In this paper Beebee argues that the problem of induction, which she describes as a genuine sceptical problem, is the same for Humeans than for Necessitarians. Neither scientific essentialists nor Armstrong can solve the problem of induction by appealing to IBE, for both arguments take an illicit inductive step.

In the not too distant past, it was common to treat Hume's skeptical doubts regarding the justification of our beliefs in causal connections—understood as necessary connections between objects or events—as having appeared per conceptionem immaculatam in his post-Cartesian mind. Thanks to recent efforts by scholars in early modern philosophy, however, we are now more informed about the roots of Hume's conclusions in Cartesian thought itself, especially the influence of Malebranche and his arguments for occasionalism. And by the (...) research of historians of Medieval philosophy we are reminded that many aspects of seventeenth-century occasionalism, in turn, have their ancestry in Latin and Arabic thought of the Middle Ages. In this paper I offer a small contribution to the overall project of illuminating the precedents in Medieval philosophy for the theses and arguments in Malebranche that so clearly influenced the most important and influential philosophical analysis of causation ever. There is a tradition here, where the goal is to undermine claims to discover real causal relations or powers in nature. I will concentrate on one particular aspect or tool of that tradition: the negative argument that we can never perceive a sufficiently necessary connection between any two natural objects or events. (shrink)

In this paper I examine whether the Humean denial of necessary connections between wholly distinct contingent existents poses problems for a theory of tropes. In section one I consider the substance-attribute theory of tropes. I distinguish first between three versions of the non-transferability of a trope from the substratum in which it inheres and then between two versions of the denial of necessary connections. I show that the most plausible combination of these views is consistent. In (...) section two I consider an objection to the bundle theory using the Humean doctrine that is advanced by Armstrong, and argue that it is unconvincing. In section three I return to the version of non-transferability that would cause obvious trouble for a substance-attribute theory, and less obvious trouble for a bundle theory. I argue that there is independent reason to reject this principle since, given a perdurantist metaphysic, it does not in fact secure what appeared to be its only benefit: namely that it allows tropes to act as truthmakers. I conclude that there is no objection to trope theory per se on the grounds that it brings commitment to necessary connections. (shrink)

In this paper I examine whether the Humean denial of necessary connections between wholly distinct contingent existents poses problems for a theory of tropes. In section one I consider the substance‐attribute theory of tropes. I distinguish first between three versions of the non‐transferability of a trope from the substratum in which it inheres and then between two versions of the denial of necessary connections. I show that the most plausible combination of these views is consistent. In (...) section two I consider an objection to the bundle theory using the Humean doctrine that is advanced by Armstrong, and argue that it is unconvincing. In section three I return to the version of non‐transferability that would cause obvious trouble for a substance‐attribute theory, and less obvious trouble for a bundle theory. I argue that there is independent reason to reject this principle since, given a perdurantist metaphysic, it does not in fact secure what appeared to be its only benefit: namely that it allows tropes to act as truthmakers. I conclude that there is no objection to trope theory per se on the grounds that it brings commitment to necessary connections. (shrink)

Malebranche presents two major arguments for occasionalism: the “no necessary connection” argument (NNC) and the “conservation is but continuous creation” argument (CCC). NNC appears prominently in his Search After Truth but virtually disappears and surrenders the spotlight to CCC in his later major work, Dialogues on Metaphysics and on Religion . This paper investigates the possible reasons and motivations behind this significant shift. I argue that the shift is no surprise if we consider the two ways in which the (...) CCC is preferable to NNC: it is not only more effective against opponents but also more consistent with his own views on freedom. (shrink)

In this paper I examine the objection to truthmaker theory, forcibly made by David Lewis and endorsed by many, that it violates the Humean denial of necessary connections between distinct existences. In Sect. 1 I present the argument that acceptance of truthmakers commits us to necessary connections. In Sect. 2 I examine Lewis’ ‘Things-qua-truthmakers’ theory which attempts to give truthmakers without such a commitment, and find it wanting. In Sects. 3–5 I discuss various formulations of the (...) denial of necessary connections and argue that each of them is either false or compatible with truthmaker theory. In Sect. 6 I show how the truthmaker theorist can resist the charge that they are committed to necessary exclusions between possible existents. I conclude that there is no good objection to truthmaker theory on the grounds that it violates the Humean dictum. (shrink)

THE aim of this paper is to refute Hume's contention that there cannot be logically necessary connections between successive events. I intend to establish, in other words, not 'Logically necessary connections do exist between successive events', but instead the rather more modest proposition: 'It may be, it is possible, as far as we can ever know for certain, that logically necessary connections do exist between successive events.' Towards the end of the paper I shall (...) say something about the implications of rejecting Hume's contention. (shrink)

This paper combines the ancient idea that causes necessitate their effects with Angelika Kratzer’s semantics of modality. On the resulting view, causal claims quantify over restricted domains of possible worlds determined by two contextually determined parameters. I argue that this view can explain a number of otherwise puzzling features of the way we use and evaluate causal language, including the difference between causing an effect and being a cause of it, the sensitivity of causal judgements to normative facts, and the (...) semantics of causal disagreements. (shrink)

The two traditional Indian Buddhist philosophers – the Mādhyamika Nāgārjuna (c.150–250) and the Sautrāntika-Vasubandhu (c. 350–430) – agree that mental causation involves a causal relationship between successive consciousness moments in which the previous moments are causes and the latter moments effects. In this chapter, I investigate the nature of this relation at stake. Is it a type of relationship that requires (1) necessary connection between successive consciousness moments in which there is an internal causal connection between the previous and (...) the latter conscious moments? (2) Alternatively, is the causal relationship between consciousness moments just a matter of constant conjunctions of intrinsic natures (svabhāvas) without any necessary causal relation? If the former, the two Buddhist philosophers need to explain which of the two truths – conventional truth or ultimate truth – does this necessary relation belong and why? If the latter, they need to explain how mental causation – a continuum of interrupted mental events in which the previous moment are causes and the subsequent moments effects – possible with intrinsic natures, absent any necessary causal connection between them? Either way, the Buddhist philosophers must address these two questions concerning causal relation adequately. (shrink)

The necessitarian solution to the problem of induction involves two claims: first, that necessary connections are justified by an inference to the best explanation; second, that the best theory of necessary connections entails the timeless uniformity of nature. In this paper, I defend the second claim. My arguments are based on considerations from the metaphysics of laws, properties, and fundamentality.

If positivism is interpreted as requiring that nothing is law that does not conform to socially accepted criteria, it is inconsistent with positive law. This is because law purports to be morally in order. Hence it is always possible to argue against a certain interpretation of the law that it is morally indefensible and there is always a certain pressure within a legal system to render it morally defensible. In that way critical morality necessarily becomes a persuasive source of law.

In this paper I will introduce a problem for at least those Humeans who believe that the future is open. More particularly, I will argue that the following aspect of scientific practice cannot be explained by openfuture- Humeanism: There is a distinction between states that we cannot bring about (which are represented in scientific models as nomologically impossible) and states that we merely happen not to bring about. Open-future-Humeanism has no convincing account of this distinction. Therefore it fails to explain (...) why we cannot bring about certain states of affairs, it cannot explain what I call the “recalcitrance of nature”. (shrink)

It has been traditional in political philosophy to take internal and external state legitimacy as resting on distinct criteria. However, this is a view that is currently being challenged. Assuming that internal and external legitimacy rely on the same criterion, a possible worry that arises is that an unacceptable amount of intervention will necessarily become justifiable. I argue that such worries are not significant and that they do not rule out this alternative to the traditional view.

In lieu of an abstract, here is a brief excerpt of the content:217 HUME'S IDEAS ABOUT NECESSARY CONNECTION 1. Introduction Hume asks, "What is our idea of necessity, when we say that two objects are necessarily connected together"? He later says that he has answered this question, but it is difficult to see what his answer is, or even to see precisely what the question was. Currently there are two main ways of understanding Hume's views about our idea of (...) necessary connection. These interpretations divide on the question whether Hume allows that we can speak meaningfully of an objective and necessary connection between two events. The one interpretation, which I will call epistemological, says that Hume does allow meaning to that phrase. On this view, justification is the only topic of Hume's negative message about necessary connection. We can mean what we say when we talk about necessary connection, but we cannot justify what we (meaningfully) say. That, according to this interpretation, is the negative outcome toward which Hume aims his investigation of the origin of our idea of necessary connection. He isn't denying we have that very idea; he is denying that its origin allows us to justify applying it to anything. The other interpretation, which I will call psychological, says that Hume does not allow meaning to the phrase, "an objective and necessary connection between two events." According to this interpretation, once we see the origin of our idea of necessary connection, we realize that we cannot mean by "necessary connection" what we thought we meant. Those words allow us to speak only of a certain 218 feeling in our minds, not of an objective feature of the world. Of course, the psychological interpretation partly resembles the epistemological one: it, too, denies that we can justify saying objective necessary connections exist. But on the psychological interpretation this follows a fortiori from the central negative claim, a claim which itself concerns meaning, not justification. In what follows, I will present these two interpretations more carefully and critically, and then I will advance my own. I think Hume was trying to express a view very different in kind from either of the two I've just mentioned. I think we can get a good idea of the kind of view Hume had by looking at Newton's treatment of gravitational force. Roughly, Newton thought that while there certainly are gravitational forces in objects, we can say nothing about them except that they are whatever it is that accounts for a specific set of observable regularities. Hume's views about necessary connection, or causal power, are roughly parallel. He does not doubt that we may speak meaningfully of objective necessary connections — rE we mean just some unknown quality in objects that underlies the constant conjunction of their sensible qualities. Inevitably we try to mean something more than this, but any such attempt is doomed to failure. Showing that we cannot mean something more is the point of investigating the origin of the "idea." I will be arguing that with this interpretation we can handle the sets of texts and problems that undercut the prevailing two interpretations, and reconcile those sets of texts with one another, despite their apparent inconsistency. This interpretation also has the advantage of attributing to Hume a view closely connected with a 219 distinctively eighteenth-century way of setting up these problems. Finally, I think the interpretation brings out nicely an instructive and central failing of Hume's views about necessary connection. 2. The Epistemological View Although there are hints of this kind of interpretation in other books, it is really articulated and defended only in Barry Stroud's book, 2 Hume. In what follows here, I mean to be sketching out and commenting on that interpretation. Hume wants to find out what our idea of necessary connection is. He conducts his investigation according to the dictum, "as we have no idea, that is not deriv'd from an impression, we must find some impression, that gives rise to this idea of necessity, if we assert we have really such an idea." (T 155) He argues, of course, that among our experiences of causes and effects, there are no impressions of necessary connection. Our experiences of... (shrink)

In this paper I deal with the relation between the disjunction thesis—that the truthmaking relation is distributed over a disjunction—and the necessary connection thesis—that the existence of some entities requires the existence of other distinct entities. I will first show that because of this very relation, the arguments for and against the disjunction thesis that overlook its metaphysical considerations will fail. Finally, I will show that the commitment produced by truthmaker maximalism to totality states of affairs, or some relevantly (...) similar things, requires one to accept a necessary connection that disaffirms the disjunction thesis. (shrink)

The following questions are discussed here. Is induction a reasonable procedure in the context of a denial of physically necessary connections? What is physical necessity? If induction does presuppose physical necessity, what amount of it is presupposed? It is argued that with logic as the only restriction on what is to count as a possible world, it is unreasonable to claim that observed connections, whether universal or statistical, will continue to hold. The concept of physical necessity is (...) no more problematic than that of logical necessity, once it is recognized that the necessity of physical and logical necessity is the same. A variant of Keynes' principle of limited independent variety answers the question of the amount of physical necessity presupposed. (shrink)

Ross Cameron puts forward a novel solution to the truthmaker problem facing presentism. I claim that, by Cameron's own lights, the view is not in fact a presentist view at all, but rather requires us to endorse a form of Priority Presentism, whereby past objects are derivative and depend for their existence upon present objects. I argue that this view should be rejected.

Ross Cameron puts forward a novel solution to the truthmaker problem facing presentism. I claim that, by Cameron's own lights, the view is not in fact a presentist view at all, but rather requires us to endorse a form of Priority Presentism, whereby past objects are derivative and depend for their existence upon present objects. I argue that this view should be rejected.

The paper offers a critical examination of Ghazali’s main arguments against the views of the philosophers on causation. The authors argue that Ghazali’s definition of miracles as "departure from the usual course of events" carries at least two meanings, only one of which is in conflict with necessary causal relations. The authors also argue that Ghazali’s desire to uphold the possibility of miracles need not constrain him to repudiate the idea of necessary connection, since he is able to (...) explain miracles in ways that are compatible with belief in causality and necessary connection. The authors conclude by examining some arguments to the effect that Ghazali’s attempt to hold on to both miracles and necessary connection is inherently unstable, and explore directions which Ghazalians may take in order to counter these arguments. (shrink)

Hume is not a philosopher who has been viewed, on the whole, with excessive sympathy. Slips and inadequacies of argument, which are the inevitable consequence of human fallibility, are treated by his critics not with charity but with delight; and there are few who think it necessary to state his argument at its strongest before proceeding to refute it. A striking example of this procedure may be found in Antony Flew's paper ‘Another Idea of Necessary Connection’. The example (...) is striking because Flew is normally one of the most sympathetic of Hume's critics and he might have been expected, in dealing with Humes view of causal necessity, to have proceeded with exceptional fairness, the incidental being identified and discarded and the essential view standing forth at its strongest. This, as I shall show, is not what occurs; but first let us consider what we are to take the essential view to be. (shrink)

In this paper, I will discuss accounts to solve the problem of induction by introducing necessary connections. The basic idea is this: if we know that there are necessary connections between properties F and G such that F -ness necessarily brings about G-ness, then we are justified to infer that all, including future or unobserved, F s will be Gs. To solve the problem of induction with ontology has been proposed by David Armstrong and Brian Ellis. (...) In this paper, I will argue that these attempts to solve the problem of induction fail. Necessary connections fail to reliably imply the respective regularities for two main reasons: Firstly, according to an argument originally presented by Helen Beebee, the respective necessary connections might be time-limited, and hence do not warrant inferences about future cases. As I will discuss, arguments against the possibility or explanatory power of time-limited necessary connections fail. Secondly, even time-unlimited necessary connections do not entail strict or non-strict regularities, and nor do they allow inferences about individual cases, which is an important function of inductive reasoning. Moreover, the proposed solution to the problem of induction would only apply to a tiny minority of inductive inferences. I argue that most inductive inferences are not easily reducible to the proposed inference pattern, as the vast majority of everyday inductive inferences do not involve necessary connections between fundamental physical properties or essences. (shrink)

Hume seems to tell us that our ideas are copies of our corresponding impres-sions, that we have an idea of necessary connection, but that we have no corresponding impression, since nothing can be known to be really necessarily connected. The paper considers two ways of reinterpreting the doctrine of the origins of ideas so as to avoid the apparent inconsistency. If we see the doctrine as concerned primarily with establishing conditions under which we possess an idea, there is no (...) need for an idea’s “corresponding” impression to be one of which the idea is true. It would be enough that the impression be in some way appropriate for making us master of the idea. Alternatively, if we see the doctrine as concerned primarily with fixing the content of ideas, we might see it operating in the case of causation rather as it must in the case of secondary qualities, conceived in a certain distinctive way. Even if there is “really” no red in the objects , we may regard the idea of red as properly ascribed to any object apt to cause typical sensations in us . Likewise, we may regard the idea of necessary connection as properly ascribed to any pair of objects apt to cause typical habits in us . This view may do justice to Hume’s wish to affirm both that there is such a thing as necessity, resident in the mind, and that there are no knowable necessary connections.Hume parece nos dizer que nossas idéias são cópias de nossas impressões correspondentes, que temos uma idéia de conexão necessária, mas que não temos nenhuma impressão correspondente, visto que nada pode ser conhecido como estando realmente conectado necessariamente. O artigo considera dois modos de se reinterpretar a doutrina das origens das idéias de forma a evitar a aparente inconsistência. Se interpretarmos a doutrina como dizendo respeito fundamentalmente ao estabelecimento das condições sob as quais possuímos uma idéia, não há nenhuma necessidade de uma impressão “correspondente” da idéia ser aquela da qual a idéia é verdadeira. Seria suficiente que a impressão fosse, de alguma maneira, apropriada para que apreendêssemos a idéia. Caso contrário, se interpretarmos a doutrina como interessada fundamentalmente em fixar o conteúdo das idéias, poderíamos ver isto como operando no caso de causação mais propriamente que no caso de qualidades secundárias, concebido de certo modo característico. Mesmo que “realmente” não exista vermelho nos objetos , nós podemos considerar a idéia de vermelho como bem aplicada a qualquer objeto capaz de causar sensações típicas em nós . Igualmente, podemos considerar a idéia de conexão necessária como bem aplicada a qualquer par de objetos apropriado para nos causar hábitos típicos . Esta visão pode fazer justiça à intenção de Hume de afirmar tanto que há tal coisa como necessidade, residente na mente, como que não há nenhuma relação necessária que se possa conhecer. (shrink)

David Hume's claim that necessary connection is essential to causality was at the expense of a useful causal distinction we sometimes note with the words ‘necessity’ and ‘contingency’. And since, as J. L. Mackie has stated, Hume made ‘the most significant and influential single contribution to the theory of causation’, subsequent writers on causality, regardless of their support for, or opposition to, Hume, have joined him in trampling this distinction. The object of this paper is not so much to (...) undermine one of Hume's conclusions as it is to describe a use of ‘necessary’ that, while surviving in popular usage, is ignored or obfuscated in the literature on causality. (shrink)

Legal positivism maintains a distinction between law as it is and law as it ought to be. In other words, for positivists, a law can be legally valid even if it is immoral. H. L. A. Hart hoped to defend legal positivism against natural law. This paper analyses Hart’s criticism of Gustav Radbruch, a natural lawyer, before suggesting that Hart’s account of legal positivism gives rise to a logical problem. It is concluded that this problem leaves logical space for a (...) theory of natural law based on moral authority rather than legal validity. (shrink)

Hume's contributions to discussions on causality and necessary connection are significant and influential. Yet they remain a source of ongoing debate among philosophers. The analysis in my book is an attempt to dissipate some of the perplexities that surround these issues. The arguments here support what I call a subjectivist interpretation of Hume's views on necessary connection. My central thesis is the suggestion that Hume identifies necessary connection or power with a specific psychological dispositon of the mind (...) "to carry our thought from one object to another". In addition to explaining and exploring this thesis, I critically investigate Hume's arguments for his powerful epistemological paradigm. (shrink)

The dynamics of general relativity is encoded in a set of ten differential equations, the so-called Einstein field equations. It is usually believed that Einstein's equations represent a physical law describing the coupling of spacetime with material fields. However, just six of these equations actually describe the coupling mechanism: the remaining four represent a set of differential relations known as Bianchi identities. The paper discusses the physical role that the Bianchi identities play in general relativity, and investigates whether these identities (...) --qua part of a physical law-- highlight some kind of a posteriori necessity in a Kripkean sense. The inquiry shows that general relativistic physics has an interesting bearing on the debate about the metaphysics of the laws of nature. (shrink)

One of the greatest of Hume's philosophical achievements, which becomes in its turn an assumption presupposed by some of the others, is perhaps best stated at the end of the First Enquiry : ‘If we reason a priori , anything may appear able to produce anything. The falling of a pebble may, for aught we know, extinguish the sun; or the wish of a man control the planets in their orbits. It is only experience, which teaches us the nature and (...) bounds of cause and effect, and enables us to infer the existence of one object from that of another’ 164). (shrink)

In this article the author adduces a non‐positivist argument for a necessary connection between law and morality; the argument is based on the claim to correctness, and it is directed to an attack stemming from Eugenio Bulygin. The heart of the controversy is the claim to correctness. The author first attempts to show that there are good reasons for maintaining that law necessarily raises a claim to correctness. He argues, second, for the thesis that this claim has moral implications. (...) Finally, he attempts to refute Bulygin's objection that the claim‐based argument for non‐positivism boils down to contradiction and triviality. (shrink)

Fred Dretske, Michael Tooley, and David Armstrong accept a theory of governing laws of nature according to which laws are atomic states of affairs that necessitate corresponding natural regularities. Some philosophers object to the Dretske/Tooley/Armstrong theory on the grounds that there is no illuminating account of the necessary connection between governing law and natural regularity. In response, Michael Tooley has provided a reductive account of this necessary connection in his book Causation (1987). In this essay, I discuss an (...) improved version of his account and argue that it fails. First, the account cannot be extended to explain the necessary connection between certain sorts of laws—namely, probabilistic laws and laws relating structural universals—and their corresponding regularities. Second, Tooley’s account succeeds only by (very subtly) incorporating primitive necessity elsewhere, so the problem of avoiding primitive necessity is merely relocated. (shrink)

Dispositional essentialists hold that the world is populated by irreducibly dispositional properties, called “potencies,” “powers,” or “dispositions.” Each of these properties is marked out by a characteristic stimulus and manifestation bound together in a metaphysically necessary connection. Dispositional essentialism faces an old objection from David Hume. Hume argues, in his Treatise of Human Nature, that we have no adequate idea of necessary connection. The epistemology of the Treatise allegedly rules the idea out. Dispositional essentialists usually respond by attacking (...) Hume’s epistemology. In this paper, I give an alternative response. I argue that we can draw an idea of necessary connection from the Treatise’s relations of ideas. We are able, therefore, to overcome Hume’s objection without needing to attack his epistemology or its related principles. (shrink)

THERE is no trap that is easier to stumble into than that of trying to show whether one philosopher did or did not answer the problem of another philosopher. The trap consists in the tendency to think that both philosophers handled the problem in precisely the same way, even though they represent two quite different traditions. This is especially true of thinkers like David Hume and Charles Sanders Peirce. John Smith has shown quite convincingly that we cannot understand the American (...) pragmatists by limiting discussion to the epistemological questions of the British empiricist tradition stemming from Hume, Mill, and Russell. And A. J. Ayer can be faulted for attempting to do just that. However, it is possible for one to treat of Peirce's answer to Hume on necessary connection without falling into the trap. First of all, both philosophers raised the same kind of question. It is clear that Peirce had Hume specifically in mind when on many an occasion he attacked nominalism and defended real connections. But they differed in that Peirce defended his position from a broader perspective enabling him to arrive at a more satisfactory conclusion. To establish this thesis, it will be necessary to focus on several aspects of their thought that bear upon the topic under discussion. Undoubtedly the task of selection and interpretation of details has many a trap of its own, but it is hoped that the more obvious ones can be avoided. (shrink)

This paper criticizes Alexy's argument on the necessary connection between law and morality. First of all, the author discusses some aspects of the notion of the claim to correctness. Basically, it is highly doubtful that all legal authorities share the same idea of moral correctness. Secondly, the author argues that the claim to correctness is not a defining characteristic of the concepts of “legal norm” and “legal system”. Hence, the thesis of a necessary connection between law and morality (...) based on such claim cannot be accepted. (shrink)

Non-naturalism—roughly the view that normative properties and facts are sui generis—may be combined either with cognitivism or with non-cognitivism. The chapter starts by explaining how the metaphysically necessary connections between the natural and the normative raise an explanatory challenge for realist non-naturalism, and how it is not at all obvious that quasi-realism offers a way of escaping the challenge. Having briefly explored different kinds of accounts of what it is to have thoughts concerning metaphysical necessity, it then proceeds (...) to argue that once we understand the explanatory challenge in the light of a quasi-realist take on normative judgments, this challenge takes the shape of a first-order normative issue, and will be answerable by the quasi-realists’ lights. When it comes to explaining the necessary connections between the normative and the natural, all will be fine, it seems, if non-naturalists just go a little quasi. (shrink)

On Berkeley’s immaterialist ontology, there are only two kinds of created entities: finite spirits and ideas. Ideas are passive, and so there is no genuine idea-idea causation. Finite spirits, by contrast, are truly causally active on Berkeley’s view, in that they can produce ideas through their volitional activity. Some commentators have argued that this account of causation is inconsistent. On their view, the unequal treatment of spirits and ideas is unfounded, for all that can be observed in either case are (...) mere patterns of regularity; Berkeley should therefore adopt a full-blown occasionalism and follow Malebranche in holding that God is the only true cause. Other commentators have argued that Berkeley denies the tenet that causes necessitate their effects – that is, the idea that causation involves necessary connection – and that in this way he can avoid inconsistency. This paper argues that Berkeley can subscribe to the thesis that finite spirits are truly causally active without falling into inconsistency, even if it is granted that Berkeleyan causes necessitate their effects. His differing treatment of spirits and of ideas is well founded, since ideas are transparent in a way our notions of spirits are not. (shrink)

In this paper, we consider choice functions that are unanimous, anonymous, symmetric, and group strategy-proof and consider domains that are single-peaked on some tree. We prove the following three results in this setting. First, there exists a unanimous, anonymous, symmetric, and group strategy-proof choice function on a path-connected domain if and only if the domain is single-peaked on a tree and the number of agents is odd. Second, a choice function is unanimous, anonymous, symmetric, and group strategy-proof on a single-peaked (...) domain on a tree if and only if it is the pairwise majority rule and the number of agents is odd. Third, there exists a unanimous, anonymous, symmetric, and strategy-proof choice function on a strongly path-connected domain if and only if the domain is single-peaked on a tree and the number of agents is odd. As a corollary of these results, we obtain that there exists no unanimous, anonymous, symmetric, and group strategy-proof choice function on a path-connected domain if the number of agents is even. (shrink)