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)

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)

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)

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. (shrink)

This paper is concerned with learners who aim to learn patterns in infinite binary sequences: shown longer and longer initial segments of a binary sequence, they either attempt to predict whether the next bit will be a 0 or will be a 1 or they issue forecast probabilities for these events. Several variants of this problem are considered. In each case, a no-free-lunch result of the following form is established: the problem of learning is a formidably difficult one, (...) in that no matter what method is pursued, failure is incomparably more common that success; and difficult choices must be faced in choosing a method of learning, since no approach dominates all others in its range of success. In the simplest case, the comparison of the set of situations in which a method fails and the set of situations in which it succeeds is a matter of cardinality (countable vs. uncountable); in other cases, it is a topological matter (meagre vs. co-meagre) or a hybrid computational-topological matter (effectively meagre vs. effectively co-meagre). (shrink)

Searching for small targets in large spaces is a common problem in the sciences. Because blind search is inadequate for such searches, it needs to be supplemented with additional information, thereby transforming a blind search into an assisted search. This additional information can be quantified and indicates that assisted searches themselves result from searching higher-level search spaces–by conducting, as it were, a search for a search. Thus, the original search gets displaced to a higher-level search. The key result in this (...) paper is a displacement theorem, which shows that successfully resolving such a higher-level search is exponentially more difficult than successfully resolving the original search. Leading up to this result, a measure-theoretic version of the No Free Lunch theorems is formulated and proven. The paper shows that stochastic mechanisms, though able to explain the success of assisted searches in locating targets, cannot, in turn, explain the source of assisted searches. (shrink)

Ravit Dotan argues that a No Free Lunch theorem from machine learning shows epistemic values are insufficient for deciding the truth of scientific hypotheses. She argues that NFL shows that the best case accuracy of scientific hypotheses is no more than chance. Since accuracy underpins every epistemic value, non-epistemic values are needed to assess the truth of scientific hypotheses. However, NFL cannot be coherently applied to the problem of theory choice. The NFL theorem Dotan’s argument relies upon is (...) a member of a family of theorems in search, optimization, and machine learning. They all claim to show that if no assumptions are made about a search or optimization problem or learning situation, then the best case performance of an algorithm is that of random search or random guessing. A closer inspection shows that these theorems all rely upon assigning uniform probabilities over problems or learning situations, which is just the Principle of Indifference. A counterexample can be crafted that shows that NFL cannot be coherently applied across different descriptions of the same learning situation. To avoid this counterexample, Dotan needs to privilege some description of the learning situation faced by scientists. However, this means that NFL cannot be applied since an important assumption about the problem is being made. So Dotan faces a dilemma: either NFL leads to incoherent best-case partial beliefs or it is inapplicable to the problem of theory choice. This negative result has implications for the larger debate over theory choice. (shrink)

Darwin's greatest accomplishment was to show how life might be explained as the result of natural selection. But does Darwin's theory mean that life was unintended? William A. Dembski argues that it does not. In this book Dembski extends his theory of intelligent design. Building on his earlier work in The Design Inference (Cambridge, 1998), he defends that life must be the product of intelligent design. Critics of Dembski's work have argued that evolutionary algorithms show that life can be explained (...) apart from intelligence. But by employing powerful recent results from the No Free Lunch Theory, Dembski addresses and decisively refutes such claims. As the leading proponent of intelligent design, Dembski reveals a designer capable of originating the complexity and specificity found throughout the cosmos. Scientists and theologians alike will find this book of interest as it brings the question of creation firmly into the realm of scientific debate. (shrink)

There is a well-known moral quandary concerning how to account for the rightness or wrongness of acts that clearly contribute to some morally significant outcome – but which each seem too small, individually, to make any meaningful difference. One consequentialist-friendly response to this problem is to deny that there could ever be a case of this type. This paper pursues this general strategy, but in an unusual way. Existing arguments for the consequentialist-friendly position are sorites-style arguments. Such arguments imagine varying (...) a subject’s predicament bit by bit until it is clear that a relevant difference has been achieved. The arguments offered in this paper are structurally different, and do not rely on any sorites series. For this reason, they are not vulnerable to objections that have been leveled against the sorites-style arguments. (shrink)

I use a theorem from machine learning, called the “No Free Lunch” theorem to support the claim that non-epistemic values are essential to theory choice. I argue that NFL entails that predictive accuracy is insufficient to favor a given theory over others, and that NFL challenges our ability to give a purely epistemic justification for using other traditional epistemic virtues in theory choice. In addition, I argue that the natural way to overcome NFL’s challenge is to use non-epistemic (...) values. If my argument holds, non-epistemic values are entangled in theory choice regardless of human limitations and regardless of the subject matter. Thereby, my argument overcomes objections to the main lines of argument revealing the role of values in theory choice. At the end of the paper, I argue that, contrary to common conception, the epistemic challenge arising from NFL is distinct from Hume’s problem of induction and other forms of underdetermination. (shrink)

Five years have elapsed since the publication of No Free Lunch. In that time, intelligent design (ID) has gone from a little-known and marginalized alternative to standard evolutionary theory to a national and international phenomenon that everyone with an interest in the biological origins debate is talking about. Gone is the former dichotomy between creationism and evolution. Leaving aside creationism’s insistence on treating Genesis as a scientific text and treating the detection and application of design as a research (...) tool for science, ID has carved out its own conceptual space and place at the table of scientific discussion. Five years ago critics of ID regularly leveled the charge that ID has no peer-reviewed publications in the biological literature. That charge is no longer supportable, with pro-ID research appearing in such journals as Protein Science, Journal of Molecular Biology, and Proceedings of the Biological Society of Washington (for details, see my expert witness report for the Dover case at www.designinference.com). (shrink)

Generating an account that can sidestep the disagreement among substantive theories of well-being, while at the same time still providing useful guidance for well-being public policy, would be a significant achievement. Unfortunately, the various attempts to remain agnostic regarding what constitutes well-being fail to either be an account of well-being, provide useful guidance for well-being policy, or avoid relying on a substantive well-being theory. There are no theory-free lunches in well-being policy. Instead, I propose an intermediate account, according to (...) which well-being is constituted by endorsed veridical experiences. This account refers back to theories of well-being but does so as agnostically as possible. An intermediate account of well-being is meant as a policy guiding compromise between the different theories of well-being that make claims regarding what constitutes well-being. An intermediate account does as well as can be hoped for in providing a basis for well-being policy. (shrink)

William Dembski (No free lunch: why specified complexity cannot be purchased without intelligence, 2002) claimed that the NFL theorems from optimization theory render darwinian biological evolution impossible. Häggström (Biology and Philosophy 22:217–230, 2007) argued that the NFL theorems are not relevant for biological evolution at all, since the assumptions of the NFL theorems are not met. Although I agree with Häggström (Biology and Philosophy 22:217–230, 2007), in this article I argue that the NFL theorems (...) should be interpreted as dealing with an extreme case within a much broader context. This broader context is in fact relevant for scientific research of certain evolutionary processes; not in the sense that the theorems can be used to draw conclusions about any intelligent design inference, but in the sense that it helps us to interpret computer simulations of evolutionary processes. As a result of this discussion, I will argue that from simulations, we do not learn much about how complexity arises in the universe. This position is in contrast with certain claims in the literature that I will discuss. (shrink)

Increasingly encompassing models have been suggested for our world. Theories range from generally accepted to increasingly speculative to apparently bogus. The progression of theories from ego- to geo- to helio-centric models to universe and multiverse theories and beyond was accompanied by a dramatic increase in the sizes of the postulated worlds, with humans being expelled from their center to ever more remote and random locations. Rather than leading to a true theory of everything, this trend faces a turning point after (...) which the predictive power of such theories decreases (actually to zero). Incorporating the location and other capacities of the observer into such theories avoids this problem and allows to distinguish meaningful from predictively meaningless theories. This also leads to a truly complete theory of everything consisting of a (conventional objective) theory of everything plus a (novel subjective) observer process. The observer localization is neither based on the controversial anthropic principle, nor has it anything to do with the quantum-mechanical observation process. The suggested principle is extended to more practical (partial, approximate, probabilistic, parametric) world models (rather than theories of everything). Finally, I provide a justification of Ockham's razor, and criticize the anthropic principle, the doomsday argument, the no free lunch theorem, and the falsifiability dogma.", . (shrink)

The autonomy thesis is the claim that one cannot get a normative statement from purely descriptive statements. But despite its intuitive appeal a precise formulation of the thesis has remained elusive. In a recent paper, Maguire makes the promising suggestion that the thesis should be understood in terms of ground. But Maguire’s formulation, I argue, is based on controversial taxonomic assumptions that make the autonomy thesis into a non-substantive claim. I develop an alternative ground-based formulation of the autonomy thesis that (...) appeals to the notion of normative relevance, which is in turn understood using the tools of truthmaker semantics. This formulation of the autonomy thesis avoids well-known counterexamples to other formulations and has significant advantages over Maguire’s formulation. (shrink)

Another look is taken at the model assumptions involved in William Dembski’s (2002a, No Free Lunch: Why Specified Complexity Cannot be Purchased without Intelligence. Roman & Littlefield, Lanham, MA) use of the NFL theorems from optimization theory to disprove the Darwinian theory of evolution by natural selection, and his argument is shown to be irrelevant to evolutionary biology.

The field of psychology, including cognitive science, is vexed by a crisis of confidence. Although the causes and solutions are varied, we focus here on a common logical problem in inference. The default mode of inference is significance testing, which has a free lunch property where researchers need not make detailed assumptions about the alternative to test the null hypothesis. We present the argument that there is no free lunch; that is, valid testing requires that researchers (...) test the null against a well-specified alternative. We show how this requirement follows from the basic tenets of conventional and Bayesian probability. Moreover, we show in both the conventional and Bayesian framework that not specifying the alternative may lead to rejections of the null hypothesis with scant evidence. We review both frequentist and Bayesian approaches to specifying alternatives, and we show how such specifications improve inference. The field of cognitive science will benefit because consideration of reasonable alternatives will undoubtedly sharpen the intellectual underpinnings of research. (shrink)

Truthmaker theorists hold that propositions about higher-level entities (e.g. the proposition that there is a heap of sand) are often made true by lower-level entities (e.g. by facts about the configuration of fundamental particles). This generates a problem: what should we say about these higher-level entities? On the one hand, they must exist (since there are true propositions about them), on the other hand, it seems that they are completely superfluous and should be banished for reasons of ontological parsimony. Some (...) truthmaker theorists—most prominently David Armstrong—have tried to solve this puzzle by arguing that these entities are ‘an ontological free lunch’, i.e. real existents that are still ‘no addition of being’. This answer is prima facie attractive, but I argue in this paper that the standard approaches to truthmaking—modal theories and grounding theories—are unable to vindicate the doctrine of the ontological free lunch, and thus fail to solve the problem of higher-level entities. Fortunately, there is a non-standard account of truthmaking available, the reductive explanation account, which succeeds where the standard approaches fail. (shrink)

The upshot of the No Free Lunch theorems is that averaged over all fitness functions, evolutionary computation does no better than blind search (see Dembski 2002, ch 4 as well as Dembski 2005 for an overview). But this raises a question: How does evolutionary computation obtain its power since, clearly, it is capable of doing better than blind search? One approach is to limit the fitness functions (see Igel and Toussaint 2001). Another, illustrated in David Fogel’s work (...) on automated checker and chess playing (see, for instance, Chellapilla and Fogel 1999 and Fogel et al. 2004) and, more recently, given a theoretical underpinning by David Wolpert and William Macready (2005), is to limit optimization problems to search spaces consisting of agents that play competitively against one another. In this brief note, I focus on the latter attempt to get around the force of No Free Lunch. (shrink)

Conway and Kochen have presented a “free will theorem” [4, 6] which they claim shows that “if indeed we humans have free will, then [so do] elementary particles.” In a more precise fashion, they claim it shows that for certain quantum experiments in which the experimenters can choose between several options, no deterministic or stochastic model can account for the observed outcomes without violating a condition “MIN” motivated by relativistic symmetry. We point out that for stochastic models this (...) conclusion is not correct, while for deterministic models it is not new. In the way the free will theorem is formulated and proved, it only concerns deterministic models. But Conway and Kochen have argued [4, 5, 6, 7] that “randomness can’t help,” meaning that stochastic models are excluded as well if we insist on the conditions “SPIN”, “TWIN”, and “MIN”. We point out a mistake in their argument. Namely, the theorem is of the form deterministic model with SPIN & TWIN & MIN ⇒ contradiction , (1) and in order to derive the further claim, which is of the form stochastic model with SPIN & TWIN & MIN ⇒ contradiction , (2) Conway and Kochen propose a method for converting any stochastic model into a deterministic one [4]. (shrink)

In this paper, the contributions to the account of meta-induction (Schurz 2019) collected in this volume are critically discussed and thereby, new insights are developed. How broad and expandable the program of meta-induction is can be learned from Ortner’s contribution. New insights about the transition from the a priori justification of meta-induction to the a posteriori justification of object-induction emerge from the reflection of Shogenji’s paper. How meta-induction may be applied also to religious prophecies and that their meta-inductive justification does (...) not fail for a priori reasons but because of missing evidence for predictive success is learned from the discussion of Pitts’ contribution. That meta-induction does not rely on a particular prior distribution, while the no free lunch theorem depends implicitly on a uniform prior, is the major conclusion drawn from the discussion of Wolpert’s article. How the problem of induction is treated in different versions of the Bayesian account is learned from the discussion of Willliamson’s paper. That meta-induction can also be employed for abduction, and that abductive theory-revision can offer meta-inductive aggregation methods is a new insight emerging from the reflection of Aliseda’s contribution. (shrink)

If the concept of “free will” is reduced to that of “choice” all physical world share the latter quality. Anyway the “free will” can be distinguished from the “choice”: The “free will” involves implicitly certain preliminary goal, and the choice is only the mean, by which it can be achieved or not by the one who determines the goal. Thus, for example, an electron has always a choice but not free will unlike a human possessing both. (...) Consequently, and paradoxically, the determinism of classical physics is more subjective and more anthropomorphic than the indeterminism of quantum mechanics for the former presupposes certain deterministic goal implicitly following the model of human freewill behavior. The choice is usually linked to very complicated systems such as human brain or society and even often associated with consciousness. In its background, the material world is deterministic and absolutely devoid of choice. However, quantum mechanics introduces the choice in the fundament of physical world, in the only way, in which it can exist: All exists in the “phase transition” of the present between the uncertain future and the well-ordered past. Thus the present is forced to choose in order to be able to transform the coherent state of future into the well-ordering of past. The concept of choice as if suggests that there is one who chooses. However quantum mechanics involves a generalized case of choice, which can be called “subjectless”: There is certain choice, which originates from the transition of the future into the past. Thus that kind of choice is shared of all existing and does not need any subject: It can be considered as a low of nature. There are a few theorems in quantum mechanics directly relevant to the topic: two of them are called “free will theorems” by their authors, Conway and Kochen, and according to them: “Do we really have free will, or, as a few determined folk maintain, is it all an illusion? We don’t know, but will prove in this paper that if indeed there exist any experimenters with a modicum of free will, then elementary particles must have their own share of this valuable commodity” “The import of the free will theorem is that it is not only current quantum theory, but the world itself that is non-deterministic, so that no future theory can return us to a clockwork universe”. Those theorems can be considered as a continuation of the so-called theorems about the absence of “hidden variables” in quantum mechanics. (shrink)

As scientists start to adopt machine learning (ML) as one research tool, the security of ML and the knowledge generated become a concern. In this paper, I explain how supervised ML can be improved with better data ontology, or the way we make categories and turn information into data. More specifically, we should design data ontology in such a way that is consistent with the knowledge that we have about the target phenomenon so that such ontology can help us make (...) the inductive leap. I do so by thinking through a thought experiment, Goodman’s New Riddle of Induction (Fact, fiction, and forecast, Harvard University Press, 1955). Goodman’s riddle helps flesh out three problems of induction: (1) the problem of equal goodies, that there are often too many equally good inductive results given the same data; (2) the problem of diverging performance, that these equally good results can give opposite predictions in the future; and (3) the problem of mediocrity, that when averaged across all equally possible datasets and tasks, no inductive algorithm outperforms any other. I show that all these three problems are manifested as real obstacles in ML practice, namely, the Rashomon effect (Breiman in Stat Sci 16(3):199–231, 2001), the problem of underspecification (D’Amour et al. in J Mach Learn Res, 2020, https://doi.org/10.48550/arXiv.2011.03395 ), and the No Free Lunch theorem (Wolpert in Neural Comput 8(7):1341–90, 1996, https://doi.org/10.1162/neco.1996.8.7.1341 ). Lastly, I argue that proper data ontology can help mitigate these problems and I demonstrate how using concrete examples from climate science. This research highlights the links between philosophers’ discussions of induction and implications in ML practice. (shrink)

The leading Intelligent Design theorist William Dembski (Rowman & Littlefield, Lanham MD, 2002) argued that the first No Free Lunch theorem, first formulated by Wolpert and Macready (IEEE Trans Evol Comput 1: 67–82, 1997), renders Darwinian evolution impossible. In response, Dembski’s critics pointed out that the theorem is irrelevant to biological evolution. Meester (Biol Phil 24: 461–472, 2009) agrees with this conclusion, but still thinks that the theorem does apply to simulations of evolutionary processes. According to Meester, the (...) theorem shows that simulations of Darwinian evolution, as these are typically set in advance by the programmer, are teleological and therefore non-Darwinian. Therefore, Meester argues, they are useless in showing how complex adaptations arise in the universe. Meester uses the term teleological inconsistently, however, and we argue that, no matter how we interpret the term, a Darwinian algorithm does not become non-Darwinian by simulation. We show that the NFL theorem is entirely irrelevant to this argument, and conclude that it does not pose a threat to the relevance of simulations of biological evolution. (shrink)

Many searches are needle-in-the-haystack problems, looking for small targets in large spaces. In such cases, blind search stands no hope of success. Success, instead, requires an assisted search. But whence the assistance required for a search to be successful? To pose the question this way suggests that successful searches do not emerge spontaneously but need themselves to be discovered via a search. The question then naturally arises whether such a higher-level “search for a search” is any easier than the original (...) search. We prove two results: (1) The Horizontal No Free Lunch Theorem, which shows that average relative performance of searches never exceeds unassisted or blind searches. (2) The Vertical No Free Lunch Theorem, which shows that the difficulty of searching for a successful search increases exponentially compared to the difficulty of the original search. (shrink)

This paper shows statistical analyses of the search-space landscape of travelling salesman problems in due consideration of stochastic optimization. It is known from existing works that travelling salesman problems have landscape called “a rugged landscape” and “big valley structure”. This work reveals more detailed structure of the landscape. We deal with the 1000 travelling salesman problems of 6 to 9 cities where the cities are arranged randomly and a travelling salesman problem of 100 cities. It is assumed that the rugged (...) landscape is a combination of the global valleylike structure and the local noiselike structure. Each of them is characterized by the statistical properties of the search-space landscape, that is, the global valleylike structure has linearity with the distance from the optimum, and the variance of the local noiselike structure increase monotonously with the distance from the optimum. On the other side correlation of the tours with the costs close upon the optimum cost is low. For this reason to combine the genetic search with the local search is supported. Even if the number of cities and the definition of the intercity cost value are changed, the structure of the landscape has the same feature. Although the number of the cities of the examined travelling salesman problems is not large, obtained results seem to be universal. It is forecasted that not only travelling salesman problems but also many practical problems have the structure which is characterized with the same measure. These results are useful to compose more effective optimization methods without trial and error. (shrink)

Maynard Smith’s defenses of adaptationism and of the value of optimization theory in evolutionary biology are both criticized. His defense does not adequately respond to the criticism of adaptationism by Gould and Lewontin. It is also argued here that natural selection cannot be interpreted as an optimization process if the objective function to be optimized is either (i) interpretable as a fitness, or (ii) correlated with the mean population fitness. This result holds even if fitnesses are frequency-independent; the problem is (...) further exacerbated in the frequency-dependent context modeled by evolutionary game theory. However, Eshel and Feldman’s new results on “long-term” evolution may provide some hope for the continuing relevance of the game-theoretic framework. These arguments also demonstrate the irrelevance of attempts by Intelligent Design creationists to use computational limits on optimization algorithms as evidence against evolutionary theory. It is pointed out that adaptation, natural selection, and optimization are not equivalent processes in the context of biological evolution. (shrink)

This article reports original research examining characteristics of the active followers of the American animal rights movement. Typical respondents were Caucasian, highly educated urban professional women approximately thirty years old with a median income of $33,000. Most activists think of themselves as Democrats or as Independents, and have moderate to liberal political views. They were often suspicious of science and made no distinctions between basic and applied science, or public versus private animal-based research. The research suggests that animal rights activism (...) is in part a symbolic manifestation of egalitarian social and political views concerning scientific and technological change. (shrink)

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)

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)

Einleitung -- Die Entwicklung des Freiheitsbegriffs in der Geschichte der antiken Philosophie -- Der Neuansatz Plotins : Die Wiederentdeckung der Metaphysik-Freiheit als metaphysisches Problem -- Plotins Konzeption menschlicher Freiheit -- Die Freiheit des göttlichen Einen als absolute Freiheit -- Mystische Freiheit - Die Vereinigung mit dem absoluten Einen als Höchstform menschlicher Freiheit - Die Nachwirkung des plotinischen Freiheitsbegriffs -- Zusammenfassung : Freiheit des Menschen - Freiheit Gottes.

The determinism-free will debate is perhaps as old as philosophy itself and has been engaged in from a great variety of points of view including those of scientific, theological, and logical character. This chapter focuses on two arguments from logic. First, there is an argument in support of determinism that dates back to Aristotle, if not farther. It rests on acceptance of the Law of Excluded Middle, according to which every proposition is either true or false, no matter whether (...) the proposition is about the past, present or future. In particular, the argument goes, whatever one does or does not do in the future is determined in the present by the truth or falsity of the corresponding proposition. The second argument coming from logic is much more modern and appeals to Gödel's incompleteness theorems to make the case against determinism and in favour of free will, insofar as that applies to the mathematical potentialities of human beings. The claim more precisely is that as a consequence of the incompleteness theorems, those potentialities cannot be exactly circumscribed by the output of any computing machine even allowing unlimited time and space for its work. The chapter concludes with some new considerations that may be in favour of a partial mechanist account of the mathematical mind. (shrink)

We present a cut-free tableau calculus with histories and variables for the EXPTIME-complete multi-modal logic of common knowledge. Our calculus constructs the tableau using only one pass, so proof-search for testing theoremhood of ϕ does not exhibit the worst-case EXPTIME-behaviour for all ϕ as in two-pass methods. Our calculus also does not contain a “finitized ω-rule” so that it detects cyclic branches as soon as they arise rather than by worst-case exponential branching with respect to the size of ϕ. (...) Moreover, by retaining the rooted-tree form from traditional tableaux, our calculus becomes amenable to the vast array of optimisation techniques which have proved essential for “practical” automated reasoning in very expressive description logics. Our calculus forms the basis for developing a uniform framework for the family of all fix-point logics of common knowledge. However, there is still no “free lunch” as, in the worst case, our method exhibits 2EXPTIME-behaviour. A prototype implementation can be found at twb.rsise.anu.edu.au which allows users to test formulae via a simple graphical interface. (shrink)

Let us recall that Raphael Robinson's Arithmetic Q is an axiom system that differs from Peano Arithmetic essentially by containing no Induction axioms [13], [18]. We will generalize the semantic-tableaux version of the Second Incompleteness Theorem almost to the level of System Q. We will prove that there exists a single rather long Π 1 sentence, valid in the standard model of the Natural Numbers and denoted as V, such that if α is any finite consistent extension of Q + (...) V then α will be unable to prove its Semantic Tableaux consistency. The same result will also apply to axiom systems α with infinite cardinality when these infinite-sized axiom systems satisfy a minor additional constraint, called the Conventional Encoding Property. Our formalism will also imply that the semantic-tableaux version of the Second Incompleteness Theorem generalizes for the axiom system IΣ 0 , as well as for all its natural extensions. (This answers an open question raised twenty years ago by Paris and Wilkie [15].). (shrink)

Reviews the book, Neurophilosophy of free will: From libertarian illusions to a concept of natural autonomy by Henrik Walter and C. Klohr . In this book, Henrik Walter applies the methodology of neurophilosophy to one of philosophy’s central challenges and enduring questions: the notion of free will. The author argues that free will is an illusion if we mean by it that under identical conditions we would be able to do or decide otherwise, while simultaneously acting only (...) for reasons and being the true originators of our actions. In place of this problematic version of free will, Walter offers what he calls “natural autonomy,” that is, self-determination unaided by supernatural powers that could exist even in an entirely determined universe. 2012 APA, all rights reserved). (shrink)

Reviews the book, Genes, genesis, and God: Values and their origins in natural and human history by Holmes Rolston III . Drawn from a series of lectures given by the author in November of 1997 at the University of Edinburgh as part of the Gifford Lectures, this book addresses the question of whether the supremely social and human phenomena of religion and ethics can be ultimately reduced to the phenomena of biology. Challenging much of what passes for unassailable truth in (...) sociobiological and similar natural science circles, Rolston argues that religion, ethics, and science—as emergent phenomena in human culture—are not only crowning and distinctive achievements in human cultural history but that it is impossible to adequately conceive of them as having resulted from simple evolutionary or biological processes. To this end, the author argues that genetic and evolutionary processes are anything but blind, selfish, and contingent. Indeed, Rolston cogently argues that not only are our sciences of nature not value free, but nature itself is laden with values. 2012 APA, all rights reserved). (shrink)

Early versions of satellite and radiosonde datasets suggested that the tropical surface had warmed more than the troposphere, while climate models consistently showed tropospheric amplification of surface warming in response to human-caused increases in greenhouse gases. We revisit such comparisons here using new observational estimates of surface and tropospheric temperature changes. We find that there is no longer a serious discrepancy between modeled and observed trends in the tropics. Our results contradict a recent claim that all simulated temperature trends in (...) the tropical troposphere are inconsistent with observations. This claim was based on the use of older radiosonde and satellite datasets and on two methodological errors: the neglect of observational trend uncertainties introduced by interannual climate variability and application of an inappropriate statistical “consistency test”.This emerging reconciliation of models and observations has two primary explanations. First, because of changes in the treatment of buoy and satellite information, new surface temperature datasets yield slightly reduced tropical warming relative to earlier versions. Second, recently developed satellite and radiosonde datasets now show larger warming of the tropical lower troposphere. In the case of a new satellite dataset from remote sensing systems, enhancedRSS warming is due to an improved procedure of adjusting for inter-satellite biases. When the RSS-derived tropospheric temperature trend is compared with four different observed estimates of surface temperature change, the surface warming is invariably amplified in the tropical troposphere, consistent with model results. Even if we use data from a second satellite dataset with smaller tropospheric warming than in remote sensing systems RSS, observed tropical lapse rates are not significantly different from those in all model simulations.Our results contradict a recent claim that all simulated temperature trends in the tropical troposphere and in tropical lapse rates are inconsistent with observations. This claim was based on the use of older radiosonde and satellite datasets and on two methodological errors: the neglect of observational trend uncertainties introduced by interannual climate variability and application of an inappropriate statistical “consistency test”. (shrink)

Using state-of-the-art observational datasets and results from a large archive of computer model simulations, a consortium of scientists from 12 different institutions has resolved a long-standing conundrum in climate science—the apparent discrepancy between simulated and observed temperature trends in the tropics. Research published by this group indicates that there is no fundamental discrepancy between modeled and observed tropical temperature trends when one accounts for: the uncertainties in observations; and the statistical uncertainties in estimating trends from observations. These results refute a (...) recent claim that model and observed tropical temperature trends “disagree to a statistically significant extent”. This claim was based on the application of a flawed statistical test and the use of older observational datasets. (shrink)

A Gedanken experiment is presented where an excited and a ground-state atom are positioned such that, within the former’s half-life time, they exchange a photon with 50% probability. A measurement of their energy state will therefore indicate in 50% of the cases that no photon was exchanged. Yet other measurements would reveal that, by the mere possibility of exchange, the two atoms have become entangled. Consequently, the “no exchange” result, apparently precluding entanglement, is non-locally established between the atoms by this (...) very entanglement. This quantum-mechanical version of the ancient Liar Paradox can be realized with already existing transmission schemes, with the addition of Bell’s theorem applied to the no-exchange cases. Under appropriate probabilities, the initially-excited atom, still excited, can be entangled with additional atoms time and again, or alternatively, exert multipartite nonlocal correlations in an interaction free manner. When densely repeated several times, this result also gives rise to the Quantum Zeno effect, again exerted between distant atoms without photon exchange. We discuss these experiments as variants of interaction-free-measurement, now generalized for both spatial and temporal uncertainties. We next employ weak measurements for elucidating the paradox. Interpretational issues are discussed in the conclusion, and a resolution is offered within the Two-State Vector Formalism and its new Heisenberg framework. (shrink)

In treatises or advanced textbooks on theoretical physics, it is apparent that the way mathematics is used is very different from what is to be found in books of mathematics. There is, for example, no close connection between books on analysis, on the one hand, and any classical textbook in quantum mechanics, for example, Schiff, [11], or quite recent books, for example Ryder, [10], on quantum field theory. The differences run a good deal deeper than the fact that the books (...) on theoretical physics are not written in the definition-theorem-proof style characteristic of pure mathematics. Although a good many propositions are proved in the books on physics, there are almost with exception no existential proofs, and consequently there is no really serious systematic use of quantifiers. Another important characteristic is the free use of infinitesimals. In fact, most results would not lose anything, from a physicist's point of view, by leaving them in approximate form, i.e., instead of strict equalities or inequalities, using equalities or inequalities only up to an infinitesimal.The discrepancy between the way mathematics is ordinarily done in theoretical physics and the way it is built up from a foundational standpoint in any of the standard modern views raises the question of whether it might be possible to construct quite directly a rigorous foundation that reflects a significant part of this standard practice in theoretical physics. Other parts of standard practice in physics, for example, the use of physically intuitive but nonrigorous arguments, are not present in our system. (shrink)