Hilbert,logicism, and mathematical existence

David Hilbert’s early foundational views, especially those corresponding to the 1890s, are analysed here. I consider strong evidence for the fact that Hilbert was a logicist at that time, following upon Dedekind’s footsteps in his understanding of pure mathematics. This insight makes it possible to throw new light on the evolution of Hilbert’s foundational ideas, including his early contributions to the foundations of geometry and the real number system. The context of Dedekind-style logicism makes it possible to offer a new analysis of the emergence of Hilbert’s famous ideas on mathematical existence, now seen as a revision of basic principles of the “naive logic” of sets. At the same time, careful scrutiny of his published and unpublished work around the turn of the century uncovers deep differences between his ideas about consistency proofs before and after 1904. Along the way, we cover topics such as the role of sets and of the dichotomic conception of set theory in Hilbert’s early axiomatics, and offer detailed analyses of Hilbert’s paradox and of his completeness axiom (Vollständigkeitsaxiom).     

Speech perception deficits by Chinese children with phonological dyslexia

Findings concerning the relation between dyslexia and speech perception deficits are inconsistent in the literature. This study examined the relation in Chinese children using a more homogeneous sample—children with phonological dyslexia. Two experimental tasks were administered to a group of Chinese children with phonological dyslexia, a group of age-matched control children, and a group of adults. In addition to a categorical perception task, a selective adaptation task was carried out. The results indicated that Chinese children with phonological dyslexia were less consistent than both the child and adult control groups in identifying stimuli within a given phonetic category. Furthermore, they did not show any significant adaptation effects in the selective adaptation task even when the adapting stimulus was identical to an endpoint stimulus in the test continuum. It seems that children with phonological dyslexia have a general deficiency in representing and processing speech stimuli.     

Logic with numbers

Many people regard utility theory as the only rigorous foundation for subjective probability, and even de Finetti thought the betting approach supplemented by Dutch Book arguments only good as an approximation to a utility-theoretic account. I think that there are good reasons to doubt this judgment, and I propose an alternative, in which the probability axioms are consistency constraints on distributions of fair betting quotients. The idea itself is hardly new: it is in de Finetti and also Ramsey. What is new is that it is shown that probabilistic consistency and consequence can be defined in a way formally analogous to the way these notions are defined in deductive (propositional) logic. The result is a free-standing logic which does not pretend to be a theory of rationality and is therefore immune to, among other charges, that of “logical omniscience”.     

Semantic transparency in free stems: The effect of Orthography-Semantics Consistency on word recognition

A largely overlooked side effect in most studies of morphological priming is a consistent main effect of semantic transparency across priming conditions. That is, participants are faster at recognizing stems from transparent sets (e.g., farm) in comparison to stems from opaque sets (e.g., fruit), regardless of the preceding primes. This suggests that semantic transparency may also be consistently associated with some property of the stem word. We propose that this property might be traced back to the consistency, throughout the lexicon, between the orthographic form of a word and its meaning, here named Orthography-Semantics Consistency (OSC), and that an imbalance in OSC scores might explain the “stem transparency” effect. We exploited distributional semantic models to quantitatively characterize OSC, and tested its effect on visual word identification relying on large-scale data taken from the British Lexicon Project (BLP). Results indicated that (a) the “stem transparency” effect is solid and reliable, insofar as it holds in BLP lexical decision times (Experiment 1); (b) an imbalance in terms of OSC can account for it (Experiment 2); and (c) more generally, OSC explains variance in a large item sample from the BLP, proving to be an effective predictor in visual word access (Experiment 3).     

Choosing what I want or keeping what I should: The effect of decision strategy on choice consistency

We examine decision-makers’ consistency vis-à-vis their own priorities in a multi-choice task, using either an inclusion or exclusion strategy to reduce a set of alternatives. Four studies demonstrate that people’s decisions are more consistent with their priorities when using an exclusion vs. an inclusion strategy to screen alternatives. Moreover, this effect was stronger for less knowledgeable than for more knowledgeable decision-makers. We examined two possible mechanisms behind this phenomenon. First, we suggest that the process of thinking about the positive aspects of the alternatives (associated with inclusion) encourages the decision-maker to more favorably evaluate options initially given low marks, resulting in less consistency with preferences. We also show that under exclusion, people tend to select the alternatives that they think they should choose, while under inclusion they tend to choose options that are more in line with what they would like to have but which may be perceived as luxuries.     

Assessing within-person personality variability via frequency estimation: More evidence for a new measurement approach

Variability in personality has been recognized in recent years as an important aspect of personality both conceptually and empirically. A relatively new and efficient method of obtaining variability information is frequency-based personality assessment (Edwards & Woehr, 2007). The purpose of the present research is to further examine the viability of frequency-based personality measurement as an alternative to traditional (Likert-type) measurement and to assess the usefulness of the variance-based parameters. Toward this end, three studies are presented. Specifically, Study 1 examined relationships between a frequency-based measure of the Big Five personality traits and several motivational variables. Study 2 examined the moderating role of temporal consistency information (provided by frequency-based measurement) on relationships between personality and peer ratings of task performance. Study 3 compared the frequency-based measure to a Likert-type measure with respect to each measure’s susceptibility to deliberate response distortion. Results indicated that consistency information increases the predictive validity of agreeableness and conscientiousness and that a frequency-based format is less susceptible to faking than a Likert-type format for conscientiousness, emotional stability, and openness to experience.     

Exploring orthographic neighborhood size effects in a computational model of Chinese character naming

Orthographic neighborhood (N) size effects have been extensively studied in English consistently producing a facilitatory effect in word naming tasks. In contrast, several recent studies on Chinese character naming have demonstrated an inhibitory effect of neighborhood size. Response latencies tend to be inhibited by inconsistent characters with large neighborhoods relative to small neighborhoods. These differences in neighborhood effects between languages may depend on the characteristics (depth) of the mapping between orthography and phonology. To explore this, we first conducted a behavioral experiment to investigate the relationship between neighborhood size, consistency and reading response. The results showed an inhibitory effect of neighborhood size for inconsistent characters but a facilitatory effect for consistent characters. We then developed two computational models based on parallel distributed processing principles to try and capture the nature of the processing that leads to these results in Chinese character naming. Simulations using models based on the triangle model of reading indicated that consistency and neighborhood size interact with the division of labor between semantics and phonology to produce these effects.     

Natural Leaders: Some Interlocutors Elicit Greater Convergence Across Conversations and Across Characteristics

Are there individual tendencies in convergence, such that some speakers consistently converge more than others? Similarly, are there natural “leaders,” speakers with whom others converge more? Are such tendencies consistent across different linguistic characteristics? We use the Switchboard Corpus to perform a large-scale convergence study of speakers in multiple conversations with different interlocutors, across six linguistic characteristics. Because each speaker participated in several conversations, it is possible to look for individual differences in speakers' likelihood of converging and interlocutors' likelihood of eliciting convergence. We only find evidence for individual differences by interlocutor, not by speaker: There are natural leaders of convergence, who elicit more convergence than others across characteristics and across conversations. The lack of similar evidence for speakers who converge more than others suggests that social factors have a stronger effect in mediating convergence than putative individual tendencies in producing convergence, or that such tendencies are characteristic-specific.     

Beyond Consistency: Contextual Dependency of Language Style in Monolog and Conversation

Language is highly dynamic: It unfolds over time, and we can use it to achieve a wide variety of communicative goals, from telling a story to trying to persuade another person. One aspect of language that has gained increasing popularity among researchers in the last several decades is the individual language style (LS) represented by an individual’s use of function words (e.g., pronouns, articles). Previous approaches to LS mostly focus on LS of one individual in isolation, paying less attention to the fact that language emerges from interaction with others. The aim of this paper is twofold: First, we integrate LS into a dynamical theoretical framework and present an innovative methodological approach. Second, this paper aims to address how interactive conversation—as an aspect of the communicative setting—changes an individual’s LS. We use recurrence quantification analysis to look at structure in patterns of LS in monologs and conversations of 118 participants. Our results showed that LS significantly differs from monolog to conversation, and post hoc analyses further revealed that the change in LS is greater for conflict than for friendly conversations. The difference between monologs and conversations is reflected more strongly in the dynamics (i.e., structure and complexity) of LS than the proportion of function words used. Theoretical implications and directions for future studies are discussed.