In this paper, a number of traditional models related to the percolation theory has been considered by means of new computational methodology that does not use Cantor’s ideas and describes infinite and infinitesimal numbers in accordance with the principle ‘The part is less than the whole’. It gives a possibility to work with finite, infinite, and infinitesimal quantities numerically by using a new kind of a compute - the Infinity Computer – introduced recently in [18]. The new approach does not (...) contradict Cantor. In contrast, it can be viewed as an evolution of his deep ideas regarding the existence of different infinite numbers in a more applied way. Site percolation and gradient percolation have been studied by applying the new computational tools. It has been established that in an infinite system the phase transition point is not really a point as with respect of traditional approach. In light of new arithmetic it appears as a critical interval, rather than a critical point. Depending on “microscope” we use this interval could be regarded as finite, infinite and infinitesimal short interval. Using new approach we observed that in vicinity of percolation threshold we have many different infinite clusters instead of one infinite cluster that appears in traditional consideration. (shrink)

Dmitri Nikulin extends his earlier study of oral dialogue (On Dialogue [Lexington, 2006]) to an investigation of dialectic, moving from a narrative of its development in Plato and the history of philosophy (ch.s 1-3) through a renewed phenomenological account of oral dialogue (ch.s 4-5) to a critique, from the perspective of oral dialogue, of the limitations of written dialectic (ch. 6). I take up some of the provocations of his bold and open-ended argument. Does his own “writing against writing” (...) constitute a performative contradiction, and if so, does this attest his critique of the limitations of dialectic or exhibit, in the elicitative force of its irony, the transcending of these limitations? How, if at all, may we reconcile Nikulin’s radical claim that oral dialogue is the very mode of being human with the drive of the turn to written dialectic to understand being itself and its relation to being human? Just insofar as the virtues distinctive of written dialectic — above all, precision, systematic elaboration, and universality — move the philosopher to suspend oral dialogue in its essential attention to a particular other and to the “who” that one emerges as for this other, may this very suspension also constitute a phase within ongoing oral dialogue? Are the last words of the “(Dialectical) Conclusion” with which Nikulin paradoxically closes his critique of dialectic really just the opening words of a conversation that the attentive reader’s very being will move him to pursue? (shrink)

Dmitri Nikulin extends his earlier study of oral dialogue (On Dialogue [Lexington, 2006]) to an investigation of dialectic, moving from a narrative of its development in Plato and the history of philosophy (ch.s 1-3) through a renewed phenomenological account of oral dialogue (ch.s 4-5) to a critique, from the perspective of oral dialogue, of the limitations of written dialectic (ch. 6). I take up some of the provocations of his bold and open-ended argument. Does his own “writing against writing” (...) constitute a performative contradiction, and if so, does this attest his critique of the limitations of dialectic or exhibit, in the elicitative force of its irony, the transcending of these limitations? How, if at all, may we reconcile Nikulin’s radical claim that oral dialogue is the very mode of being human with the drive of the turn to written dialectic to understand being itself and its relation to being human? Just insofar as the virtues distinctive of written dialectic — above all, precision, systematic elaboration, and universality — move the philosopher to suspend oral dialogue in its essential attention to a particular other and to the “who” that one emerges as for this other, may this very suspension also constitute a phase within ongoing oral dialogue? Are the last words of the “(Dialectical) Conclusion” with which Nikulin paradoxically closes his critique of dialectic really just the opening words of a conversation that the attentive reader’s very being moves him to pursue? (shrink)

I present a decision problem in which orthodox causal decision theory appears to violate weak versions of the independence of irrelevant alternatives (IIA) and normal-form extensive-form equivalence (NEE). I show that these violations lead to exploitable behavior and long-run poverty. These consequences appear damning, but I urge caution. Causalists can dispute the charge that they violate IIA and NEE in this case by carefully specifying when two options in different decision problems are similar enough to be counted as the same.

A one-boxer, Erica, and a two-boxer, Chloe, engage in a familiar debate. The debate begins with Erica asking Chloe: ‘If you’re so smart, then why ain’cha rich?’. As the debate progresses, each gets clearer about what connection they see between rational choice and long run riches. Erica says: long run riches give evidence about rationality, so long as the long run is one on which you face the same choice, and choose the same way, over and over again. Chloe objects (...) that Erica unfairly compares the long run riches of people who were afforded different opportunities. As Erica pushes Chloe to get clearer about which comparison is fair, Chloe rehearses familiar formulations of causal decision theory. She is eventually driven to reject them all, and instead endorse a novel version of causal decision theory. This new theory allows Chloe to forge a connection between rational choice and long run riches. In brief: Chloe concludes that it is not long run wealth but rather long run wealth creation which is symptomatic of rationality. (shrink)

Есть исследователи, проблематика работ и теории которых остаются актуальными длительное время и после их смерти. К числу таких, несом- ненно, относится и Николай Дмитриевич Кондратьев – замечательный российский экономист, один из тех, чье имя довольно широко известно и за рубежом. И актуальность его идей тем более важно отметить в ознаме-нование 125-летнего юбилея Н. Д. Кондратьева, который мы отпраздновали в прошлом 2017 году. Именно этой теме – связи творчества Кондратьева и проблем современной экономики и экономической науки – и посвящены многие статьи (...) данного выпуска ежегодника. Биографии и отдельным аспектам творчества ученого отведены статьи первого раздела. Тем не менее нельзя не сказать хотя бы немного об этой личности и во Введении. (shrink)

A handful of well-known arguments (the 'diachronic Dutch book arguments') rely upon theorems establishing that, in certain circumstances, you are immune from sure monetary loss (you are not 'diachronically Dutch bookable') if and only if you adopt the strategy of conditionalizing (or Jeffrey conditionalizing) on whatever evidence you happen to receive. These theorems require non-trivial assumptions about which evidence you might acquire---in the case of conditionalization, the assumption is that, if you might learn that e, then it is not the (...) case that you might learn something else that is consistent with e. These assumptions may not be relaxed. When they are, not only will non-(Jeffrey) conditionalizers be immune from diachronic Dutch bookability, but (Jeffrey) conditionalizers will themselves be diachronically Dutch bookable. I argue: 1) that there are epistemic situations in which these assumptions are violated; 2) that this reveals a conflict between the premise that susceptibility to sure monetary loss is irrational, on the one hand, and the view that rational belief revision is a function of your prior beliefs and the acquired evidence alone, on the other; and 3) that this inconsistency demonstrates that diachronic Dutch book arguments for (Jeffrey) conditionalization are invalid. (shrink)

Weisberg ([2009]) provides an argument that neither conditionalization nor Jeffrey conditionalization is capable of accommodating the holist’s claim that beliefs acquired directly from experience can suffer undercutting defeat. I diagnose this failure as stemming from the fact that neither conditionalization nor Jeffrey conditionalization give any advice about how to rationally respond to theory-dependent evidence, and I propose a novel updating procedure that does tell us how to respond to evidence like this. This holistic updating rule yields conditionalization as a special (...) case in which our evidence is entirely theory independent. 1 Introduction2 Conditionalization3 Holism and Conditionalization4 A Holistic Update5 HCondi and Dutch Books6 Commutativity and Learning about Background Theories6.1 Commutativity6.2 Learning about background theories7 In Summation. (shrink)

I present an account of deterministic chance which builds upon the physico-mathematical approach to theorizing about deterministic chance known as 'the method of arbitrary functions'. This approach promisingly yields deterministic probabilities which align with what we take the chances to be---it tells us that there is approximately a 1/2 probability of a spun roulette wheel stopping on black, and approximately a 1/2 probability of a flipped coin landing heads up---but it requires some probabilistic materials to work with. I contend that (...) the right probabilistic materials are found in reasonable initial credence distributions. I note that, with some normative assumptions, the resulting account entails that deterministic chances obey a variant of Lewis's 'principal principle'. I additionally argue that deterministic chances, so understood, are capable of explaining long-run frequencies. (shrink)

The externalist says that your evidence could fail to tell you what evidence you do or not do have. In that case, it could be rational for you to be uncertain about what your evidence is. This is a kind of uncertainty which orthodox Bayesian epistemology has difficulty modeling. For, if externalism is correct, then the orthodox Bayesian learning norms of conditionalization and reflection are inconsistent with each other. I recommend that an externalist Bayesian reject conditionalization. In its stead, I (...) provide a new theory of rational learning for the externalist. I defend this theory by arguing that its advice will be followed by anyone whose learning dispositions maximize expected accuracy. I then explore some of this theory’s consequences for the rationality of epistemic akrasia, peer disagreement, undercutting defeat, and uncertain evidence. (shrink)

I provide a theory of causation formulated within the causal modeling framework. In contrast to its predecessors, this theory is model-invariant in the following sense: if the theory says that C caused (didn't cause) E in a causal model, M, then it will continue to say that C caused (didn't cause) E once we've removed an inessential variable from M. I suggest that, if this theory is true, then we should understand a cause as something which transmits deviant or non-inertial (...) behavior to its effect. (shrink)

Accuracy-first accounts of rational learning attempt to vindicate the intuitive idea that, while rationally-formed belief need not be true, it is nevertheless likely to be true. To this end, they attempt to show that the Bayesian's rational learning norms are a consequence of the rational pursuit of accuracy. Existing accounts fall short of this goal, for they presuppose evidential norms which are not and cannot be vindicated in terms of the single-minded pursuit of accuracy. I propose an alternative account, according (...) to which learning experiences rationalize changes in the way you value accuracy, which in turn rationalize changes in belief. I show that this account is capable of vindicating the Bayesian's rational learning norms in terms of the single-minded pursuit of accuracy, so long as accuracy is rationally valued. (shrink)

Several philosophers have embraced the view that high-level events—events like Zimbabwe's monetary policy and its hyper-inflation—are causally related if their corresponding low-level, fundamental physical events are causally related. I dub the view which denies this without denying that high-level events are ever causally related causal emergentism. Several extant philosophical theories of causality entail causal emergentism, while others are inconsistent with the thesis. I illustrate this with David Lewis's two theories of causation, one of which entails causal emergentism, the other of (...) which entails its negation. I then argue for causal emergentism on the grounds that it provides the only adequate means of squaring the apparent plenitude of causal relations between low-level events with the apparent scarcity of causal relations between high-level events. This tension between the apparent abundance of low-level causation and the apparent scarcity of high-level causation has been noted before. However, it has been thought that various theses about the semantics or the pragmatics of causal claims could be used to ameliorate the tension without going in for causal emergentism. I argue that none of the suggested semantic or pragmatic strategies meet with success, and recommend emergentist theories of causality in their stead. As Lewis's 1973 account illustrates, causal emergentism is consistent with the thesis that all facts reduce to microphysical facts. (shrink)

While structural equations modeling is increasingly used in philosophical theorizing about causation, it remains unclear what it takes for a particular structural equations model to be correct. To the extent that this issue has been addressed, the consensus appears to be that it takes a certain family of causal counterfactuals being true. I argue that this account faces difficulties in securing the independent manipulability of the structural determination relations represented in a correct structural equations model. I then offer an alternate (...) understanding of structural determination, and I demonstrate that this theory guarantees that structural determination relations are independently manipulable. The account provides a straightforward way of understanding hypothetical interventions, as well as a criterion for distinguishing hypothetical changes in the values of variables which constitute interventions from those which do not. It additionally affords a semantics for causal counterfactual conditionals which is able to yield a clean solution to a problem case for the standard ‘closest possible world’ semantics. (shrink)