I explain and motivate the shutdown problem: the problem of creating artificial agents that (1) shut down when a shutdown button is pressed, (2) don’t try to prevent or cause the pressing of the shutdown button, and (3) otherwise pursue goals competently. I then propose a solution: train agents to have incomplete preferences. Specifically, I propose that we train agents to lack a preference between every pair of different-length trajectories. I suggest a way to train such agents using (...) reinforcement learning: we give the agent lower reward for repeatedly choosing same-length trajectories. (shrink)

The notion of comparative probability defined in Bayesian subjectivist theory stems from an intuitive idea that, for a given pair of events, one event may be considered “more probable” than the other. Yet it is conceivable that there are cases where it is indeterminate as to which event is more probable, due to, e.g., lack of robust statistical information. We take that these cases involve indeterminate comparative probabilities. This paper provides a Savage-style decision-theoretic foundation for indeterminate comparative probabilities.

Orthodox decision theory gives no advice to agents who hold two goods to be incommensurate in value because such agents will have incomplete preferences. According to standard treatments, rationality requires complete preferences, so such agents are irrational. Experience shows, however, that incomplete preferences are ubiquitous in ordinary life. In this paper, we aim to do two things: (1) show that there is a good case for revising decision theory so as to allow it to apply (...) non-vacuously to agents with incomplete preferences, and (2) to identify one substantive criterion that any such non-standard decision theory must obey. Our criterion, Competitiveness, is a weaker version of a dominance principle. Despite its modesty, Competitiveness is incompatible with prospectism, a recently developed decision theory for agents with incomplete preferences. We spend the final part of the paper showing why Competitiveness should be retained, and prospectism rejected. (shrink)

This paper introduces the axiom of Negative Dominance, stating that if a lottery f is strictly preferred to a lottery g, then some outcome in the support of f is strictly preferred to some outcome in the support of g. It is shown that if preferences are incomplete on a sufficiently rich domain, then this plausible axiom, which holds for complete preferences, is incompatible with an array of otherwise plausible axioms for choice under uncertainty. In particular, in (...) this setting, Negative Dominance conflicts with the standard Independence axiom. A novel theory, which includes Negative Dominance, and rejects Independence, is developed and shown to be consistent. (shrink)

More philosophical effort is spent articulating evolutionary rationales for the development of belief-like capacities than for precursors of desires or preferences. Nobody, though, seriously expects naturally evolved minds to be disinterested epistemologists. We agree that world-representing states won’t pay their way without supporting capacities that prioritise from an organism’s available repertoire of activities in light of stored (and occurrent) information. Some concede that desire-like states would be one way of solving this problem. Taking preferences as my starting point (...) instead of belief-like states, I defend two conclusions. First, psychologically real preference states, which approximately token expected utilities, have a quite general evolutionary rationale. They are a solution to the problem of efficiently allocating capacities with incompatible uses. This argument is a version of the Environmental Complexity Thesis. Second, preferences can plausibly function and naturally evolve without belief-like states, even though the converse claim is incredible. Preferences, that is, can mediate between discriminations of occurrent states (‘internal’ or ‘external’) and the processes selecting activity without mediation by stored indicative representations. By tokening expected utilities of actions conditional on discriminated state, they can increase the rate at which the ‘right thing’ is done at appropriate times, and they can do this without the support of belief-like, world-representing states. Preferences, even incomplete and noisy sets of them, are a fuel for success that will tend to be favoured when environments are complex in ways that matter to an organism, and when the organisms have complex behavioural repertoires with heterogenous returns and costs. (shrink)

A review of some major topics of debate in normative decision theory from circa 2007 to 2019. Topics discussed include the ongoing debate between causal and evidential decision theory, decision instability, risk-weighted expected utility theory, decision-making with incomplete preferences, and decision-making with imprecise credences.

Nudges are small changes in the presentation of options that make a predictable impact on people's decisions. Proponents of nudges often claim that they are justified as paternalistic interventions that respect autonomy: they lead people to make better choices, while still letting them choose for themselves. However, existing work on nudges ignores the possibility of “hard choices”: cases where a person prefers one option in some respects, and another in other respects, but has no all‐things‐considered preference between the two. In (...) this paper, I argue that many significant medical decisions are hard choices that provide patients with an opportunity to exercise a distinctive sort of “formative autonomy” by settling their preferences and committing themselves to weigh their values in a particular way. Since nudges risk infringing formative autonomy by depriving patients of this opportunity, their use in medical contexts should be sensitive to this risk. (shrink)

How should you evaluate your choices when you’re unsure what their outcomes will be? One popular answer is to rank your options in terms of their expected utilities. But what should you do when you think that the value of their respective outcomes might be incommensurable? In the face of incommensurable values, it no longer makes sense to speak of ranking your options according to expected utility. Are there any general principles to guide us when facing decisions of this kind? (...) If only! This chapter develops an impossibility result: it holds that there are a handful of independently plausible constraints that no such decision theory can jointly satisfy. The result, while depressing, can be used to helpfully classify extant approaches based on which of the constraints they violate. (shrink)

Let’s say that you regard two things as on a par when you don’t prefer one to other and aren’t indifferent between them. What does rationality require of you when choosing between risky options whose outcomes you regard as on a par? According to Prospectism, you are required to choose the option with the best prospects, where an option’s prospects is a probability-distribution over its potential outcomes. In this paper, I argue that Prospectism violates a dominance principle—which I call The (...) Principle of Predominance—because it sometimes requires you to do something that’s no better than the alternatives and might be worse. I argue that this undermines the strongest argument that’s been given in favor of Prospectism. (shrink)

Abstract: This paper defends a constraint that any satisfactory decision theory must satisfy. I show how this constraint is violated by all of the decision theories that have been endorsed in the literature that are designed to deal with cases in which opinions or values are represented by a set of functions rather than a single one. Such a decision theory is necessary to account for the existence of what Ruth Chang has called “parity” (as well as for cases in (...) which agents have incomplete preferences or imprecise credences). The problem with the all of the decision theories that have been defended to account for parity is that they are committed to a claim I call unanimity: when all of the functions in the set agree that an agent ought to do A, then an agent ought to do A. A decision theory committed to unanimity violates the constraint I defend in this paper. Thus, if parity exists, a new approach to decision theory is necessary. (shrink)

Should you be willing to forego any sure good for a tiny probability of a vastly greater good? Fanatics say you should, anti-fanatics say you should not. Anti-fanaticism has great intuitive appeal. But, I argue, these intuitions are untenable, because satisfying them in their full generality is incompatible with three very plausible principles: acyclicity, a minimal dominance principle, and the principle that any outcome can be made better or worse. This argument against anti-fanaticism can be turned into a positive argument (...) for a weak version of fanaticism, but only from significantly more contentious premises. In combination, these facts suggest that those who find fanaticism counterintuitive should favor not anti-fanaticism, but an intermediate position that permits agents to have incomplete preferences that are neither fanatical nor anti-fanatical. (shrink)

This paper presents a decision problem called the holiday puzzle. The decision problem is one that involves incommensurable goods and sequences of choices. This puzzle points to a tension between three prima facie plausible, but jointly incompatible claims. I present a way out of the trilemma which demonstrates that it is possible for agents to have incomplete preferences and to be dynamically rational. The solution also suggests that the relationship between preference and rational permission is more subtle than (...) standardly assumed. (shrink)

We present an abstract social aggregation theorem. Society, and each individual, has a preorder that may be interpreted as expressing values or beliefs. The preorders are allowed to violate both completeness and continuity, and the population is allowed to be infinite. The preorders are only assumed to be represented by functions with values in partially ordered vector spaces, and whose product has convex range. This includes all preorders that satisfy strong independence. Any Pareto indifferent social preorder is then shown to (...) be represented by a linear transformation of the representations of the individual preorders. Further Pareto conditions on the social preorder correspond to positivity conditions on the transformation. When all the Pareto conditions hold and the population is finite, the social preorder is represented by a sum of individual preorder representations. We provide two applications. The first yields an extremely general version of Harsanyi's social aggregation theorem. The second generalizes a classic result about linear opinion pooling. (shrink)

This paper will be concerned with hard choices—that is, choice situations where an agent cannot make a rationally justified choice. Specifically, this paper asks: if an agent cannot optimize in a given situation, are they facing a hard choice? A pair of claims are defended in light of this question. First, situations where an agent cannot optimize because of incompleteness of the binary preference or value relation constitute a hard choice. Second, situations where agents cannot optimize because the binary preference (...) or value relation violates acyclicity do not constitute a hard choice. (shrink)

What are economic exchanges? The received view has it that exchanges are mutual transfers of goods motivated by inverse valuations thereof. As a corollary, the standard approach treats exchanges of services as a subspecies of exchanges of goods. We raise two objections against this standard approach. First, it is incomplete, as it fails to take into account, among other things, the offers and acceptances that lie at the core of even the simplest cases of exchanges. Second, it ultimately fails (...) to generalize to exchanges of services, in which neither inverse preferences nor mutual transfers hold true. We propose an alternative definition of exchanges, which treats exchanges of goods as a special case of exchanges of services and which builds in offers and acceptances. According to this theory: (i) The valuations motivating exchanges are propositional and convergent rather than objectual and inverse; (ii) All exchanges of goods involve exchanges of services/actions, but not the reverse; (iii) Offers and acceptances, together with the contractual obligations and claims they bring about, lie at the heart of all cases of exchange. (shrink)

Nonindexical Context-Dependence and the Interpretation as Abduction Approach Inclusive nonindexical context-dependence occurs when the preferred interpretation of an utterance implies its lexically-derived meaning. It is argued that the corresponding processes of free or lexically mandated enrichment can be modeled as abductive inference. A form of abduction is implemented in Simple Type Theory on the basis of a notion of plausibility, which is in turn regarded a preference relation over possible worlds. Since a preordering of doxastic alternatives taken for itself only (...) amounts to a relatively vacuous ad hoc model, it needs to be combined with a rational way of learning from new evidence. Lexicographic upgrade is implemented as an example of how an agent might revise his plausibility ordering in light of new evidence. Various examples are given how this apparatus may be used to model the contextual resolution of context-dependent or semantically incomplete utterances. The described form of abduction is limited and merely serves as a proof of concept, but the idea in general has good potential as one among many ways to build a bridge between semantics and pragmatics since inclusive context-dependence is ubiquitous. (shrink)

It has been argued that the explanation of self-control requires positing special motivational powers. Some think that we need will-power as an irreducible mental faculty; others that we need to think of the active self as a dedicated and depletable pool of psychic energy or – in today more respectable terminology – mental resources; finally, there is the idea that self-control requires postulating a deep division between reason and passion – a deliberative and an emotional motivational system. This essay argues (...) that no such special motivational powers are necessary. Yet, at the same time, self-control does powerfully illustrate the importance of a feature of the mind. What it illustrates, I argue, is the importance of the mental activity of attention in the control of all action. It is by appeal to this mental activity that we can dispense with special motivational powers. If we think of Humeanism as the view that there is fundamentally only one kind of motivational system and that all action is based in that system, then this essay contributes to a defense of Humeanism. On the other hand, the essay also shows that any model of agency in terms of only beliefs and desires, motivational and representational states, or preferences and credences is incomplete. A different conception of Humeanism as the view that every mental state is either motivational, representational, or a combination of them, is false. (shrink)

The basic axioms or formal conditions of decision theory, especially the ordering condition put on preferences and the axioms underlying the expected utility formula, are subject to a number of counter-examples, some of which can be endowed with normative value and thus fall within the ambit of a philosophical reflection on practical rationality. Against such counter-examples, a defensive strategy has been developed which consists in redescribing the outcomes of the available options in such a way that the threatened axioms (...) or conditions continue to hold. We examine how this strategy performs in three major cases: Sen's counterexamples to the binariness property of preferences, the Allais paradox of EU theory under risk, and the Ellsberg paradox of EU theory under uncertainty. We find that the strategy typically proves to be lacking in several major respects, suffering from logical triviality, incompleteness, and theoretical insularity. To give the strategy more structure, philosophers have developed “principles of individuation”; but we observe that these do not address the aforementioned defects. Instead, we propose the method of checking whether the strategy can overcome its typical defects once it is given a proper theoretical expansion. We find that the strategy passes the test imperfectly in Sen's case and not at all in Allais's. In Ellsberg's case, however, it comes close to meeting our requirement. But even the analysis of this more promising application suggests that the strategy ought to address the decision problem as a whole, rather than just the outcomes, and that it should extend its revision process to the very statements it is meant to protect. Thus, by and large, the same cautionary tale against redescription practices runs through the analysis of all three cases. A more general lesson, simply put, is that there is no easy way out from the paradoxes of decision theory. (shrink)

Lexical views in population axiology can avoid the Repugnant Conclusion without violating Transitivity or Separability. However, they imply a dilemma: either some good life is better than any number of slightly worse lives, or else the ‘at least as good as’ relation on populations is radically incomplete. In this paper, I argue that Archimedean views face an analogous dilemma. I thus conclude that the lexical dilemma gives us little reason to prefer Archimedean views. Even if we give up on (...) lexicality, problems of the same kind remain. (shrink)

Several recent results on the aggregation of judgments over logically connected propositions show that, under certain conditions, dictatorships are the only propositionwise aggregation functions generating fully rational (i.e., complete and consistent) collective judgments. A frequently mentioned route to avoid dictatorships is to allow incomplete collective judgments. We show that this route does not lead very far: we obtain oligarchies rather than dictatorships if instead of full rationality we merely require that collective judgments be deductively closed, arguably a minimal condition (...) of rationality, compatible even with empty judgment sets. We derive several characterizations of oligarchies and provide illustrative applications to Arrowian preference aggregation and Kasher and Rubinsteinís group identification problem. (shrink)

Mechanisms for QoS provisioning in communication networks range from flow-based resource reservation schemes, providing QoS guarantees, through QoS differentiation based on reservation aggregation techniques to adaptation of applications, compensating for incomplete reservations. Scalable, aggregation-based reservations can also be combined with adaptations for a more flexible and robust overall QoS provisioning. Adaptation is particularly important in wireless networks, where reservations schemes are more difficult to realize. It is widely accepted that usability of Cellular or Mobile IP can be largely improved (...) if adaptation is incorporated. Adaptation, in turn, depends on coding techniques involved and on user requirements. Those impose certain preferences and ordering relations on QoS hierarchies or degradation paths to be followed along when adaptation is performed. With the advent of MPEG4 coding techniques, more sophisticated adaptation schemes are more likely to be supported in the future. (shrink)

This article develops a constructive criticism of methodological conventionalism. Methodological conventionalism asserts that standards of inductive risk ought to be justified in virtue of their ability to facilitate coordination in a research community. On that view, industry bias occurs when conventional methodological standards are violated to foster industry preferences. The underlying account of scientific conventionality, however, is problematically incomplete. Conventions may be justified in virtue of their coordinative functions, but often qualify for posterior empirical criticism as research advances. (...) Accordingly, industry bias does not only threaten existing conventions but may impede their empirically warranted improvement if they align with industry preferences. My empiricist account of standards of inductive risk avoids such a problem by asserting that conventional justification can be pragmatically warranted but has, in principle, only a provisional status. Methodological conventions, therefore, should not only be defended from preference-based infringements on their coordinative function but ought to be subjected to empirical criticism. (shrink)

It is widely held that under ordinal utility, utility differences are ill-defined. Allegedly, for these to be well-defined (without turning to choice under risk or the like), one should adopt as a new kind of primitive quaternary relations, instead of the traditional binary relations underlying ordinal utility functions. Correlatively, it is also widely held that the key structural properties of quaternary relations are entirely arbitrary from an ordinal point of view. These properties would be, in a nutshell, the hallmark of (...) cardinal utility. While much is obviously true in these two tenets, this note explains why, as stated, they should be abandoned. Any ordinal utility function induces a rich quaternary relation. There is such a thing as ordinal utility differences. Furthermore, this induced quaternary relation respects, apart from completeness, the most standard structural properties of quaternary relations. These properties are, from an ordinal point of view, anything but arbitrary; from a quaternary perspective only completeness should be considered the hallmark—if any—of cardinal utility. These facts are explained to be especially relevant to the critical appreciation of the ordinalist methodology. (shrink)

This paper will be concerned with hard choices—that is, choice situations where an agent cannot make a rationally justified choice. Specifically, this paper asks: if an agent cannot optimize in a given situation, are they facing a hard choice? A pair of claims are defended in light of this question. First, situations where an agent cannot optimize because of incompleteness of the binary preference or value relation constitute a hard choice. Second, situations where agents cannot optimize because the binary preference (...) or value relation violates acyclicity do not constitute a hard choice. (shrink)

If deployed, aerosol geoengineering (AG) could involve unfairness to both present and future parties. I discuss three broad risks of unfairness that an AG deployment policy might carry: (1) causing disproportionate harm to those least responsible for climate change, (2) burdening future parties with the costs and risks of AG, and (3) excluding some interested parties from contributing to AG decision-making. Yet despite these risks, it may be too hasty to reject AG deployment as a potential climate change policy. I (...) argue that since it is very unlikely that a completely fair climate change policy will be pursued, we have ethical reason to prefer some “incompletely fair” policy. Given various facts about our world, it might be the case that some AG policy is ethically preferable to many other feasible climate change policies, even if AG carries deeply problematic risks of unfairness. (shrink)

In [1] it is claimed that, based on radiation emission measurements described in [2], a certain “variant” of the Orch OR theory has been refuted. I agree with this claim. However, the significance of this result for Orch OR per se is unclear. After all, the refuted “variant” was never advocated by anyone, and it contradicts the views of Hameroff and Penrose (hereafter: HP) who invented Orch OR [3]. My aim is to get clear on this situation. I argue that (...) it is indeed reasonable to speak of “variants” here. Orch OR is not a complete model of reality but a work in progress. At its core, it claims that wavefunction collapse is a real physical event that has something to do with gravity (“OR”) and that consciousness depends on orchestrated collapses in microtubules (“Orch”). There are many ways one could make these base ideas precise hence many “variants”. Furthermore, the ways that HP aim to make these ideas precise are radical and incomplete. If they don’t work out, Orch OR will need to fall back on another variant. Thus, I believe the significance of [1-2] for Orch OR is that it cuts out a small class of possible variants and leaves behind questions and challenges for the rest, including the variant preferred by HP. (shrink)

Dâwûd al-Qarisî (Dâvûd al-Karsî) was a versatile and prolific 18th century Ottoman scholar who studied in İstanbul and Egypt and then taught for long years in various centers of learning like Egypt, Cyprus, Karaman, and İstanbul. He held high esteem for Mehmed Efendi of Birgi (Imâm Birgivî/Birgili, d.1573), out of respect for whom, towards the end of his life, Karsî, like Birgivî, occupied himself with teaching in the town of Birgi, where he died in 1756 and was buried next to (...) Birgivî. Better known for his following works on Arabic language and rhetoric and on the prophetic traditions (hadith): Sharḥu uṣûli’l-ḥadîth li’l-Birgivî; Sharḥu’l-Ḳaṣîdati’n-nûniyya (two commentaries, in Arabic and Turkish); Şarḥu’l-Emsileti’l-mukhtalifa fi’ṣ-ṣarf (two commentaries, in Arabic and Turkish); Sharḥu’l-Binâʾ; Sharḥu’l-ʿAvâmil; and Sharḥu İzhâri’l-asrâr, Karsî has actually composed textbooks in quite different fields. Hence the hundreds of manuscript copies of his works in world libraries. Many of his works were also recurrently printed in the Ottoman period. One of the neglected aspects of Karsî is his identity as a logician. Although he authored ambitious and potent works in the field of logic, this aspect of him has not been subject to modern studies. Even his bibliography has not been established so far (with scattered manuscript copies of his works and incomplete catalogue entries). This article primarily and in a long research based on manuscript copies and bibliographic sources, identifies twelve works on logic that Karsî has authored. We have clarified the works that are frequently mistaken for each other, and, especially, have definitively established his authorship of a voluminous commentary on al-Kâtibî’s al-Shamsiyya, of which commentary a second manuscript copy has been identified and described together with the other copy. Next is handled his most famous work of logic, the Sharhu Îsâghûcî, which constitutes an important and assertive ring in the tradition of commentaries on Îsâghûcî. We describe in detail the nine manuscript copies of this work that have been identified in various libraries. The critical text of Karsî’s Sharhu Îsâghûcî, whose composition was finished on 5 March 1745, has been prepared based on the following four manuscripts: (1) MS Kayseri Raşid Efendi Kütüphanesi, No. 857, ff.1v-3v, dated 1746, that is, only one year after the composition of the work; (2) MS Bursa İnebey Yazma Eser Kütüphanesi, Genel, No.794B, ff.96v-114v, dated 1755; (3) MS Millet Kütüphanesi, Ali Emiri Efendi Arapça, No. 1752, ff.48v-58r, dated 1760; (4) MS Beyazıt Yazma Eser Kütüphanesi, Beyazıt, No. 3129, ff.41v-55v, dated 8 March 1772. While preparing the critical text, we have applied the Center for Islamic Studies (İslam Araştırmaları Merkezi, İSAM)’s method of optional text choice. The critical text is preceded by a content analysis. Karsî is well aware of the preceding tradition of commentary on Îsâghûcî, and has composed his own commentary as a ‘simile’ or alternative to the commentary by Mollâ Fanârî which was famous and current in his own day. Karsî’s statement “the commentary in one day and one night” is a reference to Mollâ Fanârî who had stated that he started writing his commentary in the morning and finished it by the evening. Karsî, who spent long years in the Egyptian scholarly and cultural basin, adopted the religious-sciences-centered ‘instrumentalist’ understanding of logic that was dominant in the Egypt-Maghrib region. Therefore, no matter how famous they were, he criticized those theoretical, long, and detailed works of logic which mingled with philosophy; and defended and favored authoring functional and cogent logic texts that were beneficial, in terms of religious sciences, to the seekers of knowledge and the scholars. Therefore, in a manner not frequently encountered in other texts of its kind, he refers to the writings and views of Muhammad b. Yûsuf al-Sanûsî (d.1490), the great representative of this logical school in the Egyptian-Maghrib region. Where there is divergence between the views of the ‘earlier scholars’ (mutaqaddimûn) like Ibn Sînâ and his followers and the ‘later scholars’ (muta’akhkhirûn), i.e., post-Fakhr al-dîn al-Râzî logicians, Karsî is careful to distance himself from partisanship, preferring sometimes the views of the earliers, other times those of the laters. For instance, on the eight conditions proposed for the realization of contradiction, he finds truth to be with al-Fârâbî, who proposed “unity in the predicative attribution” as the single condition for the realization of contradiction. Similarly, on the subject matter of Logic, he tried to reconcile the mutaqaddimûn’s notion of ‘second intelligibles’ with the muta’akhkhirûn’s notion of ‘apprehensional and declarational knowledge,’ suggesting that not much difference exists between the two, on the grounds that both notions are limited to the aspect of ‘known things that lead to the knowledge of unknown things.’ Karsî asserts that established and commonly used metaphors have, according to the verifying scholars, signification by correspondence (dalâlat al-mutâbaqah), adding also that it should not be ignored that such metaphors may change from society to society and from time to time. Karsî also endorses the earlier scholars’ position concerning the impossibility of quiddity (mâhiyya) being composed of two co-extensive parts, and emphasizes that credit should not be given to later scholars’ position who see it possible. According to the verifying scholars (muhaqqîqûn), it is possible to make definition (hadd) by mentioning only difference (fasl), in which case it becomes an imperfect definition (hadd nâqis). He is of the opinion that the definition of the proposition (qadiyya) in al-Taftâzânî’s Tahdhîb is clearer and more complete: “a proposition is an expression that bears the possibility of being true or false”. He states that in the division of proposition according to quantity what is taken into consideration is the subject (mawdû‘) in categorical propositions, and the temporal aspect of the antecedent (muqaddam) in hypothetical propositions. As for the unquantified, indefinite proposition (qadiyya muhmalah), Karsî assumes that if it is not about the problems of the sciences, then it is virtually/potentially a particular proposition (qadiyya juz’iyyah); but if it is about the problems of the sciences, then it is virtually/potentially a universal proposition (qadiyya kulliyyah). This being the general rule about the ambiguous (muhmal) propositions, he nevertheless contends that, because its subject (mawdû‘) is negated, it is preferable to consider a negative ambiguous (sâliba muhmalah) proposition like “human (insân) is not standing” to be a virtually/potentially universal negative (sâliba kulliyyâh) proposition. He states that a disjunctive hypothetical proposition (shartiyya al-munfasila) that is composed of more than two parts/units is only seemingly so, and that in reality it cannot be composed of more than two units. Syllogism (qiyâs), according to Karsî, is the ultimate purpose (al-maqsad al-aqsâ) and the most valuable subject-matter of the science of Logic. For him, the entire range of topics that are handled before this one are only prolegomena to it. This approach of Karsî clearly reveals how much the ‘demonstration (burhân)-centered’ approach of the founding figures of the Muslim tradition of logic like al-Fârâbî and Ibn Sînâ has changed. al-Abharî, in his Îsâghûjî makes no mention of ‘conversion by contradiction’ (‘aks al-naqîd). Therefore, Karsî, too, in his commentary, does not touch upon the issue. However, in his Îsâghûjî al-jadîd Karsî does handle the conversion by contradiction and its rules. Following the method of Îsâghûjî, in his commentary Karsî shortly touches on the four figures (shakl) of conjuctive syllogism (qiyâs iqtirânî) and their conditions, after which he passes to the first figure (shakl), which is considered ‘the balance of the sciences’ (mi‘yâr al-‘ulûm), explaining the four moods (darb) of it. In his Îsâghûjî al-jadîd, however, Karsî handles all the four figures (shakl) with all their related moods (darb), where he speaks of fife moods (darb) of the fourth figure (shakl). The topic of ‘modal propositions’ (al-muwajjahât) and of ‘modal syllogism’ (al-mukhtalitât), both of which do not take place in the Îsâghûjî, are not mentioned by Karsî as well, either in his commentary on Îsâghûjî or in his Îsâghûjî al-jadîd. Karsî proposes that the certainties (yaqîniyyât), of which demonstration (burhân) is made, have seven, not six, divisions. After mentioning (1) axioms/first principles (awwaliyyât), (2) observata/sensuals (mushâhadât), (3) experta/empiricals (mujarrabât), (4) acumenalia (hadthiyyât), (5) testata (mutawâtirât), and (6) instictives (fitriyyât), that is, all the ‘propositions accompanied by their demonstrations,’ Karsî states that these six divisions, which do not need research and reflection (nazar), are called badîhiyyât (self-evidents), and constitute the foundations (usûl) of certainties (yaqîniyyât). As the seventh division he mentions (7) the nazariyyât (theoreticals), which are known via the badîhiyyât, end up in them, and therefore convey certainty (yaqîn). For Karsî, the nazariyyât/theoreticals, which constitute the seventh division of yaqîniyyât/certainties, are too numerous, and constitute the branches (far‘) of yaqîniyyât. Every time the concept of ‘Mughâlata’ (sophistry) comes forth in the traditional sections on the five arts usually appended to logic works, Karsî often gives examples from what he sees as extreme sûfî sayings, lamenting that these expressions are so widespread and held in esteem. He sometimes criticizes these expressions. However, it is observed that he does not reject tasawwuf in toto, but excludes from his criticism the mystical views and approaches of the truth-abiding (ahl al-haqq), shârî‘â-observant (mutasharri‘) leading sufis who have reached to the highest level of karâmah. (shrink)

Most formalisms for representing common-sense knowledge allow incomplete and potentially inconsistent information. When strong negation is also allowed, contradictory conclusions can arise. A criterion for deciding between them is needed. The aim of this paper is to investigate an inherent and autonomous comparison criterion, based on specificity as defined in [POO 85, SIM 92]. In contrast to other approaches, we consider not only defeasible, but also strict knowledge. Our criterion is context-sensitive, i. e., preference among defeasible rules is determined (...) dynamically during the dialectical analysis.We show how specificity can be defined in terms of two different approaches: activation sets and derivation trees. This allows us to get a syntactic criterion that can be implemented in a computationally attractive way. The resulting definitions may be applied in general rulebased formalisms. We present theorems linking both characterizations. Finally we discuss other frameworks for defeasible reasoning in which preference handling is considered explicitly. (shrink)

Human beings seem to capture time and the temporal properties of events and things in thought by having beliefs usually expressed with statements using tense, or notions such as ‘now’, ‘past’ or ‘future’. Tensed beliefs like these seem indispensable for correct reasoning and timely action. For instance, my belief that my root canal is over seems inexpressible with a statement that does not use tense or a temporal indexical. However, the dominant view on the nature of time is that it (...) forms, with space, a four-dimensional continuum where time does not encompass private perspectives or an absolute, fixed present. This ‘tenseless’ theory of time encounters a challenge in integrating tensed belief, because it cannot easily explain what constitutes a tensed belief in a tenseless world and how such a belief works inside our cognitive network to bring about the actions it does. Providing such an account is the main goal of this dissertation. -/- I argue here that the correct way to proceed would be to utilize philosophical theories dealing with indexicality, as the puzzling features of tensed belief are shared with beliefs expressed by first-person or spatial indexicals. In chapters II and III I expand the dominant theories about indexicality (Lewis, Perry, Kaplan) and apply them to tensed belief. I show that each is in certain respects incomplete or inadequate. -/- My preferred account critiques the preceding theories as mis-attributing the indexicality involved to a fully conceptual element in the way people think about time. I argue that we should instead connect tensed belief to not fully conceptual elements thought. For support I turn to work in perceptual psychology that connects beliefs about space to perceptions of spatial features. In chapter IV I develop an analogous argument about temporal thought and discuss how mental representations involved in perceptions are constitutively related to the formation and preservation of tensed beliefs. Combining this story with a tenseless theory of time should give us a complete, metaphysically uncontroversial, account of the way a tensed belief functions in reasoning and produces timely action. (shrink)

Abstract. The main current approach to the AI safety is AI alignment, that is, the creation of AI whose preferences are aligned with “human values.” Many AI safety researchers agree that the idea of “human values” as a constant, ordered sets of preferences is at least incomplete. However, the idea that “humans have values” underlies a lot of thinking in the field; it appears again and again, sometimes popping up as an uncritically accepted truth. Thus, it deserves (...) a thorough deconstruction, which I will do by listing and analyzing comprehensively the hidden assumptions of the idea that “humans have values.” This deconstruction of human values will be centered around the following ideas: “Human values” are useful descriptions, but not real objects; “human values” are bad predictors of behavior; the idea of a “human value system” has flaws; “human values” are not good by default; and human values cannot be separated from human minds. The method of analysis is listing hidden assumptions on which the idea of “human values” is built. I recommend that either the idea of “human values” should be replaced with something better for the goal of AI safety, or at least be used very cautiously. The approaches to AI safety which don’t use the idea of human values at all may require more attention, like the use of full brain models, boxing, and capability limiting. (shrink)

Textbook on Gödel’s incompleteness theorems and computability theory, based on the Open Logic Project. Covers recursive function theory, arithmetization of syntax, the first and second incompleteness theorem, models of arithmetic, second-order logic, and the lambda calculus.

Following Post program, we will propose a linguistic and empirical interpretation of Gödel’s incompleteness theorem and related ones on unsolvability by Church and Turing. All these theorems use the diagonal argument by Cantor in order to find limitations in finitary systems, as human language, which can make “infinite use of finite means”. The linguistic version of the incompleteness theorem says that every Turing complete language is Gödel incomplete. We conclude that the incompleteness and unsolvability theorems find limitations in our (...) finitary tool, which is our complete language. (shrink)

In this paper I offer a defence of a Russellian analysis of the referential uses of incomplete (mis)descriptions, in a contextual setting. With regard to the debate between a unificationist and an ambiguity approach to the formal treatment of definite descriptions (introduction), I will support the former against the latter. In 1. I explain what I mean by "essentially" incomplete descriptions: incomplete descriptions are context dependent descriptions. In 2. I examine one of the best versions of the (...) unificationist “explicit” approach given by Buchanan and Ostertag. I then show that this proposal seems unable to treat the normal uses of misdescriptions. I then accept the challenge of treating misdescriptions as a key to solving the problem of context dependent descriptions. In 3. I briefly discuss Michael Devitt’s and Joseph Almog’s treatments of referential descriptions, showing that they find it difficult to explain misdescriptions. In 4. I suggest an alternative approach to DD as contextuals, under a normative epistemic stance. Definite descriptions express (i) what a speaker should have in mind in using certain words in a certain context and (ii) what a normal speaker is justified in saying in a context, given a common basic knowledge of the lexicon. In 5. I define a procedure running on contextual parameters (partiality, perspective and approximation) as a means of representing the role of pragmatics as a filter for semantic interpretation. In 6. I defend my procedural approach against possible objections concerning the problem of the boundaries between semantics and pragmatics, relying on the distinction between semantics and theory of meaning. (shrink)

We investigate the conflict between the ex ante and ex post criteria of social welfare in a new framework of individual and social decisions, which distinguishes between two sources of uncertainty, here interpreted as an objective and a subjective source respectively. This framework makes it possible to endow the individuals and society not only with ex ante and ex post preferences, as is usually done, but also with interim preferences of two kinds, and correspondingly, to introduce interim forms (...) of the Pareto principle. After characterizing the ex ante and ex post criteria, we present a first solution to their conflict that extends the former as much possible in the direction of the latter. Then, we present a second solution, which goes in the opposite direction, and is also maximally assertive. Both solutions translate the assumed Pareto conditions into weighted additive utility representations, and both attribute to the individuals common probability values on the objective source of uncertainty, and different probability values on the subjective source. We discuss these solutions in terms of two conceptual arguments, i.e., the by now classic spurious unanimity argument and a novel informational argument labelled complementary ignorance. The paper complies with the standard economic methodology of basing probability and utility representations on preference axioms, but for the sake of completeness, also considers a construal of objective uncertainty based on the assumption of an exogeneously given probability measure. JEL classification: D70; D81. (shrink)

I distinguish several doctrines that economic methodologists have found attractive, all of which have a positivist flavour. One of these is the doctrine that preference assignments in economics are just shorthand descriptions of agents' choice behaviour. Although most of these doctrines are problematic, the latter doctrine about preference assignments is a respectable one, I argue. It doesn't entail any of the problematic doctrines, and indeed it is warranted independently of them.

What is the best way to make sustained societal progress over time? Non-ideal theory done on its own faces the problem of second best, but ideal theory seems unable to cope with disagreement about how to make progress. If ideal theory gives up its claims to completeness, then we can use the method of incompletely theorized agreements to make progress over time.

I argue, first, that the deprived individuals whose predicaments Nussbaum cites as examples of "adaptive preference" do not in fact prefer the conditions of their lives to what we should regard as more desirable alternatives, indeed that we believe they are badly off precisely because they are not living the lives they would prefer to live if they had other options and were aware of them. Secondly, I argue that even where individuals in deprived circumstances acquire tastes for conditions that (...) we regard as bad, they are typically better off having their acquired preferences satisfied. If they are badly off it is because they cannot get what we and they, would regard as more desirable alternatives. Preference utilitarianism explains why individuals in such circumstances are badly off whether they have adapted to their deprived circumstances or not. Even if they prefer the conditions of their lives to all other available alternatives, most would prefer alternatives that are not available to them which would, on the preferentist account, make them better off. And that, on the preferentist account, is the basis for a radical critique of unjust institutions that limit people's options and prevent them from getting what they want. (shrink)

Some common explanations of issue polarization and echo chambers rely on social or cognitive mechanisms of exclusion. Accordingly, suggested interventions like “be more open-minded” target these mechanisms: avoid epistemic bubbles and don’t discount contrary information. Contrary to such explanations, we show how a much weaker mechanism—the preference for belief—can produce issue polarization in epistemic communities with little to no mechanisms of exclusion. We present a network model that demonstrates how a dynamic interaction between the preference for belief and common structures (...) of epistemic communities can turn very small unequal distributions of initial beliefs into full-blown polarization. This points to a different class of explanations, one that emphasizes the importance of the initial spread of information. We also show how our model complements extant explanations by including a version of biased assimilation and motivated reasoning—cognitive mechanisms of exclusion. We find that mechanisms of exclusion can exacerbate issue polarization, but may not be the ultimate root of it. Hence, the recommended interventions suggested by extant literature is expected to be limited and the problem of issue polarization to be even more intractable. (shrink)

In this paper, I draw attention to comparative preference claims, i.e. sentences of the form \S prefers p to q\. I show that preference claims exhibit interesting patterns, and try to develop a semantics that captures them. Then I use my account of preference to provide an analysis of desire. The resulting entry for desire ascriptions is independently motivated, and finds support from a wide range of phenomena.

This paper is a partial review of the literature on ‘social preferences'. There are empirical findings that convincingly demonstrate the existence of social preferences, but there are also studies that indicate their fragility. So how robust are social preferences, and how exactly are they context dependent? One of the most promising insights from the literature, in my view, is an equilibrium explanation of mutually referring conditional social preferences and expectations. I use this concept of equilibrium, summarized (...) by means of a figure, to discuss a range of empirical studies. Where appropriate, I also briefly discuss a couple of insights from the (mostly parallel) evolutionary literature about cooperation. A concrete case of the Orma in Kenya will be used as a motivating example in the beginning. (shrink)

Philosophers working on time-biases assume that people are hedonically biased toward the future. A hedonically future-biased agent prefers pleasurable experiences to be future instead of past, and painful experiences to be past instead of future. Philosophers further predict that this bias is strong enough to apply to unequal payoffs: people often prefer less pleasurable future experiences to more pleasurable past ones, and more painful past experiences to less painful future ones. In addition, philosophers have predicted that future-bias is restricted to (...) first-person preferences, and that people’s third-person preferences are time-neutral. Philosophers disagree vigorously about the normative status of these preferences—i.e., they disagree about whether first-person future-bias is rationally permissible. Time-neutralists, for example, have appealed to the predicted asymmetry between first- and third-person preferences to argue for the rational impermissibility of future-bias. We empirically tested these predictions, and found that while people do prefer more past pain to less future pain, they do not prefer less future pleasure to more past pleasure. This was so in both first and third-person conditions. This suggests that future-bias is typically non-absolute, and is more easily outweighed in the case of positive events. We connect this result to the normative debate over future-bias. (shrink)

Adaptive preferences are preferences formed in response to circumstances and opportunities – paradigmatically, they occur when we scale back our desires so they accord with what is probable or at least possible. While few commentators are willing to wholly reject the normative significance of such preferences, adaptive preferences have nevertheless attracted substantial criticism in recent political theory. The groundbreaking analysis of Jon Elster charged that such preferences are not autonomous, and several other commentators have since (...) followed Elster’s lead. On a second front, Capacity Theorists Martha Nussbaum and Amartya Sen have objected that adaptive preferences lead people away from objective goods and constitute an impediment to progressive change in developing countries. In this paper I argue that the criticisms of Elster, Sen and Nussbaum fail on the one hand to take into account what may be positively said in favour of this type of preference formation, and fail on the other hand to distinguish between different types of psychological changes – with the result that many of the critiques offered have a narrower purview than is currently allowed. My analysis of adaptive preferences, even in their most ideal form, is however not entirely positive; I adduce reasons why we can be cautious about allowing adaptive preferences to play certain types of roles in political processes, even as we accept those very preferences as normative and autonomous for the agent holding them. [International scholars without access to the AJPAE are invited to email [email protected] for a pdf copy of this article.]. (shrink)

_ Source: _Page Count 30 Millions of children worldwide could benefit from adoption. One could argue that prospective parents have a pro tanto duty to adopt rather than create children. For the sake of argument, I assume there is such a duty and focus on a pressing objection to it. Prospective parents may prefer that their children are genetically related to them. I examine eight reasons prospective parents have for preferring genetic children: for parent-child physical resemblance, for family resemblance, for (...) psychological similarity, for the sake of love, to achieve a kind of immortality, for the genetic connection itself, to be a procreator, and to experience pregnancy. I argue that, with the possible exception of the pregnancy desire, these reasons fail to defeat a duty to adopt a child rather than create one, even assuming that we do have some leeway to favor our own interests. (shrink)

An important objection to preference-satisfaction theories of well-being is that these theories cannot make sense of interpersonal comparisons of well-being. A tradition dating back to Harsanyi () attempts to respond to this objection by appeal to so-called extended preferences: very roughly, preferences over situations whose description includes agents’ preferences. This paper examines the prospects for defending the preference-satisfaction theory via this extended preferences program. We argue that making conceptual sense of extended preferences is less problematic (...) than others have supposed, but that even so extended preferences do not provide a promising way for the preference satisfaction theorist to make interpersonal well-being comparisons. Our main objection takes the form of a trilemma: depending on how the theory based on extended preferences is developed, either the result will be inconsistent with ordinary preference-satisfaction theory, or it will fail to recover sufficiently rich interpersonal well-being comparisons, or it will take on a number of other arguably odd and undesirable commitments. (shrink)

Robert M. Adams claims that Leibniz’s rehabilitation of the doctrine of incomplete entities is the most sustained effort to integrate a theory of corporeal substances into the theory of simple substances. I discuss alternative interpretations of the theory of incomplete entities suggested by Marleen Rozemond and Pauline Phemister. Against Rozemond, I argue that the scholastic doctrine of incomplete entities is not dependent on a hylomorphic analysis of corporeal substances, and therefore can be adapted by Leibniz. Against Phemister, (...) I claim that Leibniz did not reduce the passivity of corporeal substances to modifications of passive aspects of simple substances. Against Adams, I argue that Leibniz’s theory of the incompleteness of the mind cannot be understood adequately without understanding the reasons for his assertion that matter is incomplete without minds. Composite substances are seen as requisites for the reality of the material world, and therefore cannot be eliminated from Leibniz’s metaphysics. (shrink)

Both Representation Theorem Arguments and Dutch Book Arguments support taking probabilistic coherence as an epistemic norm. Both depend on connecting beliefs to preferences, which are not clearly within the epistemic domain. Moreover, these connections are standardly grounded in questionable definitional/metaphysical claims. The paper argues that these definitional/metaphysical claims are insupportable. It offers a way of reconceiving Representation Theorem arguments which avoids the untenable premises. It then develops a parallel approach to Dutch Book Arguments, and compares the results. In each (...) case preferencedefects serve as a diagnostic tool, indicating purely epistemic defects. (shrink)

To eliminate incompleteness, undecidability and inconsistency from formal systems we only need to convert the formal proofs to theorem consequences of symbolic logic to conform to the sound deductive inference model. -/- Within the sound deductive inference model there is a (connected sequence of valid deductions from true premises to a true conclusion) thus unlike the formal proofs of symbolic logic provability cannot diverge from truth.

Let’s suppose all the rules of physics will change, but, before the change, we finally figured out everything there was to be figured out about physics. This means that we achieved pragmatic completeness at that point. It’s not a universal Platonic completeness, but everything there was to be expressed about the physics at that moment was expressed.

In this paper, I present the case of the discovery of complex numbers by Girolamo Cardano. Cardano acquires the concepts of (specific) complex numbers, complex addition, and complex multiplication. His understanding of these concepts is incomplete. I show that his acquisition of these concepts cannot be explained on the basis of Christopher Peacocke’s Conceptual Role Theory of concept possession. I argue that Strong Conceptual Role Theories that are committed to specifying a set of transitions that is both necessary and (...) sufficient for possession of mathematical concepts will always face counterexamples of the kind illustrated by Cardano. I close by suggesting that we should rely more heavily on resources of Anti-Individualism as a framework for understanding the acquisition and possession of concepts of abstract subject matters. (shrink)

I argue that Gauthier's constrained-maximizer rationality is problematic. But standard Maximizing Rationality means one's preferences are only rational if it would not maximize on them to adopt new ones. In the Prisoner's Dilemma, it maximizes to adopt conditionally cooperative preferences. (These are detailed, with a view to avoiding problems of circularity of definition.) Morality then maximizes. I distinguish the roles played in rational choices and their bases by preferences, dispositions, moral and rational principles, the aim of rational (...) action, and rational decision rules. I argue that Maximizing Rationality necessarily structures conclusive reasons for action. Thus conations of any sort can base rational choices only if the conations are structured like a coherent preference function; rational actions maximize on such functions. Maximization-constraining dispositions cannot integrate into a coherent preference function. (shrink)