A challenge for theories of incomplete descriptions is to capture the consistency of ‘Sobel sequences’ and to account for an asymmetry in the acceptability of utterances of Sobel sequences and ‘reverse Sobel sequences’. David Lewis’s theory of incomplete descriptions answers, unlike many other theories, the challenge from Sobel sequences, but it does not answer the challenge from reverse Sobel sequences. This article presents another asymmetry in the availability of (...) anaphoric readings of Sobel sequences and reverse Sobel sequences, and proposes an explanation of the original asymmetry on its grounds. This provides an answer to the challenge for Lewis’s theory. (shrink)

Folklore has it that Sobel sequences favor a variably strict analysis of conditionals over its plainly strict alternative. While recent discussions for or against the lore have focussed on Sobel sequences involving counterfactuals, this paper draws attention to the fact that indicative Sobel sequences are just as felicitous as are their counterfactual cousins. The fact, or so I shall argue here, disrupts the folklore: given minimal assumptions about the semantics and pragmatics of indicative conditionals, (...) a textbook variably strict analysis fails to predict that indicative Sobel sequences are felicitous. The correct lesson to draw from Sobel sequences is that their felicity challenges classical implementations of the variably strict and of the plainly strict analysis alike. In response to this challenge I develop a dynamic strict analysis of conditionals that handles indicative Sobel sequences with grace while preserving intuitive constraints on the semantics and pragmatics of their members. A discussion of how such an analysis may handle the challenge from reverse Sobel sequences is provided. (shrink)

In this paper I provide a unified analysis of a number of pragmatic anomalies that have been discussed in the literature. The paper’s main goal is to account for Sobel sequences of conditionals and sequences of disjunctive sentences, but I will also propose that this analysis can be extended to sequences of sentences with superlatives. The starting point is the observation that, while all these sequences are felicitous in one order, they are infelicitous when the (...) order is reversed. Previous proposals have focussed on particular types of infelicitous sequences Ken Hale: A life in language, MIT Press, Cambridge, 2001; Moss in Noûs 46:516–586, 2012; Lewis in Noûs 52:481–507, 2018; a.o.), or a subset of all the phenomena cited above Linguistic and psycholinguistic approaches on implicatures and presuppositions. Palgrave McMillan, Basingstoke, 2017; a.o.). I propose that sequences of sentences belonging to the same structured set of alternatives T are subject to a Specificity Constraint : sequences are acceptable if both alternatives are dominated by the same number of nodes in the structured set of alternatives T. Violations of SC can be avoided by strengthening the weaker alternative. However, covert strengthening violates an economy condition if the overtly stronger alternative is among those made salient by the preceding utterance in the sequence. I propose that the set of alternatives made salient by an utterance of a sentence s consists of s’s sisters and mother in T. I will show that the strengthening mechanism varies depending on the kind of sequence we have. (shrink)

Sobel sequences have had a huge impact on the discussion of counterfactuals. They can be composed of conditionals and mere descriptions. What is especially puzzling about them is that they are often felicitously uttered when their reversal is not. Up to now, there is no unified explanation. I examine two strategies. We might begin with conditionals and proceed to descriptions. Or we might begin with descriptions and proceed to conditionals. I argue for the latter variant and outline a (...) universal theory of Sobel sequences in terms of presuppositional anaphora. One relevant result is that the phenomenon neither counts against nor in favour of the simplified standard account of counterfactuals à la Stalnaker-Lewis. (shrink)

ABSTRACT The apparent consistency of Sobel sequences famously motivated David Lewis to defend a variably strict conditional semantics for counterfactuals. If Sophie had gone to the parade, she would have seen Pedro. If Sophie had gone to the parade and had been stuck behind someone tall, she would not have seen Pedro. But if the order of the counterfactuals in a Sobel sequence is reversed—in the example, if is asserted prior to —the second counterfactual asserted no longer (...) rings true. This is the Heim sequence problem. That the order of assertion makes this difference is surprising on the variably strict account. Some argue that this is reason to reject the Lewis-Stalnaker semantics outright. Others argue that the problem motivates a contextualist rendering of counterfactuals. Still others maintain that the explanation for the phenomenon is merely pragmatic. I argue that none of these is right, and I defend a novel way to understand the phenomenon. My proposal avoids the problems faced by the alternative analyses and enjoys independent support. There is, however, a difficulty for my view: it entails that many ordinarily accepted counterfactuals are not true. I argue that this cost is acceptable. (shrink)

Recently, von Fintel (2001) and Gillies (2007) have argued that certain sequences of counterfactuals, namely reverse Sobel sequences, should motivate us to abandon standard truth conditional theories of counterfactuals for dynamic semantic theories. I argue that we can give a pragmatic account of our judgments about counterfactuals without giving up the standard semantics. In particular, I introduce a pragmatic principle governing assertability, and I use this principle to explain a variety of subtle data concerning reverse (...) Sobel sequences. (shrink)

This paper is about Sobel sequences, which are sequences of counterfactuals that supposedly display two interesting properties: first, they are consistent, as accounted for by the famous Lewis-Stalnaker analysis; but second, they are not consistent in the reverse order, which is not accounted for by Lewis-Stalnaker. I argue that there has been an empirical oversight in the literature on these sequences: there are consistent sequences, and there are irreversible sequences, but no sequence is (...) both. The Lewis-Stalnaker theory neatly captures Sobel sequences, and also captures the inconsistency of Lewis sequences. But there is still a dynamic asymmetry at work with Lewis sequences, which I account for by appeal to the pragmatic phenomenon of imprecision. Lewis sequences seem consistent because they do not belie factual disagreements, but rather metalinguistic disagreements about how precise to be. This also accounts for their irreversibility—such metalinguistic disagreements about the standard of precision are only possible in one direction, as famously observed by Lewis, who observed them in discourses not containing counterfactuals. (shrink)

I outline and motivate a way of implementing a closest world theory of indicatives, appealing to Stalnaker's framework of open conversational possibilities. Stalnakerian conversational dynamics helps us resolve two outstanding puzzles for a such a theory of indicative conditionals. The first puzzle -- concerning so-called 'reverse Sobel sequences' -- can be resolved by conversation dynamics in a theoryneutral way: the explanation works as much for Lewisian counterfactuals as for the account of indicatives developed here. Resolving the second (...) puzzle, by contrast, relies on the interplay between the particular theory of indicative conditionals developed here and Stalnakerian dynamics. The upshot is an attractive resolution of the so-called "Gibbard phenomenon" for indicative conditionals. (shrink)

A uniform theory of conditionals is one which compositionally captures the behavior of both indicative and subjunctive conditionals without positing ambiguities. This paper raises new problems for the closest thing to a uniform analysis in the literature (Stalnaker, Philosophia, 5, 269–286 (1975)) and develops a new theory which solves them. I also show that this new analysis provides an improved treatment of three phenomena (the import-export equivalence, reverse Sobel-sequences and disjunctive antecedents). While these results concern central issues (...) in the study of conditionals, broader themes in the philosophy of language and formal semantics are also engaged here. This new analysis exploits a dynamic conception of meaning where the meaning of a symbol is its potential to change an agent’s mental state (or the state of a conversation) rather than being the symbol’s content (e.g. the proposition it expresses). The analysis of conditionals is also built on the idea that the contrast between subjunctive and indicative conditionals parallels a contrast between revising and consistently extending some body of information. (shrink)

von Fintel and Gillies : 329–360, 2007) have proposed a dynamic strict conditional account of counterfactuals as an alternative to the standard variably strict account due to Stalnaker and Lewis. Von Fintel’s view is motivated largely by so-called reverse Sobel sequences, about which the standard view seems to make the wrong predictions. More recently Moss :561–586, 2012) has offered a pragmatic/epistemic explanation that purports to explain the data without requiring abandonment of the standard view. So far the (...) small amount of subsequent literature has focused primarily on the original class of cases motivating the strict conditional view. What is needed in the debate is an examination of the predictions of the dynamic strict conditional account for a broader range of data. I undertake this task here, presenting a slew of cases that are problematic for the strict conditional view but not for Moss’s view, and considering some possible responses. Ultimately I take my contribution to constitute a significant blow to the dynamic strict conditional view, though not a decisive verdict against it. (shrink)

Ordinary speakers intuitively assign truth-values to conditional utterances in everyday conversation, but, despite the general ease with which this occurs, it is notoriously difficult to give an account of the implicit logic that is followed in making these truth-value assignments. I propose a twofold logic of the conditional – a relatively simple “factual” logic for conditionals interpreted with regard to what is actually the case, largely following the logic of the material conditional; combined with a variably strict possible-worlds counterfactual logic (...) for conditionals interpreted with regard to with what may be (or may have been) the case, incorporating a ceteris paribus clause. This theory is able to deal with a number of challenges for other prominent views of the conditional, such as counter-intuitive truth-value ascriptions provided by notions of similarity or closeness, and difficulties adequately accounting for phenomena such as reverse Sobel sequences. (shrink)

A part of Stalnaker (1968)’s influential theory of conditionals has been neglected, namely the role for an accessibility relation between worlds. I argue that the accessibility relation does not play the role intended for it in the theory as stated, and propose a minimal revision which solves the problem, and brings the theory in line with the formulation in Stalnaker & Thomason 1970.

The classic Lewis-Stalnaker semantics for counterfactuals captures that Sobel sequences are consistent sequences, for example: a.If Sophie had gone to the parade, she would have seen Pedro dance. b.But if Sophie had gone to the parade and been stuck behind someone tall, she would not have seen Pedro dance. But reverse a sequence like this one and it no longer sounds so good, which is surprising on the classic semantics. This observation motivated Kai von Fintel and (...) Thony Gillies to propose dynamic semantic accounts of counterfactual conditionals. Subsequently, Sarah Moss defended the classic semantics against the charge that it need be abandoned in the face of these order effects, arguing that the infelicity of the reverse sequences is pragmatic. I argue that both accounts are ultimately untenable, but each account has strengths. Seeing what works and what doesn't in each account points the way to the right positive view. With this in mind, I defend a contextualist account of counterfactuals that takes conversational relevance to play a central role. (shrink)

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.

The hallmark of implicit learning is that complex knowledge can be acquired unconsciously. The second order conditionals of Reed and Johnson were developed to be complex, and they are popular materials for implicit learning research. Recently, it was demonstrated that in a sequence made noisy , shared features of the SOCs may be learned explicitly . What are these shared features? We hypothesized that low reversal frequency may play a significant role. We have varied reversal frequency, and discovered that reversal (...) frequency affected response times, inclusion exclusion behavior, and recognition ratings. Not only does it appear to be important to distinguish implicit and explicit knowledge, but also to distinguish what the knowledge is of. (shrink)

One of the earliest applications of transfinite numbers is in the construction of derived sequences by Cantor [2]. In [6], the existence of derived sequences for countable closed sets is proved in ATR0. This existence theorem is an intermediate step in a proof that a statement concerning topological comparability is equivalent to ATR0. In actuality, the full strength of ATR0 is used in proving the existence theorem. To show this, we will derive a statement known to be equivalent (...) to ATR0, using only RCA0 and the assertion that every countable closed set has a derived sequence. We will use three of the subsystems of second order arithmetic defined by H. Friedman , which can be roughly characterized by the strength of their set comprehension axioms. RCA0 includes comprehension for Δmath image definable sets, ACA0 includes comprehension for arithmetical sets, and ATR0 appends to ACA0 a comprehension scheme for sets defined by transfinite recursion on arithmetical formulas. MSC: 03F35, 54B99. (shrink)

Some spatio-temporal structures are easier to transfer implicitly in sequential learning. In this study, we investigated whether the consistent reversal of triads of learned components would support the implicit transfer of their temporal structure in visuomotor sequence learning. A triad comprised three sequential button presses ([1][2][3]) and seven consecutive triads comprised a sequence. Participants learned sequences by trial and error, until they could complete it 20 times without error. Then, they learned another sequence, in which each triad was reversed (...) ([3][2][1]), partially reversed ([2][1][3]), or switched so as not to overlap with the other conditions ([2][3][1] or [3][1][2]). Even when the participants did not notice the alternation rule, the consistent reversal of the temporal structure of each triad led to better implicit transfer; this was confirmed in a subsequent experiment. These results suggest that the implicit transfer of the temporal structure of a learned sequence can be influenced by both the structure and consistency of the change. (shrink)

It has long been recognized that cancer onset and progression represent a type of reversion to an ancestral quasi‐unicellular phenotype. This general concept has been refined into the atavistic model of cancer that attempts to provide a quantitative analysis and testable predictions based on genomic data. Over the past decade, support for the multicellular‐to‐unicellular reversion predicted by the atavism model has come from phylostratigraphy. Here, we propose that cancer onset and progression involve more than a one‐off multicellular‐to‐unicellular reversion, and are (...) better described as a series of reversionary transitions. We make new predictions based on the chronology of the unicellular‐eukaryote‐to‐multicellular‐eukaryote transition. We also make new predictions based on three other evolutionary transitions that occurred in our lineage: eukaryogenesis, oxidative phosphorylation and the transition to adaptive immunity. We propose several modifications to current phylostratigraphy to improve age resolution to test these predictions. Also see the video abstract here: https://youtu.be/3unEu5JYJrQ. (shrink)

In order processing, consecutive sequences (e.g., 1‐2‐3) are generally processed faster than nonconsecutive sequences (e.g., 1‐3‐5) (also referred to as the reverse distance effect). A common explanation for this effect is that order processing operates via a memory‐based associative mechanism whereby consecutive sequences are processed faster because they are more familiar and thus more easily retrieved from memory. Conflicting with this proposal, however, is the finding that this effect is often absent. A possible explanation for these (...) absences is that familiarity may vary both within and across sequence types; therefore, not all consecutive sequences are necessarily more familiar than all nonconsecutive sequences. Accordingly, under this familiarity perspective, familiar sequences should always be processed faster than unfamiliar sequences, but consecutive sequences may not always be processed faster than nonconsecutive sequences. To test this hypothesis in an adult population, we used a comparative judgment approach to measure familiarity at the individual sequence level. Using this measure, we found that although not all participants showed a reverse distance effect, all participants displayed a familiarity effect. Notably, this familiarity effect appeared stronger than the reverse distance effect at both the group and individual level; thus, suggesting the reverse distance effect may be better conceptualized as a specific instance of a more general familiarity effect. (shrink)

This article presents a review of reverse correlation in neurophysiology. We discuss the basis of reverse correlation in linear transducers and in spiking neurons. The application of reverse correlation to measure the receptive fields of visual neurons using white noise and m‐sequences, and classical findings about spatial and color processing in the cortex resulting from such measurements, are emphasized. Finally, we describe new developments in reverse correlation, including “sub‐space” and categorical reverse‐correlation. Recent results obtained (...) by applying such methods in the orientation, spatial‐frequency and Fourier domains have revealed the importance of cortical inhibition in the establishment of sharp tuning selectivity in single neurons. (shrink)

A theory is usually said to be time reversible if whenever a sequence of states S 1 , S 2 , S 3 is possible according to that theory, then the reverse sequence of time reversed states S 3 T , S 2 T , S 1 T is also possible according to that theory; i.e., one normally not only inverts the sequence of states, but also operates on the states with a time reversal operator T . David Albert (...) and Paul Horwich have suggested that one should not allow such time reversal operations T on states. I will argue that time reversal operations on fundamental states should be allowed. I will furthermore argue that the form that time reversal operations take is determined by the type of fundamental geometric quantities that occur in nature and that we have good reason to believe that the fundamental geometric quantities that occur in nature correspond to irreducible representations of the Lorentz transformations. Finally, I will argue that we have good reason to believe that space-time has a temporal orientation. (shrink)

Reverse Mathematics (RM) is a program in the foundations of mathematics where the aim is to find the minimal axioms needed to prove a given theorem of ordinary mathematics. Generally, the minimal axioms are equivalent to the theorem at hand, assuming a weak logical system called the base theory. Moreover, many theorems are either provable in the base theory or equivalent to one of four logical systems, together called the Big Five. For instance, the Weierstrass approximation theorem, i.e., that (...) a continuous function can be approximated uniformly by a sequence of polynomials, has been classified in RM as being equivalent to weak König’s lemma, the second Big Five system. In this paper, we study approximation theorems for discontinuous functions via Bernstein polynomials from the literature. We obtain many equivalences between the latter and weak König’s lemma. We also show that slight variations of these approximation theorems fall far outside of the Big Five but fit in the recently developed RM of new ‘big’ systems, namely the uncountability of ${\mathbb R}$, the enumeration principle for countable sets, the pigeon-hole principle for measure, and the Baire category theorem. (shrink)

A theory is usually said to be time reversible if whenever a sequence of states S 1, S 2, S 3 is possible according to that theory, then the reverse sequence of time reversed states S 3 T, S 2 T, S 1 T is also possible according to that theory; i.e., one normally not only inverts the sequence of states, but also operates on the states with a time reversal operator T. David Albert and Paul Horwich have suggested (...) that one should not allow such time reversal operations T on states. I will argue that time reversal operations on fundamental states should be allowed. I will furthermore argue that the form that time reversal operations take is determined by the type of fundamental geometric quantities that occur in nature and that we have good reason to believe that the fundamental geometric quantities that occur in nature correspond to irreducible representations of the Lorentz transformations. Finally, I will argue that we have good reason to believe that space-time has a temporal orientation. (shrink)

A quasi-order Q induces two natural quasi-orders on $${\mathcal{P}(Q)}$$, but if Q is a well-quasi-order, then these quasi-orders need not necessarily be well-quasi-orders. Nevertheless, Goubault-Larrecq (Proceedings of the 22nd Annual IEEE Symposium 4 on Logic in Computer Science (LICS’07), pp. 453–462, 2007) showed that moving from a well-quasi-order Q to the quasi-orders on $${\mathcal{P}(Q)}$$ preserves well-quasi-orderedness in a topological sense. Specifically, Goubault-Larrecq proved that the upper topologies of the induced quasi-orders on $${\mathcal{P}(Q)}$$ are Noetherian, which means that they contain no (...) infinite strictly descending sequences of closed sets. We analyze various theorems of the form “if Q is a well-quasi-order then a certain topology on (a subset of) $${\mathcal{P}(Q)}$$ is Noetherian” in the style of reverse mathematics, proving that these theorems are equivalent to ACA 0 over RCA 0. To state these theorems in RCA 0 we introduce a new framework for dealing with second-countable topological spaces. (shrink)

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)

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.

Historical reversals highlight a basic methodological problem: is it possible to treat two successive periods both as independent cases to compare for causal analysis and as parts of a single historical sequence? I argue that one strategy for doing so, using models of path dependency, imposes serious limits on explanation. An alternative model which treats successive periods as contrasting solutions for recurrent problems offers two advantages. First, it more effectively combines analytical comparisons of different periods with narratives of causal (...) class='Hi'>sequences spanning two or more periods. Second, it better integrates scholarly accounts of historical reversals with actors’ own narratives of the past. (shrink)

We present evidence of a potentially serious source of error intrinsic to all spotted cDNA microarrays that use IMAGE clones of expressed sequence tags (ESTs). We found that a high proportion of these EST sequences contain 5V-end poly(dT) sequences that are remnants from the oligo(dT)-primed reverse transcription of polyadenylated mRNA templates used to generate EST cDNA for sequence clone libraries. Analysis of expression data from two single-dye cDNA microarray experiments showed that ESTs whose sequences contain repeats (...) of consecutive 5V- end dT residues appeared to be strongly coexpressed, while expression data of all other sequences exhibited no such pattern. Our analysis suggests that expression data from sequences containing 5V poly(dT) tracts are more likely to be due to systematic cross-hybridization of these poly(dT) tracts than to true mRNA coexpression. This indicates that existing data generated by cDNA microarrays containing IMAGE clone ESTs should be filtered to remove expression data containing significant 5V poly(dT) tracts. D 2003 Elsevier Inc. All rights reserved. (shrink)

A simultaneous collision that produces paradoxical indeterminism (involving N0 hypothetical particles in a classical three-dimensional Euclidean space) is described in Section 2. By showing that a similar paradox occurs with long-range forces between hypothetical particles, in Section 3, the underlying cause is seen to be that collections of such objects are assumed to have no intrinsic ordering. The resolution of allowing only finite numbers of particles is defended (as being the least ad hoc) by looking at both -sequences (in (...) the context of a very basic supertask, in Section 4) and *-sequences (reversed -sequences, in the form of paradoxical results from the recent literature). Introduction The simultaneous collision The paradox in other contexts The basic problem is N0 things The recent literature Generating N0 things. (shrink)

Suppose that 〈xk〉k∈ℕ is a countable sequence of real numbers. Working in the usual subsystems for reverse mathematics, RCA0 suffices to prove the existence of a sequence of reals 〈uk〉k∈ℕ such that for each k, uk is the minimum of {x0, x1, …, xk}. However, if we wish to prove the existence of a sequence of integer indices of minima of initial segments of 〈xk〉k∈ℕ, the stronger subsystem WKL0 is required. Following the presentation of these reverse mathematics results, (...) we will derive computability theoretic corollaries and use them to illustrate a distinction between computable analysis and constructive analysis. (shrink)

Beliefs like the Gambler's Fallacy and the Hot Hand have interested cognitive scientists, economists, and philosophers for centuries. We propose that these judgment patterns arise from the observer's mental models of the sequence-generating mechanism, moderated by the strength of belief in an a priori base rate. In six behavioral experiments, participants observed one of three mechanisms generating sequences of eight binary events: a random mechanical device, an intentional goal-directed actor, and a financial market. We systematically manipulated participants’ beliefs about (...) the base rate probabilities at which different outcomes were generated by each mechanism. Participants judged 18 sequences of outcomes produced by a mechanism with either an unknown base rate, a specified distribution of three equiprobable base rates, or a precise, fixed base rate. Six target sequences ended in streaks of between two and seven identical outcomes. The most common predictions for subsequent events were best described as pragmatic belief updating, expressed as an increasingly strong expectation that a streak of identical signals would repeat as the length of that streak increased. The exception to this pattern was for sequences generated by a random mechanical device with a fixed base rate of.50. Under this specific condition, participants exhibited a bias toward reversal of streaks, and this bias was larger when participants were asked to make a dichotomous choice versus a numerical probability rating. We review alternate accounts for the anomalous judgments of sequences and conclude with our favored interpretation that is based on Rabin's version of Tversky & Kahneman's Law of Small Numbers. (shrink)

In his twelfth century alaṃkāraśāstra, the Candrāloka, Jayadeva Pīyūṣavarṣa reverses the sequence of topics found in Mammaṭa’s Kāvyapr-akāśa, an earlier and immensely popular work. With such a structural revisionism, Jayadeva asserts the autonomy of his own work and puts forth an ambitious critique of earlier approaches to literary analysis. Jayadeva investigates the technical and aesthetic components of poetry in the first part of the Candrāloka, prior to his formal semantic investigations in the latter half of the text, thus suggesting that (...) aesthetic evaluations of poetry beneficially inform scientific investigations of language. Jayadeva’s organization of his chapters on the semantic operations, moreover, intimates that the study of suggestive and metaphoric functions of language clarifies our understanding of denotation, which is conventionally understood to be the primary and direct path of verbal designation. (shrink)

1. Setting off: An introduction. 1.1. A measure of motivation. 1.2. Computable mathematics. 1.3. Reverse mathematics. 1.4. An overview. 1.5. Further reading -- 2. Gathering our tools: Basic concepts and notation. 2.1. Computability theory. 2.2. Computability theoretic reductions. 2.3. Forcing -- 3. Finding our path: Konig's lemma and computability. 3.1. II[symbol] classes, basis theorems, and PA degrees. 3.2. Versions of Konig's lemma -- 4. Gauging our strength: Reverse mathematics. 4.1. RCA[symbol]. 4.2. Working in RCA[symbol]. 4.3. ACA[symbol]. 4.4. WKL[symbol]. (...) 4.5. [symbol]-models. 4.6. First order axioms. 4.7. Further remarks -- 5. In defense of disarray -- 6. Achieving consensus: Ramsey's theorem. 6.1. Three proofs of Ramsey's theorem. 6.2. Ramsey's theorem and the arithmetic hierarchy. 6.3. RT, ACA[symbol], and the Paris-Harrington theorem. 6.4. Stability and cohesiveness. 6.5. Mathias forcing and cohesive sets. 6.6. Mathias forcing and stable colorings. 6.7. Seetapun's theorem and its extensions. 6.8. Ramsey's theorem and first order axioms. 6.9. Uniformity -- 7. Preserving our power: Conservativity. 7.1. Conservativity over first order systems. 7.2. WKL[symbol] and II[symbol]-conservativity. 7.3. COH and r-II[symbol]-conservativity -- 8. Drawing a map: Five diagrams -- 9. Exploring our surroundings: The world below RT[symbol]. 9.1. Ascending and descending sequences. 9.2. Other combinatorial principles provable from RT[symbol]. 9.3. Atomic models and omitting types -- 10. Charging ahead: Further topics. 10.1. The Dushnik-Miller theorem. 10.2. Linearizing well-founded partial orders. 10.3. The world above ACA[symbol]. 10.4. Still further topics, and a final exercise. (shrink)

In the context of reverse mathematics, effective transfinite recursion refers to a principle that allows us to construct sequences of sets by recursion along arbitrary well orders, provided that each set is ‐definable relative to the previous stages of the recursion. It is known that this principle is provable in. In the present note, we argue that a common formulation of effective transfinite recursion is too restrictive. We then propose a more liberal formulation, which appears very natural and (...) is still provable in. (shrink)

Sequential recommendation algorithm can predict the next action of a user by modeling the user’s interaction sequence with an item. However, most sequential recommendation models only consider the absolute positions of items in the sequence, ignoring the time interval information between items, and cannot effectively mine user preference changes. In addition, existing models perform poorly on sparse data sets, which make a poor prediction effect for short sequences. To address the above problems, an improved sequential recommendation algorithm based on (...) short-sequence enhancement and temporal self-attention mechanism is proposed in this paper. In the proposed algorithm, a backward prediction model is trained first, to predict the prior items in the user sequence. Then, the reverse prediction model is used to generate a batch of pseudo-historical items before the initial items of the short sequence, to achieve the goal of enhancing the short sequence. Finally, the absolute position information and time interval information of the user sequence are modeled, and a time-aware self-attention model is adopted to predict the user’s next action and generate a recommendation list. Various experiments are conducted on two public data sets. The experimental results show that the method proposed in this paper has excellent performance on both dense and sparse data sets, and its effect is better than that of the state of the art. (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)

This paper studies categories and functors in the context of reverse and computable mathematics. In ordinary reverse mathematics, we only focuses on categories whose objects and morphisms can be represented by natural numbers. We first consider morphism sets of categories and prove several associated theorems equivalent to $$\mathrm ACA_{0}$$ over the base system $$\mathrm RCA_{0}$$. The Yoneda Lemma is a basic result in category theory and homological algebra. We then develop an effective version of the Yoneda Lemma in (...) $$\mathrm RCA_{0}$$ ; as an application, we formalize an effective version of the Yoneda Embedding in $$\mathrm RCA_{0}$$. Products and coproducts are basic notions for defining special categories like semi-additive categories and additive categories. We study properties of products and coproducts of a sequence of objects of categories and provide effective characterizations of semi-additive categories and additive categories in terms of products and coproducts. Finally, we further consider the strength of theorems of category theory that are studied in this paper by methods of higher-order reverse mathematics. (shrink)

In this paper, I argue that the recent discussion on the time - reversal invariance of classical electrodynamics (see (Albert 2000: ch.1), (Arntzenius 2004), (Earman 2002), (Malament 2004),(Horwich 1987: ch.3)) can be best understood assuming that the disagreement among the various authors is actually a disagreement about the metaphysics of classical electrodynamics. If so, the controversy will not be resolved until we have established which alternative is the most natural. It turns out that we have a paradox, namely that the (...) following three claims are incompatible: the electromagnetic fields are real, classical electrodynamics is time-reversal invariant, and the content of the state of affairs of the world does not depend on whether it belongs to a forward or a backward sequence of states of the world. (shrink)

We present evidence of a potentially serious source of error intrinsic to all spotted cDNA microarrays that use IMAGE clones of expressed sequence tags (ESTs). We found that a high proportion of these EST sequences contain 5V-end poly(dT) sequences that are remnants from the oligo(dT)-primed reverse transcription of polyadenylated mRNA templates used to generate EST cDNA for sequence clone libraries. Analysis of expression data from two single-dye cDNA microarray experiments showed that ESTs whose sequences contain repeats (...) of consecutive 5V- end dT residues appeared to be strongly coexpressed, while expression data of all other sequences exhibited no such pattern. Our analysis suggests that expression data from sequences containing 5V poly(dT) tracts are more likely to be due to systematic cross-hybridization of these poly(dT) tracts than to true mRNA coexpression. This indicates that existing data generated by cDNA microarrays containing IMAGE clone ESTs should be filtered to remove expression data containing significant 5V poly(dT) tracts. D 2003 Elsevier Inc. All rights reserved. (shrink)

We analyze the pointwise convergence of a sequence of computable elements of L1 in terms of algorithmic randomness. We consider two ways of expressing the dominated convergence theorem and show that, over the base theory RCA0, each is equivalent to the assertion that every Gδ subset of Cantor space with positive measure has an element. This last statement is, in turn, equivalent to weak weak Königʼs lemma relativized to the Turing jump of any set. It is also equivalent to the (...) conjunction of the statement asserting the existence of a 2-random relative to any given set and the principle of Σ2 collection. (shrink)

Information security is perceived as an important and vital aspect for the survival of any business. Preserving user identity and limiting the access of web resources only to the humans and restricting ‘bots’ is an ever challenging area of study. With the increase in computing power and development of newer approaches towards circumvention and reverse-engineering, the recognition gap present between the machines and the humans is said to be decreasing. Turing test and its modified versions are in place to (...) deal with such problems and ways to resolve them by developing complex algorithms for bot prevention systems like CAPTCHA (Completely Automated Public Turing test to tell Computers and Humans Apart). This paper will deal with the use of “Machine Vision” for judging the ability of the machines to compete with humans in breaking sequences of security systems like CAPTCHA. Reverse Turing test will be put to practise here. Complex image recognition technologies and novel approaches towards using Human interactive proofs (HIP) are discussed. The progress of Turing test over the past 60 years has been paid due attention at the end. After all this experimentation, it can be said that the current machine vision is quite poor and is far worse than it is expected to be. (shrink)

Two experiments involving an international collaboration of experimenters sought to replicate and extend a previously published psi experiment on precognition by Daryl Bem that has been the focus of extensive research. The experiment reverses the usual cause–effect sequence of a standard psychology experiment using priming and reaction times. The preregistered confirmatory hypothesis is that response times to incongruent stimuli will be longer than response times to congruent stimuli even though the prime has not yet appeared when the participant records their (...) judgments. The confirmatory hypothesis for Experiment 1 was not supported. Exploratory analyses indicated that those participants who completed the English-language version rather than a translation showed a significant effect, as was the case in the original study; no significant departure from chance was found in data involving non-English translations. Experiment 2 sought to enhance the predicted effect by having each participant read either a pro-psi or an anti-psi statement at the beginning of the experiment to test the pre-recorded hypothesis that a pro-psi statement would produce a larger effect than an anti-psi statement. The results did not support the primary psi hypothesis and there was no effect in the English-language sample. However, there was mixed support for the effect of the psi statement on performance; those participants who received the pro-psi statement had a greater psi score than those who received the anti-psi statement. As in the original experiment, neither the experimenters’ nor participants’ beliefs were significantly associated with the dependent measure. In sum, the pre-registered confirmatory hypotheses were not supported. The importance of the personality variable Sensation Seeking, a component of extraversion, as a correlate of psi performance is discussed as are the challenges and implications for international collaborations and replication in controversial science. Keywords: priming; expectancy effect; retrocausation; consciousness; sociology; precognition; psi; replication Two experiments involving an international collaboration of experimenters sought to replicate and extend a previously published psi experiment on precognition by Daryl Bem that has been the focus of extensive research. The experiment reverses the usual cause-effect sequence of a standard psychology experiment using priming and reaction times. The preregistered confirmatory hypothesis is that response times to incongruent stimuli will be longer than response times to congruent stimuli even though the prime has not yet appeared when the participant records his or her judgments. The confirmatory hypothesis for Study 1 was not supported. Exploratory analyses indicated that those participants who completed the English-language version rather than a translation showed a significant effect, as was the case in the original study; no significant departure from chance was found in data involving non-English translations. Study 2 sought to enhance the predicted effect by having each participant read either a pro-psi or an anti-psi statement at the beginning of the experiment to test the pre-recorded hypothesis that a pro-psi statement would produce a larger effect than an anti-psi statement. The results did not support the primary psi hypothesis and there was no observed association between belief and experience of ESP and psi outcome. However, there was mixed support for the effect of the psi statement on performance; those participants who received the pro-psi statement had a greater psi score than those who received anti-psi statement. As in the original experiment, neither the experimenters’ nor participants’ beliefs or expectations were significantly correlated with the dependent measure. In sum, the pre-registered confirmatory hypotheses were not supported. The importance of the personality variable Sensation Seeking, a component of extraversion, as a correlate of psi performance is discussed as are the challenges and implications for international collaborations and replication in controversial science. (shrink)

Gene retrocopies are generated by reverse transcription and genomic integration of mRNA. As such, retrocopies present an important exception to the central dogma of molecular biology, and have substantially impacted the functional landscape of the metazoan genome. While an estimated 8,000–17,000 retrocopies exist in the human genome reference sequence, the extent of variation between individuals in terms of retrocopy content has remained largely unexplored. Three recent studies by Abyzov et al., Ewing et al. and Schrider et al. have exploited (...) 1,000 Genomes Project Consortium data, as well as other sources of whole‐genome sequencing data, to uncover novel gene retrocopies. Here, we compare the methods and results of these three studies, highlight the impact of retrocopies in human diversity and genome evolution, and speculate on the potential for somatic gene retrocopies to impact cancer etiology and genetic diversity among individual neurons in the mammalian brain. (shrink)

We observe that Schrödinger’s equation may be written as two real coupled Hamilton–Jacobi (HJ)-like equations, each involving a quantum potential. Developing our established programme of representing the quantum state through exact free-standing deterministic trajectory models, it is shown how quantum evolution may be treated as the autonomous propagation of two coupled congruences. The wavefunction at a point is derived from two action functions, each generated by a single trajectory. The model shows that conservation as expressed through a continuity equation is (...) not a necessary component of a trajectory theory of state. Probability is determined by the difference in the action functions, not by the congruence densities. The theory also illustrates how time-reversal symmetry may be implemented through the collective behaviour of elements that individually disobey the conventional transformation (T\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm{T}$$\end{document}) of displacement (scalar) and velocity (reversal). We prove that an integral curve of the linear superposition of two vectors can be derived algebraically from the integral curves of one of the constituent vectors labelled by integral curves associated with the other constituent. A corollary establishes relations between displacement functions in diverse trajectory models, including where the functions obey different symmetry transformations. This is illustrated by showing that a (T\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm{T}$$\end{document}-obeying) de Broglie-Bohm trajectory is a sequence of points on the (non-T\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm{T}$$\end{document}) HJ trajectories, and vice versa. (shrink)

The following semantics for counterfactuals is fairly standard: for a counterfactual to be true, the closest antecedent worlds have to be consequent worlds. Closeness is measured by overall similarity of worlds to an evaluation world. There is a range of interrelated challenges to this account: counterfactual scepticism, ‘Hegel’-, ‘Sobel’-, and ‘Heim’-sequences. So far there is no unified solution to these challenges. I discuss a solution that preserves the standard semantics by writing the shifty parameter into pragmatics. The solution (...) has been suggested by Križ for Sobel- and Heim-sequences, yet I argue that it can be generalized to counterfactual scepticism. Conditionals are subject to a pattern which is familiar from descriptions. Everyday counterfactuals are semantically homogeneous and pragmatically non-maximal. Homogeneity: a counterfactual is neither true nor false if only some but not all closest antecedent worlds are consequent worlds. Non-maximality: in many contexts, not all but only practically all closest antecedent worlds have to be consequent worlds for the utterance of a counterfactual to say something true if the difference does not matter for the purposes of conversation. (shrink)

Fragile X‐linked mental retardation is an enigmatic inheritable syndrome in which severe mental retardation, a cytogenetically detectable fragile site at Xq27.3 (FraX) and a number of dysmorphic features are associated. Genetic analysis shows that the mode of inheritance is more complex than a straightforward X‐linked recessive trait and probably involves a two‐step process for which several models have been proposed. Early attempts ‘at cloning the fragile site’ provided several DNA segments lying in its general vicinity, and large scale DNA mapping (...) methods were extensively applied in an effort to generate maps including this region. These efforts were complemented by more focussed methods such as microdissection; together these approaches have now provided a number of DNA segments within a 5cM interval around FraX, and with the help of these new probes the site is indeed being cloned. Unravelling the nature of the sequence(s) responsible for the mental retardation syndrome will probably take some time, however. (shrink)

Counterfactuals are typically thought--given the force of Sobel sequences--to be variably strict conditionals. I go the other way. Sobel sequences and (what I call) Hegel sequences push us to a strict conditional analysis of counterfactuals: counterfactuals amount to some necessity modal scoped over a plain material conditional, just which modal being a function of context. To make this worth saying I need to say just how counterfactuals and context interact. No easy feat, but I have (...) something to say on the matter. (shrink)

Two reverse supertasks—one new and one invented by Pérez Laraudogoitia —are discussed. Contra Kerkvliet and Pérez Laraudogoitia, it is argued that these supertasks cannot be used to conduct fair infinite lotteries, i.e., lotteries on the set of natural numbers with a uniform probability distribution. The new supertask involves an infinity of gods who collectively select a natural number by each removing one ball from a collection of initially infinitely many balls in a reverse omega-sequence of actions.

Like most good educational interventions, problem-based learning (PBL) did not grow out of theory, but out of a practical problem. Medical students were bored, dropping out, and unable to apply what they had learned in lectures to their practical experiences a couple of years later. Neurologist Howard S. Barrows reversed the sequence, presenting students with patient problems to solve in small groups and requiring them to seek relevant knowledge in an effort to solve those problems. Out of his work, PBL (...) was born.The book is divided into four sections, each containing contributions by leaders in the field. Chapters in the first section focus on the structure of PBL and the critical elements of the approach. Articulating the underlying problems to be addressed, the role of facilitators, and the process to be followed in achieving a successful PBL intervention are all discussed. The second section explores how PBL has been adapted to function in areas outside medicine, from climate science to teacher education, while the third section explores how the methodology has been combined with other approaches to teaching and learning, such as learning by design and project-based learning. The fourth section assesses the impact of PBL techniques on improving both research and teaching. An epilogue speculates about the future of PBL, synthesizing contributions from the previous chapters and suggesting key themes for further exploration. (shrink)

Automatic detection of information changes in the visual environment is crucial for individual survival. Researchers use the oddball paradigm to study the brain’s response to frequently presented stimuli and occasionally presented stimuli. The component that can be observed in the difference wave is called visual mismatch negativity, which is obtained by subtracting event-related potentials evoked by the deviant from ERPs evoked by the standard. There are three hypotheses to explain the vMMN. The sensory fatigue hypothesis considers that weakened neural activity (...) caused by repetition results in decreased ERPs of the standard. The memory trace hypothesis proposes that vMMN results from increased responses to the deviant. The predictive coding hypothesis attributes the difference to enhanced responses for deviants and suppression for standards. However, when distinguishing between these effects, previous researchers did not consider the effect of low-level features on the vMMN. In this experiment, we used face sequences composed of different emotions and presented an oddball sequence, a reverse oddball sequence, and an equiprobable sequence to participants. The deviant of the oddball sequence was subtracted from the standard of the oddball sequence, the reverse oddball sequence, and the same type of stimulus of the equiprobable sequence to get oddball-vMMN, reverse oddball-vMMN, and equiprobable-vMMN, respectively. The results showed no significant difference between vMMN2 and vMMN3 in 100–350 ms following stimulus onset, while the vMMN effect was significant, indicating that the probability of the standard did not affect vMMN, which supported the memory trace hypothesis. Additionally, the fearful-related vMMN were more negative than the neutral-related vMMN within the range of 100–150 ms, suggesting a negative bias. We analyzed the source location of different vMMNs. There was no significant difference in brain regions between different vMMNs. Time-frequency analysis showed that the deviant had stronger theta-band oscillatory than the standard. However, there was no difference between vMORs2 and vMORs3, indicating that vMORs reflect an enhanced response to the deviant in terms of neural oscillation, supporting the memory trace hypothesis. (shrink)