Navigating to goal locations in a known environment (wayfinding) can be accomplished by different strategies, notably by taking habitual, well-learned routes (response strategy) or by inferring novel paths, such as shortcuts, from spatial knowledge of the environment's layout (place strategy). Human and animal neuroscience studies reveal that these strategies reflect different brain systems, with response strategies relying more on activation of the striatum and place strategies associated with activation of the hippocampus. In addition to individual differences in strategy, recent behavioral (...) studies show sex differences such that men use place strategies more than women, and age differences such that older adults use more response strategies than younger adults. This paper takes a comprehensive multilevel approach to understanding these differences, characterizing wayfinding as a complex information processing task. This analysis reveals factors that affect navigation strategy, including availability of the relevant type of environmental knowledge, momentary access to this knowledge, trade-offs between physical and mental effort in different navigation contexts, and risk taking. We consider how strategies are influenced by the computational demands of a navigation task and by factors that affect the neural circuits underlying navigation. We also discuss limitations of laboratory studies to date and outline priorities for future research, including relating wayfinding strategies to independent measures of spatial knowledge, and studying wayfinding strategies in naturalistic environments. (shrink)

Let the chain antichain principle (CAC) be the statement that each partial order on $\mathbb{N}$ possesses an infinite chain or an infinite antichain. Chong, Slaman, and Yang recently proved using forcing over nonstandard models of arithmetic that CAC is $\Pi^1_1$-conservative over $\text{RCA}_0+\Pi^0_1\text{-CP}$ and so in particular that CAC does not imply $\Sigma^0_2$-induction. We provide here a different purely syntactical and constructive proof of the statement that CAC (even together with WKL) does not imply $\Sigma^0_2$-induction. In detail we show using a (...) refinement of Howard's ordinal analysis of bar recursion that $\text{WKL}_0^\omega+\text{CAC}$ is $\Pi^0_2$-conservative over PRA and that one can extract primitive recursive realizers for such statements. Moreover, our proof is finitary in the sense of Hilbert's program. CAC implies that every sequence of $\mathbb{R}$ has a monotone subsequence. This Bolzano-Weierstraß}-like principle is commonly used in proofs. Our result makes it possible to extract primitive recursive terms from such proofs. We also discuss the Erdős-Moser principle, which—taken together with CAC—is equivalent to $\text{RT}^2_2$. (shrink)

I am grateful to the editors of the Canadian Journal of Philosophy for inviting me to write a comment on Kathleen Gill’s ‘On the Metaphysical Distinction Between Processes and Events’. I readily concede that she is right in the central criticism she makes of my 1978 paper: that a properly metaphysical or ontological distinction between processes and events, if it is to be made at all, cannot be sustained on the basis of the informal linguistic criteria I offered in ‘Events, (...) Processes, and States.’ My main concern in that paper was to show that discussions of the Kenny-Vendler typology of activities, performances, and states had focused too narrowly on verb types, on adverbial phrases, on the domain of human action, and on English-language intuitions. Mine was one of several voices urging in the late 1970s that issues of tense logic and of the logic of verb types had to be placed in the broader context of verb aspect — a salient and pervasive structure in natural languages generally, and one that had been studied by philologists and linguists since the nineteenth century. Captivated, as I and others had become at the time, by evidence that the distinction between count nouns and mass nouns appears to be mirrored in verb predications, I went on to make some rather venturesome ‘ontological’ claims. It is satisfying, of course, that Gill accepts not only that there is ‘substantial evidence in favor of recognizing a grammatical distinction between the language of processes and [the language of] events’ but also that ‘similarities with count and mass expressions will allow us to apply techniques for han dling nominal expressions to verbal expressions’. It is more than satisfying that the phenomenon of verb aspect is now noticed and investigated by philosophers as well as by linguists. (shrink)

We investigate the strength of the existence of a non-principal ultrafilter over fragments of higher-order arithmetic. Let [Formula: see text] be the statement that a non-principal ultrafilter on ℕ exists and let [Formula: see text] be the higher-order extension of ACA0. We show that [Formula: see text] is [Formula: see text]-conservative over [Formula: see text] and thus that [Formula: see text] is conservative over PA. Moreover, we provide a program extraction method and show that from a proof of a strictly (...) [Formula: see text] statement ∀ f ∃ g A qf in [Formula: see text] a realizing term in Gödel's system T can be extracted. This means that one can extract a term t ∈ T, such that ∀ f A qf). (shrink)

The main argument in Parmenides’ didactic poem begins with these remarks by the unnamed goddess who delivers the revelation (B2 in Diels-KranzDie Fragmente der Vorsokratiker):Come now and I shall tell you, and you listen to the account and carry it forth, which routes of inquiry (ơδοί…διζησιος, B2.2) alone are for knowing: the one (μέν, B2.3), that (…) is and that it is not possible (for …) not to be ὅπως ἔστιν τε ϰαὶ ὼς οὐϰ ἔστι μὴ είναι, B2.3) is the (...) course of Persuasion, for it attends truth; the other ἠδ; B2.5 that (…) is not and that it is right (for …) not to be (ὡς οὐϰ ἔστιυ τε ϰαὶ ὡς χρεών ἐστι μὴ εἶναι, B2.5) that one I mark for you as being a byway from which no tidings ever come (παναπευθέα ἔμμεν άταρπόυ, B2.6) For you could neither come to know (Υυοίμς, aorist, B2.7) the thing itself which is not (τό Υε μὴ έόυ), for it cannot be consummated (οὐ Υὰρ ἀνυστόυ), nor could you point it out (φράσαις, aorist, B2.8). (shrink)

This article discusses Xenophanes' “cloud astro-physics”. It analyses and explains all heavenly and meteorological phenomena in terms of clouds. It provides a view of this newer Xenophanes, who is now being recognized as an important philosopher-scientist in his own right and a crucial figure in the development of critical thought about human knowledge and its objects in the next generation of Presocratic thinkers. Xenophanes' account has been preserved in Aëtius, the doxographic compendium reconstructed by Hermann Diels late in the nineteenth (...) century mainly from two sources that show extensive parallelism: pseudo-Plutarch Placita Philosophorum or Epitome of Physical Opinions ; and Ioannes Stobaeus' Eclogae Physicae or Physical Extracts. In the Stobaeus version, which is also the one printed in the standard edition of the Pre-socratics. (shrink)

To understand how individuals adapt to and anticipate each other in joint tasks, we employ a bidirectional delay–coupled dynamical system that allows for mutual adaptation and anticipation. In delay–coupled systems, anticipation is achieved when one system compares its own time‐delayed behavior, which implicitly includes past information about the other system’s behavior, with the other system’s instantaneous behavior. Applied to joint music performance, the model allows each system to adapt its behavior to the dynamics of the other. Model predictions of asynchrony (...) between two simultaneously produced musical voices were compared with duet pianists’ behavior; each partner performed one voice while auditory feedback perturbations occurred at unpredictable times during live performance. As the model predicted, when auditory feedback from one musical voice was removed, the asynchrony changed: The pianist’s voice that was removed anticipated (preceded) the actions of their partner. When the auditory feedback returned and both musicians could hear each other, they rapidly returned to baseline levels of asynchrony. To understand how the pianists anticipated each other, their performances were fitted by the model to examine change in model parameters (coupling strength, time‐delay). When auditory feedback for one or both voices was removed, the fits showed the expected decrease in coupling strength and time‐delay between the systems. When feedback about the voice(s) returned, the coupling strength and time‐delay returned to baseline. These findings support the idea that when people perform actions together, they do so as a coupled bidirectional anticipatory system. (shrink)

In saying that sensible things exist "by convention" he does not, of course, mean that the sensible world is something we will or make up. He no doubt was aware of the fact that "sweet, bitter, hot, cold, and color" are given to us, that we do not establish them or enact them the way we establish an institution or enact a law. It is in the logic of his thesis that sensible things are appearances of atoms in configuration. They (...) exist by convention in this sense: we refer to them as if they were individuals, things; as if their character and existence were self-contained and not entirely conditioned and dependent on something else. Strictly speaking, instead of referring to "honey" we should refer to "the constellation of atoms which we experience as something sweet, fluid, etc." The mental attitude which treats animals, plants, houses, tables as ultimate, the attitude which stops with sensation is "obscure knowledge"; the attitude which sees through and beyond these is "genuine knowledge." The thesis is that we never see the world as it is; the nature of things, the reality of the world is something to be apprehended by rational inference, to be seen by a sort of mental vision. For a man who wants to know, the logically correct attitude toward the familiar sensible world is one of going beyond, penetrating beneath, transcending it. (shrink)

The comment endorses and reinforces Daniel W. Graham’s highly original and attractive proposal that early Greek cosmology develops in two stages. In what Graham calls the “meteorological stage” of the sixth century BCE, celestial objects are explained as formations either from fire or from watery exhalations in a roughly planar model of the cosmos. In the “lithic stage” of the mid- and late fifth century introduced by Anaxagoras, the model is that of a central earth around which solid stone-like celestial (...) objects revolve held aloft in a vortex. The change to the lithic stage comes about, according to Graham, as the implications of Parmenides’ epoch-making discovery that the moon is illuminated by the sun come to be understood and are then theoretically exploited. The present comment also proposes that the false explanations of lunar phases and lunar and solar eclipses in the meteorological-stage cosmologies, respectively, of Xenophanes and of Heraclitus may have played a helpful heuristic role in the theoretical breakthrough to heliophotism. (shrink)

We show how one can obtain solutions to the Arzelà‐Ascoli theorem using suitable applications of the Bolzano‐Weierstraß principle. With this, we can apply the results from and obtain a classification of the strength of instances of the Arzelà‐Ascoli theorem and a variant of it. Let be the statement that each equicontinuous sequence of functions contains a subsequence that converges uniformly with the rate and let be the statement that each such sequence contains a subsequence which converges uniformly but possibly without (...) any rate. We show that is instance‐wise equivalent, over, to the Bolzano‐Weierstraß principle and that is instance‐wise equivalent, over, to, and thus to the strong cohesive principle (). Moreover, we show that over the principles, and are equivalent. (shrink)

We show that many principles of first-order arithmetic, previously only known to lie strictly between [Formula: see text]-induction and [Formula: see text]-induction, are equivalent to the well-foundedness of [Formula: see text]. Among these principles are the iteration of partial functions of Hájek and Paris, the bounded monotone enumerations principle by Chong, Slaman, and Yang, the relativized Paris–Harrington principle for pairs, and the totality of the relativized Ackermann–Péter function. With this we show that the well-foundedness of [Formula: see text] is a (...) far more widespread than usually suspected. Further, we investigate the [Formula: see text]-iterated version of the bounded monotone iterations principle, and show that it is equivalent to the well-foundedness of the -height [Formula: see text]-tower [Formula: see text]. (shrink)

In the work of interpreting Parmenides we have witnessed in the ’sixties and ’seventies, in English language scholarship, that rarest of phenomena in the study of ancient philosophy, the emergence of a consensus. Four interpretive theses now seem quite widely shared: Parmenides deliberately suppresses the subject of esti, “is,” or einai, “to be,” in his statement of the two “routes” in B2, his intention being to allow the subject to become gradually specified as the argument unfolds. The negative route, ouk (...) esti, “is not,” or mē einai, “not to be,” is banned because sentences that adhere to it fail to refer to actual entities—the latter to be understood broadly, as will shortly be stated in thesis. The argument does not depend on a confusion between the “is” of predication and the “is” of existence. In the relevant contexts, esti and einai involve a “fused” or “veridical” use of the verb “to be”; in other words, esti or einai have the force of “is actual” or “obtains,” or “is the case,” envisaging a variable subject x that ranges over states-of-affairs. (shrink)

Let ${2-\textsf{RAN}}$ be the statement that for each real X a real 2-random relative to X exists. We apply program extraction techniques we developed in Kreuzer and Kohlenbach (J. Symb. Log. 77(3):853–895, 2012. doi:10.2178/jsl/1344862165), Kreuzer (Notre Dame J. Formal Log. 53(2):245–265, 2012. doi:10.1215/00294527-1715716) to this principle. Let ${{\textsf{WKL}_0^\omega}}$ be the finite type extension of ${\textsf{WKL}_0}$ . We obtain that one can extract primitive recursive realizers from proofs in ${{\textsf{WKL}_0^\omega} + \Pi^0_1-{\textsf{CP}} + 2-\textsf{RAN}}$ , i.e., if ${{\textsf{WKL}_0^\omega} + \Pi^0_1-{\textsf{CP}} + 2-\textsf{RAN} (...) \, {\vdash} \, \forall{f}\, {\exists}{x} A_{qf}(f,x)}$ then one can extract from the proof a primitive recursive term t(f) such that ${A_{qf}(f,t(f))}$ . As a consequence, we obtain that ${{\textsf{WKL}_0}+ \Pi^0_1 - {\textsf{CP}} + 2-\textsf{RAN}}$ is ${\Pi^0_3}$ -conservative over ${\textsf{RCA}_0}$. (shrink)

Achieving space domain awareness requires the identification, characterization, and tracking of space objects. Storing and leveraging associated space object data for purposes such as hostile threat assessment, object identification, and collision prediction and avoidance present further challenges. Space objects are characterized according to a variety of parameters including their identifiers, design specifications, components, subsystems, capabilities, vulnerabilities, origins, missions, orbital elements, patterns of life, processes, operational statuses, and associated persons, organizations, or nations. The Space Object Ontology provides a consensus-based realist framework (...) for formulating such characterizations in a computable fashion. Space object data are aligned with classes and relations in the Space Object Ontology and stored in a dynamically updated Resource Description Framework triple store, which can be queried to support space domain awareness and the needs of spacecraft operators. This paper presents the core of the Space Object Ontology, discusses its advantages over other approaches to space object classification, and demonstrates its ability to combine diverse sets of data from multiple sources within an expandable framework. Finally, we show how the ontology provides benefits for enhancing and maintaining longterm space domain awareness. (shrink)

This book presents some of the most recent trends and developments in Presocratic scholarship. A wide range of topics are covered - from the metaphysical to the moral to the methodological - as well as a broad a range of authors: from recognized figures such as Heraclitus and Parmenides to Sophistic thinkers whose place has traditionally been marginalized, such as Gorgias and the author of the Dissoi Logoi. Several of the pieces are concerned with the later reception and influence of (...) the Presocratics on ancient philosophy, an area of study important both for the light it sheds on our evidence for Presocratic thought and for understanding the philosophical power of their ideas. Drawing together contributions from distinguished authorities and internationally acclaimed scholars of ancient philosophy, this book offers new challenges to traditional interpretations in some areas of Presocratic philosophy and finds new support for traditional interpretations in other areas. (shrink)

The familiar Vendler-Kenny scheme of verb-types, viz., performances (further differentiated by Vedler into accomplishments and achievements), activities, and states, is too narrow in two important respects. First, it is narrow linguistically. It fails to take into account the phenomenon of verb aspect. The trichotomy is not one of verbs as lexical types but of predications. Second, the trichotomy is narrow ontologically. It is a specification in the context of human agency of the more fundamental, topic-neutral trichotomy, event-process-state.The central component in (...) this ontological trichotomy, event, can be sharply differentiated from its two flanking components by adapting a suggestion by Geoffrey N. Leech and others that the contrast between perfective and imperfective aspect in verbs corresponds to the count/mass distinction in the domain of nouns. With the help of two distinctions, of cardinal count adverbials versus frequency adverbials, and of occurrence versus associated occasion, two interrelated criteria for event predication are developed. Accordingly, Mary capsized the boat is an event predication because (a) it is equivalent to There was at least one capsizing of the boat by Mary, or (b) because it admits cardinal count adverbials, e.g., at least once, twice, three times. Ontologically speaking, events are defined as those occurrences that are inherently countable. (shrink)

In this paper we study with proof-theoretic methods the function(al) s provably recursive relative to Ramsey's theorem for pairs and the cohesive principle (COH). Our main result on COH is that the type 2 functional provably recursive from $RCA_0 + COH + \Pi _1^0 - CP$ are primitive recursive. This also provides a uniform method to extract bounds from proofs that use these principles. As a consequence we obtain a new proof of the fact that $WKL_0 + \Pi _1^0 - (...) CP + COH$ is $\Pi _1^0 $ -conservative over PRA. Recent work of the first author showed that $\Pi _1^0 + CP + COH$ is equivalent to a weak variant of the Bolzano-Weierstraß principle. This makes it possible to use our results to analyze not only combinatorial but also analytical proofs. For Ramsey's theorem for pairs and two colors $\left( {RT_2^2 } \right)$ we obtain the upper bounded that the type 2 functionals provable recursive relative to $RCA_0 + \sum\nolimits_2^0 {IA + RT_2^2 } $ are in T₁. This is the fragment of Gödel's system T containing only type 1 recursion—roughly speaking it consists of functions of Ackermann type. With this we also obtain a uniform method for the extraction of T₁-bounds from proofs that use RT2..... Moreover, this yields a new proof of the fact that $WKL_0 + \sum\nolimits_2^0 {IA} + RT_2^2 $ is $\Pi _1^0 $ -conservative over $RCA_0 + \sum\nolimits_2^0 { - IA} $ . The results are obtained in two steps: in the first step a term including Skolem functions for the above principles is extracted from a given proof. This is done using Gödel's functional interpretation. After this the term is normalized, such that only specific instances of the Skolem functions are used. In the second step this term is interpreted using $\Pi _1^0 $ -comprehension. The comprehension is then eliminated in favor of induction using either elimination of monotone Skolem functions (for COH) or Howard's ordinal analysis of bar recursion (for $RT_2^2 $. (shrink)

Analyzes the poem "On Nature" by Parmenides, arguing that is actually a philosophical argument disguised as Homer-like mythological journey. Original.

This chapter contains sections titled: Criteria Used for the Concept of the Universal Some Conceptual Barriers to Early Grasp of the Universal Empedocles: Formulae for Compounds; Biological Forms; Type‐Identities across Cycles Philolaus: Genus, Species, and the Relation to Particulars Democritus: An Infinity of Atomic Types, Atomic Tokens Comments by Democritus on the Universal Democritus and Aristotle: Origins of the Type–Token Distinction Democritus and Plato Bibliography.

Mourelatos’ study of the fragments of Parmenides’ poem combines traditional philological reconstruction with the approaches of literary criticism and philosophical analysis in order to reveal the thought structure and expressive unity of the best preserved and most important, influential, and coherent text of Greek philosophy before Plato. Through philosophical, philological, and literary analysis, Mourelatos examines the morphology of images and metaphors in Parmenides’ text with the aim of articulating and interpreting the poem’s key concepts and component arguments. Relevant antecedents and (...) parallels from the tradition of epic poetry, especially from Homer’s Odyssey, are explored in depth. (shrink)

The Covid-19 pandemic reveals a new phenomenon, unaddressed by the existing literature on “price gouging” in times of emergency. While merchants – getting large remuneration for providing desperately needed goods – evoke public moral outrage for assumed “price gouging”, employees – getting large remuneration for providing desperately needed services – do not cause such outrage but rather experience moral appraisal for their valuable commitment. To address this inherent inconsistency of moral judgment, we propose to embrace insights from research on folk (...) economics. By understanding the folk perception underlying public outrage at “price gougers,” business ethics might better enlighten the moral legitimacy of anti-“price gouging” measures. (shrink)

As indicated by Kahn's use of the pronoun "whatever," the thesis has the force of universality. Let me condense the formulation into a single proposition.