This paper is a discussion of Gabriel, Hülser and Schlotter’s 2009 article on a possible causal relation between Stoic logic and Frege. The paper provides detailed argument for why Rudolf Hirzel should not be taken as the qualified middleman in philosophical discussion with whom Frege learned what he ‘borrowed’ without acknowledgement from Stoic logic. Additionally, this paper offers some modest findings about some aspects of Frege's and Hirzel's lives and work habits, which may help us understand a little better Frege's (...) connection to Hirzel and to Stoic logic as well as Frege’s failure to acknowledge the Stoics. This paper is a purely historical offshoot of my essay ‘Frege plagiarized the Stoics’. Zero direct insights into either Frege’s or Stoic philosophy are offered. OPEN ACCESS. Choose 'without proxy' below. (shrink)

This very brief paperli provides plausible answers to the two residual questions that Jamie Tappenden states, but leaves unanswered, in his 2024 paper ‘Following Bobzien: Some notes on Frege’s development and engagement with his environment’, namely, why Frege read Sigwart’s Logik and what caused Frege to read Prantl. (This paperli is merely historical and offers no special philosophical insights of any sort.) ---------- OPEN ACCESS. Choose 'without proxy' below.

Although artificial intelligence has been given an unprecedented amount of attention in both the public and academic domains in the last few years, its convergence with other transformative technologies like cloud computing, robotics, and augmented/virtual reality is predicted to exacerbate its impacts on society. The adoption and integration of these technologies within industry and manufacturing spaces is a fundamental part of what is called Industry 4.0, or the Fourth Industrial Revolution. The impacts of this paradigm shift on the human operators (...) who continue to work alongside and symbiotically with these technologies in the industry bring with it novel ethical issues. Therefore, how to design these technologies for human values becomes the critical area of intervention. This paper takes up the case study of robotic AI-based assistance systems to explore the potential value implications that emerge due to current design practices and use. The design methodology known as Value Sensitive Design (VSD) is proposed as a sufficient starting point for designing these technologies for human values to address these issues. (shrink)

Suppose several individuals (e.g., experts on a panel) each assign probabilities to some events. How can these individual probability assignments be aggregated into a single collective probability assignment? This article reviews several proposed solutions to this problem. We focus on three salient proposals: linear pooling (the weighted or unweighted linear averaging of probabilities), geometric pooling (the weighted or unweighted geometric averaging of probabilities), and multiplicative pooling (where probabilities are multiplied rather than averaged). We present axiomatic characterisations of each class of (...) pooling functions (most of them classic, but one new) and argue that linear pooling can be justified procedurally, but not epistemically, while the other two pooling methods can be justified epistemically. The choice between them, in turn, depends on whether the individuals' probability assignments are based on shared information or on private information. We conclude by mentioning a number of other pooling methods. (shrink)

ABSTRACT: Recently a bold and admirable interpretation of Chrysippus’ position on the Sorites has been presented, suggesting that Chrysippus offered a solution to the Sorites by (i) taking an epistemicist position1 which (ii) made allowances for higher-order vagueness. In this paper I argue (i) that Chrysippus did not take an epistemicist position, but − if any − a non-epistemic one which denies truth-values to some cases in a Sorites-series, and (ii) that it is uncertain whether and how he made allowances (...) for higher-order vagueness, but if he did, this was not grounded on an epistemicist position. (shrink)

We introduce a “reason-based” framework for explaining and predicting individual choices. It captures the idea that a decision-maker focuses on some but not all properties of the options and chooses an option whose motivationally salient properties he/she most prefers. Reason-based explanations allow us to distinguish between two kinds of context-dependent choice: the motivationally salient properties may (i) vary across choice contexts, and (ii) include not only “intrinsic” properties of the options, but also “context-related” properties. Our framework can accommodate boundedly rational (...) and sophisticatedly rational choice. Since properties can be recombined in new ways, it also offers resources for predicting choices in unobserved contexts. (shrink)

There is a trade-off between specificity and accuracy in existing models of belief. Descriptions of agents in the tripartite model, which recognizes only three doxastic attitudes—belief, disbelief, and suspension of judgment—are typically accurate, but not sufficiently specific. The orthodox Bayesian model, which requires real-valued credences, is perfectly specific, but often inaccurate: we often lack precise credences. I argue, first, that a popular attempt to fix the Bayesian model by using sets of functions is also inaccurate, since it requires us to (...) have interval-valued credences with perfectly precise endpoints. We can see this problem as analogous to the problem of higher order vagueness. Ultimately, I argue, the only way to avoid these problems is to endorse Insurmountable Unclassifiability. This principle has some surprising and radical consequences. For example, it entails that the trade-off between accuracy and specificity is in-principle unavoidable: sometimes it is simply impossible to characterize an agent’s doxastic state in a way that is both fully accurate and maximally specific. What we can do, however, is improve on both the tripartite and existing Bayesian models. I construct a new model of belief—the minimal model—that allows us to characterize agents with much greater specificity than the tripartite model, and yet which remains, unlike existing Bayesian models, perfectly accurate. (shrink)

This paper examines three cases of the clash between science and philosophy: Zeno’s paradoxes, the Frame Problem, and a recent attempt to experimentally refute skepticism. In all three cases, the relevant science claims to have resolved the purported problem. The sciences, construing the term broadly, are mathematics, artificial intelligence, and psychology. The goal of this paper is to show that none of the three scientific solutions work. The three philosophical problems remain as vibrant as ever in the face of robust (...) scientific attempts to dispel them. The paper concludes by examining some consequences of this persistence. (shrink)

How can different individuals' probability assignments to some events be aggregated into a collective probability assignment? Classic results on this problem assume that the set of relevant events -- the agenda -- is a sigma-algebra and is thus closed under disjunction (union) and conjunction (intersection). We drop this demanding assumption and explore probabilistic opinion pooling on general agendas. One might be interested in the probability of rain and that of an interest-rate increase, but not in the probability of rain or (...) an interest-rate increase. We characterize linear pooling and neutral pooling for general agendas, with classic results as special cases for agendas that are sigma-algebras. As an illustrative application, we also consider probabilistic preference aggregation. Finally, we compare our results with existing results on binary judgment aggregation and Arrovian preference aggregation. This paper is the first of two self-contained, but technically related companion papers inspired by binary judgment-aggregation theory. (shrink)

In response to recent work on the aggregation of individual judgments on logically connected propositions into collective judgments, it is often asked whether judgment aggregation is a special case of Arrowian preference aggregation. We argue for the converse claim. After proving two impossibility theorems on judgment aggregation (using "systematicity" and "independence" conditions, respectively), we construct an embedding of preference aggregation into judgment aggregation and prove Arrow’s theorem (stated for strict preferences) as a corollary of our second result. Although we thereby (...) provide a new proof of Arrow’s theorem, our main aim is to identify the analogue of Arrow’s theorem in judgment aggregation, to clarify the relation between judgment and preference aggregation, and to illustrate the generality of the judgment aggregation model. JEL Classi…cation: D70, D71.. (shrink)

Behaviourism is the view that preferences, beliefs, and other mental states in social-scientific theories are nothing but constructs re-describing people's behaviour. Mentalism is the view that they capture real phenomena, on a par with the unobservables in science, such as electrons and electromagnetic fields. While behaviourism has gone out of fashion in psychology, it remains influential in economics, especially in ‘revealed preference’ theory. We defend mentalism in economics, construed as a positive science, and show that it fits best scientific practice. (...) We distinguish mentalism from, and reject, the radical neuroeconomic view that behaviour should be explained in terms of brain processes, as distinct from mental states. (shrink)

Except for a patina of twenty-first century modernity, in the form of logic and language, philosophy is exactly the same now as it ever was; it has made no progress whatsoever. We philosophers wrestle with the exact same problems the Pre-Socratics wrestled with. Even more outrageous than this claim, though, is the blatant denial of its obvious truth by many practicing philosophers. The No-Progress view is explored and argued for here. Its denial is diagnosed as a form of anosognosia, a (...) mental condition where the affected person denies there is any problem. The theories of two eminent philosophers supporting the No-Progress view are also examined. The final section offers an explanation for philosophy 's inability to solve any philosophical problem, ever. The paper closes with some reflections on philosophy 's future. (shrink)

The aggregation of individual judgments over interrelated propositions is a newly arising field of social choice theory. I introduce several independence conditions on judgment aggregation rules, each of which protects against a specific type of manipulation by agenda setters or voters. I derive impossibility theorems whereby these independence conditions are incompatible with certain minimal requirements. Unlike earlier impossibility results, the main result here holds for any (non-trivial) agenda. However, independence conditions arguably undermine the logical structure of judgment aggregation. I therefore (...) suggest restricting independence to premises, which leads to a generalised premise-based procedure. This procedure is proven to be possible if the premises are logically independent. (shrink)

The new field of judgment aggregation aims to merge many individual sets of judgments on logically interconnected propositions into a single collective set of judgments on these propositions. Judgment aggregation has commonly been studied using classical propositional logic, with a limited expressive power and a problematic representation of conditional statements ("if P then Q") as material conditionals. In this methodological paper, I present a simple unified model of judgment aggregation in general logics. I show how many realistic decision problems can (...) be represented in it. This includes decision problems expressed in languages of classical propositional logic, predicate logic (e.g. preference aggregation problems), modal or conditional logics, and some multi-valued or fuzzy logics. I provide a list of simple tools for working with general logics, and I prove impossibility results that generalise earlier theorems. (shrink)

The contemporary theory of epistemic democracy often draws on the Condorcet Jury Theorem to formally justify the ‘wisdom of crowds’. But this theorem is inapplicable in its current form, since one of its premises – voter independence – is notoriously violated. This premise carries responsibility for the theorem's misleading conclusion that ‘large crowds are infallible’. We prove a more useful jury theorem: under defensible premises, ‘large crowds are fallible but better than small groups’. This theorem rehabilitates the importance of deliberation (...) and education, which appear inessential in the classical jury framework. Our theorem is related to Ladha's (1993) seminal jury theorem for interchangeable (‘indistinguishable’) voters based on de Finetti's Theorem. We also prove a more general and simpler such jury theorem. (shrink)

Which rules for aggregating judgments on logically connected propositions are manipulable and which not? In this paper, we introduce a preference-free concept of non-manipulability and contrast it with a preference-theoretic concept of strategy-proofness. We characterize all non-manipulable and all strategy-proof judgment aggregation rules and prove an impossibility theorem similar to the Gibbard--Satterthwaite theorem. We also discuss weaker forms of non-manipulability and strategy-proofness. Comparing two frequently discussed aggregation rules, we show that “conclusion-based voting” is less vulnerable to manipulation than “premise-based voting”, (...) which is strategy-proof only for “reason-oriented” individuals. Surprisingly, for “outcome-oriented” individuals, the two rules are strategically equivalent, generating identical judgments in equilibrium. Our results introduce game-theoretic considerations into judgment aggregation and have implications for debates on deliberative democracy. (shrink)

ABSTRACT: For the Stoics, a syllogism is a formally valid argument; the primary function of their syllogistic is to establish such formal validity. Stoic syllogistic is a system of formal logic that relies on two types of argumental rules: (i) 5 rules (the accounts of the indemonstrables) which determine whether any given argument is an indemonstrable argument, i.e. an elementary syllogism the validity of which is not in need of further demonstration; (ii) one unary and three binary argumental rules which (...) establish the formal validity of non-indemonstrable arguments by analysing them in one or more steps into one or more indemonstrable arguments (cut type rules and antilogism). The function of these rules is to reduce given non-indemonstrable arguments to indemonstrable syllogisms. Moreover, the Stoic method of deduction differs from standard modern ones in that the direction is reversed (similar to tableau methods). The Stoic system may hence be called an argumental reductive system of deduction. In this paper, a reconstruction of this system of logic is presented, and similarities to relevance logic are pointed out. (shrink)

There is a surprising disconnect between formal rational choice theory and philosophical work on reasons. The one is silent on the role of reasons in rational choices, the other rarely engages with the formal models of decision problems used by social scientists. To bridge this gap, we propose a new, reason-based theory of rational choice. At its core is an account of preference formation, according to which an agent’s preferences are determined by his or her motivating reasons, together with a (...) ‘weighing relation’ between different combinations of reasons. By explaining how someone’s preferences may vary with changes in his or her motivating reasons, our theory illuminates the relationship between deliberation about reasons and rational choices. Although primarily positive, the theory can also help us think about how those preferences and choices ought to respond to normative reasons. (shrink)

In the theory of judgment aggregation, it is known for which agendas of propositions it is possible to aggregate individual judgments into collective ones in accordance with the Arrow-inspired requirements of universal domain, collective rationality, unanimity preservation, non-dictatorship and propositionwise independence. But it is only partially known (e.g., only in the monotonic case) for which agendas it is possible to respect additional requirements, notably non-oligarchy, anonymity, no individual veto power, or implication preservation. We fully characterize the agendas for which there (...) are such possibilities, thereby answering the most salient open questions about propositionwise judgment aggregation. Our results build on earlier results by Nehring and Puppe (2002), Nehring (2006), Dietrich and List (2007a) and Dokow and Holzman (2010a). (shrink)

Under the independence and competence assumptions of Condorcet’s classical jury model, the probability of a correct majority decision converges to certainty as the jury size increases, a seemingly unrealistic result. Using Bayesian networks, we argue that the model’s independence assumption requires that the state of the world (guilty or not guilty) is the latest common cause of all jurors’ votes. But often – arguably in all courtroom cases and in many expert panels – the latest such common cause is a (...) shared ‘body of evidence’ observed by the jurors. In the corresponding Bayesian network, the votes are direct descendants not of the state of the world, but of the body of evidence, which in turn is a direct descendant of the state of the world. We develop a model of jury decisions based on this Bayesian network. Our model permits the possibility of misleading evidence, even for a maximally competent observer, which cannot easily be accommodated in the classical model. We prove that (i) the probability of a correct majority verdict converges to the probability that the body of evidence is not misleading, a value typically below 1; (ii) depending on the required threshold of ‘no reasonable doubt’, it may be impossible, even in an arbitrarily large jury, to establish guilt of a defendant ‘beyond any reasonable doubt’. (shrink)

In this extended essay, I argue that Frege plagiarized the Stoics --and I mean exactly that-- on a large scale in his work on the philosophy of logic and language as written mainly between 1890 and his death in 1925 (much of which published posthumously) and possibly earlier. I use ‘plagiarize' (or 'plagiarise’) merely as a descriptive term. The essay is not concerned with finger pointing or casting moral judgement. The point is rather to demonstrate carefully by means of detailed (...) evidence that there are numerous (over a hundred) and extensive parallels both in formulation and --more importantly-- in content between the Stoics and Frege, parallels so plentiful that one would be hard pressed to brush them off as coincidence. These parallels include several that appear to occur in no other modern works that were published before Frege’s own and were accessible to him. Additionally, a cluster of corroborating historical data is adduced to support the suggestion, showing how easy it would have to been for Frege to plagiarize the Stoics. This (first) part of the essay is easy to read and vaguely entertaining, or so I hope. -/- (Corrigendum: At school, Frege likely had seven, not ten, years of intensive Latin and four years of intensive ancient Greek courses.). (shrink)

I propose a relevance-based independence axiom on how to aggregate individual yes/no judgments on given propositions into collective judgments: the collective judgment on a proposition depends only on people’s judgments on propositions which are relevant to that proposition. This axiom contrasts with the classical independence axiom: the collective judgment on a proposition depends only on people’s judgments on the same proposition. I generalize the premise-based rule and the sequential-priority rule to an arbitrary priority order of the propositions, instead of a (...) dichotomous premise/conclusion order resp. a linear priority order. I prove four impossibility theorems on relevance-based aggregation. One theorem simultaneously generalizes Arrow’s Theorem (in its general and indifference-free versions) and the well-known Arrow-like theorem in judgment aggregation. (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)

Advocates of dynamic systems have suggested that higher mental processes are based on continuous representations. In order to evaluate this claim, we first define the concept of representation, and rigorously distinguish between discrete representations and continuous representations. We also explore two important bases of representational content. Then, we present seven arguments that discrete representations are necessary for any system that must discriminate between two or more states. It follows that higher mental processes require discrete representations. We also argue that discrete (...) representations are more influenced by conceptual role than continuous representations. We end by arguing that the presence of discrete representations in cognitive systems entails that computationalism (i.e., the view that the mind is a computational device) is true, and that cognitive science should embrace representational pluralism. (shrink)

The widely discussed "discursive dilemma" shows that majority voting in a group of individuals on logically connected propositions may produce irrational collective judgments. We generalize majority voting by considering quota rules, which accept each proposition if and only if the number of individuals accepting it exceeds a given threshold, where different thresholds may be used for different propositions. After characterizing quota rules, we prove necessary and sufficient conditions on the required thresholds for various collective rationality requirements. We also consider sequential (...) quota rules, which ensure collective rationality by adjudicating propositions sequentially and letting earlier judgments constrain later ones. Sequential rules may be path-dependent and strategically manipulable. We characterize path-independence and prove its essential equivalence to strategy-proofness. Our results shed light on the rationality of simple-, super-, and sub-majoritarian decision-making. (shrink)

This paper argues for a noncognitiveist computationalism in the philosophy of mind. It further argues that both humans and computers have intentionality, that is, their mental states are semantical -- they are about things in their worlds.

The purpose of this paper is to challenge some widespread assumptions about the role of the modal axiom 4 in a theory of vagueness. In the context of vagueness, axiom 4 usually appears as the principle ‘If it is clear (determinate, definite) that A, then it is clear (determinate, definite) that it is clear (determinate, definite) that A’, or, more formally, CA → CCA. We show how in the debate over axiom 4 two different notions of clarity are in play (...) (Williamson-style "luminosity" or self-revealing clarity and concealeable clarity) and what their respective functions are in accounts of higher-order vagueness. On this basis, we argue first that, contrary to common opinion, higher-order vagueness and S4 are perfectly compatible. This is in response to claims like that by Williamson that, if vagueness is defined with the help of a clarity operator that obeys axiom 4, higher-order vagueness disappears. Second, we argue that, contrary to common opinion, (i) bivalence-preservers (e.g. epistemicists) can without contradiction condone axiom 4 (by adopting what elsewhere we call columnar higher-order vagueness), and (ii) bivalence-discarders (e.g. open-texture theorists, supervaluationists) can without contradiction reject axiom 4. Third, we rebut a number of arguments that have been produced by opponents of axiom 4, in particular those by Williamson. (The paper is pitched towards graduate students with basic knowledge of modal logic.). (shrink)

ABSTRACT: I argue that there is no evidence that Epicurus dealt with the kind of free-will problem he is traditionally associated with; i.e. that he discussed free choice or moral responsibility grounded on free choice, or that the "swerve" was involved in decision processes. Rather, for Epicurus, actions are fully determined by the agent's mental disposition at the outset of the action. Moral responsibility presupposes not free choice but that the person is unforced and causally responsible for the action. This (...) requires the agent's ability to influence causally, on the basis of their beliefs, the development of their behavioral dispositions. The "swerve" was intended to explain the non-necessity of agency without undermining Epicurus' atomistic explanation of the order in the universe, viz. by making the mental dispositions of adults non-necessary. (shrink)

ABSTRACT: Stewart Shapiro recently argued that there is no higher-order vagueness. More specifically, his thesis is: (ST) ‘So-called second-order vagueness in ‘F’ is nothing but first-order vagueness in the phrase ‘competent speaker of English’ or ‘competent user of “F”’. Shapiro bases (ST) on a description of the phenomenon of higher-order vagueness and two accounts of ‘borderline case’ and provides several arguments in its support. We present the phenomenon (as Shapiro describes it) and the accounts; then discuss Shapiro’s arguments, arguing that (...) none is compelling. Lastly, we introduce the account of vagueness Shapiro would have obtained had he retained compositionality and show that it entails true higher-order vagueness. (shrink)

If a group is modelled as a single Bayesian agent, what should its beliefs be? I propose an axiomatic model that connects group beliefs to beliefs of group members, who are themselves modelled as Bayesian agents, possibly with different priors and different information. Group beliefs are proven to take a simple multiplicative form if people’s information is independent, and a more complex form if information overlaps arbitrarily. This shows that group beliefs can incorporate all information spread over the individuals without (...) the individuals having to communicate their (possibly complex and hard-to-describe) private information; communicating prior and posterior beliefs sufices. JEL classification: D70, D71.. (shrink)

In the framework of judgment aggregation, we assume that some formulas of the agenda are singled out as premisses, and that both Independence (formula-wise aggregation) and Unanimity Preservation hold for them. Whether premiss-based aggregation thus defined is compatible with conclusion-based aggregation, as defined by Unanimity Preservation on the non-premisses, depends on how the premisses are logically connected, both among themselves and with other formulas. We state necessary and sufficient conditions under which the combination of both approaches leads to dictatorship (resp. (...) oligarchy), either just on the premisses or on the whole agenda. This framework is inspired by the doctrinal paradox of legal theory and arguably relevant to this field as well as political science and political economy. When the set of premisses coincides with the whole agenda, a limiting case of our assumptions, we obtain several existing results in judgment aggregation theory. (shrink)

How can the propositional attitudes of several individuals be aggregated into overall collective propositional attitudes? Although there are large bodies of work on the aggregation of various special kinds of propositional attitudes, such as preferences, judgments, probabilities and utilities, the aggregation of propositional attitudes is seldom studied in full generality. In this paper, we seek to contribute to filling this gap in the literature. We sketch the ingredients of a general theory of propositional attitude aggregation and prove two new theorems. (...) Our first theorem simultaneously characterizes some prominent aggregation rules in the cases of probability, judgment and preference aggregation, including linear opinion pooling and Arrovian dictatorships. Our second theorem abstracts even further from the specific kinds of attitudes in question and describes the properties of a large class of aggregation rules applicable to a variety of belief-like attitudes. Our approach integrates some previously disconnected areas of investigation. (shrink)

In this paper, we identify a new and mathematically well-defined sense in which the coherence of a set of hypotheses can be truth-conducive. Our focus is not, as usual, on the probability but on the confirmation of a coherent set and its members. We show that, if evidence confirms a hypothesis, confirmation is “transmitted” to any hypotheses that are sufficiently coherent with the former hypothesis, according to some appropriate probabilistic coherence measure such as Olsson’s or Fitelson’s measure. Our findings have (...) implications for scientific methodology, as they provide a formal rationale for the method of indirect confirmation and the method of confirming theories by confirming their parts. (shrink)

ABSTRACT: This paper serves two purposes: (i) it can be used by students as an introduction to chapters 1-5 of book iii of the NE; (ii) it suggests an answer to the unresolved question what overall objective this section of the NE has. The paper focuses primarily on Aristotle’s theory of what makes us responsible for our actions and character. After some preliminary observations about praise, blame and responsibility (Section 2), it sets out in detail how all the key notions (...) of NE iii 1-5 are interrelated (Sections 3-9). The setting-out of these interconnections makes it then possible to provide a comprehensive interpretation of the purpose of the passage. Its primary purpose is to explain how agents are responsible for their actions not just insofar as they are actions of this kind or that, but also insofar as they are noble or base: agents are responsible for their actions qua noble or base, because, typically via choice, their character dispositions are a causal factor of those actions (Section 10). The paper illustrates the different ways in which agents can be causes of their actions by means of Aristotle’s four basic types of agents (Section 11). A secondary purpose of NE iii 1-5 is to explain how agents can be held responsible for consequences of their actions (Section 12), in particular for their character dispositions insofar as these are noble or base, i.e. virtues or vices (Section 13). These two goals are not the only ones Aristotle pursues in the passage. But they are the ones Aristotle himself indicates in its first sentence and summarizes in its last paragraph; and the ones that give the passage a systematic unity. The paper also briefly consider the issues of freedom-to-do-otherwise, free choice and free-will in the contexts in which they occur (i.e. in the final paragraphs of Sections 6, 7, 12, 13). (shrink)

ABSTRACT: A very brief summary presentation of western ancient logic for the non-specialized reader, from the beginnings to Boethius. For a much more detailed presentation see my "Ancient Logic" in the Stanford Encyclopedia of Philosopy (also on PhilPapers).

Imagine a group that faces a decision problem but does not agree on which decision procedure is appropriate. In that case, can a decision be reached that respects the procedural concerns of the group? There is a sense in which legitimate decisions are possible even if people disagree on which procedure to use. I propose to decide in favour of an option which maximizes the number of persons whose judged-right procedure happens to entail this decision given the profile. This decision (...) rule is based not only ona profile in the standard sense, but in addition on a profile of judged-right procedures. To justify this decision rule, I present a set of simple axioms leading to it as the only solution. (shrink)

ABSTRACT: This paper argues that the so-called paradoxes of higher-order vagueness are the result of a confusion between higher-order vagueness and the distribution of the objects of a Sorites series into extensionally non-overlapping non-empty classes.

ABSTRACT: This paper traces the earliest development of the most basic principle of deduction, i.e. modus ponens (or Law of Detachment). ‘Aristotelian logic’, as it was taught from late antiquity until the 20th century, commonly included a short presentation of the argument forms modus (ponendo) ponens, modus (tollendo) tollens, modus ponendo tollens, and modus tollendo ponens. In late antiquity, arguments of these forms were generally classified as ‘hypothetical syllogisms’. However, Aristotle did not discuss such arguments, nor did he call any (...) arguments ‘hypothetical syllogisms’. The Stoic indemonstrables resemble the modus ponens/tollens arguments. But the Stoics never called them ‘hypothetical syllogisms’; nor did they describe them as ponendo ponens, etc. The tradition of the four argument forms and the classification of the arguments as hypothetical syllogisms hence need some explaining. In this paper, I offer some explanations by tracing the development of certain elements of Aristotle’s logic via the early Peripatetics to the logic of later antiquity. I consider the questions: How did the four argument forms arise? Why were there four of them? Why were arguments of these forms called ‘hypothetical syllogisms’? On what grounds were they considered valid? I argue that such arguments were neither part of Aristotle’s dialectic, nor simply the result of an adoption of elements of Stoic logic, but the outcome of a long, gradual development that begins with Aristotle’s logic as preserved in his Topics and Prior Analytics; and that, as a result, we have a Peripatetic logic of hypothetical inferences which is a far cry both from Stoic logic and from classical propositional logic, but which sports a number of interesting characteristics, some of which bear a cunning resemblance to some 20th century theories. (shrink)

The new …eld of judgment aggregation aims to …nd collective judgments on logically interconnected propositions. Recent impossibility results establish limitations on the possibility to vote independently on the propositions. I show that, fortunately, the impossibility results do not apply to a wide class of realistic agendas once propositions like “if a then b” are adequately modelled, namely as subjunctive implications rather than material implications. For these agendas, consistent and complete collective judgments can be reached through appropriate quota rules (which decide (...) propositions using acceptance thresholds). I characterise the class of these quota rules. I also prove an abstract result that characterises consistent aggregation for arbitrary agendas in a general logic. (shrink)

In judgment aggregation, unlike preference aggregation, not much is known about domain restrictions that guarantee consistent majority outcomes. We introduce several conditions on individual judgments su¢ - cient for consistent majority judgments. Some are based on global orders of propositions or individuals, others on local orders, still others not on orders at all. Some generalize classic social-choice-theoretic domain conditions, others have no counterpart. Our most general condition generalizes Sen’s triplewise value-restriction, itself the most general classic condition. We also prove a (...) new characterization theorem: for a large class of domains, if there exists any aggregation function satisfying some democratic conditions, then majority voting is the unique such function. Taken together, our results provide new support for the robustness of majority rule. (shrink)

Rational choice theory analyzes how an agent can rationally act, given his or her preferences, but says little about where those preferences come from. Preferences are usually assumed to be fixed and exogenously given. Building on related work on reasons and rational choice, we describe a framework for conceptualizing preference formation and preference change. In our model, an agent's preferences are based on certain "motivationally salient" properties of the alternatives over which the preferences are held. Preferences may change as new (...) properties of the alternatives become salient or previously salient properties cease to be salient. Our approach captures endogenous preferences in various contexts and helps to illuminate the distinction between formal and substantive concepts of rationality, as well as the role of perception in rational choice. (shrink)

We argue that the extant evidence for Stoic logic provides all the elements required for a variable-free theory of multiple generality, including a number of remarkably modern features that straddle logic and semantics, such as the understanding of one- and two-place predicates as functions, the canonical formulation of universals as quantified conditionals, a straightforward relation between elements of propositional and first-order logic, and the roles of anaphora and rigid order in the regimented sentences that express multiply general propositions. We consider (...) and reinterpret some ancient texts that have been neglected in the context of Stoic universal and existential propositions and offer new explanations of some puzzling features in Stoic logic. Our results confirm that Stoic logic surpasses Aristotle’s with regard to multiple generality, and are a reminder that focusing on multiple generality through the lens of Frege-inspired variable-binding quantifier theory may hamper our understanding and appreciation of pre-Fregean theories of multiple generality. (shrink)

Bayesian epistemology tells us with great precision how we should move from prior to posterior beliefs in light of new evidence or information, but says little about where our prior beliefs come from. It offers few resources to describe some prior beliefs as rational or well-justified, and others as irrational or unreasonable. A different strand of epistemology takes the central epistemological question to be not how to change one’s beliefs in light of new evidence, but what reasons justify a given (...) set of beliefs in the first place. We offer an account of rational belief formation that closes some of the gap between Bayesianism and its reason-based alternative, formalizing the idea that an agent can have reasons for his or her (prior) beliefs, in addition to evidence or information in the ordinary Bayesian sense. Our analysis of reasons for belief is part of a larger programme of research on the role of reasons in rational agency (Dietrich and List, Nous, 2012a, in press; Int J Game Theory, 2012b, in press). (shrink)

How can different individuals' probability functions on a given sigma-algebra of events be aggregated into a collective probability function? Classic approaches to this problem often require 'event-wise independence': the collective probability for each event should depend only on the individuals' probabilities for that event. In practice, however, some events may be 'basic' and others 'derivative', so that it makes sense first to aggregate the probabilities for the former and then to let these constrain the probabilities for the latter. We formalize (...) this idea by introducing a 'premise-based' approach to probabilistic opinion pooling, and show that, under a variety of assumptions, it leads to linear or neutral opinion pooling on the 'premises'. This paper is the second of two self-contained, but technically related companion papers inspired by binary judgment-aggregation theory. (shrink)

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

All existing impossibility theorems on judgment aggregation require individual and collective judgment sets to be consistent and complete, arguably a demanding rationality requirement. They do not carry over to aggregation functions mapping profiles of consistent individual judgment sets to consistent collective ones. We prove that, whenever the agenda of propositions under consideration exhibits mild interconnections, any such aggregation function that is "neutral" between the acceptance and rejection of each proposition is dictatorial. We relate this theorem to the literature.

ABSTRACT: In antiquity we encounter a distinction of two types of hypothetical syllogisms. One type are the ‘mixed hypothetical syllogisms’. The other type is the one to which the present paper is devoted. These arguments went by the name of ‘wholly hypothetical syllogisms’. They were thought to make up a self-contained system of valid arguments. Their paradigm case consists of two conditionals as premisses, and a third as conclusion. Their presentation, either schematically or by example, varies in different authors. For (...) instance, we find ‘If (it is) A, (it is) B; if (it is) B, (it is) C; therefore, if (it is) A, (it is) C’. The main contentious point about these arguments is what the ancients thought their logical form was. Are A, B, C schematic letters for terms or propositions? Is ‘is’, where it occurs, predicative, existential, or veridical? That is, should ‘A esti’ be translated as ‘it is an A’, ‘A exists’, ‘As exist’ or ‘It is true/the case that A’? If A, B, C are term letters, and ‘is’ is predicative, are the conditionals quantified propositions or do they contain designators? If one cannot answer these questions, one can hardly claim to know what sort of arguments the wholly hypothetical syllogisms were. In fact, all the above-mentioned possibilities have been taken to describe them correctly. In this paper I argue that it would be mistaken to assume that in antiquity there was one prevalent understanding of the logical form of these arguments - even if the ancients thought they were all talking about the same kind of argument. Rather, there was a complex development in their understanding, starting from a term-logical conception and leading to a propositional-logical one. I trace this development from Aristotle to Philoponus and set out the deductive system on which the logic of the wholly hypothetical syllogisms was grounded. (shrink)

According to standard rational choice theory, as commonly used in political science and economics, an agent's fundamental preferences are exogenously fixed, and any preference change over decision options is due to Bayesian information learning. Although elegant and parsimonious, such a model fails to account for preference change driven by experiences or psychological changes distinct from information learning. We develop a model of non-informational preference change. Alternatives are modelled as points in some multidimensional space, only some of whose dimensions play a (...) role in shaping the agentís preferences. Any change in these "motivationally salient" dimensions can change the agent's preferences. How it does so is described by a new representation theorem. Our model not only captures a wide range of frequently observed phenomena, but also generalizes some standard representations of preferences in political science and economics. (shrink)

This paper contends that Stoic logic (i.e. Stoic analysis) deserves more attention from contemporary logicians. It sets out how, compared with contemporary propositional calculi, Stoic analysis is closest to methods of backward proof search for Gentzen-inspired substructural sequent logics, as they have been developed in logic programming and structural proof theory, and produces its proof search calculus in tree form. It shows how multiple similarities to Gentzen sequent systems combine with intriguing dissimilarities that may enrich contemporary discussion. Much of Stoic (...) logic appears surprisingly modern: a recursively formulated syntax with some truth-functional propositional operators; analogues to cut rules, axiom schemata and Gentzen’s negation-introduction rules; an implicit variable-sharing principle and deliberate rejection of Thinning and avoidance of paradoxes of implication. These latter features mark the system out as a relevance logic, where the absence of duals for its left and right introduction rules puts it in the vicinity of McCall’s connexive logic. Methodologically, the choice of meticulously formulated meta-logical rules in lieu of axiom and inference schemata absorbs some structural rules and results in an economical, precise and elegant system that values decidability over completeness. (shrink)

Economic models describe individuals in terms of underlying characteristics, such as taste for some good, sympathy level for another player, time discount rate, risk attitude, and so on. In real life, such characteristics change through experiences: taste for Mozart changes through listening to it, sympathy for another player through observing his moves, and so on. Models typically ignore change, not just for simplicity but also because it is unclear how to incorporate change. I introduce a general axiomatic framework for defining, (...) analysing and comparing rival models of change. I show that seemingly basic postulates on modelling change together have strong implications, like irrelevance of the order in which someone has his experiences and ‘linearity’ of change. This is a step towards placing the modelling of change on solid axiomatic grounds and enabling non-arbitrary incorporation of change into economic models. (shrink)