The halting problem for Turing machines is decidable on a set of asymptotic probability one. The proof is sensitive to the particular computational models.

A method is presented for deciding whether correct predictions about other people are based on simulation or theory use. The differentiating power of this method was assessed with cognitive estimation biases (e.g. estimating the area of Brazil) in two variations. Experiments 1 and 2 operated with the influence of response scales of different length. Experiment 3 used the difference between free estimates that tended to be far off the true value and estimates constrained by an appropriate response scale, where estimates (...) became greatly more realistic. The critical question is how well observer subjects can predict these target biases under two different presentation conditions. Response scale biases (Experiments 1 and 2) were more strongly predicted when observer subjects were presented with the two scales juxtaposed, than when responses for each scale were given independently. This speaks for the use of a theory, since simulation should, if there is any difference at all, be made more difficult by the juxtaposition of conditions. The difference between free and constrained estimations (Experiment 3) was more strongly predicted under independent than under juxtaposed presentation. This speaks for the use of simulation since use of a theory should, if anything, be helped by juxtaposition of problems since it helps highlight the theoretically relevant factor. Results are discussed in view of recent proposals about when simulation is likely to be used, i.e. for belief fixation but not action prediction (Stich and Nichols, 1995b), for content fixation (Heal, 1996a), and for rational effects only (Heal, 1996b). (shrink)

We study the parameterized complexity of the problem to decide whether a given natural number n satisfies a given $\Delta _0$ -formula $\varphi (x)$ ; the parameter is the size of $\varphi $. This parameterization focusses attention on instances where n is large compared to the size of $\varphi $. We show unconditionally that this problem does not belong to the parameterized analogue of $\mathsf {AC}^0$. From this we derive that certain natural upper bounds on the complexity of our parameterized (...) problem imply certain separations of classical complexity classes. This connection is obtained via an analysis of a parameterized halting problem. Some of these upper bounds follow assuming that $I\Delta _0$ proves the MRDP theorem in a certain weak sense. (shrink)

I show that Eric Winsberg’s principles of model-building given in Science in the Age of Computer Simulation are insufficient to argue for the external validation of simulation data in cases in which simulation results conflict, and that laboratory experiments have an advantage over simulations because conflicting experimental results can be decided between on the basis of reproducibility. I also argue that robustness of predictions serves the same function for simulations as repeatability does for laboratory experiments in either adjudicating between conflicting (...) results or allowing us to say that we do not have sufficient justification to validate the results. Finally, I argue for an interpretation of the argument from robustness that appeals to the convergence of many well-built and diverse models rather than the more common interpretation which appeals to the probability that one of a set of models is likely to be true. (shrink)

The uniform halting problem (UH) can be stated as follows:Give a decision procedure which for any given Turing machine (TM) will decide whether or not it has an immortal instantaneous description (ID).An ID is called immortal if it has no terminal successor. As it is generally the case in the literature (see e.g. Minsky [4, p. 118]) we assume that in an ID the tape must be blank except for some finite number of squares. If we remove this restriction the (...) UH becomes the immortality problem (IP). (shrink)

Deliberative analysis enables us to weigh features, simulate futures, and arrive at good, tractable decisions. So why do we so often eschew deliberation, and instead rely on more intuitive, gut responses? We propose that intuition might be prescribed for some decisions because people’s folk theory of decision-making accords a special role to authenticity, which is associated with intuitive choice. Five pre-registered experiments find evidence in favor of this claim. In Experiment 1 (N = 654), we show that participants prescribe intuition (...) and deliberation as a basis for decisions differentially across domains, and that these prescriptions predict reported choice. In Experiment 2 (N = 555), we find that choosing intuitively vs. deliberately leads to different inferences concerning the decision-maker’s commitment and authenticity—with only inferences about the decision-maker’s authenticity showing variation across domains that matches that observed for the prescription of intuition in Experiment 1. In Experiment 3 (N = 631), we replicate our prior results and rule out plausible confounds. Finally, in Experiment 4 (N = 177) and Experiment 5 (N = 526), we find that an experimental manipulation of the importance of authenticity affects the prescribed role for intuition as well as the endorsement of expert human or algorithmic advice. These effects hold beyond previously recognized influences on intuitive vs. deliberative choice, such as computational costs, presumed reliability, objectivity, complexity, and expertise. (shrink)

The uniform halting problem (UH) can be stated as follows.Give a decision procedure which for any given Turing machine (TM) will decide whether or not it has an immortal instantaneous description (ID).An ID is called immortal if it has no terminal successor. As it is generally the case in the literature (see e.g. Minsky [3, p. 118]) we assume that in an ID the tape must be blank except for some finite numbers of squares. If we remove this restriction the (...) UH becomes the immortality problem (IP). The UH should not be confused with the initialised uniform halting problem (whether or not a TM has an immortal ID when started in a specified state) which can easily be shown to be undecidable (see e.g. Minsky [3, p. 151]). (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Willing and DecidingHegel on Irony, Evil, and the Sovereign ExceptionAndrew NorrisIf political decisionism is the claim that the most important political decisions cannot be regulated by rational norms and instead require a confrontation with the exception, Carl Schmitt remains its most notorious advocate. While Schmitt distanced himself from decisionism when he joined the Nazi party in the 1930s, his critics insist that his role in the events leading to (...) Hitler’s assumption of power and his own membership in the party were only attempts “to put... into practice” his earlier theoretical attack on legal positivism and what he vaguely termed “liberalism.”1 Even for those who reject such sweeping claims, the teaching laid out in his 1922 Political Theology remains deeply disturbing. On Schmitt’s account, “Sovereign is he who decides on the exception” [Political Theology 5]. This decision is not a matter of recognizing an exception that already exists; rather it has a performative quality whereby the sovereign decision that names a given event to be an exception is the necessary precondition for the existence of the exception as such—as well as, by extension, the legal system from which it is excepted or removed. The exception is, as it were, called into being by the sovereign, whose decision on it is unregulated by the standards of law or, indeed, of normal life itself.The exception is that which cannot be subsumed; it defies general codification, but it simultaneously reveals a specifically juristic element—the decision in its absolute purity. The exception appears in its absolute form when a situation in which legal prescriptions can be valid must first be brought about. Every general norm demands a normal, everyday frame of life to which it can be factually applied and which is subjected to its regulations. The norm requires a homogenous medium.... For a legal order to make sense, a normal situation must exist, and he is sovereign who definitively decides whether this normal situation actually exists.[Political Theology 13]2 [End Page 135]As the ability to decide on the exception (and hence the norm and the normal) in this sense is what defines the sovereign, sovereignty only appears in its “absolute purity” in the act of naming the exception. Schmitt’s sovereign is a creature of the border: “although he stands outside the normally valid legal system, he nevertheless belongs to it, for it is he who decides when the constitution needs to be suspended in its entirety” [Political Theology 7].3 But while the sovereign’s decision on the exception seems to range back and forth over the borders of the legal order, this movement is in fact the oscillation of the borders themselves—an oscillation that bears the two names sovereignty and exception. Though it makes sense in one way to speak of the sovereign overstepping the limits he lays down, in a deeper sense he, as the moment of decision, is himself the limit. On this account, George W. Bush was more accurate than he could have known in his recent halting suggestion that he is not just the nation’s “decider,” but also himself “a decision.” Or, as he more regularly if quietly maintains, an exception.4While Schmitt’s celebratory analysis of the exception is the best-known today, he is hardly the inventor of this problematic: as he himself emphasizes in Political Romanticism (1919), the question of the decision lies at the heart of nineteenth-century Continental Romanticism, which celebrated an “occasionalism” derived from Malebranche in which the self and its whims take precedence over any substantive commitments that self might take up.5 Karl Löwith has demonstrated that Schmitt’s 1920s decisionism is, rather ironically, open in many aspects to his earlier attack upon this Romantic occasionalism [see Löwith]. Löwith was perhaps as attuned to this as he was on account of being a keen student of Hegel, as well as of Heidegger. Indeed, many features of Schmitt’s own attack upon the Romantics are anticipated in Hegel’s fierce critique of this movement and, in particular, his attack upon Friedrich Schlegel’s role in it. But if Hegel’s critique of Schlegel casts... (shrink)

The ability of ordinary differential equations (ODEs) to simulate discrete machines with a universal computing power indicates a new source of difficulties for event detection problems. Indeed, nearly any kind of event detection is algorithmi- cally undecidable for infinite or finite half-open time intervals, and explicitly given “well-behaved” ODEs (see [18]). Practical event detection, however, usually takes place on finite closed time intervals. In this paper the undecidability of general event detection is extended to such intervals. On the other hand, (...) on finite closed time in- tervals event detection in a certain approximate sense is quite generally decidable, which partly saves the case for practicable event detection. The capability of simulat- ing universal Turing machines is still there, and is used to give complexity lower bounds in terms of accuracy of event detection. The ODEs used here are of course quite complicated, but not artificial, in that even from the point of view of practical event detection it would appear difficult to find criteria to exclude them. (shrink)

According to the "experimenter's regress", disputes about the validity of experimental results cannot be closed by objective facts because no conclusive criteria other than the outcome of the experiment itself exist for deciding whether the experimental apparatus was functioning properly or not. Given the frequent characterization of simulations as "computer experiments", one might worry that an analogous regress arises for computer simulations. The present paper analyzes the most likely scenarios where one might expect such a "simulationist's regress" to surface, and, (...) in doing so, discusses analogies and disanalogies between simulation and experimentation. I conclude that, on a properly broadened understanding of robustness, the practice of simulating mathematical models can be seen to have sufficient internal structure to avoid any special susceptibility to regress-like situations. (shrink)

We show that given a finite, transitive and reflexive Kripke model 〈 W , ≼, ⟦ ⋅ ⟧ 〉 and $${w \in W}$$ , the property of being simulated by w (i.e., lying on the image of a literalpreserving relation satisfying the ‘forth’ condition of bisimulation) is modally undefinable within the class of S4 Kripke models. Note the contrast to the fact that lying in the image of w under a bi simulation is definable in the standard modal language even (...) over the class of K4 models, a fairly standard result for which we also provide a proof. We then propose a minor extension of the language adding a sequent operator $${\natural}$$ (‘tangle’) which can be interpreted over Kripke models as well as over topological spaces. Over finite Kripke models it indicates the existence of clusters satisfying a specified set of formulas, very similar to an operator introduced by Dawar and Otto. In the extended language $${{\sf L}^+ = {\sf L}^{\square\natural}}$$ , being simulated by a point on a finite transitive Kripke model becomes definable, both over the class of (arbitrary) Kripke models and over the class of topological S4 models. As a consequence of this we obtain the result that any class of finite, transitive models over finitely many propositional variables which is closed under simulability is also definable in L + , as well as Boolean combinations of these classes. From this it follows that the μ -calculus interpreted over any such class of models is decidable. (shrink)

We characterise explicitly the decidable predicates on integers of Infinite Time Turing machines, in terms of admissibility theory and the constructible hierarchy. We do this by pinning down ζ, the least ordinal not the length of any eventual output of an Infinite Time Turing machine (halting or otherwise); using this the Infinite Time Turing Degrees are considered, and it is shown how the jump operator coincides with the production of mastercodes for the constructible hierarchy; further that the natural ordinals associated (...) with the jump operator satisfy a Spector criterion, and correspond to the L ζ -stables. It also implies that the machines devised are "Σ 2 Complete" amongst all such other possible machines. It is shown that least upper bounds of an "eventual jump" hierarchy exist on an initial segment. (shrink)

In this response, I do four things. First, I defend the claim that the action compatibility effect does not distinguish between embodied and traditional accounts of language comprehension. Second, I present neuroimaging and neuropsychological results that seem to support the traditional account. Third, I argue that metaphorical language poses no special challenge to the arguments I gave against embodied theories of comprehension. Fourth, I lay out the architecture of language I advocate and suggest the sorts of data that would decide (...) between traditional and embodied accounts.Keywords: Language; Comprehension; Perception; Action; Embodied cognition; Representation. (shrink)

An empirical interaction potential has been developed primarily to simulate displacement cascades in a UO 2 matrix. After a bibliographical survey revealed that the potentials discussed in the literature are not entirely suitable for describing point defects and their migration, we decided to adapt the most representative of the existing potentials. Our objective was specifically to reproduce transport phenomena, which are fundamental to a satisfactory description of atomic displacement cascades. The modified potential more correctly describes the experimental energies of formation (...) and migration of point defects as well as the oxygen diffusion coefficients in the superionic phase. Thermal expansion, heat capacity and enthalpy are also better modelled over a wide temperature range. The new potential is much more transferable than earlier potentials fitted mainly to the properties of perfect crystals. The initial simulated atomic displacement cascades showed that this potential is well suited to the description of structural effects created by decelerating recoil nuclei in a UO 2 matrix. (shrink)

An innovative approach to improve the fidelity of low-frequency lateral motion cueing within full-flight simulators for non-maneuvering aircraft is presented. On the basis of the perception peculiarities by the human vestibular system of movement along the roll, the problem of low-frequency motion cueing of lateral movement by motion systems of flight simulators was formulated and solved. The critical challenge of simulating the set of angular motion cues that pilots perceive during flights is decided. This research highlights two key outcomes. (...) The fourth-order low-pass filter effectively extracts low-frequency motion cues from aircraft motion kinematic parameters, enhancing simulation accuracy. Secondly, proposed method significantly expands the range of simulated motion cues while ensuring their synchronization with high-frequency motion cues along relevant degrees of freedom. This formulation of the problem increases the range of simulated motion cues to ±0,3nz, which practically corresponds to the range of simulated motion cues of a transport aircraft, and thus increases the quality of motion cueing. The implementation of the developed method on the An-72TK-200 full flight simulator confirmed its effectiveness. In conclusion, this study introduces a promising methodology that enhances the quality of motion cueing, thus rendering flight simulations more realistic and beneficial for both pilots and aerospace engineering researchers in the real of non-maneuvering aircraft flight simulators. (shrink)

We contribute to the empirical debate on whether we understand and predict mental states by using simulation (simulation theory) or by relying on a folk psychological theory (theory theory). To decide between these two fundamental positions, it has been argued that failure to predict other people’s choices would be challenging evidence against the simulation view. We test the specific claim that people prefer the rightmost position in choosing among equally valued objects, and whether or not this position bias can be (...) correctly predicted. A series of experiments shows that the bias appears only in a specific spatial arrangement and that it can be correctly predicted given adequate imaginative input. In concert with other recent findings on the correct prediction of choices these findings do actually strengthen, rather than challenge, the simulation account on the prediction of mental states. (shrink)

We contribute to the empirical debate on whether we understand and predict mental states by using simulation (simulation theory) or by relying on a folk psychological theory (theory theory). To decide between these two fundamental positions, it has been argued that failure to predict other people's choices would be challenging evidence against the simulation view. We test the specific claim that people prefer the rightmost position in choosing among equally valued objects, and whether or not this position bias can be (...) correctly predicted. A series of experiments shows that the bias appears only in a specific spatial arrangement and that it can be correctly predicted given adequate imaginative input. In concert with other recent findings on the correct prediction of choices these findings do actually strengthen, rather than challenge, the simulation account on the prediction of mental states. (shrink)

In an attempt at fleshing out the thesis that religious (and other similar) experiences cannot be attributed to an individual on the basis of outer behaviour alone, the hypothesis is entertained of somebody who decides, at a certain point in his life, to fool everybody into beUeving that he is a reUgious beUever. This person, it is claimed, lacks the inner conviction that is crucial to religious experiences. Does this claim fall prey to Wittgenstein-like objections to the possibility of a (...) private language? It is argued that it does not, by distinguishing between what counts empirically, and what conceptually, as a private language. (shrink)

ABSTRACT George Gargov was an active pioneer in the ‘Sofia School’ of modal logicians. Starting in the 1970s, he and his colleagues expanded the scope of the subject by introducing new modal expressive power, of various innovative kinds. The aim of this paper is to show some general patterns behind such extensions, and review some very general results that we know by now, 20 years later. We concentrate on simulation invariance, decidability, and correspondence. What seems clear is that ‘modal logic’ (...) as a genre of logical systems has a much wider scope than originally conceived, and that we have not reached its limits yet. (shrink)

Accelerating Turing machines are Turing machines of a sort able to perform tasks that are commonly regarded as impossible for Turing machines. For example, they can determine whether or not the decimal representation of contains n consecutive 7s, for any n; solve the Turing-machine halting problem; and decide the predicate calculus. Are accelerating Turing machines, then, logically impossible devices? I argue that they are not. There are implications concerning the nature of effective procedures and the theoretical limits of computability. Contrary (...) to a recent paper by Bringsjord, Bello and Ferrucci, however, the concept of an accelerating Turing machine cannot be used to shove up Searle's Chinese room argument. (shrink)

All known structural extensions of the substructural logic $\textbf{FL}_{\textbf{e}}$, the Full Lambek calculus with exchange/commutativity (corresponding to subvarieties of commutative residuated lattices axiomatized by $\{\vee, \cdot, 1\}$ -equations), have decidable theoremhood; in particular all the ones defined by knotted axioms enjoy strong decidability properties (such as the finite embeddability property). We provide infinitely many such extensions that have undecidable theoremhood, by encoding machines with undecidable halting problem. An even bigger class of extensions is shown to have undecidable deducibility problem (the (...) corresponding varieties of residuated lattices have undecidable word problem); actually with very few exceptions, such as the knotted axioms and the other prespinal axioms, we prove that undecidability is ubiquitous. Known undecidability results for non-commutative extensions use an encoding that fails in the presence of commutativity, so and-branching counter machines are employed. Even these machines provide encodings that fail to capture proper extensions of commutativity, therefore we introduce a new variant that works on an exponential scale. The correctness of the encoding is established by employing the theory of residuated frames. (shrink)

The paper presents an exploration of conceptual issues that have arisen in the course of investigating speed-up and slowdown phenomena in small Turing machines, in particular results of a test that may spur experimental approaches to the notion of computational irreducibility. The test involves a systematic attempt to outrun the computation of a large number of small Turing machines (3 and 4 state, 2 symbol) by means of integer sequence prediction using a specialized function for that purpose. The experiment prompts (...) an investigation into rates of convergence of decision procedures and the decidability of sets in addition to a discussion of the (un)predictability of deterministic computing systems in practice. We think this investigation constitutes a novel approach to the discussion of an epistemological question in the context of a computer simulation, and thus represents an interesting exploration at the boundary between philosophical concerns and computational experiments. (shrink)

In a theoretical simulation the cooperation of two insects is investigated who share a large number of maximally entangled EPR-pairs to correlate their probabilistic actions. Specifically, two distant butterflies must find each other. Each butterfly moves in a chaotic form of short flights, guided only by the weak scent emanating from the other butterfly. The flight directions result from classical random choices. Each such decision of an individual is followed by a read-out of an internal quantum measurement on a spin, (...) the result of which decides whether the individual shall do a short flight or wait. These assumptions reflect the scarce environmental information and the small brains’ limited computational capacity. The quantum model is contrasted to two other cases: In the classical case the coherence between the spin pairs gets lost and the two butterflies act independently. In the super classical case the two butterflies read off their decisions of whether to fly or to wait from the same internal list so that they always take the same decision as if they were super correlated. The numerical simulation reveals that the quantum entangled butterflies find each other with a much shorter total flight path than in both classical models. (shrink)

When deciding on an online purchase, consumers often face a plethora of information. Yet, individuals consumers differ greatly in the amount of information they are willing and able to acquire and process before making purchasing decisions. Extensively processing all available information does not necessarily promote good decisions. Instead, the empirical evidence suggests that reviewing too much information or too many choice alternatives can impair decision quality. Using simulated contract conclusion scenarios, we identify distinctive types of information processing styles and find (...) that certain search and selection strategies predict the quality of the final choice. Participants chose a cellular service contract in a web-based environment that closely resembled actual online settings in the country of study. Using information processing data obtained with tracking software, we identify three consumer segments differing along two dimensions – the extent dimension, referring to the overall effort invested in information processing, and the focus dimension, referring to the degree to which someone focuses on the best available options. The three subgroups of respondents can be characterized as follows: consumers with a low-effort and low-focus information processing strategy ; consumers with a moderate-effort and high-focus information processing strategy ; and consumers with high-effort and low-focus information processing strategy. The three groups differed not only in their information processing but also in the quality of their decisions. In line with the assumption of ecological rationality, most successful search strategies were not exhaustive, but instead involved the focused selection and processing of a medium amount of information. Implications for effective consumer information are provided. (shrink)

We performed three experiments to investigate whether adjectives can modulate the sensorimotor activation elicited by nouns. In Experiment 1, nouns of graspable objects were used as stimuli. Participants had to decide if each noun referred to a natural or artifact, by performing either a precision or a power reach‐to‐grasp movement. Response grasp could be compatible or incompatible with the grasp typically used to manipulate the objects to which the nouns referred. The results revealed faster reaction times (RTs) in compatible than (...) in incompatible trials. In Experiment 2, the nouns were combined with adjectives expressing either disadvantageous information about object graspability (e.g., sharp) or information about object color (e.g., reddish). No difference in RTs between compatible and incompatible conditions was found when disadvantageous adjectives were used. Conversely, a compatibility effect occurred when color adjectives were combined with nouns referring to natural objects. Finally, in Experiment 3 the nouns were combined with adjectives expressing tactile or shape proprieties of the objects (e.g., long or smooth). Results revealed faster RTs in compatible than in incompatible condition for both noun categories. Taken together, our findings suggest that adjectives can shape the sensorimotor activation elicited by nouns of graspable objects, highlighting that language simulation goes beyond the single‐word level. (shrink)

Assume that a person who is suspected of either murdering X or raping Y credibly and voluntarily confesses to have committed ‘a terrible crime’ but immediately after this utterance decides to remain silent. The remaining available evidence cannot prove beyond reasonable doubt the exact offence which he committed. Should such an accused be acquitted of both offences and evade the law or should a way be found to allow a conviction, although no specific offence can be proven beyond reasonable doubt? (...) Harel and Porat suggest that such an accused should be convicted of an unspecific offence. This paper reaches entirely different conclusions, according to which the prevailing insistence of most Criminal justice systems on offence specificity is justified. It is argued that offence specificity stems from the cognitive psychological difficulties associated with simulating the event in question if the accused is convicted of an unspecific offence. The reason is that fact-finders are unable to simulate the details of an unspecific offence while retaining a confidence level sufficiently high to satisfy the standard of ‘beyond reasonable doubt’. The fact-finder faces a choice between a proven offence which is difficult to simulate and a group of unproven offences which are easy to simulate. These difficulties also give rise to a more solid expressivist justification for offence specificity than that conceded by Harel and Porat. Unspecific offences undermine the efficacy of condemnation because the message that corresponding convictions would broadcast to members of the public would be either blurred and ineffective or based on scenarios none of which was proven beyond reasonable doubt. This paper therefore offers two independent justifications for the prevailing insistence on offence specificity, both of which are based on the cognitive psychological difficulties of simulation, as found by the fact-finder and the public respectively. (shrink)

In our everyday social interactions, we try to make sense of what people are thinking, why they act as they do, and what they are likely to do next. This process is called mindreading. Mindreading, Shannon Spaulding argues in this book, is central to our ability to understand and interact with others. Philosophers and cognitive scientists have converged on the idea that mindreading involves theorizing about and simulating others’ mental states. She argues that this view of mindreading is limiting (...) and outdated. Most contemporary views of mindreading vastly underrepresent the diversity and complexity of mindreading. She articulates a new theory of mindreading that takes into account cutting edge philosophical and empirical research on in-group/out-group dynamics, social biases, and how our goals and the situational context influence how we interpret others’ behavior. -/- Spaulding's resulting theory of mindreading provides a more accurate, comprehensive, and perhaps pessimistic view of our abilities to understand others, with important epistemological and ethical implications. Deciding who is trustworthy, knowledgeable, and competent are epistemically and ethically fraught judgments: her new theory of mindreading sheds light on how these judgments are made and the conditions under which they are unreliable. -/- This book will be of great interest to students of philosophy of psychology, philosophy of mind, applied epistemology, cognitive science and moral psychology, as well as those interested in conceptual issues in psychology. (shrink)

It is shown that many different problems have the same degree of unsolvability. Among these problems are: THE INDUCTIVE INFERENCE PROBLEM. Infer in the limit an index for a recursive function f presented as f(0), f(1), f(2),.... THE RECURSIVE INDEX PROBLEM. Decide in the limit if i is the index of a total recursive function. THE ZERO NONVARIANT PROBLEM. Decide in the limit if a recursive function f presented as f(0), f(1), f(2),... has value unequal to zero for infinitely many (...) arguments. Finally, it is shown that these unsolvable problems are strictly easier than the halting problem. (shrink)

Does Nature permit the implementation of behaviours that cannot be simulated computationally? We consider the meaning of physical computation in some detail, and present arguments in favour of physical hypercomputation: for example, modern scientific method does not allow the specification of any experiment capable of refuting hypercomputation. We consider the implications of relativistic algorithms capable of solving the (Turing) Halting Problem. We also reject as a fallacy the argument that hypercomputation has no relevance because non-computable values are indistinguishable from sufficiently (...) close computable approximations. In addition to considering the nature of computability relative to any given physical theory, we can consider the relationship between versions of computability corresponding to different models of physics. Deutsch and Penrose have argued on mathematical grounds that quantum computation and Turing computation have equivalent formal power. We suggest this equivalence is invalid when considered from the physical point of view, by highlighting a quantum computational behaviour that cannot meaningfully be considered feasible in the classical universe. (shrink)

A true Turing machine (TM) requires an infinitely long paper tape. Thus a TM can be housed in the infinite world of Newtonian spacetime (the spacetime of common sense), but not necessarily in our world, because our world-at least according to our best spacetime theory, general relativity-may be finite. All the same, one can argue for the "existence" of a TM on the basis that there is no such housing problem in some other relativistic worlds that are similar ("close") to (...) our world. But curiously enough-and this is the main point of this paper-some of these close worlds have a special spacetime structure that allows TMs to perform certain Turing unsolvable tasks. For example, in one kind of spacetime a TM can be used to solve first-order predicate logic and the halting problem. And in a more complicated spacetime, TMs can be used to decide arithmetic. These new computers serve to show that Church's thesis is a thoroughly contingent claim. Moreover, since these new computers share the fundamental properties of a TM in ordinary operation (e.g. intuitive, finitely programmed, limited in computational capability), a computability theory based on these non-Turing computers is no less worthy of investigation than orthodox computability theory. Some ideas about this new mathematical theory are given. (shrink)

Problem of truth and reality is age old in the field of philosophy as well as in the field of science. People very often confuse between ‘Truth’ and ‘Reality’ Most people think them to be one and the same, but there are differences. Whatever exist is real, reality and existence are interchangeable words. We can say truth, which is unchangeable and reality, which exist but change. False, which is not exist at all. People have suggested various taste to decide the (...) truth falsity of our description of reality. Some suggested Pragmatic theory and some other have suggested Coherence as a test of truth. Realism is also an ontological theory and has been probably the most ancient one. According to ancient man, real is that which perceived. Latter on, due to religious impact the knower became more important then the knowing object. Barkeley developed an extreme position that the objective material world does not exist at all. Dewey has developed the position called Instrumentalism. Halt, Perry, Marvin, Pitkin are the chief advocates of this position. Philosophers such as Darke, Lovejoy, Cellars, and Santayana held a position of Critical Realism. These people hold that mind does not see the object directly as they are but only through their representatives, as regards the object of knowledge is concerned, the Neo Realist are monist while Critical Realist are dualist. Indian rationalist philosopher Dr. D.D. Bandiste introduces a new concept of reality Radical Realism. He proved that knowledge change the knower not the object. to him every new knowledge make some change or other inthe knowing person. Epistemological position of john Dewey called instrumentalism. According to him knowledge is an instrument of action and a meaningful action is always of a problem-solving type. Every knowledge is an instrument to serve some need or other, neither is any knowledge final, nor is any truth final. Not only everything in the world is changing, their mutual relations also change. Knowledge is not a goal, but only a instrument to achieve this or that goal. In my paper I haves discussed various theories regarding whether knowledge change the object known. In this contest I have discussed varieties of realism, Idealismand so on, but importantly I have also discussed a new theory Radical Realism. (shrink)

Using a simulated, two-party negotiation, we examined how characteristics of the actor, target, and situation affected deception. To trigger deception, we used an issue that had no value for one of the two parties (indifference issue). We found support for an opportunistic betrayal model of deception: deception increased when the other party was perceived as benevolent, trustworthy, and as having integrity. Negotiators’ goals also affected the use of deception. Individualistic, cooperative, and mixed dyads responded differently to information about the other (...) party’s trustworthiness, benevolence, and integrity when deciding to either misrepresent or leverage their indifference issue. Mixed dyads displayed opportunistic betrayal. Negotiators in all-cooperative and all-individualistic dyads used different information in deciding whether to leverage their indifference issues and used the same information (benevolence) differently in deciding whether to misrepresent the value of their indifference issue. (shrink)

A critique of algorithmic rationalisation offers at best some initial reasons and preliminary ideas. Critique is understood as a reflection on validity. It is limited to an “epistemological investigation” of the limits of the calculable or of what appears “knowable” in the mode of the algorithmic. The argumentation aims at the mathematical foundations of computer science and goes back to the so-called “foundational crisis of mathematics” at the beginning of the 20th century with the attempt to formalise concepts such as (...) calculability, decidability and provability. The Gödel theorems and Turing’s halting problem prove to be essential for any critical approach to “algorithmic rationalisation”. Both, however, do not provide unambiguous results, at best they run towards what later became known as “Gödel’s disjunction”. The chosen path here, however, suggests the opposite way, insofar as, on the one hand, the topos of creativity appear constitutive for what can be regarded as cognitive “algorithmic rationalisation” and which encounters systematic difficulties in the evaluation of non-trivial results. On the other hand, the investigations lead to a comparison between the “mediality” of formally generated structures, which have to distinguish between object-and metalanguages, and the “volatile” differentiality of human thought, which calls for syntactically non-simulatable sense structures. (shrink)

Philosophers of science frequently bemoan (or cheer) the fact that today, with the supposed collapse of logical empiricism, there are now ;;10 grand systems. However, although this mayor may not be true, and if true mayor may not be a cause for delight, no one should conclude that the philosophy of science has ground to a halt, its problems exhausted and its practioners dispirited. In fact, in this post­ Kuhnian age the subject has never been more alive, as we (...) work with enthusiasm on special topics, historical and conceptual. And no topic has grown and thrived quite like the philosophy of biology, which now has many students in the field producing high-quality articles and monographs. The success of this subject is due above all to the work and influence of one man: David Hull. In his own writings and in the support he has given to others, he has shown true leadership, in the best Platonic sense. It is now twenty years since Hull fnt gave his seminal paper 'What the philosophy of biology is not', and to mark that point and to show our respect, gratitude and affection to its author, a number of us who owe much to Hull decided to produce a volume of essays on and around themes to which Hull has spoken. (shrink)

I develop a theory of counterfactuals about relative computability, i.e. counterfactuals such as 'If the validity problem were algorithmically decidable, then the halting problem would also be algorithmically decidable,' which is true, and 'If the validity problem were algorithmically decidable, then arithmetical truth would also be algorithmically decidable,' which is false. These counterfactuals are counterpossibles, i.e. they have metaphysically impossible antecedents. They thus pose a challenge to the orthodoxy about counterfactuals, which would treat them as uniformly true. What’s more, I (...) argue that these counterpossibles don’t just appear in the periphery of relative computability theory but instead they play an ineliminable role in the development of the theory. Finally, I present and discuss a model theory for these counterfactuals that is a straightforward extension of the familiar comparative similarity models. (shrink)

Social context shapes negotiators’ actions, including their willingness to act unethically. We use a simulated negotiation to test how three dimensions of social context—dyadic gender composition, negotiation strategy, and trust—interact to influence one micro-ethical decision, the use of deception. Deception in all-male dyads was relatively unaffected by trust or the other negotiator’s strategy. In mixed-sex dyads, negotiators consistently increased their use of deception when three forms of trust were low and opponents used an accommodating strategy. However, in all-female dyads, negotiators (...) appeared to use multiple and shifting reference points in deciding when to deceive the other party. In these dyads, the use of deception increased when a competitive strategy combined with low benevolence-based trust or an accommodating strategy combined with high identity-based trust. Deception in all-female dyads decreased when a competitive strategy was used in the context of low deterrence-based trust. (shrink)

Effective inseparability of pairs of sets is an important notion in logic and computer science. We study the effective inseparability of sets which appear as index sets of subsets of an effectively given topological T0-space and discuss its consequences. It is shown that for two disjoint subsets X and Y of the space one can effectively find a witness that the index set of X cannot be separated from the index set of Y by a recursively enumerable set, if X (...) intersects the topological closure of an effectively enumerable subset of Y. As a consequence of a more general parametric inseparability result a theorem of Rice-Shapiro type is obtained. Moreover, under some additional requirements it follows that nonopen subsets have productive index sets. This implies a generalized Rice theorem: Connected spaces have only trivial completely recursive subsets. As application some decision problems in computable analysis and domain theory are studied. It follows that the complement of the halting problem can be reduced to the problem to decide of a number whether it is a computable irrational. The same is true for the problems to decide whether two numbers are equal, whether one is not greater than the other, and whether a number is equal to a given number. In the case of an effectively given continuous complete partial order the complexity of the last problem depends on whether the given element is the smallest element, in which case the complement of the halting problem is reducible to it, whether it is a base element and maximal, then the decision problem is recursively isomorphic to the halting problem, or whether it is none of these. In this case, both the halting problem and its complement are reducible to the problem. The same is true in nontrivial cases for the problems whether an element belongs to the basis, whether two elements of the partial order are equal, or whether one approximates the other. In general, for any nonempty proper subset of the partial order either the halting problem or its complement can be reduced to the membership problem of the subset. (shrink)

In October 2013, Missouri officials abandoned a plan to execute a convicted murderer using a novel method—an injection of propofol. The name of this drug became a household word after propofol played a role in singer Michael Jackson's death, but this has been a popular therapeutic drug for many years. Clinicians use it in intensive care, surgery, and common procedures like colonoscopy. After deciding to halt the execution, Missouri governor Jay Nixon told corrections officials to come up with a (...) different lethal injection protocol. But that was not a simple assignment. Missouri had proposed using propofol because officials had faced barriers to obtaining the drugs previously used for executions. Corrections officials in death penalty states are finding it harder to secure drugs for lethal injection. (shrink)

RésuméSelon K. Gödel, les restrictions méthodologiques des constructivistes sont aberrantes, et le point de vue réaliste est beaucoup plus fécond: il est hi‐même parvenu à ses résultats logiques fondarnentaux en donnant une place à la notion de vérite, qui n'est pas de type combinatoire. Le premier théorème d'incomplétude est hi‐même un argument décisif en faveur du réalisme, si l'on accepte le principe d'«accessibilité» en vertu duquel nous pouvons décider de toutes les propriétés de nos constructions intellectuelles. Par ailleurs, il existe (...) un large spectre d'arguments permettant de statuer sur un énoncé indécidable dans un système formel. La thèse mécaniste, selon laquelle l'intelligence humaine peut être pensée sans distorsion significative sur le modèle d'une machine de Turing, est donc inacceptable.SummaryAccording to K. Gödel, the methodological restrictions of the constructivists are aberrant, and the realist point of view is much more fruitful. He reached these fundamental logical results himself by making place for a non‐cornbinatorial notion of truth. The first incompletness theorem is itself a decisive argument in favor of realism, provided that the principle of «accessibility» is accepted, by virtue of which we are capable of determining all the properties of our intellectual constructions. Moreover, there are numerous arguments that permit the evaluation of an undecidable statement in a formal system. The mechanistic thesis, according to which the functioning of the human mind, without significant distorsion, can be compared to a Turing machine, is now unacceptable.ZusammenfassungNach Gödel sind die methodologischen Einschränkungen der Konstruktivisten irrig, und er hält den realistischen Standpuukt für viel fruchtbarer. Er selbst erreichte seine grundlegenden logischen Ergebnisse dadurch, dass er Platz machte für einen nichtkombinatorischen Begriff der Wahrheit. Das erste Unvollständigkeitstheorem ist selbst ein entscheidendes Argument zugunsten des Realismus, sofern das «Zugänglichkeitsprinzip» akzeptiert wird, wonach wir fähig sind, alle Eigenschaften unserer intellektuellen Konstruktionen zu bestinmen. Zudem gibt es zahlreiche Argumente, die die Beurteilung einer unentscheidbaren Aussage in einem formalen System erlauben. Die mechanistische These, nach welcher das Funktionieren des menschlichen Geistes ohne wesentliche Verzerrung mit einer Turingmaschine verglichen werden kann, ist heute nicht mehr annehmbar. (shrink)

We argue for teleology as a description of the way in which we ordinarily understand others’ intentional actions. Teleology starts from the close resemblance between the reasoning involved in understanding others’ actions and one’s own practical reasoning involved in deciding what to do. We carve out teleology’s distinctive features more sharply by comparing it to its three main competitors: theory theory, simulation theory, and rationality theory. The plausibility of teleology as our way of understanding others is underlined by developmental data (...) in its favour. (shrink)

The main purpose of this paper, which takes the form of an essay, is an attempt to answer the question of the limits of artificial intelligence (AI). In the introductory section, we present the key milestones in AI development, both historical and future projections, in which two terms – Artificial Human (AH) and Artificial ‘god’ (AG) – play a special role. In the second section, we clarify the question of the limits of AI by indicating the hypothetical goal of AI (...) development. The third section develops the argument proposed by C. F. Weizsäcker, originally formulated for cybernetics. The conclusion of this argument is optimistic about limitations to the possibilities of cybernetic simulations. We apply this argument to AI and subject it to a critique which ultimately undermines the legitimacy of its conclusion. We base the critique on two well-known results: the theorem of the unsolvability of the halting problem and Gödel’s first incompleteness theorem, and we formulate two objections interpreted without adopting Church’s thesis. In the crucial fourth section, we present a third objection in the form of a hypothesis for which we argue that AI (AH), understood as a subject, will always be solipsistic. (shrink)

: Autonomous driving systems promise important changes for future of transport, primarily through the reduction of road accidents. However, ethical concerns, in particular, two central issues, will be key to their successful development. First, situations of risk that involve inevitable harm to passengers and/or bystanders, in which some individuals must be sacrificed for the benefit of others. Secondly, and identification responsible parties and liabilities in the event of an accident. Our work addresses the first of these ethical problems. We are (...) interested in investigating how humans respond to critical situations and what reactions they consider to be morally right or at least preferable to others. Our experimental approach relies on the trolley dilemma and knowledge gained from previous research on this. More specifically, our main purpose was to test the difference between what human drivers actually decide to do in an emergency situations whilst driving a realistic simulator and the moral choices they make when they pause to consider what they would do in the same situation and to better understand why these choices may differs. Keywords: Self-driving Cars; Trolley Problem; Moral Choices; Moral Responsibility; Virtual Reality Dilemmi morali nelle automobili a guida autonoma Riassunto: I sistemi di guida autonomi promettono importanti cambiamenti per il futuro dei trasporti, principalmente attraverso la riduzione degli incidenti stradali. Tuttavia, vi sono preoccupazioni etiche, in particolare due questioni centrali, fondamentali per il loro sviluppo. In primo luogo, le situazioni di rischio che comportano inevitabili danni ai passeggeri e/o ai pedoni, ovvero situazioni in cui alcune persone devono essere sacrificate a beneficio di altri. In secondo luogo, l’identificazione delle parti responsabili in caso di incidente. Il nostro lavoro affronta il primo di questi problemi etici. Siamo interessati a studiare come gli umani rispondono a situazioni critiche e quali reazioni considerano moralmente giuste o almeno preferibili. Il nostro approccio sperimentale si basa sul trolley problem e sulle conoscenze acquisite da precedenti ricerche su questo ambito. Più specificamente, il nostro scopo principale è quello di testare la differenza tra ciò che i conducenti umani decidono effettivamente di fare in una situazione di emergenza, mentre guidano un simulatore realistico, e le scelte morali che compiono se posti nella stessa situazione e hanno la possibilità di decidere senza limiti di tempo. Lo scopo è inoltre comprendere come e perché queste scelte possono differire. Parole chiave: Automobili a guida autonoma; Trolley problem; Scelte morali; Responsabilità morale, Realtà virtuale. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Prelude to Tackling Contemporary Crises: William James and a Psychological Springboard to Political ChangePaul Croce (bio)“That selective industry of the mind,... incessantly deciding, among many things,... which ones for it shall be realities.”—William James, 1892 (PBC, 167)“[N]either the whole of truth, nor the whole of good, is revealed to any single observer.”—William James, 1899 (TT, 149)The modern world has witnessed tremendous increases in prosperity, and that material abundance has (...) spurred great achievements. But these successes have also brought enormous and troubling side effects. Climate change, biodiversity loss, social inequality, and more problems have grown into crises with potential to challenge the achievements themselves. Alongside these challenges, many outstanding proposals have also emerged for dealing with our present crises. The crises and the insights for addressing them are in a harrowing competition, reminiscent of what H. G. Wells called “a race between education and catastrophe.” During recent chapters of this contest, especially in the United States, sound suggestions for halting or reversing environmental deterioration and for reducing class and racial inequities have gained some public and political support but have also met considerable resistance.1 While direct work to [End Page 26] address the crises is important, those efforts can be supported with understanding of the people and ideologies resisting that work. In fact, neglect of these impediments, which can further enable them to reduce abilities or willingness to address problems or even notice them, may be the biggest crisis of all.Just as medication can directly heal an illness while rest and self-care can build up general strength to support recovery, so coping with crises calls for both grappling with them directly and also consideration of the impediments that reduce the strength of those steps toward social healing. The inquiry here serves as a complement to sound proposals for immediate action by diagnosing what has hindered their realization. Outcries against injustice and creative interventions address the acute conditions of current crises, while cultural assessments of ways those responses gain or lose attention serve as prescriptions for addressing the chronic conditions that have exacerbated the crises through distraction. As with medical issues, long-term and preventive care of chronic problems can support acute treatment, even as they do not displace the need for immediate action.This article confronts a puzzle about why so many people do not pay attention to such large problems in nature and society and what steps can be taken to bridge that divide between the committed and the distracted. The emphasis here on attention shifts focus away from ideological differences and toward the values selections that drive the ideological differences. This article portrays James’s own path as he learned from differences before explaining how his theories offer insights on how selective choices shape the assumptions supporting ideologies that so often form into hostile contrasts.2 In addition to these alerts about the challenges of disagreement, he also presents methods to encourage listening across differences for chances to turn some of those commitments into constructive possibilities rather than treating them as reasons [End Page 27] to fight. These ways to evaluate cultural and political debates and increase understanding about selective choices can shed light on how so many people have been unwilling or unable to pay attention to the mounting problems, and through encouragement of more listening with respect, these methods can encourage more support for addressing the crises themselves.I. Jamesian Ways to Listen Across DifferencesCharles Taylor calls William James (1842–1910) “our great philosopher of the cusp.” This brief, elegant expression depicts a borderland thinker adept at mediating contrasting ideas. James’s often-difficult experiences in development toward that way of thinking and that reputation provide more depth about the contrasts that he experienced on the way toward his creative syntheses in psychology and philosophy.3 His wrestling with different interpretations serves as a microcosm for the challenges and rewards of listening for potential insights on each side of even hostile contrasts. He designed deliberate ways to reckon with differences, considering each to be a partial yet valuable window into the human condition. In his youth, he was torn between the competing perspectives of religious thought... (shrink)

There are various ways to reach a group decision on a factual yes–no question. One way is to vote and decide what the majority votes for. This procedure receives some epistemological support from the Condorcet Jury Theorem. Alternatively, the group members may prefer to deliberate and will eventually reach a decision that everybody endorses—a consensus. While the latter procedure has the advantage that it makes everybody happy, it has the disadvantage that it is difficult to implement, especially for larger groups. (...) Besides, the resulting consensus may be far away from the truth. And so we ask: Is deliberation truth-conducive in the sense that majority voting is? To address this question, we construct a highly idealized model of a particular deliberation process, inspired by the movie Twelve Angry Men, and show that the answer is ‘yes’. Deliberation procedures can be truth-conducive just as the voting procedure is. We then explore, again on the basis of our model and using agent-based simulations, under which conditions it is better epistemically to deliberate than to vote. Our analysis shows that there are contexts in which deliberation is epistemically preferable and we will provide reasons for why this is so. (shrink)

Logic in Action/Doron Avital Nothing is more difficult, and therefore more precious, than to be able to decide (Napoleon Bonaparte) Introduction -/- This book was born on the battlefield and in nights of secretive special operations all around the Middle East, as well as in the corridors and lecture halls of Western Academia best schools. As a young boy, I was always mesmerized by stories of great men and women of action at fateful cross-roads of decision-making. Then, like as today, (...) I felt the full weight of the moment of truth as it confronts the individual, the man or woman of action, with the imminent necessity to decide. Alongside, as I was climbing up the ladder of education, I found myself just as well captivated by the great intellectual stories of our times, in particular 20th century analytic philosophy and, at its core, the machinery of modern logic. How do then the cool contemplative modes of the philosophical and analytic outlooks, that are better fitting of the philosopher's armchair at the fireplace, hang together with the heat of the battlefield or the angst of the ticking clock of time left to the completion of a daring special operation? Growing up I was pondering exactly that. Not accidently, and in fact as consequence, I have chosen a course in life that challenged me to visit the poles of both theory and practice. I set myself on a mission to unravel the tension between the contemplative inquiry, supposedly theoretical, aiming at the logical structure of things, and the uncompromising test of life and action. The puzzle of the gap between theory and practice has become ever since the guiding question of my life. -/- Not long ago, I met two friends, Avner Shor, a veteran combat soldier of the special forces unit I eventually commanded, and Aviram Halevi, a fellow officer with whom I served. Why will we not put into writing the ideas that guided us during our years of military action, we wondered. At that time, I used to deliver the keynote lectures to the senior officers' course of Israel central intelligence organization, the Mossad. For this I already had to put some of these ideas in writing. Avner was quick to introduce me with a notable publisher and even helped me write the first chapter. With Aviram I sat to many meetings, where he would challenge me with key questions, and we followed them with memories of operations and battles, aiming to draw the required lessons. This served me well when I finally sat down to write the first draft of the book. The result was more extensive than me and my friends had expected. I had to add a particularly long chapter dealing with the story of modern philosophy and logic. This was required, I felt, as no decision-making process lives in an intellectual vacuum. Knowingly or subconsciously, the intellectual climate of the time guides us for better or worse with the decisions we finally take. The initial draft was naturally cumbersome and inaccessible. But here I had the privilege of meeting a particularly talented editor, Rami Rothholtz. I found in Rami both an editor and a critical reader. As an infantry combat soldier at youth and now a senior journalist and editor, Rami insisted on simplifying and refining my ideas. Had it not been for his work, this book would have been literally unreadable. *** I opened my book with a brief description of a single night of a special operation deep at the Lebanon Bekaa valley, far away from Israel northern border. The mission was to kidnap a senior terror leader known to be holding in captivity an Israeli pilot. This was also the last special operation I commanded in my military career. A single special operation night, but what had to precede it? For sure, many months of intense and skillful preparations. What is Planning? This is the question with which I open up chapter (2) of the book. I confront in this chapter two approaches to planning. The first is the one I saw as a mission to myself to cultivate in my many years of military service. The second is the one I saw as representing a deep-rooted fallacy that holds a firm grip on today's conventional wisdom about planning. To further examine the logic of the competing models, I was required in chapter (3) to analyze the concept of "The Standard". I argue that the false model of planning has its roots in an attitude of an uncompromising adherence to the power of literal obedience to standards and rules. The standard, or what is outlined by a rule as prescribing a future course of action, is seen as an answer to the fundamental tension between theory (planning) and practice (execution). I argue in contrast that the standard does not produce an answer but rather what I call: "A Well-Defined Question". In essence, it is a meticulously-well-planned invitation to exercise a fresh judgment. A judgement that has as an anchor the default answer that the standard produces but is open to extension as it confronts the new frame of reference of the test of reality. In chapter (4), I present a new tool for planning and execution: "The Polygon of Risks" or "The Polygon of Execution". The Polygon is a geometric illustration of the underlying tension that exists between all dimensions of the operational project. The construction and conceptualization of the trade-offs that exist between the various dimensions - segments of the polygon - is the first topic on the planner's agenda. I position the concepts of "Daring" and "Taking Proactive and Well-Informed Risks" as necessary logical constituents of the polygon and show how in contrast the false model of planning is responsible for an operational culture that is risk-averse. It encourages, in fact, the piling up of false securities at the segments' level that eventually lead to the collapse of the polygon. The necessary trade-offs relationships that exist between the segments of the polygon express the fundamental tension between partnership and competition: partnership in a joint goal and competition over resources, both material and abstract. When this tension is not managed well, that is, when the players' local optimizations overshadow the global optimization required for the success of the project, the execution polygon collapses. In this scenario, we may find the setting of the bar of "High Standards" in a players' spheres of responsibility to conceal a hidden agenda of personal insurances taken against a possible failure. Once the overall risk is not mitigated by way of collaborative joint executional dialogue, the process that leads to a collapse of the polygon is literally unstoppable. *** In chapter (5), I discuss "(Fateful) Decisions". I examine the way in which we should translate the polygon into sequential critical decisions on the timeline. The execution polygon is not a rigid scaffolding but a dynamic conceptual illustration of the -/- project. It will need now to be converted into successive decision junctions. We will find the content of a decision and its timing on the timeline to be inseparable. The right decision is the one that is taken at the right time. The moment of decision is in fact the last moment of deliberation, the first moment available for action, i.e. the first possible "Can" is also the latest possible "Must". Deciding too soon is analog to the "Jumping of the Gun". The decision maker is forcing a pre-conceived answer to a state of affairs not ripe for an answer, e.g. the target in the shooting range is not yet erected. Late to decide and the decision maker may envision what he or she should have done but reality is no longer available for them to harness it right, e.g. consider a tennis player's frustration when reviewing a too-late-to-react move in the video replay. I review in this chapter many fateful decisions, both historical, from Napoleon's Waterloo, to a Bridge Too Far of WWII, to the failed rescue attempt of American hostages at the time of the Iranian Revolution, as well as fateful decisions I had to take in the course of my military life, both in combat and in special operations, and show the sense in which they all answer to our analysis. The theme of chapter (6) is "The Moment of Truth". This is the moment when everything is on the line and from which there is no turning back. I discuss the formative repetitive structure of the schooling and simulation phase and contrast it with the "One Shot, One Opportunity" nature of the moment of truth. This is extremely helpful when we analyze the logical structure of failures as unwarranted repetitions of past lessons. The schooling curriculum indeed consists of important abstractions drawn from lessons of the past. However, it is when we project them in a fashion that is literal or mechanical that we cross path with the possibility of a failure. The paradox of education is that what we must repeat in school and simulation must be extended and not repeated in real life. What is required of us so we do not fall into the fallacy of repetition in face of the moment of truth is the core subject of the discussion of this chapter. In chapter (7), I took a lengthy philosophical detour surveying the intellectual drama of modern logic, and in general, the story of 20th century analytic philosophy. Readers who choose to bypass the somehow demanding narrative of this drama can do so and still keep the argumentative thread of the book. However, even by way of skipping the more technical parts, I would still urge the readers to delve into the discussion in this chapter as I believe this would grant them a deeper understanding of the overall conceptual framework. I explore here the work of two key figures: the logician Kurt Gödel and the philosopher Ludwig Wittgenstein, both were crowned in 2000 by TIME Magazine, as the leading Logician and Philosopher, respectively, of the 20th Century. I review the fascinating logical result of Gödel's Incompleteness Theorem and examine its relevance as setting a theoretical limit to the power of formalization. This amazing logical result - a result that shakes the logical foundations of 20th century thought in as much as the discovery of irrational numbers shook the foundations of the Pythagorean program of the ancient Greeks - bears significantly on the question of action and the blind trust we place in the power of formalization in the form of protocols and rules. It is here that Wittgenstein's philosophy enters in full force. We follow Wittgenstein as he dismantles our conception of rules as if there were "Railroads to Infinite", i.e. as prescribing for us in-advance their proper employments in all possible -/- future eventualities. Instead we propose that the dilemma of action demands of us an extension of rules rather than a mechanical or blind repetition of their literal imperative. In turn, this extension can serve as a new lesson added to the curriculum of school and simulation. The theme of chapter (8), the concluding chapter, is Strategy, Logic, and Ethics. The chapter comes to place the ethical dilemma in the conceptual map we presented in the book. I discuss here the tension between strategy as a process of setting goals and deriving backward as it were the steps that are necessary for achieving these goals, to the inescapable dictation of the ethical imperative. This unavoidable tension is particularly important against the backdrop of contemporary culture that is guided by a vision of personal success and achievement that may threaten our ability to do what is right. Most of all, I am troubled in this chapter, with the role logic may play, first as a liberating force enabling a change that is tuned to the ethical imperative, and second, as a force designed to justify on logical grounds, as it were, the existing power structure. It is in this junction that brave individuals will be called to challenge the governing logic of the zeitgeist - logic that operates now as an oppressive force that serves the vested interest of beneficials of the existing order. When success is favored over doing what is right, as we must admit is the prevailing cultural mood of our times, that the words of Emanuel Kant carry their full weight: "Do the Right thing and leave the Consequences to God". For this we need heroes and heroines that challenge the time by bearing the full weight of responsibility that comes with the doing of what is Right. *** This book was written more than anything from the perspective of the heroes and heroines of action. Sometimes they may be missing the exact words or the full insight into the solid logical complexity that stands between them and the doing of what is right. They feel what is right to do on the battlefield of life, whether in real battle, in political or economic life or whether in the life of creativity and the quest of the intellect. They do need, in analogy, proper logical and intellectual artillery. I hope they will find the logical cannons they require as they travel through the pages of this book. The rest is in their hands at the Moment of Truth. -/- Doron Avital, Tel Aviv 2011 -/- . (shrink)

We investigate the question of whether one can characterize complexity classes in terms of efficient reducibility to the set of Kolmogorov-random strings . This question arises because and , and no larger complexity classes are known to be reducible to in this way. We show that this question cannot be posed without explicitly dealing with issues raised by the choice of universal machine in the definition of Kolmogorov complexity. What follows is a list of some of our main results.• Although (...) Kummer showed that, for every universal machine U there is a time bound t such that the halting problem is disjunctive truth-table reducible to in time t, there is no such time bound t that suffices for every universal machine U. We also show that, for some machines U, the disjunctive reduction can be computed in as little as doubly-exponential time.• Although for every universal machine U, there are very complex sets that are -reducible to , it is nonetheless true that . • Any decidable set that is polynomial-time monotone-truth-table reducible to is in .• Any decidable set that is polynomial-time truth-table reducible to via a reduction that asks at most f queries on inputs of size n lies in. (shrink)

ABSTRACT According to Lyman Tower Sargent, utopias are repositories for individual and collective hopes and fears, which sometimes unleash energies that can achieve at least part of what is hoped for. The Australian green bans movement of 1971–75 can be understood as a utopian project in this sense. During this period, the construction workers organized in the New South Wales branch of a labor union, known as the Builders Labourers' Federation, refused to work on ecologically or socially harmful projects and (...) publicly argued for their collective right to socially responsible labor. Coining the term “green bans” to describe environmentally motivated withdrawals of labor, they halted projects worth five billion Australian dollars at 1970s prices. When enthusiastic resident action groups mobilized in support of these bans, the union grew into the core of a more general social movement. The success of the green bans movement suggests that the power of subversive imagining can be especially effective if coupled with the power of workers at the point of production. The movement's basic premise—that workers, acting in the general public interest, should decide what can be built and where—represented a direct challenge to the dominant power relations. Ultimately, such impossible demands could not be conceded either by the employers or by the state. But the practical effects of this utopianism nonetheless secured substantial environmental improvements, which brought the green bans activists significantly closer to their dreams. (shrink)

Recent empirical evidence indicates that people tend to believe that they possess indeterminist free will, and people’s experience of choosing and deciding is that they possess such freedom. Some also maintain that people’s belief in indeterminist free will has its source in their experience of choosing and deciding. Yet there seem to be good reasons to resist endorsing. Despite this, I maintain that belief in indeterminist free will really does have its source in experience. I explain how this is so (...) by appeal to the phenomenon of prospection, which is the mental simulation of future possibilities for the purpose of guiding action. Crucially, prospection can be experienced. And because of the way in which prospection models choice, it is easy for agents to experience and to believe that their choice is indeterministic. Yet this belief is not justified; the experience of prospection, and hence of free will as being indeterminist, is actually consistent with determinism. (shrink)

Two key research issues in the field of causal learning are how people acquire causal knowledge when observing data that are presented sequentially, and the level of abstraction at which learning takes place. Does sequential causal learning solely involve the acquisition of specific cause-effect links, or do learners also acquire knowledge about abstract causal constraints? Recent empirical studies have revealed that experience with one set of causal cues can dramatically alter subsequent learning and performance with entirely different cues, suggesting that (...) learning involves abstract transfer, and such transfer effects involve sequential presentation of distinct sets of causal cues. It has been demonstrated that pre-training can modulate classic causal learning phenomena such as forward and backward blocking. To account for these effects, we propose a Bayesian theory of sequential causal learning. The theory assumes that humans are able to consider and use several alternative causal generative models, each instantiating a different causal integration rule. Model selection is used to decide which integration rule to use in a given learning environment in order to infer causal knowledge from sequential data. Detailed computer simulations demonstrate that humans rely on the abstract characteristics of outcome variables to select a causal integration rule, which in turn alters causal learning in a variety of blocking and overshadowing paradigms. When the nature of the outcome variable is ambiguous, humans select the model that yields the best fit with the recent environment, and then apply it to subsequent learning tasks. Based on sequential patterns of cue-outcome co-occurrence, the theory can account for a range of phenomena in sequential causal learning, including various blocking effects, primacy effects in some experimental conditions, and apparently abstract transfer of causal knowledge. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:The National Commission on AIDSDonald S. Goldman (bio) and Jeff Stryker (bio)A decade after the first cases were recognized in the United States, AIDS continues to vex policymakers and fascinate the public. It has been said that AIDS acts as a prism, refracting a spectrum of controversial topics. For bioethicists, these topics include: equity in the allocation of resources for treatment and research; forgoing life-sustaining care and proxy decision (...) making; informed consent in the context of HIV testing and screening; the ethical duties of health care workers to provide care for persons with HIV disease; and competing obligations of health care professionals to patients and to third parties who may be put at risk.The Role of CommissionsIf AIDS is the quintessential case study for bioethicists, it is a potential quagmire for politicians. The association of HIV disease with drug use and sexual behavior makes it a topic that all but the most courageous (or the most homophobic) politicians shy away from. A frequent political response is to form a commission.Alexander Capron, who was executive director of the President's Commission for the Study of Ethical Problems in Medicine, has described some roles commissions play: a watchdog, overseeing the work of particular government agencies; a crucible, providing a means for "publicly hammering out conclusions on controversial issues when consensus, both in the public and in the relevant disciplines, is not yet apparent"; and "a lightning rod for public concern—or viewed less charitably, dumping ground for an issue that is too difficult for the ordinary political process to handle" (Capron 1983, p. 9).Nearly every state has created a gubernatorial-level task force or commission on AIDS. The National Commission on AIDS was established under the Health Omnibus Program Extension (HOPE) Act of 1988, which was signed by President Reagan on November 4, 1988. The official charter of the commission was approved August 2, 1989 and its original two-year term was extended for a third year. The mission statement crafted by the commission to reflect its Congressional mandate reads: [End Page 339]The National Commission on Acquired Immune Deficiency Syndrome is an independent body of 15 members created to advise the President and Congress. The Commission seeks to build a broad public understanding on the magnitude, scope and urgency of the HIV/AIDS epidemic; provide and inspire leadership at all levels of both the public and private sectors; empower individuals and communities; and advocate for effective, cooperative and non-discriminatory resources required for prevention, comprehensive care, and the research necessary to halt the epidemic.As the mission statement implies, the National Commission on AIDS has viewed itself from the outset not only as a crucible for policy analysis, but also as a forum for those affected by HIV disease. In site visits and hearings the commissioners have met with hundreds of people living with HIV disease, and with caregivers on the front lines. This odyssey has taken the commission on visits to homeless shelters in New York City; to "shooting galleries" where intravenous drug users congregate in Seattle; to Native American communities in four states; to private homes in rural Georgia; and to hospitals, HIV antibody testing centers, drug treatment clinics, and hemophilia treatment centers throughout the nation. It quickly became clear during the commission's travels that HIV disease cannot be understood outside the context of the racism, homophobia, poverty and unemployment that provide the medium that fosters its spread. It also became apparent that issues of HIV prevention, care and treatment, and clinical research are inextricably intertwined and must be dealt with as such.Early InitiativesUnder the leadership of Chairperson June Osborn and Vice-chairperson David Rogers, the commission decided that the problems it saw in its first few meetings were too urgent to await a full-length annual report. Hence the commission entered the fray with a series of brief interim reports on particular aspects of AIDS. These reports enabled the commission to draw attention to urgent problems of limitations in access to health care and to underscore the plight of people with HIV disease who might otherwise garner little media attention, such as prisoners and drug users (National Commission... (shrink)