Graham Priest argued that all the paradoxes of set theory and logic fall under one schema; and hence they should be solved by one kind of solution. This reply addresses both claims, and counters that in fact at least one paradox escapes the schema, and also some apparently "safe" theorems fall within it; and even for the range of paradoxes so captured by the schema, the assumption of a common solution is not obvious; each paradox surely depends upon the theory (...) and context in which it arises. Details of Priest's proposed solution are also sought. (shrink)

In this article, I provide a close analysis of the resolutions to God as first known in Bonaventure’s Itinerarium mentis in Deum and the Collationes in Hexaemeron. Hardly any methodological reflection has been given to the fact that there are two accounts of God as first known in each of these works. Myanalysis shows that there exists a structural similarity between the Itinerarium and the Hexaemeron with regard to their treatment of Deus primum cognitum. In both texts, Bonaventure’s (...) doctrine on God as first known exhibits a dynamic character, which I relate to the fact that both texts present a spiritual discourse dealing with the gradual transformation of the soul, in which the resolutions are embedded. Each of the two resolutions is part of a different stage of the development ofknowledge that corresponds to this transformation. (shrink)

We establish some similarities/analogies between uncountable cardinals or powersets and the class V of all sets. They concern mainly the Boolean algebras, for a regular cardinal κ, and (the class of subclasses of the universe V), endowed with some ideals, especially the ideal for, and the ideal of sets V for.

In the debate about the nature and identity of possible worlds, philosophers have neglected the parallel questions about the nature and identity of moments of time. These are not questions about the structure of time in general, but rather about the internal structure of each individual time. Times and worlds share the following structural similarities: both are maximal with respect to propositions (at every world and time, either p or p is true, for every p); both are consistent; both (...) are closed (every modal consequence of a proposition true at a world is also true at that world, and every tense-theoretic consequence of a proposition true at a time is also true at that time); just as there is a unique actual world, there is a unique present moment; and just as a proposition is necessarily true iff true at all worlds, a proposition is eternally true iff true at all times. In this paper, I show that a simple extension of my theory of worlds yields a theory of times in which the above structural similarities between the two are consequences. (shrink)

Humphreys and Forde (H&F) propose that greater within- category structural similarity makes living things more difficult to name. However, recent studies show that normal subjects find it easier to name living than nonliving things when these are matched across category for potential artefacts. Additionally, at the level of single pixels, visual overlap appears to be greater for nonliving things.

We propose and investigate an Analogy Principle in the context of Unary Inductive Logic based on a notion of support by structural similarity which is often employed to motivate scientific conjectures.

In organisms, ribonucleic acid plays an essential role. Its function is being discovered more and more. Due to the conserved nature of RNA sequences, its function mainly depends on the RNA secondary structure. The discovery of an approximate relationship between two RNA secondary structures helps to understand their functional relationship better. It is an important and urgent task to explore structural similarities from the graphical representation of RNA secondary structures. In this paper, a novel graphical analysis method based on (...) the triple vector curve representation of RNA secondary structures is proposed. A combinational method involving a discrete wavelet transform and fractal dimension with sliding window is introduced to analyze and compare the graphs derived from feature extraction; after that, the distance matrix is generated. Then, the distance matrix is analyzed by clustering and visualized as a clustering tree. RNA virus and noncoding RNA datasets are applied to perform experiments and analyze the clustering tree. The results show that the proposed method yields more accurate results in the comparison of RNA secondary structures. (shrink)

The expression of physical motion (the spider crawls across the net) and metaphorical motion (the fear crawls across her heart) shows strong inter-typological differences between language types (German, an S-language vs. Spanish, a V-language) and more subtle intra-typological differences within a language type (German vs. Polish, both S-languages). However, we know relatively less about the extension of these patterns to translated texts. In this study, we focused on physical and metaphorical motion descriptions in written texts in original language and their (...) translations to a language that belongs to the same or a different typological group, to determine whether motion expression in translated texts shows the same patterns of inter-typological and intra-typological variability as it does in original texts. We investigated this question by extracting 450 physical motion (150/language) and 450 metaphorical motion (150/language) descriptions from novels originally written in German, Polish, or Spanish and their translations to typologically different (i.e. inter-typological; German to Spanish, Spanish to German) or typologically similar (i.e. intra-typological; German to Polish, Polish to German) languages. Our results provided evidence for similar patterns of strong inter-typological and more subtle intra-typological variability in translations akin to those observed in original texts – with translated texts largely following the patterns of the target language in their expression of physical and metaphorical motion. Our results also highlighted specificity of event expression in a language as an important factor in the attainment of target language patterns in translated texts. (shrink)

The concept of emergence is commonly invoked in modern physics but rarely defined. Building on recent influential work by Jeremy Butterfield, I provide precise definitions of emergence concepts as they pertain to properties represented in models, applying them to some basic examples from space-time and thermostatistical physics. The chief formal innovation I employ, similarity structure, consists in a structured set of similarity relations among those models under analysis—and their properties—and is a generalization of topological structure. Although motivated from (...) physics, this similarity-structure-based account of emergence applies to any science that represents its possibilia with models. (shrink)

Does y obtain under the counterfactual supposition that x? The answer to this question is famously thought to depend on whether y obtains in the most similar world in which x obtains. What this notion of ‘similarity’ consists in is controversial, but in recent years, graphical causal models have proved incredibly useful in getting a handle on considerations of similarity between worlds. One limitation of the resulting conception of similarity is that it says nothing about what would (...) obtain were the causal structure to be different from what it actually is, or from what we believe it to be. In this paper, we explore the possibility of using graphical causal models to resolve counterfactual queries about causal structure by introducing a notion of similarity between causal graphs. Since there are multiple principled senses in which a graph G* can be more similar to a graph G than a graph G**, we introduce multiple similarity metrics, as well as multiple ways to prioritize the various metrics when settling counterfactual queries about causal structure. (shrink)

I provide a formally precise account of diachronic emergence of properties as described within scientific theories, extending a recent account of synchronic emergence using similarity structure on the theories’ models. This similarity structure approach to emergent properties unifies the synchronic and diachronic types by revealing that they only differ in how they delineate the domains of application of theories. This allows it to apply also to cases where the synchronic/diachronic distinction is unclear, such as spacetime emergence from theories (...) of quantum gravity. In addition, I discuss two further case studies—finite periodicity in van der Pol oscillators and two-dimensional quasiparticles in the fractional quantum Hall effect—to facilitate comparison of this approach to others in the literature on concepts of emergence applicable to the sciences. My discussion of the fractional quantum Hall effect in particular may be of independent interest to philosophers of physics concerned with its interpretation. (shrink)

Theories of analogical reasoning have viewed relational structure as the dominant determinant of analogical mapping and inference, while assigning lesser importance to similarity between individual objects. An experiment is reported in which these two sources of constraints on analogy are placed in competition under conditions of high relational complexity. Results demonstrate equal importance for relational structure and object similarity, both in analogical mapping and in inference generation. The human data were successfully simulated using a computational analogy model (LISA) (...) that treats both relational correspondences and object similarity as soft constraints that operate within a limited-capacity working memory; but not with a model (SME) that treats relational structure as pre-eminent. (shrink)

Political sociologists interested in corporate power have focused increasingly on the extent to which the business community is cohesive. Studies of cohesion, however, frequently contain either no definition or operational definitions with little theoretical rationale. This paper examines the uses of the term cohesion in the power structure literature as well as in classical and contemporary sociological theory. I argue that: (1) cohesion is most appropriately defined as an objective characteristic of a social structure; (2) to understand a group's power, (...) we should focus on the extent to which its members behave similarly; and (3) the concept of structural equivalence may be as likely to capture the processes of interest to power structure researchers as the concept of cohesion. Findings from a study of corporate political behavior are presented to illustrate this argument. (shrink)

While language is presumably unique to humans, there are possible pre-linguistic features that developed in the course of human evolution which predate features of language, and might have even been essential for its evolution. A number of such possible preadaptations for human language have been discussed, like the permanent lowering of the larynx, the ability to control one’s breath, or the inclination of humans to imitate. In this paper I would like to point out another candidate for a preadaptation, namely (...) the functional differentiation of the hands and the way in which they cooperate in manual actions. (shrink)

Previous research has demonstrated how emotion resembling cues in the face help shape impression formation. Perhaps most notable in the literature to date, has been work suggesting that gender-related appearance cues are visually confounded with certain stereotypic expressive cues. Only a couple studies to date have used computer vision to directly map out and test facial structural resemblance to emotion expressions using facial landmark coordinates to estimate face shape. In one study using a Bayesian network classifier trained to detect (...) emotional expressions structural resemblance to a specific expression on a non-expressive face was found to influence trait impressions of others. In another study, a connectionist model trained to detect emotional expressions found different emotion-resembling cues in male vs. female faces. Despite this seminal work, direct evidence confirming the theoretical assertion that humans likewise utilize these emotion-resembling cues when forming impressions has been lacking. Across four studies, we replicate and extend these prior findings using new advances in computer vision to examine gender-related, emotion-resembling structure, color, and texture and their impact on gender-stereotypic impression formation. We show that all three are meaningfully related to human impressions of emotionally neutral faces. Further when applying the computer vision algorithms to experimentally manipulate faces, we show that humans derive similar impressions from them as did the computer. (shrink)

Recently, interest has surged in similarity-based epistemologies of possibility. However, it has been pointed out that the notion of ‘relevant similarity’ is not properly developed in this literature. In this paper, I look at the research done in the field of analogical reasoning, where we find that one of the most promising ways of capturing relevance in similarity reasoning is by relying on the predictive analogy similarity relation. This takes relevant similarity to be based on (...) shared properties that have structural relations to the property of interest. I argue that if we base our epistemology of possibility on similarity reasoning on the predictive analogy similarity relation, we require prior knowledge of the specifics of these structural relations. I discuss a number of possible responses to this on behalf of the similarity theorists given their methodological approach to the epistemology of modality more generally. They could either opt for making explicit the metaphysics underlying these structural relations, in which case they need to spell out how we can come to know these relations. Or they could opt for developing a theory that explains why we do not need to have explicit knowledge of these structural relations; for example by suggesting that we make use of epistemic shortcuts. (shrink)

Recently, interest has surged in similarity-based epistemologies of possibility. However, it has been pointed out that the notion of ‘relevant similarity’ is not properly developed in this literature. In this paper, I look at the research done in the field of analogical reasoning, where we find that one of the most promising ways of capturing relevance in similarity reasoning is by relying on the predictive analogy similarity relation. This takes relevant similarity to be based on (...) shared properties that have structural relations to the property of interest. I argue that if we base our epistemology of possibility on similarity reasoning on the predictive analogy similarity relation, we require prior knowledge of the specifics of these structural relations. I discuss a number of possible responses to this on behalf of the similarity theorists given their methodological approach to the epistemology of modality more generally. They could either opt for making explicit the metaphysics underlying these structural relations, in which case they need to spell out how we can come to know these relations. Or they could opt for developing a theory that explains why we do not need to have explicit knowledge of these structural relations; for example by suggesting that we make use of epistemic shortcuts. (shrink)

Properties of mental representation are related to findings in cognitive science and ideas in shamanism. A selective review of research in cognitive science suggests visual images and spatial memory preserve important functional information regarding physical principles and the behavior of objects in the natural world, and notions of second‐order isomorphism and the perceptual cycle developed to account for such findings are related to shamanic experience. Possible roles of implicit processes in shamanic cognition, and the idea that shamanic experience may involve (...) normally unconscious information becoming temporarily available to consciousness, are considered. The existence of a cognitive module dedicated to processing information relevant to social knowledge and social interaction is consistent with cognitive science and with shamanism, and may help account for the extension of intentionality and meaning that characterize shamanic practice. Overall, findings from cognitive science and ideas from shamanism exhibit a number of correspondences and similarities regarding basic properties of cognition, and this suggests that shamanic and nonshamanic cognition may not be fundamentally different. (shrink)

Categories, as mental structures, are more than simply sums of property frequencies. A number of recent studies have supported the view that the properties of categories may be organised along functional lines and possibly dependency structures more generally. The study presented here investigates whether earlier findings reflect something unique in the English language/North American culture or whether the functional structuring of categories is a more universal phenomenon. A population of English-speaking Americans was compared to a population of Cantonese-speaking Hong Kong (...) Chinese. The findings clearly support the view that functional influences on category centrality are universal (or at least common to Cantonese-speaking Hong Kong Chinese and English-speaking Americans), albeit with specific cross-cultural/cross-linguistic group differences in the particular properties that are considered central to categories. (shrink)

A promising approach to more refined models consistent with the Caplan & Waters hypothesis is based on similarity-based interference, a general principle that applies across working memory domains. This may explain both the fine details of syntactic working memory phenomena and the gross fractionation for which Caplan & Waters have found evidence. Detailed models of syntactic processing that embody similarity-based interference fare well cross-linguistically.

Apart from the computationally appealing properties of representation by similarities, it is possible to extend this form of representation when needed to include object parts as well as the correspondence between subobject parts.

Similarity-based cognition is commonplace. It occurs whenever an agent or system exploits the similarities that hold between two or more items—e.g., events, processes, objects, and so on—in order to perform some cognitive task. This kind of cognition is of special interest to cognitive neuroscientists. This paper explicates how similarity-based cognition can be understood through the lens of radical enactivism and why doing so has advantages over its representationalist rival, which posits the existence of structural representations or S-representations. (...) Specifically, it is argued that there are problems both with accounting for the content of S-representations and with understanding how neurally-based structural similarities can work as representations in guiding intelligent behavior. Finally, with these clarifications in place, it is revealed how radical enactivism can commit to an account of similarity-based cognition in its understanding of neurodynamics. (shrink)

The aim of this paper is to elucidate the relationship between Aristotelian conceptual oppositions, commutative diagrams of relational structures, and Galois connections.This is done by investigating in detail some examples of Aristotelian conceptual oppositions arising from topological spaces and similarity structures. The main technical device for this endeavor is the notion of Galois connections of order structures.

Similarity is one of the most important relations humans perceive, arguably subserving category learning and categorization, generalization and discrimination, judgment and decision making, and other cognitive functions. Researchers have proposed a wide range of representations and metrics that could be at play in similarity judgment, yet have not comprehensively compared the power of these representations and metrics for predicting similarity within and across different semantic categories. We performed such a comparison by pairing nine prominent vector semantic representations (...) with seven established similarity metrics that could operate on these representations, as well as supervised methods for dimensional weighting in the similarity function. This approach yields a factorial model structure with 126 distinct representation‐metric pairs, which we tested on a novel dataset of similarity judgments between pairs of cohyponymic words in eight categories. We found that cosine similarity and Pearson correlation were the overall best performing unweighted similarity functions, and that word vectors derived from free association norms often outperformed word vectors derived from text (including those specialized for similarity). Importantly, models that used human similarity judgments to learn category‐specific weights on dimensions yielded substantially better predictions than all unweighted approaches across all types of similarity functions and representations, although dimension weights did not generalize well across semantic categories, suggesting strong category context effects in similarity judgment. We discuss implications of these results for cognitive modeling and natural language processing, as well as for theories of the representations and metrics involved in similarity. (shrink)

Although the mapping between form and meaning is often regarded as arbitrary, there are in fact well-known constraints on words which are the result of functional pressures associated with language use and its acquisition. In particular, languages have been shown to encode meaning distinctions in their sound properties, which may be important for language learning. Here, we investigate the relationship between semantic distance and phonological distance in the large-scale structure of the lexicon. We show evidence in 100 languages from a (...) diverse array of language families that more semantically similar word pairs are also more phonologically similar. This suggests that there is an important statistical trend for lexicons to have semantically similar words be phonologically similar as well, possibly for functional reasons associated with language learning. (shrink)

Similarity-based cognition is commonplace. It occurs whenever an agent or system exploits the similarities that hold between two or more items—e.g., events, processes, objects, and so on—in order to perform some cognitive task. This kind of cognition is of special interest to cognitive neuroscientists. This paper explicates how similarity-based cognition can be understood through the lens of radical enactivism and why doing so has advantages over its representationalist rival, which posits the existence of structural representations or S-representations. (...) Specifically, it is argued that there are problems both with accounting for the content of S-representations and with understanding how neurally-based structural similarities can work as representations in guiding intelligent behavior. Finally, with these clarifications in place, it is revealed how radical enactivism can commit to an account of similarity-based cognition in its understanding of neurodynamics. (shrink)