If a proposition is typically true, given your evidence, then you should believe that proposition; or so I argue here. In particular, in this paper, I propose and defend a principle of rationality---call it the `Typical Principle'---which links rational belief to facts about what is typical. As I show, this principle avoids several problems that other, seemingly similar principles face. And as I show, in many cases, this principle implies the verdicts of the Principal Principle: so ultimately, the Typical Principle (...) may be the more fundamental of the two. (shrink)

Dreams of chase or pursuit, falling, sex, flying, nudity, failing an examination, one's own and other's death, fire, teeth falling out and some other themes experienced, even if only rarely, by many people all over the world have been labelled 'typical dreams'. This essay argues that typical dreaming, rather a syndrome of themes than monothematic, reflects an extraordinary state of mind and brain. Odd and particularly memorable perceptions, as well as emerging awareness of sleep and dreaming -- i.e. parallels to (...) lucid dreaming, sleep paralysis, complex partial seizure, epileptic and migraine auras, and aspects of dreaming after trauma -- can be traced with some plausibility in all prominent variants of typical dreaming. When viewed from this perspective, for example, dream pursuers are much more a shadow of the bodily self than a metaphor for the psycho- biographical situation or evolutionarily implemented sparring partners who make dreamers fit for the struggle for survival during waking hours. (shrink)

Why do systems prepared in a non-equilibrium state approach, and eventually reach, equilibrium? An important contemporary version of the Boltzmannian approach to statistical mechanics answers this question by an appeal to the notion of typicality. The problem with this approach is that it comes in different versions, which are, however, not recognised as such, much less clearly distinguished, and we often find different arguments pursued side by side. The aim of this paper is to disentangle different versions of (...) class='Hi'>typicality-based explanations of thermodynamic behaviour and evaluate their respective success. My conclusion will be that the boldest version fails for technical reasons, while more prudent versions leave unanswered essential questions. (shrink)

Bohmian mechanics represents the universe as a set of paths with a probability measure defined on it. The way in which a mathematical model of this kind can explain the observed phenomena of the universe is examined in general. It is shown that the explanation does not make use of the full probability measure, but rather of a suitable set function deriving from it, which defines relative typicality between single-time cylinder sets. Such a set function can also be derived (...) directly from the standard quantum formalism, without the need of an underlying probability measure. The key concept for this derivation is the quantum typicality rule, which can be considered as a generalization of the Born rule. The result is a new formulation of quantum mechanics, in which particles follow definite trajectories, but which is based only on the standard formalism of quantum mechanics. (shrink)

An important contemporary version of Boltzmannian statistical mechanics explains the approach to equilibrium in terms of typicality. The problem with this approach is that it comes in different versions, which are, however, not recognized as such and not clearly distinguished. This article identifies three different versions of typicality‐based explanations of thermodynamic‐like behavior and evaluates their respective successes. The conclusion is that the first two are unsuccessful because they fail to take the system's dynamics into account. The third, however, (...) is promising. I give a precise formulation of the proposal and present an argument in support of its central contention. †To contact the author, please write to: Department of Philosophy, Logic, and Scientific Method, London School of Economics, Houghton Street, London WC2A 2AE, England; e‐mail: [email protected]. (shrink)

Typicality is routinely invoked in everyday contexts: bobcats are typically short-tailed; people are typically less than seven feet tall. Typicality is invoked in scientific contexts as well: typical gases expand; typical quantum systems exhibit probabilistic behaviour. And typicality facts like these support many explanations, both quotidian and scientific. But what is it for something to be typical? And how do typicality facts explain? In this paper, I propose a general theory of typicality. I analyse the (...) notion of a typical property. I provide a formalism for typicality explanations, and I give an account of why typicality explanations are explanatory. Along the way, I show how typicality facts explain a variety of phenomena, from everyday phenomena to the statistical mechanical behaviour of gases. Finally, I argue that typicality is not the same thing as probability. (shrink)

Certain results, most famously in classical statistical mechanics and complex systems, but also in quantum mechanics and high-energy physics, yield a coarse-grained stable statistical pattern in the long run. The explanation of these results shares a common structure: the results hold for a 'typical' dynamics, that is, for most of the underlying dynamics. In this paper I argue that the structure of the explanation of these results might shed some light --a different light-- on philosophical debates on the laws of (...) nature. In the explanation of such patterns, the specific form of the underlying dynamics is almost irrelevant. The conditions required, given a free state-space evolution, suffice to account for the coarse-grained lawful behaviour. An analysis of such conditions might thus provide a different account of how regular behaviour can occur. This paper focuses on drawing attention to this type of explanation, outlining it in the diverse areas of physics in which it appears, and discussing its limitations and significance in the tractable setting of classical statistical mechanics. (shrink)

This paper addresses theoretical problems arising from the vagueness of language terms, and intuitions of the vagueness of the concepts to which they refer. It is argued that the central intuitions of prototype theory are sufficient to account for both typicality phenomena and psychological intuitions about degrees of membership in vaguely defined classes. The first section explains the importance of the relation between degrees of membership and typicality (or goodness of example) in conceptual categorization. The second and third (...) section address arguments advanced by Osherson and Smith (1997), and Kamp and Partee (1995), that the two notions of degree of membership and typicality must relate to fundamentally different aspects of conceptual representations. A version of prototype theory—the Threshold Model—is proposed to counter these arguments and three possible solutions to the problems of logical selfcontradiction and tautology for vague categorizations are outlined. In the final section graded membership is related to the social construction of conceptual boundaries maintained through language use. (shrink)

The recent use of typicality in statistical mechanics for foundational purposes has stirred an important debate involving both philosophers and physicists. While this debate customarily focuses on technical issues, in this paper I try to approach the problem from an epistemological angle. The discussion is driven by two questions: (1) What does typicality add to the concept of measure? (2) What kind of explanation, if any, does typicality yield? By distinguishing the notions of `typicality-as-vast-majority' and ` (...) class='Hi'>typicality-as-best-exemplar', I argue that the former goes beyond the concept of measure. Furthermore, I also argue that typicality aims at providing us with a form of causal explanation of equilibrium. (shrink)

A sentence of the usual language of set theory is said to be stratified if it is obtained by “erasing” type indices in a sentence of the language of Russell's Simple Theory of Types. In this paper we give an alternative presentation of a proof the ambiguity theorem stating that any provable stratified sentence has a stratified proof. To this end, we introduce a new set of ambiguity axioms, inspired by Fraïssé's characterization of elementary equivalence; these axioms can be naturally (...) used to give different proofs of the ambiguity theorem . MSC: 03B15, 03F50, 03F55. (shrink)

Hugh Everett III's pure wave mechanics is a deterministic physical theory with no probabilities. He nevertheless sought to show how his theory might be understood as making the same statistical predictions as the standard collapse formulation of quantum mechanics. We will consider Everett's argument for pure wave mechanics, how it depends on the notion of branch typicality, and the relationship between the predictions of pure wave mechanics and the standard quantum probabilities.

The paper uses the concept of typicality to spell out an argument against Humean supervenience and the best system account of laws. It proves that, in a very general and robust sense, almost all possible Humean worlds have no Humean laws. They are worlds of irreducible complexity that do not allow for any systematization. After explaining typicality reasoning in general, the implications of this result for the metaphysics of laws are discussed in detail.

Why do systems prepared in a non-equilibrium state approach, and eventually reach, equilibrium? An important contemporary version of the Boltzmannian approach to statistical mechanics answers this question by an appeal to the notion of typicality. The problem with this approach is that it comes in different versions, which are, however, not recognised as such, much less clearly distinguished, and we often find different arguments pursued side by side. The aim of this paper is to disentangle different versions of (...) class='Hi'>typicality-based explanations of thermodynamic behaviour and evaluate their respective success. My conclusion will be that the boldest version fails for technical reasons, while more prudent versions leave unanswered essential questions. (shrink)

While most chemists agree on what is a metal and what is a non-metal there is a disagreement with respect to what is a metalloid and what is a transition metal. It is believed that this problem can be solved if two new terms are adopted: typical and less typical metals. These new terms will also help reconcile the European Periodic Table versus the North American regarding numbering of groups as well as the IUPAC numbering which could be as well (...) abandoned in favour of group names as will be shown in the manuscript. (shrink)

The aim of this paper is to systematically analyze Schutz’s phenomenological account of the typicality and habituality of everyday cognitive experience, and to identify the Husserlian leitmotifs that inform it. In order to do so, I will proceed in three steps. First, I will briefly present the main lines of Schutz’s theoretical project; second, I will scrutinize his Husserlian account of typification as a passive sort of interpretation; and finally, I will examine his –also Husserl-inspired– analysis of the structure (...) and genesis of the habitualized stock of knowledge at hand. (shrink)

In the Typic chapter of the Critique of Practical Reason, Kant aims to enable moral judgment by means of the law of nature, which serves as the ‘type’, or formal analogue, of moral law. The present monograph is the first comprehensive study of this key text. It provides a detailed commentary on the Typic, situates it within Kant’s ethics and his theory of symbolic representation, and critically engages with the relevant secondary literature.

We discuss the content and significance of John von Neumann’s quantum ergodic theorem (QET) of 1929, a strong result arising from the mere mathematical structure of quantum mechanics. The QET is a precise formulation of what we call normal typicality, i.e., the statement that, for typical large systems, every initial wave function ψ0 from an energy shell is “normal”: it evolves in such a way that |ψt ψt| is, for most t, macroscopically equivalent to the micro-canonical density matrix. The (...) QET has been mostly forgotten after it was criticized as a dynamically vacuous statement in several papers in the 1950s. However, we point out that this criticism does not apply to the actual QET, a correct statement of which does not appear in these papers, but to a different (indeed weaker) statement. Furthermore, we formulate a stronger statement of normal typicality, based on the observation that the bound on the deviations from the average specified by von Neumann is unnecessarily coarse and a much tighter (and more relevant) bound actually follows from his proof. (shrink)

Instances of the law of large numbers are used to model many different physical systems. In this paper, I argue for a particular interpretation, of those instances of that law, which appeals to typicality. As I argue, the content of that law, when used to model physical systems, is that the probability of an event typically—rather than probably—approximates the frequency with which that event occurs.

We discuss Boltzmann’s probabilistic explanation of the second law of thermodynamics providing a comprehensive presentation of what is called today the typicality account. Countering its misconception as an alternative explanation, we examine the relation between Boltzmann’s H-theorem and the general typicality argument demonstrating the conceptual continuity between the two. We then discuss the philosophical dimensions of the concept of typicality and its relevance for scientific reasoning in general, in particular for understanding the reduction of macroscopic laws to (...) microscopic laws. Finally, we reply to various common criticisms of the typicality account. (shrink)

If we are to constrain our place in the world, two principles are often appealed to in science. According to the Copernican Principle, we do not occupy a privileged position within the Universe. The Cosmological Principle, on the other hand, says that our observations would roughly be the same, if we were located at any other place in the Universe. In our paper we analyze these principles from a logical and philosophical point of view. We show how they are related, (...) how they can be supported and what use is made of them. Our main results are: 1. There is a logical gap between both principles insofar as the Cosmological Principle is significantly stronger than the Copernican Principle. 2. A step that is often taken for establishing the Cosmological Principle on the base of the Copernican Principle and observations is not incontestable as it stands, but can be supplemented with a different argument. 3. The Cosmological Principle might be crucial for cosmology to the extent it is not supported by empirical evidence. (shrink)

Generic statements play a crucial role in concept learning, communication and education. Despite many efforts, the semantics of generics remain a controversial issue, as they do not seem to fit our standard theories of meaning. In this article, we attempt to shed light on this problem by focusing on how these sentences function in reasoning. Drawing on a distinction between property and diagnostic generics, we defend three theses: First, property generics are not about facts but express relations between concepts. Second, (...) generics play an important role in everyday reasoning by interacting with our expectations about the world. Third, diagnostic generics emphasise properties that separate the category in the generics from other categories in the same contrast class. We use the theory of conceptual spaces to advance measures of typicality and diagnosticity capable of modelling different aspects of generics and apply them to the modifier effect and the inverse conjunction fallacy. Finally, we discuss the pragmatics of generics. (shrink)

This essay examines the sanitary policies for the protection of overseas communities that Italian fascism employed during the empire. From 1935–1936, the vast scale of the Ethiopian campaign, as well as intensive colonisation programmes, gave new political visibility to the issue of safeguarding Italian settlers from the risks of the tropical climate. In this period, the problem of how Italians could adapt to overseas environments moved beyond the boundaries of scientific discussion to become a major concern of colonial rule. Analysing (...) both the medical literature and archival sources, this essay examines the concepts and practices that underpinned the fascist project for the “reclamation” of the empire: from the intensification of hygienic propaganda, to the redefinition of the medical-geographical boundaries of tropical risk, and to the expansion of social security benefits, which were extended to harms caused by tropical diseases. Finally, it investigates how the notion of acclimatisation was transformed within the context of the regime's imperial ideology, showing how the conception of the tropics as a pathogenic space remained widespread, fuelled by the regime's organicistic vision and its concerns for upholding the racial prestige of Italians in the colony. (shrink)

Cimpian et al. observed that we accept generic statements of the form ‘Gs are f’ on relatively weak evidence, but that if we are unfamiliar with group G and we learn a generic statement about it, we still treat it inferentially in a much stronger way: all Gs are f. This paper makes use of notions like ‘representativeness’, ‘contingency’ and ‘relative difference’ from psychology to provide a uniform semantics of generics that explains why people accept generics based on weak evidence. (...) The spirit of the approach has much in common with Leslie’s cognition-based ideas about generics, but the semantics will be grounded on a strengthening of Cohen’s relative readings of generic sentences. In contrast to Leslie and Cohen, we propose a uniform semantic analysis of generics. The basic intuition is that a generic of the form ‘Gs are f’ is true because f is typical for G, which means that f is valuably associated with G. We will make use of Kahneman and Tversky’s Heuristics and Biases approach, according to which people tend to confuse questions about probability with questions about representativeness, to explain pragmatically why people treat many generic statements inferentially in a much stronger way. (shrink)

We work with a finite relational vocabulary with at least one relation symbol with arity at least 2. Fix any integer m > 1. For almost all finite structures such that at least m elements are moved by some automorphisms, the automorphism group is i\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${^{i}}$$\end{document} for some i≤/2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${i \leq /2}$$\end{document}; and if some relation symbol has arity at least 3, then the automorphism (...) group is almost always Z2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{Z}_{2}}$$\end{document}. (shrink)

Certain results, most famously in classical statistical mechanics and complex systems, but also in quantum mechanics and high-energy physics, yield a coarse-grained stable statistical pattern in the long run. The explanation of these results shares a common structure: the results hold for a ‘typical’ dynamics, that is, for most of the underlying dynamics. In this paper I argue that the structure of the explanation of these results might shed some light—a different light—on philosophical debates on the laws of nature. In (...) the explanation of such patterns, the specific form of the underlying dynamics is almost irrelevant. The constraints required, given a free state-space evolution, suffice to account for the coarse-grained lawful behaviour. An analysis of such constraints might thus provide a different account of how regular behaviour can occur. This paper focuses on drawing attention to this type of explanation, outlining it in the diverse areas of physics in which it appears, and discussing its limitations and significance in the tractable setting of classical statistical mechanics. (shrink)

A gas prepared in a non-equilibrium state will approach equilibrium and stay there. An influential contemporary approach to Statistical Mechanics explains this behaviour in terms of typicality. However, this explanation has been criticised as mysterious as long as no connection with the dynamics of the system is established. We take this criticism as our point of departure. Our central claim is that Hamiltonians of gases which are epsilon-ergodic are typical with respect to the Whitney topology. Because equilibrium states are (...) typical, we argue that there follows the desired conclusion that typical initial conditions approach equilibrium and stay there. (shrink)

This paper is about the epistemology of quantum theory. We establish a new result about a limitation to knowledge of its central object---the quantum state of the universe. We show that, if the universal quantum state can be assumed to be a typical unit vector from a high-dimensional subspace of Hilbert space (such as the subspace defined by a low-entropy macro-state as prescribed by the Past Hypothesis), then no observation can determine (or even just narrow down significantly) which vector it (...) is. Typical state vectors, in other words, are observationally indistinguishable from each other. Our argument is based on a typicality theorem from quantum statistical mechanics. We also discuss how theoretical considerations that go beyond the empirical evidence might bear on this fact and on our knowledge of the universal quantum state. (shrink)

In extracting predictions from theories that describe a multiverse, we face the difficulty that we must assess probability distributions over possible observations, prescribed not just by an underlying theory, but by a theory together with a conditionalization scheme that allows for selection effects. This means we usually need to compare distributions that are consistent with a broad range of possible observations, with actual experimental data. One controversial means of making this comparison is by invoking the 'principle of mediocrity': that is, (...) the principle that we are typical of the reference class implicit in the conjunction of the theory and the conditionalization scheme. In this paper, I quantitatively assess the principle of mediocrity in a range of cosmological settings, employing 'xerographic distributions' to impose a variety of assumptions regarding typicality. I find that for a fixed theory, the assumption that we are typical gives rise to higher likelihoods for our observations. If, however, one allows both the underlying theory and the assumption of typicality to vary, then the assumption of typicality does not always provide the highest likelihoods. Interpreted from a Bayesian perspective, these results support the claim that when one has the freedom to consider different combinations of theories and xerographic distributions, one should favor the framework that has the highest posterior probability; and then from this framework one can infer, in particular, how typical we are. In this way, the invocation of the principle of mediocrity is more questionable than has been recently claimed. (shrink)

The dynamics inherent to the life activity of all living systems presents itself in the form of regular patterns viewed by the observer as taking place in an extended timeline. Routines, rituals and celebrations, each in their own way, are defined by the typical cyclical behavioural patterns exhibited by individuals embedded in specific semiospheres. The particular nature of these semiospheres will determine the distinct patterns of behaviour to be adopted in different life contexts so that existential functions are fulfilled. The (...) restricted and protected family circle normally provides the initial learning environment where the definition of the individual’s Umwelt (von Uexküll 1909, 1934; Ferreira, Biosemiotics 3(1):107–130, 2010, 2011) his/her meaningful world, starts to take shape. This learning process comprehends the progressive identification of distinct physical entities, the development of basic patterns of physical and social behaviour- the incorporation of basic routines and the assignment of meaning to particular events. (shrink)

According to the so-called Classical Theory, concepts are mentally represented by individually necessary and jointly sufficient application conditions. One of the principal empirical objections against this view stems from evidence that people judge some instances of a concept to be more typical than others. In this paper we present and discuss four empirical studies that investigate the extent to which this ‘typicality effect’ holds for the concept of basic needs. Through multiple operationalizations of typicality, our studies yielded evidence (...) for a strong effect of this kind: Participants tended to recall the same core examples of the concept in a free-listing task. They judged some basic needs to be more typical than others. The items that were judged to be more typical were listed more frequently in the free-listing task. These items were listed earlier on in the free-listing task. Typical basic needs, as well as non needs, were classified faster than atypical basic needs in a reaction time study. These findings suggest that the concept of basic needs may have a non-classical structure. If so, the quest for a simple and robust intensional analysis of the concept may be futile. (shrink)

In this paper we analyze the relation between the notion of typicality and the notion of probability and the related question of how the choice of measure in deterministic theories in physics may be justified. Recently it has been argued that although the notion of typicality is not a probabilistic notion, it plays a crucial role in underwriting probabilistic statements in classical statistical mechanics and in Bohm’s theory. We argue that even in theories with deterministic dynamics, like classical (...) statistical mechanics and Bohm’s theory, the notion of probability can be understood as fundamentally objective, and that it is the notion of probability rather than typicality that may have an explanatory value. (shrink)

A popular view in contemporary Boltzmannian statistical mechanics is to interpret the measures as typicality measures. In measure-theoretic dynamical systems theory measures can similarly be interpreted as typicality measures. However, a justification why these measures are a good choice of typicality measures is missing, and the paper attempts to fill this gap. The paper first argues that Pitowsky's (2012) justification of typicality measures does not fit the bill. Then a first proposal of how to justify (...) class='Hi'>typicality measures is presented. The main premises are that typicality measures are invariant and are related to the initial probability distribution of interest (which are translation-continuous or translation-close). The conclusions are two theorems which show that the standard measures of statistical mechanics and dynamical systems are typicality measures. There may be other typicality measures, but they agree about judgements of typicality. Finally, it is proven that if systems are ergodic or epsilon-ergodic, there are uniqueness results about typicality measures. (shrink)

This paper’s purpose is to provide a foundation for viewing critical thinking as both a maximal and typical performance construct. While maximal performance measures the best a person can do, typical performance measures what the person is most likely to do. An overview of maximal performance, including its history and limitations, will be given. The role of maximal and typical performance in cognitive development will be demonstrated through an exploration of the relationships between behavior, the environment, personality, crystallized intelligence, and (...) fluid intelligence. Furthermore, these topics will be related to the development and use of critical thinking skills. Discussion will conclude with directions for future research. (shrink)

We propose a nonmonotonic Description Logic of typicality able to account for the phenomenon of combining prototypical concepts, an open problem in the fields of AI and cognitive modelling. Our logic extends the logic of typicality ALC + TR, based on the notion of rational closure, by inclusions p :: T(C) v D (“we have probability p that typical Cs are Ds”), coming from the distributed semantics of probabilistic Description Logics. Additionally, it embeds a set of cognitive heuristics (...) for concept combination. We show that the complexity of reasoning in our logic is EXPTIME-complete as in ALC. (shrink)

Next SectionIn recent years, the interpretation of scalar terms in embedded environments has been investigated extensively. Some experimentalists have been concerned with sentences like (1), in which a scalar term is embedded under a universal quantifier. The controversy involves the question whether ‘some’ in these sentences is interpreted as ‘some but not all’, thus leading to the embedded upper-bounded inference that no square is connected to all of the circles. (1) All the squares are connected with some of the circles.Geurts (...) & Pouscoulous (2009) conducted a verification task that seemed to prove that the inference is not licensed. In response, Clifton & Dube (2010) and Chemla & Spector (2011) gathered evidence suggesting the opposite conclusion. By experimentally investigating the typicality structure of complex quantified sentences like (1) above, I show how the results of the latter two experiments can be explained as typicality effects. Typicality plays a significant role in the comprehension of quantified sentences, thus complicating the interpretation of data from the kinds of experiments that have been employed to test between theories of upper-bounded inferences. (shrink)

In the literature, the term code-mixing/switching refers to instances of language mixing in which speakers/signers combine properties of two or more languages in their utterances. Such a linguistic behavior is typically discussed in the context of multilinguals, and experts commonly focus on the form of language mixing/switching and its cross-linguistic commonalities. Not much is known, however, about how the knowledge of code-mixing comes about. How come any speaker/signer having access to more than one externalization channel (spoken or signed) code-mixes spontaneously? (...) Likewise, why do both neurotypical speakers/signers and certain neuro-atypical speakers/signers produce structurally similar mixing types? This paper offers some answers to these questions arguing that the cognitive process underlying code-mixing is a basic property of the human learning device: recombination, a fully automated cognitive process. Recombination is innate: it allows learners to select relevant linguistic features from heterogeneous inputs, and recombine them into new syntactic objects as part of their mental grammars whose extensions, arguably individual idiolects, represents what Aboh (2015b, a, 2019b) characterizes as hybrid grammars. (shrink)