The 'no-supervenience' theorem (Reason, 2019; Reason and Shah, 2021) is a proof that no fully self-aware system can entirely supervene on any objectively observable system. I here present a simple, non-technical summary of the proof and demonstrate its implications for four separate theories of consciousness: the 'property dualism' theory of David Chalmers; the 'reflexive monism' of Max Velmans; Galen Strawson's 'realistic monism'; and the 'illusionism' of Keith Frankish. It is shown that all are ruled out in their current (...) form by the no-supervenience theorem, except for Chalmers' theory, which I show requires humans to behave irrationally. (shrink)

Conscious macrostates are usually assumed to be emergent from the underlying physical microstates comprising the brain and nervous system of biological organisms. However, a major problem with this assumption is that consciousness is essentially nonmeasurable unlike all other proven emergent properties of physical systems. In an earlier paper, using a no-go theorem, it was shown that conscious states cannot be comprised of processes that are physical in nature (Reason, 2019). Combining this result with another unrelated work on causal emergence (...) in physical systems (Hoel, Albantakis and Tononi, 2013), we show in this paper that conscious macrostates are not emergent from physical systems and they also do not supervene on physical microstates. An important implication of our work is that there must be some form of violation of energy conservation in biological systems that are conscious. (shrink)

How can a virtual machine X be implemented in a physical machine Y? We know the answer as far as compilers, editors, theorem-provers, operating systems are concerned, at least insofar as we know how to produce these implemented virtual machines, and no mysteries are involved. This paper is about extrapolating from that knowledge to the implementation of minds in brains. By linking the philosopher's concept of supervenience to the engineer's concept of implementation, we can illuminate both. In particular, (...) by showing how virtual machines can be implemented in causally complete physical machines, and still have causal powers, we remove some philosophical problems about how mental processes can be real and can have real effects in the world even if the underlying physical implementation has no causal gaps. This requires a theory of ontological levels. (shrink)

There is a strong formal analogy between proposition-wise supervenience of collective doxastic rationality on individual doxasticrationality and supervenience of social choice functions on individual choice functions. In light of this analogy, the basis for List and Pettit’s impossibility theorems can fruitfully be compared with the basis for Arrow’s. This helps to explain why List and Pettit can derive no impossibility theorem for set-wise supervenience. However, there are empirical reasons for doubting that set-wise supervenience of collective (...) doxastic rationality on individual doxastic rationality is necessary; a systematic feedback relationship between the former and some individual behavioral dispositions is probably sufficient to dissolve mysteries about group agency. Group doxastic rationality need not supervene on individual rationality. (shrink)

Recent experiments have shown that certain fluid-mechanical systems, namely oil droplets bouncing on oil films, can mimic a wide range of quantum phenomena, including double-slit interference, quantization of angular momentum and Zeeman splitting. Here I investigate what can be learned from these systems concerning no-go theorems as those of Bell and Kochen-Specker. In particular, a model for the Bell experiment is proposed that includes variables describing a ‘background’ field or medium. This field mimics the surface wave that accompanies the droplets (...) in the fluid-mechanical experiments. It appears that quite generally such a model can violate the Bell inequality and reproduce the quantum statistics, even if it is based on local dynamics only. The reason is that measurement independence is not valid in such models. This opens the door for local ‘background-based’ theories, describing the interaction of particles and analyzers with a background field, to complete quantum mechanics. Experiments to test these ideas are also proposed. (shrink)

I argue that our judgements regarding the locally causal models that are compatible with a given constraint implicitly depend, in part, on the context of inquiry. It follows from this that certain quantum no-go theorems, which are particularly striking in the traditional foundational context, have no force when the context switches to a discussion of the physical systems we are capable of building with the aim of classically reproducing quantum statistics. I close with a general discussion of the possible implications (...) of this for our understanding of the limits of classical description, and for our understanding of the fundamental aim of physical investigation. _1_ Introduction _2_ No-Go Results _2.1_ The CHSH inequality _2.2_ The GHZ equality _3_ Classically Simulating Quantum Statistics _3.1_ GHZ statistics _3.2_ Singlet statistics _4_ What Is a Classical Computer Simulation? _5_ Comparing the All-or-Nothing GHZ with Statistical equalities _6_ General Discussion _7_ Conclusion. (shrink)

In the history of quantum physics several no-go theorems have been proved, and many of them have played a central role in the development of the theory, such as Bell’s or the Kochen–Specker theorem. A recent paper by F. Laudisa has raised reasonable doubts concerning the strategy followed in proving some of these results, since they rely on the standard framework of quantum mechanics, a theory that presents several ontological problems. The aim of this paper is twofold: on the (...) one hand, I intend to reinforce Laudisa’s methodological point by critically discussing Malament’s theorem in the context of the philosophical foundation of quantum field theory; secondly, I rehabilitate Gisin’s theorem showing that Laudisa’s concerns do not apply to it. (shrink)

The asymmetry is the view in population ethics that, while we ought to avoid creating additional bad lives, there is no requirement to create additional good ones. The question is how to embed this intuitively compelling view in a more complete normative theory, and in particular one that treats uncertainty in a plausible way. While arguing against existing approaches, I present new and general principles for thinking about welfarist choice under uncertainty. Together, these reduce arbitrary choices to uncertainty-free ones, regardless (...) of how the latter should be made. I illustrate these principles by developing two theories of the asymmetry, reflecting different views about the non-identity problem. In doing so, I clarify some other major choice-points, presenting new arguments that creating additional good lives can justify (but not require) doing harm. Finally, I consider what the developed theories have to say about the importance of extinction risk and the long-run future. (shrink)

Our conscious minds exist in the Universe, therefore they should be identified with physical states that are subject to physical laws. In classical theories of mind, the mental states are identified with brain states that satisfy the deterministic laws of classical mechanics. This approach, however, leads to insurmountable paradoxes such as epiphenomenal minds and illusionary free will. Alternatively, one may identify mental states with quantum states realized within the brain and try to resolve the above paradoxes using the standard Hilbert (...) space formalism of quantum mechanics. In this essay, we first show that identification of mind states with quantum states within the brain is biologically feasible, and then elaborating on the mathematical proofs of two quantum mechanical no-go theorems, we explain why quantum theory might have profound implications for the scientific understanding of one's mental states, self identity, beliefs and free will. (shrink)

Modal interpretations take quantum mechanics as a theory which assigns at all times definite values to magnitudes of quantum systems. In the case of single systems, modal interpretations manage to do so without falling prey to the Kochen and Specker no-go theorem, because they assign values only to a limited set of magnitudes. In this paper I present two further no-go theorems which prove that two modal interpretations become nevertheless problematic when applied to more than one system. The first (...) theorem proves that the modal interpretation proposed by Kochen and by Dieks cannot correlate the values simultaneously assigned to three systems. The second and new theorem proves that the atomic modal interpretation proposed by Bacciagaluppi and Dickson and by Dieks cannot correlate the values simultaneously and sequentially assigned to two systems if one assumes that these correlations are uniquely related to the dynamics of the state of the systems. (shrink)

Correlations of spins in a system of entangled particles are inconsistent with Kolmogorov’s probability theory (KPT), provided the system is assumed to be non-contextual. In the Alice–Bob EPR paradigm, non-contextuality means that the identity of Alice’s spin (i.e., the probability space on which it is defined as a random variable) is determined only by the axis $\alpha _{i}$ chosen by Alice, irrespective of Bob’s axis $\beta _{j}$ (and vice versa). Here, we study contextual KPT models, with two properties: (1) Alice’s (...) and Bob’s spins are identified as $A_{ij}$ and $B_{ij}$ , even though their distributions are determined by, respectively, $\alpha _{i}$ alone and $\beta _{j}$ alone, in accordance with the no-signaling requirement; and (2) the joint distributions of the spins $A_{ij},B_{ij}$ across all values of $\alpha _{i},\beta _{j}$ are constrained by fixing distributions of some subsets thereof. Of special interest among these subsets is the set of probabilistic connections, defined as the pairs $\left( A_{ij},A_{ij'}\right) $ and $\left( B_{ij},B_{i'j}\right) $ with $\alpha _{i}\not =\alpha _{i'}$ and $\beta _{j}\not =\beta _{j'}$ (the non-contextuality assumption is obtained as a special case of connections, with zero probabilities of $A_{ij}\not =A_{ij'}$ and $B_{ij}\not =B_{i'j}$ ). Thus, one can achieve a complete KPT characterization of the Bell-type inequalities, or Tsirelson’s inequalities, by specifying the distributions of probabilistic connections compatible with those and only those spin pairs $\left( A_{ij},B_{ij}\right) $ that are subject to these inequalities. We show, however, that quantum-mechanical (QM) constraints are special. No-forcing theorem says that if a set of probabilistic connections is not compatible with correlations violating QM, then it is compatible only with the classical–mechanical correlations. No-matching theorem says that there are no subsets of the spin variables $A_{ij},B_{ij}$ whose distributions can be fixed to be compatible with and only with QM-compliant correlations. (shrink)

Within the framework of general relativity, in some cases at least, it is a delicate and interesting question just what it means to say that an extended body is or is not "rotating". It is so for two reasons. First, one can easily think of different criteria of rotation. Though they agree if the background spacetime structure is sufficiently simple, they do not do so in general. Second, none of the criteria fully answers to our classical intuitions. Each one exhibits (...) some feature or other that violates those intuitions in a significant and interesting way. The principal goal of the paper is to make the second claim precise in the form of a modest no-go theorem. (shrink)

Modal interpretations take quantum mechanics as a theory which assigns at all times definite values to magnitudes of quantum systems. In the case of single systems, modal interpretations manage to do so without falling prey to the Kochen and Specker no-go theorem, because they assign values only to a limited set of magnitudes. In this paper I present two further no-go theorems which prove that two modal interpretations become nevertheless problematic when applied to more than one system. The first (...) theorem proves that the modal interpretation proposed by Kochen and by Dieks cannot correlate the values simultaneously assigned to three systems. The second and new theorem proves that the atomic modal interpretation proposed by Bacciagaluppi and Dickson and by Dieks cannot correlate the values simultaneously and sequentially assigned to two systems if one assumes that these correlations are uniquely related to the dynamics of the state of the systems. (shrink)

The aim of the paper is to investigate the role played by causality, and more specifically the no-signaling condition, in the assessment of the quantum theory. To this end, we discuss why it is important that even a non-relativistic theory such as Quantum Mechanics doesn’t imply a violation of this condition. Then, we use this argument to prove an original result stating that the destructive behaviour of the measurement process on the entanglement properties of quantum systems is a necessary and (...) unavoidable feature of the quantum theory. Finally, we critically review the no-cloning theorem. The original formulation of the theorem states that a linear quantum cloning machine, designed in order to successfully clone states that coincide with appropriate basis vectors, fails to copy states that are a non-trivial superposition of those basis vectors; we will furthermore prove that such a linear cloning device, even with the hypothesis that it can only clone basis vectors successfully, may provide a violation of the no-signaling condition and therefore cannot exist. (shrink)

This paper derives a no-trade theorem under Knightian uncertainty, which generalizes the theorem of Milgrom and Stokey by allowing general preference relations. It is shown that the no-trade theorem holds true as long as agents' preferences are dynamically consistent in the sense of Machina and Schmeidler, and satisfies the so-called piece-wise monotonicity axiom. A preference satisfying the piece-wise monotonicity axiom does not necessarily imply the additive utility representation, nor is necessarily based on beliefs.

Uncertainty about the actual orientation of the measurement device has been claimed to open a loophole for hidden variable models of quantum mechanics. In this paper I describe the statistics of inaccurate spin measurements by unsharp spin observables. A no‐go theorem for hidden variable models of the inaccurate measurement statistics follows: There is a finite set of directions for which not all results of inaccurate spin measurements can be predetermined in a non‐contextual way. In contrast to an earlier (...) class='Hi'>theorem (Breuer 2002) this result does not rely on the assigment of approximate truth values, and it holds under weaker assumptions on the measurement inaccuracy. (shrink)

Uncertainty about the actual orientation of the measurement device has been claimed to open a loophole for hidden variable models of quantum mechanics. In this paper I describe the statistics of inaccurate spin measurements by unsharp spin observables. A no-go theorem for hidden variable models of the inaccurate measurement statistics follows: There is a finite set of directions for which not all results of inaccurate spin measurements can be predetermined in a non-contextual way. In contrast to an earlier (...) class='Hi'>theorem [Breuer, Phys. Rev. Lett. 88(2002), 240402] this result does not rely on the assigment of approximate truth values, and it holds under weaker assumptions on the measurement inaccuracy. (shrink)

Modal interpretations take quantum mechanics as a theory which assigns at all times definite values to magnitudes of quantum systems. In the case of single systems, modal interpretations manage to do so without falling prey to the Kochen and Specker no-go theorem, because they assign values only to a limited set of magnitudes. In this paper I present two further no-go theorems which prove that two modal interpretations become nevertheless problematic when applied to more than one system. The first (...) theorem proves that the modal interpretation proposed by Kochen and by Dieks cannot correlate the values simultaneously assigned to three systems. The second and new theorem proves that the atomic modal interpretation proposed by Bacciagaluppi and Dickson and by Dieks cannot correlate the values simultaneously and sequentially assigned to two systems if one assumes that these correlations are uniquely related to the dynamics of the state of the systems. (shrink)

A recent no-go theorem gives an extension of the Wigner’s Friend argument that purports to prove the “Quantum theory cannot consistently describe the use of itself.” The argument is complex and thought provoking, but fails in a straightforward way if one treats QM as a statistical theory in the most fundamental sense, i.e. if one applies the so-called ensemble interpretation. This explanation is given here at an undergraduate level, which can be edifying for experts and students alike. A recent (...) paper has already shown that the no-go theorem is incorrect with regard to the de Broglie Bohm theory and misguided in some of its general claims. This paper’s contribution is three fold. It shows how the extended Wigner’s Friend argument fails in the ensemble interpretation. It also makes more evident how natural a consistent statistical treatment of the wave function is. In this way, the refutation of the argument is useful for bringing out the core statistical nature of QM. It, in addition, manifests the unnecessary complications and problems introduced by the collapse mechanism that is part of the Copenhagen interpretation. The paper uses the straightforwardness of the ensemble interpretation to make the no-go argument and its refutation more accessible. (shrink)

It seems to me that it is among the most sure-footed of quantum physicists, those who have it in their bones, that one finds the greatest impatience with the idea that the ‘foundations of quantum mechanics’ might need some attention. Knowing what is right by instinct, they can become a little impatient with nitpicking distinctions between theorems and assumptions. —John Stewart Bell [4, p. 33].

In this paper we address a deeply interesting debate that took place at the end of the last millennia between David Mermin, Adan Cabello and Michiel Seevinck, regarding the meaning of relationalism within quantum theory. In a series of papers, Mermin proposed an interpretation in which quantum correlations were considered as elements of physical reality. Unfortunately, the very young relational proposal by Mermin was too soon tackled by specially suited no-go theorems designed by Cabello and Seevinck. In this work we (...) attempt to reconsider Mermin's program from the viewpoint of the Logos Categorical Approach to QM. Following Mermin's original proposal, we will provide a redefinition of quantum relation which not only can be understood as a preexistent element of physical reality but is also capable to escape Cabello’s and Seevinck's no-go-theorems. In order to show explicitly that our notion of ontological quantum relation is safe from no-go theorems we will derive a non-contextuality theorem. We end the paper with a discussion regarding the physical meaning of quantum relationalism. (shrink)

We begin by considering two principles, each having the form causal completeness ergo screening-off. The first concerns a common cause of two or more effects; the second describes an intermediate link in a causal chain. They are logically independent of each other, each is independent of Reichenbach's principle of the common cause, and each is a consequence of the causal Markov condition. Simple examples show that causal incompleteness means that screening-off may fail to obtain. We derive a stronger result: in (...) a rather general setting, if the composite cause C1 & C2 & … & Cn screens-off one event from another, then each of the n component causes C1, C2, …, Cn must fail to screen-off. The idea that a cause may be ordinally invariant in its impact on different effects is defined; it plays an important role in establishing this no-go theorem. Along the way, we describe how composite and component causes can all screen-off when ordinal invariance fails. We argue that this theorem is relevant to assessing the plausibility of the two screening-off principles. The discovery of incomplete causes that screen-off is not evidence that causal completeness must engender screening-off. Formal and epistemic analogies between screening-off and determinism are discussed. (shrink)

Applications of quantum mechanics in the computational and information processing tasks is a recent research interest among the researchers. Certain operations which are impossible to achieve in the description of quantum mechanics are known as no-go theorems. One such theorem is no-splitting theorem of quantum states. The no-splitting theorem states that the information in an unknown quantum bit is an inseparable entity and cannot be split into two complementary qubits. In this work, we try to find out (...) the class of operators for which the splitting is possible in a probabilistic way. The work also aims to find the connection between the unitary operators and probabilistic splitting. (shrink)

Our response amplifies our case for scientific realism and the unity of science and clarifies our commitments to scientific unity, nonreductionism, behaviorism, and our rejection of talk of “emergence.” We acknowledge support from commentators for our view of physics and, responding to pressure and suggestions from commentators, deny the generality supervenience and explain what this involves. We close by reflecting on the relationship between philosophy and science.

The present paper investigates the philosophical relationship between John von Neumann’s Nohidden-variable theorem and Bell’s inequalities. Bell erroneously takes the axiomatic method as implying a finality claim and thus ignores von Neumann’s strongly pragmatist stance towards mathematical physics. If one considers, however, Hilbert’s axiomatic method as a critical enterprise, Bell’s theorem improves von Neumann’s by defining a more appropriate notion of ‘ hidden variable’ that permits one to include Bohm’s interpretation which recovers the predictive content of quantum mechanics. (...) Contrary to Bell’s belief, accepting this model does not require adopting the metaphysically realist Böhm picture. If one takes the latter as a physical research programme one sees that it only partly disputes a common domain of facts with the mathematically oriented research programme of von Neumann. (shrink)

Some recent work in the philosophy of quantum mechanics has suggested that quantum systems can be thought of as non-separable and therefore non-individual, in some sense, in Bell and E.P.R. type situations. This suggestion is set in the context of previous work regarding the individuality of quantal particles and it is argued that such entities can be considered as individuals if their non-classical statistical correlations are understood in terms of non-supervenient relations holding between them. We conclude that such relations are (...) strongly non-supervenient in Cleland's sense and note a possible connection between this idea and the realist quantum logic programme. (shrink)

The no-free-lunch theorems promote a skeptical conclusion that all possible machine learning algorithms equally lack justification. But how could this leave room for a learning theory, that shows that some algorithms are better than others? Drawing parallels to the philosophy of induction, we point out that the no-free-lunch results presuppose a conception of learning algorithms as purely data-driven. On this conception, every algorithm must have an inherent inductive bias, that wants justification. We argue that many standard learning algorithms should rather (...) be understood as model-dependent: in each application they also require for input a model, representing a bias. Generic algorithms themselves, they can be given a model-relative justification. (shrink)

Without invoking macrorealism, we derive a contradiction between the quantum mechanical predictions forsquid's and two intuitive conditions. First, we assume that asquid can be measured without significantly disturbing its subsequent macroscopic behavior. Second, we assume a trivial realism condition much weaker than Leggett's macrorealism. Quantum mechanics itself obeys our realism assumption. This proof suggests that althoughsquid experiments cannot rule out macrorealism, they can rule out most theories that allow noninvasive measurements.

Recent attempts to resolve the truthmaker objection to presentism employ a fundamentally tensed account of the relationship between truth and being. On this view, the truth of a proposition concerning the past supervenes on how things are, in the present, along with how things were, in the past. This tensed approach to truthmaking arises in response to pressure placed on presentists to abandon the standard response to the truthmaker objection, whereby one invokes presently existing entities as the supervenience base (...) for the truth of past-directed propositions. In this paper, I argue that a fundamentally tensed approach to truthmaking is implausible because it requires the existence of cross-temporal supervenience relations, which are anathema to presentism. (shrink)

The no free lunch theorem is a radicalized version of Hume’s induction skepticism. It asserts that relative to a uniform probability distribution over all possible worlds, all computable prediction algorithms—whether ‘clever’ inductive or ‘stupid’ guessing methods —have the same expected predictive success. This theorem seems to be in conflict with results about meta-induction. According to these results, certain meta-inductive prediction strategies may dominate other methods in their predictive success. In this article this conflict is analyzed and dissolved, by (...) means of probabilistic analysis and computer simulation. (shrink)

We give a new characterization of the strict $$\forall {\Sigma^b_j}$$ sentences provable using $${\Sigma^b_k}$$ induction, for 1 ≤ j ≤ k. As a small application we show that, in a certain sense, Buss’s witnessing theorem for strict $${\Sigma^b_k}$$ formulas already holds over the relatively weak theory PV. We exhibit a combinatorial principle with the property that a lower bound for it in constant-depth Frege would imply that the narrow CNFs with short depth j Frege refutations form a strict hierarchy (...) with j, and hence that the relativized bounded arithmetic hierarchy can be separated by a family of $$\forall {\Sigma^b_1}$$ sentences. (shrink)

In this paper we show that ψ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\psi$$\end{document}-ontic models, as defined by Harrigan and Spekkens (HS), cannot reproduce quantum theory. Instead of focusing on probability, we use information theoretic considerations to show that all pure states of ψ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\psi$$\end{document}-ontic models must be orthogonal to each other, in clear violation of quantum mechanics. Given that (i) Pusey, Barrett and Rudolph (PBR) previously showed that ψ\documentclass[12pt]{minimal} \usepackage{amsmath} (...) \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\psi$$\end{document}-epistemic models, as defined by HS, also contradict quantum mechanics, and (ii) the HS categorization is exhausted by these two types of models, we conclude that the HS categorization itself is problematic as it leaves no space for models that can reproduce quantum theory. (shrink)

White proposes an a priori justification of the reliability of inductive prediction methods based on his thesis of induction-friendliness. It asserts that there are by far more induction-friendly event sequences than induction-unfriendly event sequences. In this paper I contrast White's thesis with the famous no free lunch theorem. I explain two versions of this theorem, the strong NFL theorem applying to binary and the weak NFL theorem applying to real-valued predictions. I show that both versions refute (...) the thesis of induction-friendliness. In the conclusion I argue that an a priori justification of the reliability of induction based on a uniform probability distribution over possible event sequences is impossible. In the outlook I consider two alternative approaches: justification externalism and optimality justifications. (shrink)

Carter and Leslie (1996) have argued, using Bayes's theorem, that our being alive now supports the hypothesis of an early 'Doomsday'. Unlike some critics (Eckhardt 1997), we accept their argument in part: given that we exist, our existence now indeed favors 'Doom sooner' over 'Doom later'. The very fact of our existence, however, favors 'Doom later'. In simple cases, a hypothetical approach to the problem of 'old evidence' shows that these two effects cancel out: our existence now yields no (...) information about the coming of Doom. More complex cases suggest a move from countably additive to non-standard probability measures. (shrink)

The Bell–Kochen–Specker contradiction is presented using continuous observables in infinite dimensional Hilbert space. It is shown that the assumption of the existence of putative values for position and momentum observables for one single particle is incompatible with quantum mechanics.

We prove a uniqueness theorem showing that, subject to certain natural constraints, all 'no collapse' interpretations of quantum mechanics can be uniquely characterized and reduced to the choice of a particular preferred observable as determine (definite, sharp). We show how certain versions of the modal interpretation, Bohm's 'causal' interpretation, Bohr's complementarity interpretation, and the orthodox (Dirac-von Neumann) interpretation without the projection postulate can be recovered from the theorem. Bohr's complementarity and Einstein's realism appear as two quite different proposals (...) for selecting the preferred determinate observable--either settled pragmatically by what we choose to observe, or fixed once and for all, as the Einsteinian realist would require, in which case the preferred observable is a 'beable' in Bell's sense, as in Bohm's interpretation (where the preferred observable is position in configuration space). (shrink)

The important recent book by Schurz ( 2019 ) appreciates that the no-free-lunch theorems (NFL) have major implications for the problem of (meta) induction. Here I review the NFL theorems, emphasizing that they do not only concern the case where there is a uniform prior—they prove that there are “as many priors” (loosely speaking) for which any induction algorithm _A_ out-generalizes some induction algorithm _B_ as vice-versa. Importantly though, in addition to the NFL theorems, there are many _free lunch_ theorems. (...) In particular, the NFL theorems can only be used to compare the expected performance of an induction algorithm _A_, considered in isolation, with the expected performance of an induction algorithm _B_, considered in isolation. There is a rich set of free lunches which instead concern the statistical _correlations_ among the generalization errors of induction algorithms. As I describe, the meta-induction algorithms that Schurz advocates as a “solution to Hume’s problem” are simply examples of such a free lunch based on correlations among the generalization errors of induction algorithms. I end by pointing out that the prior that Schurz advocates, which is uniform over bit frequencies rather than bit patterns, is contradicted by thousands of experiments in statistical physics and by the great success of the maximum entropy procedure in inductive inference. (shrink)

No-free-lunch theorems are important theoretical result in the fields of machine learning and artificial intelligence. Researchers in this fields often claim that the theorems are based on Hume’s argument about induction and represent a formalisation of the argument. This paper argues that this is erroneous but that the theorems correspond to and formalise Goodman’s new riddle of induction. To demonstrate the correspondence among the theorems and Goodman’s argument, a formalisation of the latter in the spirit of the former is sketched.

Vardanyan's theorem states that the set of PA-valid principles of Quantified Modal Logic, QML, is complete Π0 2. We generalize this result to a wide class of theories. The crucial step in the generalization is avoiding the use of Tennenbaum's Theorem.

Humean supervenience is the conjunction of three theses: Truth supervenes on being, Anti‐haecceitism, and Spatiotemporalism. The first clause is a core part of Lewis's metaphysics. The second clause is related to Lewis's counterpart theory. The third clause says there are no fundamental relations beyond the spatiotemporal, or fundamental properties of extended objects. Supervenience is classified into strong modal Humean supervenience, local modal Humean supervenience and familiar modal Humean supervenience which states that: for any two "worlds (...) like ours", if the spatiotemporal distribution of fundamental qualities is the same at each world, the contingent facts are also the same. The fact that quantum mechanics raises problems for Humean supervenience does not undercut the philosophical significance of Lewis's defense of Humean supervenience. Humean supervenience says that in a world like ours, the fundamental properties are local qualities: perfectly natural intrinsic properties of points, or of point‐sized occupants of points. (shrink)

This paper is a survey of the supervenience challenge to non-naturalist moral realism. I formulate a version of the challenge, consider the most promising non-naturalist replies to it, and suggest that no fully effective reply has yet been given.

The debate over the question whether quantum mechanics should be considered as a complete account of microphenomena has a long and deeply involved history, a turning point in which has been certainly the Einstein-Bohr debate, with the ensuing charge of incompleteness raised by the Einstein-Podolsky-Rosen argument. In quantum mechanics, physical systems can be prepared in pure states that nevertheless have in general positive dispersion for most physical quantities; hence in the EPR argument, the attention is focused on the question whether (...) the account of the microphysical phenomena provided by quantum mechanics is to be regarded as an exhaustive description of the physical reality to which those phenomena are supposed to refer, a question to which Einstein himself answered in the negative. However, there is a mathematical side of the completeness issue in quantum mechanics, namely the question whether the kind of states with positive dispersion can be represented as a different, dispersion-free kind of states in a way consistent with the mathematical constraints of the quantum mechanical formalism. From this point of view, the other source of the completeness issue in quantum mechanics is the no hidden variables theorem formulated by John von Neumann in his celebrated book on the mathematical foundations of quantum mechanics, the preface of which already anticipates the program and the conclusion concerning the possibility of ‘neutralizing’ the statistical character of quantum mechanics. (shrink)