In this paper, the problem of compatibility between the two parts of the poem by Parmenides of Elea is addressed. This is done on the basis of a number of fragments from the poem – B 8, 9, 12, 16 and others – and a study of their ancient testimonia. In this way, the Parmenidean conception of the world and of human perceptive and gnoseological activity within it is reconstructed. Furthermore, starting from textual clues that show a certain need to (...) go beyond this view of the world, an attempt has been made to argue how τὸ ἐόν can be understood as the All, i.e. as the universe, but seen in its unity. In order to do so, a tempative answer was proposed, using the philosophical category of limit, to recent aporias raised by interpreters. (shrink)

Sequential Time Theory (STT) defines time as a metrological quantity realized by operational procedures (record, count, resolution), distinct from the coordinate time parameter in spacetime geometry. Starting from the primitive definition Δτ(n)=n k ΔQ_unit, STT internalizes time metrology (L2) and treats spacetime geometry (L1) as a representation of protocol constraints, rendering block-universe interpretations optional rather than required for physical derivations. Physics is reframed as STT-Core + Bridge axioms + Θ_sys, where Θ_sys is an explicit, auditable bundle of system-specific auxiliary assumptions. (...) Within this scheme, SR and GR kinematics arise as representation theorems for defect-free and defect-bearing clock networks; GR curvature is interpreted as a measurable holonomy defect density. Quantum interference is treated as U(1) phase holonomy in sequential update, and a Gaussian diffusion kernel is derived from minimal sequentiality assumptions. The framework is used to compare candidate quantum-gravity routes via Θ-auditing. (shrink)

In this paper I propose a reconstruction of the onto-cosmological perspective of Plato’s Timaeus and suggest an interpretation of it in the light of some contemporary approaches to ontology and logic, i.e. “ontological sequentialism” and “fuzzy logic”, attempting to use the categories and language of present-day ontology and logic to examine from a different point of view some aspects of the Timaeus onto-cosmology and of its logical scaffolding.

Sequential Time Theory (STT) is developed as a metrological reconstruction of physical time grounded in the operational act of counting distinguishable events. The theory argues that time is not an ontological dimension but a constructed variable derived from event generation. This framework dissolves long-standing paradoxes concerning the Arrow of Time, the reversibility of physical laws, and the Block Universe by distinguishing the logical sequential index from physical state evolution. STT interprets relativistic time dilation as a delay in event completion and (...) quantum measurement as the generator of temporal advancement. The resulting theory offers a parsimonious alternative to entropy-based, cosmological, or multiverse explanations of temporal asymmetry. (shrink)

This monograph presents Sequential Time Theory (STT), an operational reconstruction of physical time based on the counting of discrete, distinguishable events. The framework resolves classical paradoxes surrounding the arrow of time, relativistic time dilation, and quantum measurement by treating time as a constructed variable rather than an ontological dimension. STT argues that irreversibility arises logically from event accumulation, that relativistic effects reflect delays in event generation, and that quantum collapse represents the registration of discrete physical changes. The theory offers a (...) parsimonious alternative to entropy-based, cosmological, and multiverse explanations of temporal asymmetry. (shrink)

The standard cosmological model (Lambda-CDM) postulates the existence of Dark Energy to explain the accelerating expansion of the universe. While statistically robust, the model lacks a fundamental physical origin for this energy and faces the persistent "Hubble Tension." -/- This paper applies Sequential Time Theory (STT) to cosmology, proposing a paradigm shift where the physical unit of time is not invariant but evolves due to the changing cosmic gravitational potential and quantum coherence scales. We construct a unified model integrating General (...) Relativistic time dilation with a Quantum Damping term derived from STT Vol.2. This model was tested against the full Pantheon+ Unbinned Supernovae dataset (N=1590), utilizing the full covariance matrix including systematic errors. -/- The results reveal that the STT model achieves a goodness-of-fit (chi-squared = 1402.71) that is statistically indistinguishable from the standard Lambda-CDM model (chi-squared = 1402.92) using SNe alone. Significantly, the derived quantum transition scale z_dec = 1.50 (+0.42 / -0.33) is consistent with the peak epoch of cosmic star formation. This suggests that "cosmic acceleration" could be reinterpreted as an illusion caused by the phase transition of time from a quantum-coherent regime to a gravity-dominated classical regime, potentially offering an alternative to the standard Dark Energy hypothesis. (shrink)

Sequential Time Theory (STT) provides a metrological foundation for physics, defining time through operational procedures rather than as a geometric coordinate. STT CR (Metrological Completion of Relativity) established a formal framework: Physics = (STT-Core -> Bridge -> L1) -> Θ_sys Physical Systems, where L1 is the formal language of dynamics, L2 (STT-Core) is the operational definition of time, and Θ_sys is the mapping rule to specific physical systems. This paper applies this framework to audit the Standard Model (Θ_SM), focusing on (...) the Higgs mechanism. -/- We propose that mass is not a primitive quantity but is defined through the time unit process: m = h * (c^2 * ΔQ_unit)^-1. From Bridge axiom B4 (local calibration consistency), we derive that mass must be determined by a spatially uniform Lorentz-scalar quantity. From metrological constraints on ΔQ_unit -- positivity (C1), finiteness (C2), and statistical reproducibility (C3) -- together with an explicit minimality assumption (Θ_minimal), we derive the form of the Higgs potential V(φ) = -μ^2 |φ|^2 + λ |φ|^4, where the derivation is conditional on the stated assumptions. -/- We show that, for UV-complete fundamental descriptions, renormalizability is a metrological necessity: otherwise the operational distribution of clock-ticks becomes resolution-dependent in a way that cannot be removed by finitely many calibrations (violating C3 and B4). Effective-field descriptions can still satisfy C3 within a finite resolution window. -/- Finally, we present a testable prediction distinguishing STT from standard quantum mechanics: intrinsic clock fluctuations scale as σ_Q ∝ m^-2, predicting the ratio σ_Q(e) : σ_Q(μ) ≈ m_μ : m_e ≈ 207 for electrons versus muons. (shrink)

Bell-type experiments confront us with a threefold demand: any satisfactory account must preserve Bell-inequality violation, operational no-signalling, and consistency with relativistic causal structure. Standard discussions often treat this situation as if it required a physically meaningful transit time for a collapse-like influence between spacelike separated measurement events. In this paper, I argue that this presupposition is false. -/- Working within Sequential Time Theory (STT), I formulate admissibility conditions for temporal variables in Bell configurations and prove that no state-independent and foliation-independent (...) calibration map exists that could define a physical collapse-transit time between spacelike separated local record-completion events. The quantity required to define a collapse speed is therefore not extremely small; it is non-constructible. -/- To establish this result, I reconstruct a Bell experiment as a partially ordered record structure consisting of source events, local record events at each wing, and later comparison events. Local measurements are represented by compatible instruments on admissible hypersurface descriptions. I then show that Bell-inequality violation and operational no-signalling remain fully intact without any admissible collapse-transit variable. -/- What is eliminated is not the empirical Bell phenomenon, but only the pseudo-variable that would redescribe a correlation structure as though it were a directed transport process between the two wings. The resulting claim is narrower than a complete relativistic theory of quantum measurement, but stronger than a merely interpretive remark. The paper yields a theorem-level boundary condition on future measurement theory: any successful extension may model local detector dynamics, irreversible amplification, delayed recording, or moving-frame configurations, but it must not reintroduce a state-independent and foliation-independent collapse-transit time between spacelike separated local record-completion events. In STT terms, Bell nonlocality does not force superluminal propagation; it forces the abandonment of an inadmissible temporal variable. (shrink)

This paper does not challenge the observational fact of LIGO’s gravitational-wave detections. Instead, it examines a maximal interpretation often associated with those detections: that LIGO strongly supports the physical reality of spacetime and thereby naturally motivates a four-dimensional ontology. Using the audit vocabulary of STT-CR, the paper reformulates the LIGO case in terms of the relation among observable output OOO, measurement protocols PPP, calibration structure CCC, and theoretical variables Θsys\Theta_{\mathrm{sys}}Θsys. Within STT-CR, explanatory accountability is carried by the map (Θsys,P,C)→O(\Theta_{\mathrm{sys}},P,C)\to O(Θsys,P,C)→O, (...) while elements that do not participate in this map are treated as OverΘ\ThetaΘ. The paper shows that both general relativity and Sequential Time Theory can, at the level of the LIGO observational core, be cast as isomorphic observation maps. On the STT side, time is defined as an accumulation of local state-transitions, allowing the interferometric phase difference to be reconstructed without assuming that a four-dimensional spacetime ontology is observationally mandatory. The conclusion is limited but precise: LIGO strongly supports the predictive core of general relativity, yet LIGO data alone do not uniquely force a block-universe interpretation. (shrink)

This paper extends the temporal concept of Sequential Time Theory (STT) to the problem of metrology in the quantum domain. In STT, a time interval Δt is constructed by a counter n representing the number of realizations of a standard displacement ΔQ_unit, while time t serves as a coordinate label assigned to this sequence. STT explicitly posits that "time is a scaling of physical change" and that "time is constructed solely by clock phenomena subject to the same conditions within a (...) local system." Consequently, in regimes where ΔQ is indistinguishable, time does not "cease to exist" but becomes "unconstructible (undefined)." Based on these definitions and axioms, this paper (i) organizes criteria for distinguishing between science and metaphysics, (ii) identifies conceptual confusions arising from the implicit assumption of an external classical clock in quantum theory, and (iii) proposes a relativity principle regarding differences in observation scale (e.g., macroscopic observation of microscopic systems). We demonstrate that issues such as measurement, classicality, and tunneling time can be unifiedly organized as problems of "choice of clock (ΔQ)" and "recording (event-token) protocols.". (shrink)

This article develops a constructive theological account of sequential knowledge as a valid mode of Christian revelation by bringing African numerological traditions into dialogue with Valentinian Christianity. Focusing on Alexandria as an African center of Christian thought within the Greater Middle East, the study argues that both traditions share an understanding of revelation as ordered, knowledge as formative, and salvation as a process that unfolds through stages rather than as a single act of belief. The work does not claim historical (...) transmission or direct influence between African numerological systems and Valentinian theology. Instead, it employs a comparative theological approach that examines how each tradition answers similar questions about how divine truth is known and how human beings are shaped by that knowledge. African numerological traditions are treated as structured ways of knowing in which number communicates divine order, learning requires moral preparation, and access to deeper truth depends on initiation and growth. When read alongside these traditions, Valentinianism appears not simply as a rejected movement but as an African Christian attempt to express salvation through order, pattern, and graded instruction within the Alexandrian school. The article places these findings within the history of African Christianity, paying attention to theological schools, debates over heresy, and the formation of Christian communities. It also addresses present concerns, including rapid growth, mission, theological education, and relations between different Christian groups. The study concludes by proposing a Christian theology of sacred sequence that supports deeper formation and sustained faith amid expanding and diverse Christian contexts. Keywords: African Christianity, African theology, theological epistemology, sequential knowledge, Valentinianism, Alexandria, heresy in Africa. (shrink)

According to T. M. Scanlon’s anti-aggregation principle, it is wrong to save a larger number of people from minor harms rather than a smaller number from much more serious harms. This principle is a central part of many influential and anti-utilitarian ethical theories. According to the sequential-dominance principle, one does something wrong if one knowingly performs a sequence of acts whose outcome would be worse for everyone than the outcome of an alternative sequence of acts. The intuitive appeal of the (...) sequential-dominance principle should be obvious; everyone is knowingly made worse off if it is violated. In this paper, I present a number of cases where one is forced to violate either the anti-aggregation principle or the sequential-dominance principle. I show that these principles conflict regardless of whether one accepts a counterfactual or a temporal, worsening view of harm. Moreover, I show that this result holds regardless of how much worse a harm has to be in order to count as a much more serious harm. (shrink)

This paper redefines time not as a primitive background quantity in physical theory, but as a quantity constructed under metrological conditions. In standard theoretical descriptions, time is often introduced as a continuous independent variable. Yet every measurement of time depends on some physical reference process. Concealing this dependence at the starting point of theory obscures the foundation of the concept of time. -/- The paper first formulates a metrological principle prior to the construction of time. It then defines a clock (...) as a physical system that provides a comparable reference process and whose change can be unitized and calibrated. Proper time is constructed from the sequential count of that reference process. On this basis, state description, rates of change, kinematics, and dynamics are reformulated. -/- Within this framework, Newtonian mechanics, analytical mechanics, electromagnetism, relativity, and quantum mechanics are reread not as theories that presuppose a primitive time variable, but as theories that rely on a time parameter constructed through clocks, unitization, calibration, and sequential ordering. The claim of this paper is not that time does not exist. The more limited claim is that time is not self-evidently given at the beginning of a theory, but should be treated as a quantity constructed through physical clocks and calibration relations. -/- From this standpoint, part of what has traditionally been discussed under the headings of the flow of time, the block universe, and the problem of time in quantum gravity can be relocated from metaphysical claims to questions about the constitutive conditions internal to physical theory. (shrink)

Causal Decision Theory reckons the choice-worthiness of an option to be completely independent of its evidential bearing on its non-effects. But after one has made a choice this bearing is relevant to future decisions. Therefore it is possible to construct problems of sequential choice in which Causal Decision Theory makes a guaranteed loss. So Causal Decision Theory is wrong. The source of the problem is the idea that agents have a special perspective on their own contemplated actions, from which evidential (...) connections that observers can see are either irrelevant or invisible. (shrink)

It is known that – assuming the axiom of choice – for subsets A of ℝ the following hold: (a) A is compact iff it is sequentially compact, (b) A is complete iff it is closed in ℝ, (c) ℝ is a sequential space. We will show that these assertions are not provable in the absence of the axiom of choice, and that they are equivalent to each.

Prediction‐based processes appear to play an important role in language. Few studies, however, have sought to test the relationship within individuals between prediction learning and natural language processing. This paper builds upon existing statistical learning work using a novel paradigm for studying the on‐line learning of predictive dependencies. Within this paradigm, a new “prediction task” is introduced that provides a sensitive index of individual differences for developing probabilistic sequential expectations. Across three interrelated experiments, the prediction task and results thereof are (...) used to bridge knowledge of the empirical relation between statistical learning and language within the context of nonadjacency processing. We first chart the trajectory for learning nonadjacencies, documenting individual differences in prediction learning. Subsequent simple recurrent network simulations then closely capture human performance patterns in the new paradigm. Finally, individual differences in prediction performances are shown to strongly correlate with participants’ sentence processing of complex, long‐distance dependencies in natural language. (shrink)

Text classification involves deciding whether or not a document is about a given topic. It is an important problem in machine learning, because automated text classifiers have enormous potential for application in information retrieval systems. It is also an interesting problem for cognitive science, because it involves real world human decision making with complicated stimuli. This paper develops two models of human text document classification based on random walk and accumulator sequential sampling processes. The models are evaluated using data from (...) an experiment where participants classify text documents presented one word at a time under task instructions that emphasize either speed or accuracy, and rate their confidence in their decisions. Fitting the random walk and accumulator models to these data shows that the accumulator provides a better account of the decisions made, and a “balance of evidence” measure provides the best account of confidence. Both models are also evaluated in the applied information retrieval context, by comparing their performance to established machine learning techniques on the standard Reuters‐21578 corpus. It is found that they are almost as accurate as the benchmarks, and make decisions much more quickly because they only need to examine a small proportion of the words in the document. In addition, the ability of the accumulator model to produce useful confidence measures is shown to have application in prioritizing the results of classification decisions. (shrink)

Rational individuals who perceive information sequentially are confronted to cognitive dissonance and dynamic uncertainty in a way that sets a natural limit to the ex post efficiency of their choices. From the normative perspective which ignores this dynamic uncertainty, their rationality seems limited. Sequential perception is assumed in a model of Bayesian revision of the contingent preference in a repeated choice. This model predicts both the cognitive dissonance phenomenon studied by Festinger and the formation of stable habits. It also shows (...) how an ordinary man can be rational with bounded informational and computational abilities and, for the same reasons, give a disproportionate weight to impressions without any normative value in his own choices and judgments. Sequential perception and cognitive consistency offer a credible alternative to the cognitive bias paradigm for predicting anomalies in choice and game behavior.Des individus logiques percevant l’information de manière séquentielle sont soumis à une dissonance cognitive et une incertitude dynamique qui limitent naturellement l’efficacité ex post de leurs choix. Du point de vue normatif, qui ignore cette incertitude dynamique, leur rationalité apparaît limitée. L’hypothèse de perception séquentielle est introduite dans un modèle de révision bayésienne de la préférence contingente lors d’un choix répété. Ce modèle prédit à la fois le phénomène de dissonance cognitive étudié par Festinger et la formation d’une habitude stable. Il montre aussi comment un homme ordinaire peut être rationnel sans disposer de capacités d’information et de calcul démesurées et, pour les mêmes raisons, subir l’influence disproportionnée d’impressions dénuées de valeur normative dans les choix ou les jugements qu’il porte. La perception séquentielle et la cohérence cognitive offrent une alternative crédible au paradigme des biais cognitifs pour expliquer tous les comportements humains qui réfutent la théorie normative des choix et des jeux. (shrink)

It is shown that in any model of constructive mathematics in which a certain omniscience principle is false, for strongly extensional functions on an interval the distinction between sequentially continuous and regulated disappears. It follows, without the use of Markov's Principle, that any recursive function of bounded variation on a bounded closed interval is recursively sequentially continuous.

We show that the property of sequential compactness for subspaces of.

We introduce a new allocation rule, called the sequential equal surplus division for rooted forest TU-games. We provide two axiomatic characterizations for this allocation rule. The first one uses the classical property of component efficiency plus an edge deletion property. The second characterization uses standardness, an edge deletion property applied to specific rooted trees, a consistency property, and an amalgamation property. We also provide an extension of the sequential equal surplus division applied to the problem of sharing a river with (...) bifurcations. (shrink)

The main result of this paper is a weak constructive version of the uniform continuity theorem for pointwise continuous, real-valued functions on a convex subset of a normed linear space. Recursive examples are given to show that the hypotheses of this theorem are necessary. The remainder of the paper discusses conditions which ensure that a sequentially continuous function is continuous. MSC: 03F60, 26E40, 46S30.

The effect of recent experience on current behavior has been studied extensively in simple laboratory tasks. We explore the nature of sequential effects in the more naturalistic setting of automobile driving. Driving is a safety-critical task in which delayed response times may have severe consequences. Using a realistic driving simulator, we find significant sequential effects in pedal-press response times that depend on the history of recent stimuli and responses. Response times are slowed up to 100 ms in particular cases, a (...) delay that has dangerous practical consequences. Further, we observe a significant number of history-related pedal misapplications, which have recently been noted as a cause for concern in the automotive safety community. By anticipating these consequences of sequential context, driver assistance systems could mitigate the effects of performance degradations and thus critically improve driver safety. (shrink)

In the first author's thesis [10], a sequential language, LRT, for real number computation is investigated. That thesis includes a proof that all polynomials are programmable, but that work comes short of giving a complete characterization of the expressive power of the language even for first‐order functions. The technical problem is that LRT is non‐deterministic. So a natural characterization of its expressive power should be in terms of relations rather than in terms of functions. In [2], Brattka examines a formalization (...) of recursive relations in the style of Kleene's recursive functions on the natural numbers. This paper is an expanded version of [13] which establishes the expressive power of LRTp, a variant of LRT, in terms of Brattka's recursive relations. Because Brattka already did the work of establishing the precise connection between his recursive relations and Type 2 Theory of Effectivity, we thus obtain a complete characterization of first‐order definability in LRTp. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim). (shrink)

In this paper we suggest a model of sequential auctions with endogenous participation where each bidder conjectures about the number of participants at each round. Then, after learning his value, each bidder decides whether or not to participate in the auction. In the calculation of his expected value, each bidder uses his conjectures about the number of participants for each possible subgroup. In equilibrium, the conjectured probability is compatible with the probability of staying in the auction. In our model, players (...) face participation costs, bidders may buy as many objects as they wish and they are allowed to drop out at any round. Bidders can drop out at any time, but they cannot come back to the auction. In particular we can determine the number of participants and expected prices in equilibrium. We show that for any bidding strategy, there exists such a probability of staying in the auction. For the case of stochastically independent objects, we show that in equilibrium every bidder who decides to continue submits a bid that is equal to his value at each round. When objects are stochastically identical, we are able to show that expected prices are decreasing. (shrink)

This paper introduces and conceptualizes ecoexperiential sequentialism (EcoSeq), defined as multi-stage engagement in reflecting on interrelated experiences that track how the granularity of sense-making unfolds over time. EcoSeq has procedural (operationalizing the stages of inquiry) and conceptual (justifying the need for experiential engagement) components that guide it from an interpretative phenomenological analysis perspective. After explaining the theoretical and methodological dimensions, I report on three English language teachers’ engagement in EcoSeq, which involved collecting data from three rounds of semi-structured interviews (...) and narrative frames focused on their sense-making of parental demands. The study concludes with implications on how EcoSeq might be used in research on human experiences, especially in teacher education courses and teachers’ daily lives. (shrink)

Independence is the condition that, if X is preferred to Y, then a lottery between X and Z is preferred to a lottery between Y and Z given the same probability of Z. Is it rationally required that one’s preferences conform to Independence? The main objection to this requirement is that it would rule out the alleged rationality of Allais and Ellsberg Preferences. In this paper, I put forward a sequential dominance argument with fairly weak assumptions for a variant of (...) Independence (called Independence for Constant Prospects), which shows that Allais and Ellsberg Preferences are irrational. Hence this influential objection (that is, the alleged rationality of Allais and Ellsberg Preferences) can be rebutted. I also put forward a number of sequential dominance arguments that various versions of Independence are requirements of rationality. One of these arguments is based on very minimal assumptions, but the arguments for the versions of Independence which are strong enough to serve in the standard axiomatization of Expected Utility Theory need notably stronger assumptions. (shrink)

Uniform sequential continuity, a property classically equivalent to sequential continuity on compact sets, is shown, constructively, to be a consequence of strong continuity on a metric space. It is then shown that in the case of a separable metric space, uniform sequential continuity implies strong continuity if and only if one adopts a certain boundedness principle that, although valid in the classical, recursive and intuitionistic setting, is independent of Heyting arithmetic.

Sequential decision problems are studied in which there are two decision-makers, or players, who are trying to control the same stochastic system in order to minimize their own individual expected losses. The standard linear model for the stochastic control process and standard quadratic loss functions are assumed. The players take turns choosing the value of the control variable, and each player has his own sequence of targets and his own loss function. Optimal pure competitive strategies are derived by backward induction, (...) and limiting strategies and equilibria are determined. Myopic strategies are introduced and shown to yield smaller losses for each player than the pure competitive strategies. Coefficients of cooperation are then defined, and various cooperative sequential strategies based on them are shown to be mutually beneficial to both players. (shrink)

Sequential quantum logic is an extension of the well-known system of usual quantum logic8 to sequentially connected sentences. The usual quantum logic establishes the implication relation between logically connected quantum mechanical sentences. These sentences can be interpreted by means of yes-no experiments (in the sense of Jauch and Piron) as tests for elementary propositions and by means of dialogic proof procedures for compound propositions.11 Sequentially connected sentences (also called sequential sentences) exceed the class of logically connected sentences. They are interpreted (...) by means of dialogic proof procedures which are more fundamental than the proof procedures for logically connected propositions. A detailed investigation of sequential sentences in the language of quantum physics can be found in14. (shrink)

It is widely assumed that language in some form or other originated by piggybacking on pre-existing learning mechanism not dedicated to language. Using evolutionary connectionist simulations, we explore the implications of such assumptions by determining the effect of constraints derived from an earlier evolved mechanism for sequential learning on the interaction between biological and linguistic adaptation across generations of language learners. Artificial neural networks were initially allowed to evolve “biologically” to improve their sequential learning abilities, after which language was introduced (...) into the population. We compared the relative contribution of biological and linguistic adaptation by allowing both networks and language to change over time. The simulation results support two main conclusions: First, over generations, a consistent head-ordering emerged due to linguistic adaptation. This is consistent with previous studies suggesting that some apparently arbitrary aspects of linguistic structure may arise from cognitive constraints on sequential learning. Second, when networks were selected to maintain a good level of performance on the sequential learning task, language learnability is significantly improved by linguistic adaptation but not by biological adaptation. Indeed, the pressure toward maintaining a high level of sequential learning performance prevented biological assimilation of linguistic-specific knowledge from occurring. (shrink)

Psychological Sequentialism holds that no causal constraint is necessary for the preservation of what matters in survival; rather, it is sufficient for preservation if two groups of mental states are similar enough and temporally close enough. Suppose that one’s body is instantaneously dematerialized and subsequently, by an amazing coincidence, a collection of molecules is configured to form a qualitatively identical human body. According to Psychological Sequentialism, these events preserve what matters in survival. In this article, I examine some (...) of the main arguments for the view and argue that they fail to establish that no causal constraint is necessary. I also argue that Psychological Sequentialism yields implausible consequences that render it hard to accept the view. (shrink)

We deal with situations incongruent with our automatic response tendencies much better right after having done so on a previous trial than after having reacted to a congruent trial. The nature of the mechanisms responsible for these sequential congruency effects is currently a hot topic of debate. According to the conflict monitoring model these effects depend on the adjustment of control triggered by the detection of conflict on the preceding situation. We tested whether these conflict monitoring processes can operate implicitly (...) in an implicit learning procedure, modulating the expression of knowledge of which participants are not aware. We reanalyze recently published data, and present an experiment with a probabilistic sequence learning procedure, both showing consistent effects of implicit sequence learning. Despite being implicit, the expression of learning was reduced or completely eliminated right after trials incongruent with the learned sequence, thus showing that sequential congruency effects can be obtained even when the source of congruency itself remains implicit. (shrink)

Neural network models of memory are notorious for catastrophic interference: Old items are forgotten as new items are memorized (French, 1999; McCloskey & Cohen, 1989). While working memory (WM) in human adults shows severe capacity limitations, these capacity limitations do not reflect neural network style catastrophic interference. However, our ability to quickly apprehend the numerosity of small sets of objects (i.e., subitizing) does show catastrophic capacity limitations, and this subitizing capacity and WM might reflect a common capacity. Accordingly, computational investigations (...) (Knops, Piazza, Sengupta, Eger & Melcher, 2014; Sengupta, Surampudi & Melcher, 2014) suggest that mutual inhibition among neurons can explain both kinds of capacity limitations as well as why our ability to estimate the numerosity of larger sets is limited according to a Weber ratio signature. Based on simulations with a saliency map‐like network and mathematical proofs, we provide three results. First, mutual inhibition among neurons leads to catastrophic interference when items are presented simultaneously. The network can remember a limited number of items, but when more items are presented, the network forgets all of them. Second, if memory items are presented sequentially rather than simultaneously, the network remembers the most recent items rather than forgetting all of them. Hence, the tendency in WM tasks to sequentially attend even to simultaneously presented items might not only reflect attentional limitations, but also an adaptive strategy to avoid catastrophic interference. Third, the mean activation level in the network can be used to estimate the number of items in small sets, but it does not accurately reflect the number of items in larger sets. Rather, we suggest that the Weber ratio signature of large number discrimination emerges naturally from the interaction between the limited precision of a numeric estimation system and a multiplicative gain control mechanism. (shrink)

Many theorems of mathematics have the form that for a certain problem, e.g. a differential equation or polynomial (in)equality, there exists a solution. The sequential version then states that for a sequence of problems, there is a sequence of solutions. The original and sequential theorem can often be proved via the same (or similar) proof and often have the same (or similar) logical properties, esp. if everything is formulated in the language of second-order arithmetic. In this paper, we identify basic (...) theorems of third-order arithmetic, e.g. concerning semi-continuous functions, such that the sequential versions have very different logical properties. In particular, depending on the constructive status of the original theorem, very different and independent choice principles are needed. Despite these differences, the associated Reverse Mathematics, working in Kohlenbach’s higher-order framework, is rather elegant and is still based at the core on weak König’s lemma. (shrink)

This article analyses the sequential ordering of multi-modal discussions in real-time online classes in postgraduate education contexts. The article explores the ways that text and verbal talk are organized by the participants as inter-connecting modes of interaction. Focusing on Initiation, Response and Feedback sequences as an example of a form of exchange, the article shows that the interaction was comparatively disorderly where conducted across talk and text modes. For instance, written responses to questions or to encouragement turns often overlapped with (...) verbal answers from other students or with encouragement turns from the tutor. However, through the withholding of speech turns, the close latching of speech to written talk, and the ceasing of written turns at points where the topics or speakers changed, the participants showed a concern with re-establishing sequential order across the modalities. (shrink)

In _The Sequential Imperative_ William Edmondson describes the functional specification of the brain. This new approach to Cognitive Science depends on detailed understanding of speech, but the outcome is an understanding of the functionality of the brain in any species.

We relate two sequential models of PCF: the sequential algorithm model due to Berry and Curien and the strongly stable model due to Bucciarelli and the author. More precisely, we show that all the morphisms araising in the strongly stable model of PCF are sequential in the sense that they are the “extensional projections” of some sequential algorithms. We define a model of PCF where morphisms are “extensional” sequential algorithms and prove that any equation between PCF terms which holds in (...) this model also holds in the strongly stable model. (shrink)

The constructions of sequential calculi are based on the idea of application to the deduction process not only single logical constants but complexes of them as well. Surely, making use of this idea is not obligatory in paraconsistent logic. Nevertheless, using it in this field gives us a convenient tool for seeking proofs in formulation of many paraconsistent logics. Each of sequential propositional logics discussed in this paper is obtained as a result of a transformation of a starting calculus GCL (...) – one of sequential formalizations of classical propositional logic. Let α be a standard propositional language with a vocabulary {p1, p2, p3, . . . , −,∨, &, ⊃,¬,), we shall denote any formulas of α and by the letters Γ,∆, Σ, Θ finite sets of α-formulas. (shrink)

Working within Bishop-style constructive mathematics, we derive a number of results relating the nonconstructive LPO and sequential compactness property on the one hand, and the intuitionistically reasonable anti-Specker property on the other.

We respond to recent comments on our proposal to improve justice in ventilator triage, in which we used as an example New Jersey’s publicly available and legally binding Directive Number 2020-03. We agree with Bernard Lo and Doug White that equity implications of triage frameworks should be continually reassessed, which is why we offered six concrete options for improvement, and called for monitoring the consequences of adopted triage models. We disagree with their assessment that we mis-characterised their Model Guidance, as (...) included in the NJ Directive, in ways that undermine our conclusions. They suggest we erroneously described their model as a two-criterion allocation framework; that recognising other operant criterion reveals it ‘likely mitigate[s] rather than exacerbate[s] racial disparities during triage’, and allege that concerns about inequitable outcomes are ‘without evidence’. We highlight two major studies robustly demonstrating why concerns about disparate outcomes are justified. We also show that White and Lo seek to retrospectively—and counterfactually—correct the version of the Model Guideline included in the NJ Directive. However, as our facsimile reproductions show, neither the alleged four-criteria form, nor other key changes, such as dropping the Sequential Organ Failure Assessment score, are found in the Directive. These points matter because our conclusions hence stand, because the public version of the Model Guidance had not been updated to reduce the risk of inequitable outcomes until June 2021 and NJ’s Directive still does not reflect these revisions, and, hence, represents a less equitable version, as acknowledged by its authors. We comment on broader policy implications and call for ways of ensuring accurate, transparent and timely updates for users of high-stakes guidelines. (shrink)

By examining the activity of direction-giving and asking we can discover some of the sequential and other structures which characterize the activity. The insertion sequence, as a sequential structure, can be found to be used by interactants in more than one way to accomplish different results. We can therefore consider the insertion sequence as a sequential structure and, by attending to the activity in which the interactants are engaged, discover the relation between sequential and activity system structures. In this way (...) we can relate what persons are doing and how they are doing it (i.e. the activity being accomplished in and through their talk) to some of the basic structures of conversational interaction (e.g. insertion sequences). (shrink)

With reference to Mead, Peirce, speech act theory, conversation analysis, and Luhmann's phenomenological grounded version of systems theory, the paper tries to reconstruct actions as products of communication. A triadic sequence is identified as the elementary unit for the intersubjective constitution of an act. This unit combines three achievements: (a) the constitution of meaning by sequential attribution, (b) the intersubjective coordination of attributed meanings, and (c) the reproduction of rules, guiding the process of constitution and coordination of attributed meanings. Then, (...) using the tools of systems theory and applying them to empirical results of ethnomethodology and conversation analysis, it is shown how the rule scheme is integrated in a triadic sequence, functioning on three different levels of communication. Finally, a specific form of repair after next turn is discussed, relating it to the function of preserving the structure of conversational types. The analysis of such conversational types opens a possible realm of cooperation between conversation analysis and Luhmann's version of systems theory. (shrink)