-reflection result for X ⊆ Vλ+1, thus focusing the (...) study of L generalizations on L. (shrink)

The contributions to this volume originate from a symposium in honour of Hermann von Helmholtz. The authors are concerned with different aspects of the inverse methodology being a powerful tool in modern science. There is emphasized its role for understanding the concept of physical observation, for interpreting experimental results and for developing constructive strategies as well.

Although to live is to face problems, the general concept of a problem has been significantly understudied. So much so, that the publication of Polya’s delightful How to Solve It caused quite a stir. And, although the concept of a conceptual problem is philosophical because it is deep and occurs across fields, from mathematics to politics, no philosophers have produced any memorable studies of it. Moreover, the word ‘problem’ is absent from most philosophical reference works. There are plenty of texts (...) on particular problems such as those of evil and induction, but none on the general concept of a conceptual problem—as if it were not a problematic concept. Worse, we are seldom told that doing original mathematics, science or technology is to wrestle with original problems. Nor have we been told that the hardest problems are likely to be inverse, in that they go from effect to cause, or from sketch to implementation, or from conclusion to premises—as in diagnosing disease from symptoms, looking for a westward passage from Europe to Asia, and designing public policies to attack social issues. The existence of this significant gap in the philosophical literature justifies the publication of the present study. (shrink)

This essay brings together the inversion of intentionality in Levinas and the later Heidegger. In light of the later Heidegger’s traversal of the intentional horizon through the articulation of the withdrawal of Ereignis , it argues that the earlier Levinasian critique of the understanding proper to Heideggerian ontology is assuaged. In both Levinas and the post- Kehre Heidegger, Husserlian intentionality is expanded beyond the so called representational features that were criticized by both post-Husserlian figures.

William Lane Craig has argued that there cannot be actual infinities because inverse operations are not well-defined for infinities. I point out that, in fact, there are mathematical systems in which inverse operations for infinities are well-defined. In particular, the theory introduced in John Conway's *On Numbers and Games* yields a well-defined field that includes all of Cantor's transfinite numbers.

Let U be an initial segment of $^*{\mathbb N}$ closed under addition (such U is called a cut) with uncountable cofinality and A be a subset of U, which is the intersection of U and an internal subset of $^*{\mathbb N}$ . Suppose A has lower U-density α strictly between 0 and 3/5. We show that either there exists a standard real $\epsilon$ > 0 and there are sufficiently large x in A such that | (A+A) ∩ [0, 2x]| > (...) (10/3+ $\epsilon$ ) | A ∩ [0, x]| or A is a large subset of an arithmetic progression of difference greater than 1 or A is a large subset of the union of two arithmetic progressions with the same difference greater than 2 or A is a large subset of the union of three arithmetic progressions with the same difference greater than 4. (shrink)

In this article I propose what I call the inverse spaceship paradox. The article's interest lies in the fact that, contrary to what appears to be an implicit agreement in the literature on indeterminism, it shows that coming from infinity can be a perfectly predictable and therefore deterministic process in a classical universe.

It is proved that for every countable structure and a computable successor ordinal α there is a countable structure which is ‐least among all countable structures such that is Σ‐definable in the αth jump. We also show that this result does not hold for the limit ordinal. Moreover, we prove that there is no countable structure with the degree spectrum for.