It has been well documented how language‐specific cues may be used for word segmentation. Here, we investigate what role a language‐independent phonological universal, the sonority sequencing principle (SSP), may also play. Participants were presented with an unsegmented speech stream with non‐English word onsets that juxtaposed adherence to the SSP with transitional probabilities. Participants favored using the SSP in assessing word‐hood, suggesting that the SSP represents a potentially powerful cue for word segmentation. To ensure the SSP influenced the (...) segmentation process (i.e., during learning), we presented two additional groups of participants with either (a) no exposure to the stimuli prior to testing or (b) the same stimuli with pauses marking word breaks. The SSP did not influence test performance in either case, suggesting that the SSP is important for word segmentation during the learning process itself. Moreover, the fact that SSP‐independent segmentation of the stimulus occurred (in the latter control condition) suggests that universals are best understood as biases rather than immutable constraints on learning. (shrink)

It has been well documented how language-specific cues may be used for word segmentation. Here, we investigate what role a language-independent phonological universal, the sonority sequencing principle (SSP), may also play. Participants were presented with an unsegmented speech stream with non-English word onsets that juxtaposed adherence to the SSP with transitional probabilities. Participants favored using the SSP in assessing word-hood, suggesting that the SSP represents a potentially powerful cue for word segmentation. To ensure the SSP influenced the (...) segmentation process (i.e., during learning), we presented two additional groups of participants with either (a) no exposure to the stimuli prior to testing or (b) the same stimuli with pauses marking word breaks. The SSP did not influence test performance in either case, suggesting that the SSP is important for word segmentation during the learning process itself. Moreover, the fact that SSP-independent segmentation of the stimulus occurred (in the latter control condition) suggests that universals are best understood as biases rather than immutable constraints on learning. (shrink)

We analyze the axiomatic strength of the following theorem due to Rival and Sands [28] in the style of reverse mathematics. Every infinite partial order P of finite width contains an infinite chain C such that every element of P is either comparable with no element of C or with infinitely many elements of C. Our main results are the following. The Rival–Sands theorem for infinite partial orders of arbitrary finite width is equivalent to $\mathsf {I}\Sigma ^0_{2} + \mathsf {ADS}$ (...) over $\mathsf {RCA}_0$. For each fixed $k \geq 3$, the Rival–Sands theorem for infinite partial orders of width $\leq \!k$ is equivalent to $\mathsf {ADS}$ over $\mathsf {RCA}_0$. The Rival–Sands theorem for infinite partial orders that are decomposable into the union of two chains is equivalent to $\mathsf {SADS}$ over $\mathsf {RCA}_0$. Here $\mathsf {RCA}_0$ denotes the recursive comprehension axiomatic system, $\mathsf {I}\Sigma ^0_{2}$ denotes the $\Sigma ^0_2$ induction scheme, $\mathsf {ADS}$ denotes the ascending/descending sequence principle, and $\mathsf {SADS}$ denotes the stable ascending/descending sequence principle. To the best of our knowledge, these versions of the Rival–Sands theorem for partial orders are the first examples of theorems from the general mathematics literature whose strength is exactly characterized by $\mathsf {I}\Sigma ^0_{2} + \mathsf {ADS}$, by $\mathsf {ADS}$, and by $\mathsf {SADS}$. Furthermore, we give a new purely combinatorial result by extending the Rival–Sands theorem to infinite partial orders that do not have infinite antichains, and we show that this extension is equivalent to arithmetical comprehension over $\mathsf {RCA}_0$. (shrink)

Cognitive Science, Volume 46, Issue 7, July 2022.

Five recursively axiomatizable theories extending Kleene's intuitionistic theory FIM of numbers and numbertheoretic sequences are introduced and shown to be consistent, by a modified relative realizability interpretation which verifies that every sequence classically defined by a Π11 formula is unavoidable and that no sequence can fail to be classically Δ11. The analytical form of Markov's Principle fails under the interpretation. The notion of strongly inadmissible rule of inference is introduced, with examples.

We propose a new method for constructing Turing ideals satisfying principles of reverse mathematics below the Chain–Antichain (CAC) Principle. Using this method, we are able to prove several new separations in the presence of Weak König’s Lemma (WKL), including showing that CAC+WKL does not imply the thin set theorem for pairs, and that the principle “the product of well-quasi-orders is a well-quasi-order” is strictly between CAC and the Ascending/Descending Sequences principle, even in the presence of WKL.

We give an overview of the role of equicontinuity of sequences of real-valued functions on [0,1] and related notions in classical mathematics, intuitionistic mathematics, Bishop’s constructive mathematics, and Russian recursive mathematics. We then study the logical strength of theorems concerning these notions within the programme of Constructive Reverse Mathematics. It appears that many of these theorems, like a version of Ascoli’s Lemma, are equivalent to fan-theoretic principles.

Fusion genes formed by chromosomal rearrangements are common drivers of cancer. Recent innovations in the field of next‐generation sequencing (NGS) have seen a dynamic shift from traditional fusion detection approaches, such as visual characterization by fluorescence, to more precise multiplexed methods. There are many different NGS‐based approaches to fusion gene detection and deciding on the most appropriate method can be difficult. Beyond the experimental approach, consideration needs to be given to factors such as the ease of implementation, processing time, (...) associated costs, and the level of expertise required for data analysis. Here, the different NGS‐based methods for fusion gene detection, the basic principles underlying the techniques, and the benefits and limitations of each approach are reviewed. This article concludes with a discussion of how NGS will impact fusion gene detection in a clinical context and from where the next innovations are evolving. (shrink)

It is shown that, relative to Bishop-style constructive mathematics, the boundedness principle BD-N is equivalent both to a general result about the convergence of double sequences and to a particular one about Cauchyness in a semi-metric space.

Salmon genomics is an emerging field that represents a convergence between socially important scientific innovation and a politically volatile topic of significant interest to the public. These factors provide a strong rationale for public input. This report describes such input from a public engagement event based on the principles of deliberative democracy. The event involved a random, demographically stratified sample of 25 British Columbians (Canada). While some participants opposed sequencing the salmon genome on principle, on the whole participants (...) responded favourably, citing the value of increased knowledge of human impacts on salmon, potentially slowing or reversing this impact, and assisting sustainable management of salmon resources. Participants discussed many of the potential implications of the sequencing project and formulated recommendations pertaining to regulations, international treaties, public education and engagement. Overall, the project illustrates that the specific design and implementation of this event is capable of producing sound policy advice from the general public on genomic-related issues. (shrink)

A bounded monotone sequence of reals without a limit is called a Specker sequence. In Russian constructive analysis, Church's Thesis permits the existence of a Specker sequence. In intuitionistic mathematics, Brouwer's Continuity Principle implies it is false that every bounded monotone sequence of real numbers has a limit. We claim that the existence of Specker sequences crucially depends on the properties of intuitionistic decidable sets. We propose a schema about intuitionistic decidability that asserts “there exists an intuitionistic enumerable set (...) that is not intuitionistic decidable” and show that the existence of a Specker sequence is equivalent to ED. We show that ED is consistent with some certain well known axioms of intuitionistic analysis as Weak Continuity Principle, bar induction, and Kripke Schema. Thus, the assumption of the existence of a Specker sequence is conceivable in intuitionistic analysis. We will also introduce the notion of double Specker sequence and study the existence of them. (shrink)

In this paper we discuss a particular example of the passage from the informal, but rigorous description of a concept to the axiomatic formulation of principles holding for the concept; in particular, we look at the principles of continuity and lawlike choice in the theory of lawless sequences. Our discussion also leads to a better understanding of the rôle of the so-called density axiom for lawless sequences.

We investigate the complexity of various combinatorial theorems about linear and partial orders, from the points of view of computability theory and reverse mathematics. We focus in particular on the principles ADS (Ascending or Descending Sequence), which states that every infinite linear order has either an infinite descending sequence or an infinite ascending sequence, and CAC (Chain-AntiChain), which states that every infinite partial order has either an infinite chain or an infinite antichain. It is well-known that Ramsey's Theorem for pairs (...) (RT₂²) splits into a stable version (SRT₂²) and a cohesive principle (COH). We show that the same is true of ADS and CAC, and that in their cases the stable versions are strictly weaker than the full ones (which is not known to be the case for RT₂² and SRT₂²). We also analyze the relationships between these principles and other systems and principles previously studied by reverse mathematics, such as WKL₀, DNR, and BΣ₂. We show, for instance, that WKL₀ is incomparable with all of the systems we study. We also prove computability-theoretic and conservation results for them. Among these results are a strengthening of the fact, proved by Cholak, Jockusch, and Slaman, that COH is Π₁¹-conservative over the base system RCA₀. We also prove that CAC does not imply DNR which, combined with a recent result of Hirschfeldt, Jockusch, Kjos-Hanssen, Lempp, and Slaman, shows that CAC does not imply SRT₂² (and so does not imply RT₂²). This answers a question of Cholak, Jockusch, and Slaman. Our proofs suggest that the essential distinction between ADS and CAC on the one hand and RT₂² on the other is that the colorings needed for our analysis are in some way transitive. We formalize this intuition as the notions of transitive and semitransitive colorings and show that the existence of homogeneous sets for such colorings is equivalent to ADS and CAC, respectively. We finish with several open questions. (shrink)

We introduce strong Goodstein principles which are true but unprovable in strong impredicative theories like IDn.

Most interpreting theories claim that different interpreting types should involve varied processing mechanisms and procedures. However, few studies have examined their underlying differences. Even though some previous results based on quantitative approaches show that different interpreting types yield outputs of varying lexical and syntactic features, the grammatical parsing approach is limited. Language sequences that form without relying on parsing or processing with a specific linguistic approach or grammar excel other quantitative approaches at revealing the sequential behavior of language production. As (...) a non-grammatically-bound unit of language sequences, frequency motif can visualize the local distribution of content and function words, and can also statistically classify languages and identify text types. Thus, the current research investigates the distribution, length and position-dependent properties of frequency motifs across different interpreting outputs in pursuit of the sequential generation behaviors. It is found that the distribution, the length and certain position-dependent properties of the specific language sequences differ significantly across simultaneous interpreting and consecutive interpreting output. The features of frequency motifs manifest that both interpreting output is produced in the manner that abides by the least effort principle. The current research suggests that interpreting types can be differentiated through this type of language sequential unit and offers evidence for how the different task features mediate the sequential organization of interpreting output under different demand to achieve cognitive load minimization. (shrink)

We present a new proof of the existence of Morley sequences in simple theories. We avoid using the Erdős–Rado theorem and instead use only Ramsey’s theorem and compactness. The proof shows that the basic theory of forking in simple theories can be developed using only principles from “ordinary mathematics,” answering a question of Grossberg, Iovino, and Lessmann, as well as a question of Baldwin.

The ability to process events in their temporal and sequential context is a fundamental skill made mandatory by constant interaction with a dynamic environment. Sequence learning studies have demonstrated that subjects exhibit detailed — and often implicit — sensitivity to the sequential structure of streams of stimuli. Current connectionist models of performance in the so-called Serial Reaction Time Task (SRT), however, fail to capture the fact that sequence learning can be based not only on sensitivity to the sequential associations between (...) successive stimuli, but also on sensitivity to the associations between successive responses, and on the predictive relationships that exist between these sequences of responses and their effects in the environment. In this paper, we offer an initial exploration of an alternative architecture for sequence learning, based on the principles of Forward Models. (shrink)

We establish the consistency of the failure of the diamond principle on a cardinal [Formula: see text] which satisfies a strong simultaneous reflection property. The result is based on an analysis of Radin forcing, and further leads to a characterization of weak compactness of [Formula: see text] in a Radin generic extension.

In the author's Relative lawlessness in intuitionistic analysis [this JOURNAL. vol. 52 (1987). pp. 68-88] and An intuitionistic theory of lawlike, choice and lawless sequences [Logic Colloquium '90. Springer-Verlag. Berlin. 1993. pp. 191-209] a notion of lawless ness relative to a countable information base was developed for classical and intuitionistic analysis. Here we simplify the predictability property characterizing relatively lawless sequences and derive it from the new axiom of closed data (classically equivalent to open data) together with a natural (...) class='Hi'>principle of invariance under finite translation. We characterize relative lawlessness in terms of a notion of forcing. Finally, we study relative lawlessness on an arbitrary fan and show that the collection of lawless binary sequences (which is comeager in the sense of Baire) has probability measure zero. The reasoning is predominantly constructive. (shrink)

When Kleene extended his recursive realizability interpretation from intuitionistic arithmetic to analysis, he was forced to use more than recursive functions to interpret sequences and conditional constructions. In fact, he used what classically appears to be the full continuum. We describe here a generalization to higher type of Kleene's realizability, one case of which, -realizability, uses general recursive functions throughout, both to realize theorems and to interpret choice sequences. -realizability validates a version of the bar theorem and the usual continuity (...) principles, while also providing naturally, as Kleene's 1965 realizability does not, for versions of lawless sequence axioms, as well as of Church's Thesis. (shrink)

Intuitionistically. a set has to be given by a finite construction or by a construction-project generating the elements of the set in the course of time. Quantification is only meaningful if the range of each quantifier is a well-circumscribed set. Thinking upon the meaning of quantification, one is led to insights?in particular, the so-called continuity principles?which are surprising from a classical point of view. We believe that such considerations lie at the basis of Brouwer?s reconstruction of mathematics. The predicate ?α (...) is lawless? is not acceptable, the lawless sequences do not form a well-circumscribed intuitionistic set, and quantification over lawless sequences does not make sense. (shrink)

The purpose of this paper is to present several applications of combinatorial principles, well-known in Set Theory, to the geometry of infinite dimensional Banach spaces, particularly to the existence of certain basic sequences. We mention also some open problems where set-theoretical techniques are relevant.

In this thesis, we study transfer principles in the context of certain Henselian valued fields, namely Henselian valued fields of equicharacteristic $0$, algebraically closed valued fields, algebraically maximal Kaplansky valued fields, and unramified mixed characteristic Henselian valued fields with perfect residue field. First, we compute the burden of such a valued field in terms of the burden of its value group and its residue field. The burden is a cardinal related to the model theoretic complexity and a notion of dimension (...) associated to $\text {NTP}_2$ theories. We show, for instance, that the Hahn field $\mathbb {F}_p^{\text {alg}})$ is inp-minimal, and that the ring of Witt vectors $W$ over $\mathbb {F}_p^{\text {alg}}$ is not strong. This result extends previous work by Chernikov and Simon and realizes an important step toward the classification of Henselian valued fields of finite burden. Second, we show a transfer principle for the property that all types realized in a given elementary extension are definable. It can be written as follows: a valued field as above is stably embedded in an elementary extension if and only if its value group is stably embedded in the corresponding extension of value groups, its residue field is stably embedded in the corresponding extension of residue fields, and the extension of valued fields satisfies a certain algebraic condition. We show, for instance, that all types over the power series field $\mathbb {R})$ are definable. Similarly, all types over the quotient field of $W$ are definable. This extends previous work of Cubides and Delon and of Cubides and Ye.These distinct results use a common approach, which has been developed recently. It consists of establishing first a reduction to an intermediate structure called the leading term structure, or $\operatorname {\mathrm {RV}}$ -sort, and then of reducing to the value group and residue field. This leads us to develop similar reduction principles in the context of pure short exact sequences of abelian groups.prepared by Pierre Touchard.E-mail: [email protected]: https://miami.uni-muenster.de/Record/a612cf73-0a2f-42c4-b1e4-7d28934138a9. (shrink)

We shall investigate certain set-theoretic pigeonhole principles which arise as generalizations of the usual pigeonhole principle; and we shall show that many of them are equivalent to full AC. We discuss also several restricted cases and variations of those principles and relate them to restricted choice principles. In this sense the pigeonhole principle is a rich source of weak choice principles. It is shown that certain sequences of restricted pigeonhole principles form implicational hierarchies with respect to ZF. We (...) state also several open problems in order to indicate the extent to which the whole subject of pigeonhole principles requires further exploration. (shrink)

Several authors believe that there are certain facts that are striking and cry out for explanation—for instance, a coin that is tossed many times and lands in the alternating sequence HTHTHTHTHTHT…. According to this view, we have prima facie reason to believe that such facts are not the result of chance. I call this view the striking principle. Based on this principle, some have argued for far-reaching conclusions, such as that our universe was created by intelligent design, that (...) there are many universes other than the one we inhabit, and that there are no mathematical or normative facts. Appealing as the view may initially seem, I argue that we lack sufficient reason to accept it. (shrink)

We investigate the interaction between compactness principles and guessing principles in the Radin forcing extensions. In particular, we show that in any Radin forcing extension with respect to a measure sequence on [Formula: see text], if [Formula: see text] is weakly compact, then [Formula: see text] holds. This provides contrast with a well-known theorem of Woodin, who showed that in a certain Radin extension over a suitably prepared ground model relative to the existence of large cardinals, the diamond principle (...) fails at a strongly inaccessible Mahlo cardinal. Refining the analysis of the Radin extensions, we consistently demonstrate a scenario where a compactness principle, stronger than the diagonal stationary reflection principle, holds yet the diamond principle fails at a strongly inaccessible cardinal, improving a result from [O. B. -Neria, Diamonds, compactness, and measure sequences, J. Math. Log. 19(1) (2019) 1950002]. (shrink)

In set theory without the Axiom of Choice, we investigate the set-theoretic strength of the principle NDS which states that there is no function f on the set ω of natural numbers such that for everyn ∈ ω, f ≺ f, where for sets x and y, x ≺ y means that there is a one-to-one map g : x → y, but no one-to-one map h : y → x. It is a long standing open problem whether NDS (...) implies AC. In this paper, among other results, we show that NDS is a strong axiom by establishing that ACLO ↛ NDS in ZFA set theory. The latter result provides a strongly negative answer to the question of whether “every Dedekind-finite set is finite” implies NDS addressed in G. H. Moore “Zermelo’s Axiom of Choice. Its Origins, Development, and Influence” and in P. Howard–J. E. Rubin “Consequences of the Axiom of Choice”. We also prove that ACWO ↛ NDS in ZF and that “for all infinite cardinals m, m + m = m” ↛ NDS in ZFA. (shrink)

1. Generalising a given set of examples is essential in many machine learning techniques. In principle, a machine learning algorithm builds an abstract model that represents a set of examples. But...

On the occasion of its recent centennial, we trace the remarkable history of Herbert Spencer's 2,240 page Principles of Sociology , the most inductive, systematic, and comprehensive study of human society ever attempted. Spencer's bold aim was to establish empirically and then to explain (after the manner of the natural sciences) the 'relations of co-existence and sequence' among social phenomena. The database ('mass of evidence') required was so vast that it was published as a separate work, some eight folio volumes (...) called Descriptive Sociology . A major force in the making of both scientific sociology and anthropology in the last quarter of the nineteenth century, Spencer's magnum opus was all but lost to these fields by the early decades of the twentieth century. The present generation, however, is witnessing a growing revival of interest in Spencer's thought. For many, his confident vision of a natural science of society still offers the best hope for understanding human societies and how they have come to be as they are. (shrink)

Elementary Recursive Nonstandard Analysis, in short ERNA, is a constructive system of nonstandard analysis proposed around 1995 by Patrick Suppes and Richard Sommer, who also proved its consistency inside PRA. It is based on an earlier system developed by Rolando Chuaqui and Patrick Suppes, of which Michal Rössler and Emil Jeřábek have recently proposed a weakened version. We add a Π₁-transfer principle to ERNA and prove the consistency of the extended theory inside PRA. In this extension of ERNA a (...) σ₁-supremum principle 'up-to-infinitesimals', and some well-known calculus results for sequences are deduced. Finally, we prove that transfer is 'too strong' for finitism by reconsidering Rössler and Jeřábek's conclusions. (shrink)

We introduce the $\Sigma _1$ -definable universal finite sequence and prove that it exhibits the universal extension property amongst the countable models of set theory under end-extension. That is, the sequence is $\Sigma _1$ -definable and provably finite; the sequence is empty in transitive models; and if M is a countable model of set theory in which the sequence is s and t is any finite extension of s in this model, then there is an end-extension of M to a (...) model in which the sequence is t. Our proof method grows out of a new infinitary-logic-free proof of the Barwise extension theorem, by which any countable model of set theory is end-extended to a model of $V=L$ or indeed any theory true in a suitable submodel of the original model. The main theorem settles the modal logic of end-extensional potentialism, showing that the potentialist validities of the models of set theory under end-extensions are exactly the assertions of S4. Finally, we introduce the end-extensional maximality principle, which asserts that every possibly necessary sentence is already true, and show that every countable model extends to a model satisfying it. (shrink)

There are two principles that lend Brouwer's mathematics the extra power beyond arithmetic. Both are presented in Brouwer's writings with little or no argument. One, the principle of bar induction, will not concern us here. The other, the continuity principle for numbers, occurs for the first time in print in [4]. It is formulated and immediately applied to show that the set of numerical choice sequences is not enumerable. In fact, the idea of the continuity property can be (...) dated fairly precisely, it is to be found in the margin of Brouwer's notes for his course on Pointset Theory of 1915/16. The course was repeated in 1916/17 and he must have inserted his first formulation of the continuity principle in the fall of 1916 as new material right at the beginning of the course.In modern language, the principle readswhere α and β range over choice sequences of natural numbers, m and x over natural numbers, and stands for ⟨α, α, …, α⟩, the initial segment of α of length m.An immediate consequence of WC-N is that all full functions are continuous, and, as a corollary, that the continuum is unsplittable [28]. Note that WC-N is incompatible with Church's thesis, [22], section 4.6.After Brouwer asserted WC-N, Troelstra was the first to ask in print for a conceptual motivation, but he remained an exception; most authors followed Brouwer by simply asserting it, cf. [18].Let us note first that in one particular case the principle is obvious indeed, namely in the case of the lawless sequences. The notion of lawless sequence surfaced fairly late in the history of intuitionism. Kreisel introduced it in [17] for metamathematical purposes. There is a letter from Brouwer to Heyting in which the phenomenon also occurs [7]. This is an important and interesting fact since it is the only time that Brouwer made use of a possibility expressly stipulated in, e.g., [5], see below. (shrink)

The aim of this paper is to determine the logical and computational strength of instances of the Bolzano-Weierstraß principle and a weak variant of it.We show that BW is instance-wise equivalent to the weak König’s lemma for Σ01-trees . This means that from every bounded sequence of reals one can compute an infinite Σ01-0/1-tree, such that each infinite branch of it yields an accumulation point and vice versa. Especially, this shows that the degrees d ≫ 0′ are exactly those (...) containing an accumulation point for all bounded computable sequences.Let BWweak be the principle stating that every bounded sequence of real numbers contains a Cauchy subsequence . We show that BWweak is instance-wise equivalent to the cohesive principle and—using this—obtain a classification of the computational and logical strength of BWweak. Especially we show that BWweak does not solve the halting problem and does not lead to more than primitive recursive growth. Therefore it is strictly weaker than BW. We also discuss possible uses of BWweak. © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim. (shrink)

Motivated by a characterization of weakly compact cardinals due to Todorcevic, we introduce a new cardinal characteristic, the C-sequence number, which can be seen as a measure of the compactness of a regular uncountable cardinal. We prove a number of ZFC and independence results about the C-sequence number and its relationship with large cardinals, stationary reflection, and square principles. We then introduce and study the more general C-sequence spectrum and uncover some tight connections between the C-sequence spectrum and the strong (...) coloring principle U(. . .), introduced in Part I of this series. (shrink)

This article argues that a successful answer to Hume's problem of induction can be developed from a sub-genre of philosophy of science known as formal learning theory. One of the central concepts of formal learning theory is logical reliability: roughly, a method is logically reliable when it is assured of eventually settling on the truth for every sequence of data that is possible given what we know. I show that the principle of induction (PI) is necessary and sufficient for (...) logical reliability in what I call simple enumerative induction. This answer to Hume's problem rests on interpreting PI as a normative claim justified by a non-empirical epistemic means-ends argument. In such an argument, a rule of inference is shown by mathematical or logical proof to promote a specified epistemic end. Since the proof concerning PI and logical reliability is not based on inductive reasoning, this argument avoids the circularity that Hume argued was inherent in any attempt to justify PI. (shrink)

We introduce three families of diagonal reflection principles for matrices of stationary sets of ordinals. We analyze both their relationships among themselves and their relationships with other known principles of simultaneous stationary reflection, the strong reflection principle, and the existence of square sequences.

The Pauli exclusion principle is interpreted using a geometrical theory of electrons. Spin and spatial motion are described together in an eight dimensional spinor coordinate space. The field equation derives from the assumption of conformal waves. The Dirac wave function is a gradient of the scalar wave in spinor space. Electromagnetic and gravitational interactions are mediated by conformal transformations. An electron may be followed through a sequence of creation and annihilation processes. Two electrons are branches of a single particle. (...) Each satisfies a Dirac equation, but together they are a solution of the curvature condition. As two so identified electrons approach each other, the exclusion principle develops from the boundary conditions in spinor space. The gradient motion does not allow the particles to overlap. Since the spinor-gradient of the scalar wave function is odd in the coordinates, the sign of the wave function must change at the electron-electron boundary. The exclusion principle becomes geometry intrinsic and all electrons are combined into one field. Further applications are proposed including the possibility of improved numerical calculations in atomic and molecular systems. There also may be extensions to nuclear or particle physics. Implications are expected for the properties of rotating objects in a gravitational field. (shrink)

The aim of this paper is to show that it’s not a good idea to have a theory of truth that is consistent but ω-inconsistent. In order to bring out this point, it is useful to consider a particular case: Yablo’s Paradox. In theories of truth without standard models, the introduction of the truth-predicate to a first order theory does not maintain the standard ontology. Firstly, I exhibit some conceptual problems that follow from so introducing it. Secondly, I show that (...) in second order theories with standard semantics the same procedure yields a theory that doesn’t have models. So, while having an ω- inconsistent theory is a bad thing, having an unsatisfiable theory of truth is actually worse. This casts doubts on whether the predicate in question is, after all, a truthpredicate for that language. Finally, I present some alternatives to prove an inconsistency adding plausible principles to certain theories of truth. (shrink)

There are two principles that lend Brouwer's mathematics the extra power beyond arithmetic. Both are presented in Brouwer's writings with little or no argument. One, the principle of bar induction, will not concern us here. The other, the continuity principle for numbers, occurs for the first time in print in [4]. It is formulated and immediately applied to show that the set of numerical choice sequences is not enumerable. In fact, the idea of the continuity property can be (...) dated fairly precisely, it is to be found in the margin of Brouwer's notes for his course on Pointset Theory of 1915/16. The course was repeated in 1916/17 and he must have inserted his first formulation of the continuity principle in the fall of 1916 as new material right at the beginning of the course.In modern language, the principle readswhere α and β range over choice sequences of natural numbers, m and x over natural numbers, and stands for ⟨α, α, …, α⟩, the initial segment of α of length m.An immediate consequence of WC-N is that all full functions are continuous, and, as a corollary, that the continuum is unsplittable [28]. Note that WC-N is incompatible with Church's thesis, [22], section 4.6.After Brouwer asserted WC-N, Troelstra was the first to ask in print for a conceptual motivation, but he remained an exception; most authors followed Brouwer by simply asserting it, cf. [18].Let us note first that in one particular case the principle is obvious indeed, namely in the case of the lawless sequences. The notion of lawless sequence surfaced fairly late in the history of intuitionism. Kreisel introduced it in [17] for metamathematical purposes. There is a letter from Brouwer to Heyting in which the phenomenon also occurs [7]. This is an important and interesting fact since it is the only time that Brouwer made use of a possibility expressly stipulated in, e.g., [5], see below. (shrink)

The fundamental Hennigian principle, grouping solely on synapomorphy, is seldom used in modern phylogenetics. In the submitted paper, we apply this principle in reanalyzing five datasets comprising 197 complete plastid genomes (plastomes). We focused on the latter because plastome-based DNA sequence data gained dramatic popularity in molecular systematics during the last decade. We show that pattern-cladistic analyses based on complete plastid genome sequences can successfully resolve affinities between plant taxa, simultaneously simplifying both the genomic and analytical frameworks of (...) phylogenetic studies. We developed “Matrix to Newick” (M2N), a program to represent the standard molecular alignment of plastid genomes in the form of trees or relationships directly. Thus, massive plastome-based DNA sequence data can be successfully represented in a relational form rather than as a standard molecular alignment. Application of methods of median supertree construction (the Average Consensus method has been used as an example in this study) or Maximum Parsimony analysis to relational representations of plastome sequence data may help systematist to avoid the complicated assumption-based frameworks of Maximum Likelihood or Bayesian phylogenetics that are most used today in massive plastid sequence data analyses. We also found that significant amounts of pure genomic information that typically accommodate the majority of current plastid phylogenomic studies can be effectively dropped by systematists if they focus on the pattern-cladistics or relational analyses of plastome-based molecular data. The proposed pattern-cladistic approach is a powerful and straightforward heuristic alternative to modern plastome-based phylogenetics. (shrink)

We investigate the relationship between weak square principles and simultaneous reflection of stationary sets.

We discuss the philosophical implications of formal results showing the con- sequences of adding the epsilon operator to intuitionistic predicate logic. These results are related to Diaconescu’s theorem, a result originating in topos theory that, translated to constructive set theory, says that the axiom of choice (an “existence principle”) implies the law of excluded middle (which purports to be a logical principle). As a logical choice principle, epsilon allows us to translate that result to a logical setting, (...) where one can get an analogue of Diaconescu’s result, but also can disentangle the roles of certain other assumptions that are hidden in mathematical presentations. It is our view that these results have not received the attention they deserve: logicians are unlikely to read a discussion because the results considered are “already well known,” while the results are simultaneously unknown to philosophers who do not specialize in what most philosophers will regard as esoteric logics. This is a problem, since these results have important implications for and promise signif i cant illumination of contem- porary debates in metaphysics. The point of this paper is to make the nature of the results clear in a way accessible to philosophers who do not specialize in logic, and in a way that makes clear their implications for contemporary philo- sophical discussions. To make the latter point, we will focus on Dummettian discussions of realism and anti-realism. Keywords: epsilon, axiom of choice, metaphysics, intuitionistic logic, Dummett, realism, antirealism. (shrink)

The main result of this paper is a formal argument for the principle of maximizing expected utility that does not rely on the law of large numbers. Unlike the well-known arguments by Savage and von Neumann & Morgenstern, this argument does not presuppose the sure-thing principle or the independence axiom. The principal idea is to use the concept of transformative decision rules for decomposing the principle of maximizing expected utility into a sequence of normatively reasonable subrules. It (...) is shown that this procedure provides a resolution of Allais's paradox that cannot be obtained by Savage-style or von Neumann & Morgenstern-style arguments. (shrink)

The precautionary principle justifies postponing the implementation of development projects to await better information about their environmental impacts. But if implementation capacity is congestible, as is often the case in practical settings, a postponed project may have to vie for implementation priority with projects that arrive later. Limitations of implementation capacity create two risks. First, it may sometimes not make sense to go back to a postponed project, even if it is later revealed to be a good one. Second, (...) the planner may find it worthwhile to go back to it, but at the expense of undesirable delay of subsequent projects. We consider a planner facing a sequence of projects that vary stochastically in their (1) importance and (2) improvability, but knowing that implementation capacity is congestible. The scope for congestion implies a ‘bonus’ for earlier-than-otherwise decisions, in common parlance ‘keeping the desk clear’, which works against the well-understood option value that encourages postponement. The optimal decision rule depends upon the stochastic environment whereby future projects are generated, in ways that are not obvious. The value of the bonus is increasing in the expected importance of future projects but decreasing in their expected improvability. Higher variability of the importance of projects, in the sense of mean-preserving spread, increases the size of the bonus, but variability in their improvability has a generally ambiguous impact. We characterize the adjusted decision rule and note its implications for the conduct of cost-benefit informed policy. (shrink)

This thesis first introduces the basic principles of model-based image sequence coding technology, then discusses in detail the specific steps in various implementation algorithms, and proposes a basic feature point calibration required in three-dimensional motion and structure estimation. This is a simple and effective solution. Aiming at the monocular video image sequence obtained by only one camera, this paper introduces the 3D model of the sculpture building into the pose tracking framework to provide initial depth information. The whole posture tracking (...) framework can be divided into three parts, namely, the construction of the initial sculpture model, the posture tracking between frames, and the robustness processing during continuous tracking. In order to reduce the complexity of calculation, this paper proposes a new three-dimensional mesh model and a moving image restoration algorithm based on this model. At the same time, the influence of the intensity and direction factors in the scene is added, the simulation results are given, and the next step is discussed. The optimization work that needs to be done. (shrink)