The Modal Logic of Gödel Sentences

The modal logic of Gödel sentences, termed as GS, is introduced to analyze the logical properties of ‘true but unprovable’ sentences in formal arithmetic. The logic GS is, in a sense, dual to Grzegorczyk’s Logic, where modality can be interpreted as ‘true and provable’. As we show, GS and Grzegorczyk’s Logic are, in fact, mutually embeddable. We prove Kripke completeness and arithmetical completeness for GS. GS is also an extended system of the logic of ‘Essence and Accident’ proposed by Marcos (Bull Sect Log 34(1):43–56, 2005). We also clarify the relationships between GS and the provability logic GL and between GS and Intuitionistic Propositional Logic.     

Congruence Lattices of Semilattices with Operators

The duality between congruence lattices of semilattices, and algebraic subsets of an algebraic lattice, is extended to include semilattices with operators. For a set G of operators on a semilattice S, we have \({{\rm Con}(S,+,0,G) \cong^{d} {{\rm S}_{p}}(L,H)}\), where L is the ideal lattice of S, and H is a corresponding set of adjoint maps on L. This duality is used to find some representations of lattices as congruence lattices of semilattices with operators. It is also shown that these congruence lattices satisfy the Jónsson–Kiefer property.     

The Structure Group of a Generalized Orthomodular Lattice

Orthomodular lattices with a two-valued Jauch–Piron state split into a generalized orthomodular lattice (GOML) and its dual. GOMLs are characterized as a class of L-algebras, a quantum structure which arises in the theory of Garside groups, algebraic logic, and in connections with solutions of the quantum Yang–Baxter equation. It is proved that every GOML X embeds into a group G(X) with a lattice structure such that the right multiplications in G(X) are lattice automorphisms. Up to isomorphism, X is uniquely determined by G(X), and the embedding \(X\hookrightarrow G(X)\) is a universal group-valued measure on X.     

The scope of formal explanation

The existence of multiple modes of explanation means that a crucial step in the process of generating explanations has to be selecting a particular mode. The present article identifies the key conceptual, as well as some pragmatic and epistemological, considerations that license the use of the formal mode of explanation, and thus that enter into the process of selecting and generating a formal explanation. Formal explanations explain the presence of certain properties in an instance of a kind by reference to the kind of thing it is (e.g. That has four legs because it is a dog). As such, this mode of explanation is intrinsically tied to kind representations and is applicable domain-generally. Although it is possible for formal explanation to apply domain-generally, for any given kind it is selective in its application, in that it can explain some, but not all, properties of the instances of a kind. It also appears that different types of properties can receive formal explanations across different domains. This article provides a sketch of a theory of the selectivity of formal explanation that results from the manner in which kinds of different types are distinguished. The present discussion also suggests how the mechanisms underlying formal explanations may contribute to the illusion of explanatory depth Keil (Trends in Cognitive Sciences, 7, 368–373,2003), the operation of the inherence heuristic Cimpian & Salomon (Behavioral and Brain Sciences, 37, 461–480, 2014a; Behavioral and Brain Sciences, 37, 506–527,2014b), and psychological essentialism (Gelman, 2003).     

Reasoning defeasibly about probabilities

In concrete applications of probability, statistical investigation gives us knowledge of some probabilities, but we generally want to know many others that are not directly revealed by our data. For instance, we may know prob(P/Q) (the probability of P given Q) and prob(P/R), but what we really want is prob(P/Q&;R), and we may not have the data required to assess that directly. The probability calculus is of no help here. Given prob(P/Q) and prob(P/R), it is consistent with the probability calculus for prob(P/Q&;R) to have any value between 0 and 1. Is there any way to make a reasonable estimate of the value of prob(P/Q&;R)? A related problem occurs when probability practitioners adopt undefended assumptions of statistical independence simply on the basis of not seeing any connection between two propositions. This is common practice, but its justification has eluded probability theorists, and researchers are typically apologetic about making such assumptions. Is there any way to defend the practice? This paper shows that on a certain conception of probability—nomic probability—there are principles of “probable probabilities” that license inferences of the above sort. These are principles telling us that although certain inferences from probabilities to probabilities are not deductively valid, nevertheless the second-order probability of their yielding correct results is 1. This makes it defeasibly reasonable to make the inferences. Thus I argue that it is defeasibly reasonable to assume statistical independence when we have no information to the contrary. And I show that there is a function Y(r, s, a) such that if prob(P/Q) = r, prob(P/R) = s, and prob(P/U) = a (where U is our background knowledge) then it is defeasibly reasonable to expect that prob(P/Q&;R) = Y(r, s, a). Numerous other defeasible inferences are licensed by similar principles of probable probabilities. This has the potential to greatly enhance the usefulness of probabilities in practical application.     

Arithmetical Completeness Theorem for Modal Logic $$\mathsf{}$$

We prove that for any recursively axiomatized consistent extension T of Peano Arithmetic, there exists a \(\Sigma _2\) provability predicate of T whose provability logic is precisely the modal logic \(\mathsf{K}\). For this purpose, we introduce a new bimodal logic \(\mathsf{GLK}\), and prove the Kripke completeness theorem and the uniform arithmetical completeness theorem for \(\mathsf{GLK}\).     

Group Agents and Their Responsibility

Group agents are able to act but are not literally agents. Some group agents, e.g., we-mode groups and corporations, can, however, be regarded as functional group agents that do not have “intrinsic” mental states and phenomenal features comparable to what their individual members on biological and psychological grounds have. But they can have “extrinsic” mental states, states collectively attributed to them—primarily by their members. In this paper, we discuss the responsibility of such group agents. We defend the view that if the group members have accepted the group agent’s (attributed) attitudes and are committed to them, we can favorably compare the situation with the case of individual human agents and a group agent can be regarded as morally responsible for its intentional activities.     

A class of k-modes algorithms for extracting knowledge structures from data

One of the most crucial issues in knowledge space theory is the construction of the so-called knowledge structures. In the present paper, a new data-driven procedure for large data sets is described, which overcomes some of the drawbacks of the already existing methods. The procedure, called k-states, is an incremental extension of the k-modes algorithm, which generates a sequence of locally optimal knowledge structures of increasing size, among which a “best” model is selected. The performance of k-states is compared to other two procedures in both a simulation study and an empirical application. In the former, k-states displays a better accuracy in reconstructing knowledge structures; in the latter, the structure extracted by k-states obtained a better fit.     

Understanding the Heart-Mind Within the Heart-Mind of the <Emphasis Type="Italic">Nèiyè</Emphasis> (<Emphasis Type="Italic">Inward Training</Emphasis>)

The Nèiyè 內業 (Inward Training) talks of “a heart-mind (xīn 心) within a heart-mind” that is somehow connected to or prior to language. In the context of the overall advice on looking “inward” or “internally” as part of the meditation and mysticism practice that the Nèiyè introduces, this talk of a heart-mind within a heart-mind arguably invites comparisons with a Cartesian “inner theater” conception of mentality. In this paper, I examine the “inner” talk of the Nèiyè in order to tease out its identifiable commitments in philosophical psychology. I consider the ways in which the “inner” talk of the text might be read as marking out one or more of three different inner/outer distinctions, and I argue that we can consistently read the Nèiyè without seeing it as marking any inner/outer distinction that is related to what is often referred to in English as “inner experience.”     

Antisocial Process Screening Device Subscales Predict Recidivism in an Australian Juvenile Offender Sample

The present study is the first to examine the psychometric properties of the self-report Antisocial Process Screening Device (APSD-SR), and the predictive utility of its subscales for reoffending, among Australian juvenile offenders (N?= 308, M age = 17.00, SD?=?1.49). Exploratory factor analysis supported a modified three-factor structure in which four items loaded differently to prior studies. Total APSD-SR and modified subscale scores were positively associated with criminal history and mental health problems (e.g., internalizing and externalizing problems, alcohol and substance abuse/dependence). Survival analyses indicated that youth scoring high on the APSD-SR total score were faster to reoffend nonviolently (Hazard Ratio [HR]?= 1.31, p?=?.0003) and violently (HR?=?1.42, p?=?.0003) than those scoring low. Whereas the modified grandiose-manipulative subscale predicted faster time to nonviolent recidivism (HR?=?1.18, p?=?.026) as a single predictor, when all subscales were simultaneously entered into the model only callous-unemotional (CU) traits and impulsivity predicted nonviolent recidivism (HR?=?1.19, p?=?.026 and 1.22, p?=?.015, respectively), and only impulsivity predicted violent recidivism (HR?=?1.26, p?=?.014). Findings inform current understanding of the relative contribution of adolescent psychopathy dimensions to designating a particularly high-risk group of Australian youth in custody.     

Scientific Realism Within Perspectivism and Perspectivism Within Scientific Realism

Perspectivism is often understood as a conception according to which subjective conditions inevitably affect our knowledge and, therefore, we are never confronted with reality and facts but only with interpretations. Hence, subjectivism and anti-realism are usually associated with perspectivism. The thesis of this paper is that, especially in the case of the sciences, perspectivism can be better understood as an appreciation of the cognitive attitude that consists in considering reality only from a certain ‘point of view’, in a way that can avoid subjectivism. Whereas the way of conceiving a notion is strictly subjective, the way of using it is open to intersubjective agreement, based on the practice of operations whose nature is neither mental nor linguistic. Therefore, intersubjectivity (that is a ‘weak’ sense of objectivity) is possible within perspectivism. Perspectivism can also help understand the notion of ‘scientific objects’ in a referential sense: they are those ‘things’ that become ‘objects’ of a certain science by being investigated from the ‘point of view’ of that science. They are ‘clipped out’ of things (and constitute the ‘domain of objects’ or the ‘regional ontology’ of that particular science) by means of standardized operations which turn out to be the same as those granting intersubjectivity. Therefore this ‘strong’ sense of objectivity, which is clearly realist, coincides with the ‘weak’ one. The notion of truth appears fully legitimate in the case of the sciences, being clearly defined for the regional ontology of each one of them and, since this truth can be extended in an analogical sense to the theories elaborated in each science, it follows that are real also the unobservable entities postulated by those theories.     

Age and Gender Variations in Healthy Immigrant Effect: a Population Study of Immigrant Well-Being in Canada

The healthy immigrant effect (HIE) is the phenomenon in which immigrants show better health than their native-born counterparts but this healthier condition declines with length of residence. This study investigated whether (1) immigrants also show better adaptation than non-immigrants as well as better health, (2) length of residence affects their health and adaptation differently, and (3) differential outcomes are found for different age and gender groups. Utilizing the Canadian Community Health Survey (2011–2012) data, immigrants (N?=?17,555) and non-immigrants (N?=?103,579) were divided into adolescents (15–19 years old), adults (20–49), older adults (50–64), and seniors (65–74) to examine their subjective general and mental health, diagnosed chronic and psychological illnesses, and self-reported daily stress, life satisfaction and sense of belonging. After controlling for key demographics, HIE was found to be more robust in health than adaptation. In general, recent immigrants reported better health conditions than long-term immigrants; however, the two did not differ with daily stress or life satisfaction. The older adult immigrants were the only segment of the immigrant population who did not display HIE; within the immigrant population, working-aged long-term adult immigrants were those experiencing negative well-being in both health and adaptation compared to the same-aged recent immigrants. Regarding diagnosed psychological illnesses, immigrants yielded no difference by age, gender, or length of residence, indicating ‘reluctant’ views on seeking professional help for mental health were persistently held by both recent and long-immigrants. The findings suggest that health policy needs to take into consideration age-related life stages, and enhancement of mental health awareness for immigrant well-being.     

Imposing Order to See the Disorder: Student Depression and T.S. Eliot’s <Emphasis Type="Italic">The Waste Land:</Emphasis> A (Mis)reading/Diagnosis

Sometime ago, I found myself using the diagnosis of a student’s depression as a critical tool of interpretation, searching for signs of mental illness in her essay that explored order and disorder in T. S. Eliot’s The Waste Land. I realised that my reading had become a creative act, combining poem, poet, student essay and author to create, in a sense, one (un)readable text. The present paper is a reflection upon the processes of order and disorder located in a diagnosis of “madness” and the readings of writer and text this diagnosis initiated. I look to deconstruct acts of reading and diagnosis.     

Efficient estimation of Weber’s <Emphasis Type="Italic">W</Emphasis>

Many studies rely on estimation of Weber ratios (W) in order to quantify the acuity an individual’s approximate number system. This paper discusses several problems encountered in estimating W using the standard methods, most notably low power and inefficiency. Through simulation, this work shows that W can best be estimated in a Bayesian framework that uses an inverse (1/W) prior. This beneficially balances a bias/variance trade-off and, when used with MAP estimation is extremely simple to implement. Use of this scheme substantially improves statistical power in examining correlates of W.     

Subjunctive Conditional Probability

There seem to be two ways of supposing a proposition: supposing “indicatively” that Shakespeare didn’t write Hamlet, it is likely that someone else did; supposing “subjunctively” that Shakespeare hadn’t written Hamlet, it is likely that nobody would have written the play. Let P(B//A) be the probability of B on the subjunctive supposition that A. Is P(B//A) equal to the probability of the corresponding counterfactual, A □→B? I review recent triviality arguments against this hypothesis and argue that they do not succeed. On the other hand, I argue that even if we can equate P(B//A) with P(A □→B), we still need an account of how subjunctive conditional probabilities are related to unconditional probabilities. The triviality arguments reveal that the connection is not as straightforward as one might have hoped.     

Higher-order theories of consciousness and what-it-is-like-ness

Ambitious higher-order theories of consciousness aim to account for conscious states when these are understood in terms of what-it-is-like-ness. This paper considers two arguments concerning this aim, and concludes that ambitious theories fail. The misrepresentation argument against HO theories aims to show that the possibility of radical misrepresentation—there being a HO state about a state the subject is not in—leads to a contradiction. In contrast, the awareness argument aims to bolster HO theories by showing that subjects are aware of all their conscious states. Both arguments hinge on how we understand two related notions which are ubiquitous in discussions of consciousness: those of what-it-is-like-ness and there being something it is like for a subject to be in a mental state. This paper examines how HO theorists must understand the two crucial notions if they are to reject the misrepresentation argument but assert the awareness argument. It shows that HO theorists can and do adopt an understanding—the HO reading—which seems to give them what they want. But adopting the HO reading changes the two arguments. On this reading, the awareness argument tells us nothing about those states there is something it is like to be in, and so offers no support to ambitious HO theories. And to respond to the misrepresentation understood according to the HO reading is to simply ignore the argument presented, and so to give no response at all. As things stand, we should deny that HO theories can account for what-it-is-like-ness.     

Episodic-like memory in zebrafish

Episodic-like memory tests often aid in determining an animal’s ability to recall the what, where, and which (context) of an event. To date, this type of memory has been demonstrated in humans, wild chacma baboons, corvids (Scrub jays), humming birds, mice, rats, Yucatan minipigs, and cuttlefish. The potential for this type of memory in zebrafish remains unexplored even though they are quickly becoming an essential model organism for the study of a variety of human cognitive and mental disorders. Here we explore the episodic-like capabilities of zebrafish (Danio rerio) in a previously established mammalian memory paradigm. We demonstrate that when zebrafish were presented with a familiar object in a familiar context but a novel location within that context, they spend more time in the novel quadrant. Thus, zebrafish display episodic-like memory as they remember what object they saw, where they saw it (quadrant location), and on which occasion (yellow or blue walls) it was presented.