Modern insolubility proofs of the measurement problem in quantum mechanics not only differ in their complexity and degree of generality, but also reveal a lack of agreement concerning the fundamental question of what constitutes such a proof. A systematic reworking of the (incomplete) 1970 Fine theorem is presented, which is intended to go some way toward clarifying the issue.

This is a supplement my original 2005 article "Insolubles" in the Stanford Encyclopedia of Philosophy.

I present a very general and simple argument—based on the no-signalling theorem—showing that within the framework of the unitary Schrödinger equation it is impossible to reproduce the phenomenological description of quantum mechanical measurements (in particular the collapse of the state of the measured system) by assuming a suitable mixed initial state of the apparatus. The thrust of the argument is thus similar to that of the ‘insolubility theorems’ for the measurement problem of quantum mechanics (which, however, focus on the impossibility (...) of reproducing the macroscopic measurement results). Although I believe this form of the argument is new, I argue it is essentially a variant of Einstein’s reasoning in the context of the EPR paradox—which is thereby illuminated from a new angle. (shrink)

Soldiers encounter extremely difficult ethical dilemmas during wars, as they must make decisions about how to follow the laws of war and their rules of engagement while still protecting themselves and accomplishing their missions. Scholarship on just war theory and military ethics generally describe soldiers' dilemmas as being ethical challenges that soldiers can overcome by using the correct ethical reasoning process. However, this essay argues that some of the apparent ethical dilemmas that soldiers confront are actually ethically insoluble dilemmas that (...) cannot be solved using ethical reasoning processes. Dilemmas are ethically insoluble when soldiers do not have sufficient knowledge of a situation or control over it to apply an ethical decision procedure. In these situations soldiers must guess at the right course of action and leave the outcome to luck. (shrink)

Evocatively referred to by Alain Badiou as a “final unravelling” and an “insoluble enigma” that “form[s] an integral part of his enigmatic legacy,” Lacan’s dissolution has long been regarded as a q...

The traditional problem of the social contract defies solution. Agents with the motivations traditionally assumed would not in the circumstances traditionally assumed voluntarily arrive at a contract or voluntarily keep it up, as we can now understand, more clearly than our illustrious predecessors, by treating the problem in terms not available to them: the terms of Prisoner's Dilemma and of the theory of public goods.

Central topics in medieval logic are here treated in a way that is congenial to the modern reader, without compromising historical reliability. The achievements of medieval logic are made available to a wider philosophical public then the medievalists themselves. The three genres of logica moderna arising in a later Middle Ages are covered: obligations, insolubles and consequences - the first time these have been treated in such a unified way. The articles on obligations look at the role of logical (...) consistence in medieval disputation techniques. Those on insolubles concentrate on medieval solutions to the Liar Paradox. There is also a systematic account of how medieval authors described the logical content of an inference, and how they thought that the validity of an inference could be guaranteed. (shrink)

An interesting question is whether deflationism about truth (and falsity) extends to related properties and relations on truthbearers. Lionel Shapiro (2011) answers affirmatively by arguing that a certain deflationism about truth is as plausible as an analogous version of deflationism about logical consequence. I argue that the argument fails on two counts. First, it trivializes to any relation between truthbearers, including substantive ones; in other words, his argument can be used to establish that deflationism about truth is as plausible as (...) deflationism about an arbitrary sentential relation. Second, the alleged analogy between the arguments for deflationism about truth and deflationism about consequence fails. Along the way I consider what implications the failure of the equiplausibility thesis has for deflationism about falsity. (shrink)

This paper provides a philosophical analysis and a new edition of an anonymous Epitome of John Dumbleton’s solution to the semantic paradoxes. The first part of this paper briefly presents Dumbleton’s cassationist solution to the semantic paradoxes, which the English philosopher proposes in his Summa Logicae, written in the 1330s–40s. The second part investigates the solution to various types of insolubles proposed by the anonymous author of the Epitome. The third part provides a new critical edition of the Latin (...) text – a first edition was edited by Bottin in 1978 – and an English translation. (shrink)

The focus of the paper is a sophism based on the proposition ‘This is Socrates’ found in a short treatise on obligational casus attributed to William Heytesbury. First, the background to the puzzle in Walter Burley’s traditional account of obligations (the responsio antiqua), and the objections and revisions made by Richard Kilvington and Roger Swyneshed, are presented. All six types of obligations described by Burley are outlined, including sit verum, the type used in the sophism. Kilvington and Swyneshed disliked the (...) dynamic nature of the responsio antiqua, and Kilvington proposed a revision to the rules for irrelevant propositions. This allowed him to use a form of reasoning, the “disputational meta-argument”, which is incompatible with Burley’s rules. Heytesbury explicitly rejected Kilvington’s revision and the associated meta-argument. Swyneshed also revised Burley’s account of obligations, formulating the so-called responsio nova, characterised by the apparently surprising thesis that a conjunction can be denied both of whose conjuncts are granted. On closer inspection, however, his account is found to be less radical than first appears. (shrink)

In his Quadratura, Paul of Venice considers a sophism involving time and tense which appears to show that there is a valid inference which is also invalid. His argument runs as follows: consider this inference concerning some proposition A: A will signify only that everything true will be false, so A will be false. Call this inference B. Then B is valid because the opposite of its conclusion is incompatible with its premise. In accordance with the standard doctrine of ampliation, (...) Paul takes A to be equivalent to 'Everything that is or will be true will be false'. But he proceeds to argue that it is possible that B's premise ('A will signify only that everything true will be false') could be true and its conclusion false, so B is not only valid but also invalid. Thus A and B are the basis of an insoluble. In his Logica Parva, a self-confessedly elementary text aimed at students and not necessarily representing his own view, and in the Quadratura, Paul follows the solution found in the Logica Oxoniensis, which posits an implicit assertion of its own truth in insolubles like B. However, in the treatise on insolubles in his Logica Magna, Paul develops and endorses Swyneshed's solution, which stood out against this ''multiple-meanings'' approach in offering a solution that took insolubles at face value, meaning no more than is explicit in what they say. On this account, insolubles imply their own falsity, and that is why, in so falsifying themselves, they are false. We consider how both types of solution apply to B and how they complement each other. On both, B is valid. But on one (following Swyneshed), B has true premises and false conclusion, and contradictories can be false together; on the other (following the Logica Oxoniensis), the counterexample is rejected. (shrink)

The Oxford Calculator Roger Swyneshed put forward three provocative claims in his treatise on insolubles, written in the early 1330s, of which the second states that there is a formally valid inference with true premises and false conclusion. His example deployed the Liar paradox as the conclusion of the inference: ‘The conclusion of this inference is false, so this conclusion is false’. His account of insolubles supported his claim that the conclusion is false, and so the premise, referring (...) to the conclusion, would seem to be true. But what is his account of validity that can allow true premises to lead to a false conclusion? This article considers Roger’s own account, as well as that of Paul of Venice, writing some sixty years later, whose account of the truth and falsehood of insolubles followed Roger’s closely. Paul endorsed Roger’s three claims. But their accounts of validity were different. The question is whether these accounts are coherent and support Paul’s claim in his Logica Magna that he endorsed all the normal rules of inference. (shrink)

This book reports the proceedings of the International Congress on the Education of Teachers of Physics in Secondary Schools, held in Eger, Hungary, during September 1970.

This paper examines an insoluble Cartesian problem for classical AI, namely, how linguistic understanding involves knowledge and awareness of u’s meaning, a cognitive process that is irreducible to algorithms. As analyzed, Descartes’ view about reason and intelligence has paradoxically encouraged certain classical AI researchers to suppose that linguistic understanding suffices for machine intelligence. Several advocates of the Turing Test, for example, assume that linguistic understanding only comprises computational processes which can be recursively decomposed into algorithmic mechanisms. Against this background, in (...) the first section, I explain Descartes’ view about language and mind. To show that Turing bites the bullet with his imitation game, in the second section I analyze this method to assess intelligence. Then, in the third section, I elaborate on Schank and Abelsons’ Script Applier Mechanism (SAM, hereby), which supposedly casts doubt on Descartes’ denial that machines can think. Finally, in the fourth section, I explore a challenge that any algorithmic decomposition of linguistic understanding faces. This challenge, I argue, is the core of the Cartesian problem: knowledge and awareness of meaning require a first-person viewpoint which is irreducible to the decomposition of algorithmic mechanisms. (shrink)

The protein folding problem is one of the foundational problems of biochemistry and it is still considered unsolved. It basically consists of two main questions: what are the factors determining the stability of the protein’s native structure and how does the protein acquire it starting from an unfolded state. Since its first formulation, two main explanatory approaches have dominated the field of protein folding research: a thermodynamic approach focused on energetic features and a kinetic approach focused on the temporal development (...) of protein chains and structural considerations. Although these two approaches are tightly intertwined in biochemical practice and largely agree on which are the parts and activities in which the phenomenon under study should be decomposed to, there nevertheless exist important contrasts that have had repercussions on the development of the field and still engender vigorous debate. We shall analyse the historical development of the field and crucial aspects of current scientific debates. On this basis, we argue that the main sources of disagreement centre on the causal interpretation of thermodynamic and kinetic explanations, on the explanatory relevance assigned to different features of the phenomena under study and on the status of the ontological assumptions concerning the entities under study. (shrink)

ABSTRACT In their contribution to the first part of this special issue Craig Bourn and Emily Caddick Bourne claim to have solved a puzzle I put forward in my ‘An Insoluble Problem’. Here I argue that their attempt fails.

This paper offers an analysis of a hitherto neglected text on insoluble propositions dating from the late XiVth century and puts it into perspective within the context of the contemporary debate concerning semantic paradoxes. The author of the text is the italian logician Peter of Mantua (d. 1399/1400). The treatise is relevant both from a theoretical and from a historical standpoint. By appealing to a distinction between two senses in which propositions are said to be true, it offers an unusual (...) solution to the paradox, but in a traditional spirit that contrasts a number of trends prevailing in the XiVth century. It also counts as a remarkable piece of evidence for the reconstruction of the reception of English logic in italy, as it is inspired by the views of John Wyclif. Three approaches addressing the Liar paradox (Albert of Saxony, William Heytesbury and a version of strong restrictionism) are first criticised by Peter of Mantua, before he presents his own alternative solution. The latter seems to have a prima facie intuitive justification, but is in fact acceptable only on a very restricted understanding, since its generalisation is subject to the so-called revenge problem. (shrink)

Paul of Venice joined the Austin Friars at an early age and was sent by them from Padua to study at Oxford in 1390. When he returned, full of ideas and laden with books, he began his prodigious writing career with several books on logic, including the Logica Magna, which runs to some half a million words. The current volume contains the final treatise, on insolubles - that is, logical paradoxes. After surveying fifteen previous solutions, Paul develops his own, (...) based on the idea that such propositions falsify themselves. Besides a critical edition of the Latin text, the volume also contains an English translation, a detailed commentary, excerpts from two other logical works of Paul, and a substantial introduction. The introduction describes the fourteenth-century background to Paul's treatise; it also gives a detailed rebuttal of a recent claim that the Logica Magna is not by Paul because its content clashes with genuine works of his. All in all, the volume greatly enhances our understanding of the development of logic, in particular of the semantics of propositions, during a crucial century in its history. (shrink)

ABSTRACT In 'An Insoluble Problem', Storrs McCall presents an argument which he takes to reveal the real problem with backwards time travel. McCall asks us to imagine a scenario in which a renowned artist produces his famous works by copying them from reproductions brought back to him by a time-travelling art critic. The novelty of the scenario lies in its introduction of aesthetic constraints on the possibility of time travel, something which sets it apart from other time travel cases. McCall (...) states that 'The puzzle lies... in finding where artistic creativity enters the equation', and that 'Unlike the traditional "paradoxes of time travel", this problem has no solution'. We offer four responses to McCall's puzzle. Whilst we show that the puzzle is not insoluble, we also argue that it reveals something about the proper relationship between copying and creativity, which may not have been apparent without considering time travel. (shrink)

This is a public philosophy article that aims to make available an idea about abortion from my Sex, Love, and Gender book.

The paper is concerned with the epistemological status of testimony and the question of what may confer justification on true testimonial beliefs and enable us to call such beliefs knowledge. In particular, it addresses certain anti-reductionist arguments in the epistemology of testimony and their incompatibility with the grammatical categories of egophoricity (conjunct/disjunct marking) and evidentiality (information source marking) present in the architecture of natural languages. First, the tradition of epistemological individualism and its rationale are discussed, as well as certain attempts (...) within this tradition to include testimony-based beliefs in the body of legitimate and rational beliefs. The next section is concerned with the anti-reductionist approach to testimonial beliefs and some arguments supporting ‘the credulity principle’ grounded in Thomas Reid's philosophy of common sense. The last two sections show how the anti-reductionist argumentation is threatened with an insoluble dilemma when considered in the context of languages with the grammatical categories of egophoricity (conjunct/disjunct marking) and evidentiality (information source marking). Special attention is paid to the justificatory role of egophoric and evidential marking; how these grammatical categories may influence the process of belief formation, and consequently, how this bears upon the nature of justification for testimonial beliefs. The final conclusion of the paper is that the anti-reductionist claim concerning the directness and non-inferential nature of testimonial knowledge is bound to meet objections grounded in the structure of many natural languages. This leads to a paradox: in discussion with reductionism, anti-reductionists do seek support for their arguments in common sense beliefs reflected in everyday language, and, on the other hand, their claims are incompatible with the linguistic data found in a number of natural languages. (shrink)