The current studies (N = 255, children ages 4–5 and adults) explore patterns of age‐related continuity and change in conceptual representations of social role categories (e.g., “scientist”). In Study 1, young children's judgments of category membership were shaped by both category labels and category‐normative traits, and the two were dissociable, indicating that even young children's conceptual representations for some social categories have a “dual character.” In Study 2, when labels and traits were contrasted, adults and children based their category‐based induction (...) decisions on category‐normative traits rather than labels. Study 3 confirmed that children reason based on category‐normative traits because they view them as an obligatory part of category membership. In contrast, adults in this study viewed the category‐normative traits as informative on their own (not only as a cue to obligations). Implications for continuity and change in representations of social role categories will be discussed. (shrink)

Viale introduced covering matrices in his proof that SCH follows from PFA. In the course of the proof and subsequent work with Sharon, he isolated two reflection principles, CP and S, which, under certain circumstances, are satisfied by all covering matrices of a certain shape. Using square sequences, we construct covering matrices for which CP and S fail. This leads naturally to an investigation of square principles intermediate between □κ and □ for a regular cardinal κ. We provide a detailed (...) picture of the implications between these square principles. (shrink)

This third volume of Boston Studies in the Philosophy of Science contains papers which are based upon Colloquia from 1964 to 1966. In most cases, they have been substantially modified subsequent to presentation and discussion. Once again we publish work which goes beyond technical analysis of scientific theories and explanations in order to include philo sophical reflections upon the history of science and also upon the still problematic interactions between metaphysics and science. The philo sophical history of scientific ideas has (...) increasingly been recognized as part of the philosophy of science, and likewise the cultural context of the genesis of such ideas. There is no school or attitude to be taken as de fining the scope or criteria of our Colloquium, and so we seek to under stand both analytic and historical aspects of science. This volume, as the previous two, constitutes a substantial part of our final report to the U. S. National Science Foundation, which has continued its support of the Boston Colloquium for the Philosophy of Science by a grant to Boston University. That report will be concluded by a subse quent volume of these Studies. It is a pleasure to record our thanks to the Foundation for its confidence and funds. We dedicate this book to the memory of Norwood Russell Hanson. During this academic year of 1966-67, this beloved and distinguished American philosopher participated in our Colloquium, and he did so before. (shrink)

In the context of continuous first-order logic, special attention is often given to theories that are somehow continuous in an ‘essential’ way. A common feature of such theories is that they do not interpret any infinite discrete structures. We investigate a stronger condition that is easier to establish and use it to give an example of a strictly simple continuous theory that does not interpret any infinite discrete structures: the theory of richly branching [Formula: see text]-forests with generic binary predicates. (...) We also give an example of a superstable theory that fails to satisfy this stronger condition but nevertheless does not interpret any infinite discrete structures. (shrink)

Arthur Diamond comments that "it is not clear how a donor distributes money through Hanson's market". Let me try again to be clear. Imagine David Levy were to seek funding for the regression he suggests in his comments, on the relative impact of sports versus science spending on aggregate productivity. Consider what might happen under three different funding institutions.

How do people gather samples of evidence to learn about the world? Adults often prefer to sample evidence from diverse sources—for example, choosing to test a robin and a turkey to find out if something is true of birds in general. Children below age 9, however, often do not consider sample diversity, instead treating non‐diverse samples (e.g., two robins) and diverse samples as equivalently informative. The current study (N = 247) found that this discontinuity stems from developmental changes in standards (...) for evaluating evidence—younger children chose to learn from samples that best approximate idealized views of what category members are supposed to be like (e.g., the fastest cheetahs), with a gradual shift across age toward samples that cover more within‐category variation (e.g., cheetahs of varying speeds). These findings have implications for the relation between conceptual structure and inductive reasoning, and for the mechanisms underlying inductive reasoning more generally. (shrink)

We give a formalism for approximate isomorphism in continuous logic simultaneously generalizing those of two papers by Ben Yaacov [2] and by Ben Yaacov, Doucha, Nies, and Tsankov [6], which are largely incompatible. With this we explicitly exhibit Scott sentences for the perturbation systems of the former paper, such as the Banach‐Mazur distance and the Lipschitz distance between metric spaces. Our formalism is simultaneously characterized syntactically by a mild generalization of perturbation systems and semantically by certain elementary classes of two‐sorted (...) structures that witness approximate isomorphism. As an application, we show that the theory of any ‐tree or ultrametric space of finite radius is stable, improving a result of Carlisle and Henson [8]. (shrink)

We investigate questions involving Aronszajn trees, square principles, and stationary reflection. We first consider two strengthenings of introduced by Brodsky and Rinot for the purpose of constructing κ‐Souslin trees. Answering a question of Rinot, we prove that the weaker of these strengthenings is compatible with stationary reflection at κ but the stronger is not. We then prove that, if μ is a singular cardinal, implies the existence of a special ‐tree with a cf(μ)‐ascent path, thus answering a question of Lücke.

[Anne:] “I can't, I'm in the depths of despair. Can you eat when you are in the depths of despair?”“I've never been in the depths of despair, so I can't say,” said Marilla.“Weren't you? Well did you ever try to imagine you were in the depths of despair?”” No, I didn't.”“Then I don't think you can understand what it's like. It's a very uncomfortable feeling indeed. When you try to eat a lump comes right up in your throat and you (...) can't swallow anything, not even if it was a chocolate caramel.”—L.M. Montgomery, Anne of Green Gables.Emotion, as a “suprarational” property, transcends rationality in that it can be thought of as a group, contextual rather than as a solely individual trait, and thus is a higher order property, as the above quote suggests. This proposal arises from a metatheoretical analysis of models available to broach questions of emotion. I use metatheoretical in the sense of both the context of theory production and the theory of theory. From the first arose the idea that emotion, through the use of irrationality, has surfaced as a working equivalent to inexplicability or rational relativity, and can be modelled more adequately as suprarational, with a unique nature in its own right. The latter led me to propose that the concept of emotion as contextual, a higher order group level property, is possible and tentatively profitable. (shrink)

If we are not to conclude that most planets like Earth have evolved life as intelligent as we are, we must presume Earth is not random. This selection effect, however, also implies that the origin of life need not be as easy as the early appearance of life on Earth suggests. If a series of major evolutionary transitions were required to produce intelligent life, selection implies that a subset of these were “critical steps,” with durations that are similarly distributed. The (...) time remaining from now until simple life is no longer possible on Earth must also be similarly distributed. I show how these results provide timing tests to constrain models of critical evolutionary transitions. (shrink)

In this 1958 book, Professor Hanson turns to an equally important but comparatively neglected subject, the philosophical aspects of research and discovery.

Until recently, technology has happened to allow for cheap wiretaps. New digital telephone technologies, however, may soon make wiretaps more difficult, and new encryption technologies may soon make them almost impossible. This may be good news to privacy buffs, but it worries U.S. police agencies -- since 1968 the law has explicitly allowed police wiretaps. And it worries U.S. spy agencies -- since 1978 the law has explicitly allowed them to wiretap foreigners.

Hypertext publishing, the integration of a large body (perhaps billions) of public writings into a unified hypertext environment, will require the simultaneous solution of problems involving very wide database distribution, royalties, freedom of speech, and privacy. This paper describes these problems and presents, for criticism and discussion, an abstract design which seems to solve many of them. This design, called LinkText, is presented both as a specification and as design approaches grouped around various levels of electronic publishing.

We explore approximate categoricity in the context of distortion systems, introduced in our previous paper (Hanson in Math Logic Q 69(4):482–507, 2023), which are a mild generalization of perturbation systems, introduced by Yaacov (J Math Logic 08(02):225–249, 2008). We extend Ben Yaacov’s Ryll-Nardzewski style characterization of separably approximately categorical theories from the context of perturbation systems to that of distortion systems. We also make progress towards an analog of Morley’s theorem for inseparable approximate categoricity, showing that if there is (...) some uncountable cardinal $$\kappa $$ such that every model of size $$\kappa $$ is ‘approximately saturated,’ in the appropriate sense, then the same is true for all uncountable cardinalities. Finally we present some examples of these phenomena and highlight an apparent interaction between ordinary separable categoricity and inseparable approximate categoricity. (shrink)

We continue our study of strongly unbounded colorings, this time focusing on subadditive maps. In Part I of this series, we showed that, for many pairs of infinite cardinals $\theta < \kappa $, the existence of a strongly unbounded coloring $c:[\kappa ]^2 \rightarrow \theta $ is a theorem of $\textsf{ZFC}$. Adding the requirement of subadditivity to a strongly unbounded coloring is a significant strengthening, though, and here we see that in many cases the existence of a subadditive strongly unbounded coloring (...) $c:[\kappa ]^2 \rightarrow \theta $ is independent of $\textsf{ZFC}$. We connect the existence of subadditive strongly unbounded colorings with a number of other infinitary combinatorial principles, including the narrow system property, the existence of $\kappa $ -Aronszajn trees with ascent paths, and square principles. In particular, we show that the existence of a closed, subadditive, strongly unbounded coloring $c:[\kappa ]^2 \rightarrow \theta $ is equivalent to a certain weak indexed square principle $\boxminus ^{\operatorname {\mathrm {ind}}}(\kappa, \theta )$. We conclude the paper with an application to the failure of the infinite productivity of $\kappa $ -stationarily layered posets, answering a question of Cox. (shrink)

Is there such a thing as a ‘Logic of Discovery’? Do we even have a consistent idea of such a thing? The approved answer to this seems to be “No.” Thus Popper argues “The initial stage, the act of conceiving or inventing a theory, seems to me neither to call for logical analysis nor to be susceptible of it.” Again, “… there is no such thing as a logical method of having new ideas, or a logical reconstruction of this process.” (...) Reichenbach writes that philosophy of science “… cannot be concerned with [reasons for suggesting hypotheses], but only with [reasons for accepting hypotheses].” Braithwaite elaborates: “The solution of these historical problems involves the individual psychology of thinking and the sociology of thought. None of these questions are our business here.”. (shrink)

In this paper I argue that there can be genuine (as opposed to merely verbal) disputes about whether a sentence form is logically true or an argument form is valid. I call such disputes ?cases of deviance?, of which I distinguish a weak and a strong form. Weak deviance holds if one disputant is right and the other wrong, but the available evidence is insufficient to determine which is which. Strong deviance holds if there is no fact of the matter. (...) In section 2 I argue that weak deviance need not be trivial and may even be interesting. Section 3 considers what it could mean to say that logic is determined by a theory, especially a theory of meaning, an idea that arises in section 2. In section 4 I discuss the dispute between classical and relevance logicians over entailment and argue that it is a case of strong deviance. Finally, in section 5 I show that the result of the previous section is not absolute but relative to the background logic used in reaching it. (shrink)

Portrayals of humanoid robots in television series draw heavily from the historical and cultural mythology of robots. This mythology is expressed in two contemporary television series, Almost Human and Humans, in which robots are depicted as closely resembling humans in physical appearance and behavior and as fulfilling social roles usually occupied by humans. The robots are imagined with characteristics associated with human consciousness, such as emotions, individuality, and free will. An analysis of the robots in these series, using Jean Paul (...) Sartre’s theories of consciousness and the Other, demonstrates that when the robots are depicted as conscious, the relationship between a human and robot is portrayed as one of human-to-human (or human-to-Other), not human-to-technology. Sartre’s philosophy helps describe the human characters’ fascination and fear of the robots as resulting from their perceptions of the Other’s shifting status of object and subject and the unpredictability associated with the Other’s freedom. Thus, it is not the machine aspects of the robot that are desired and feared, but the humanness within the machine. Viewed in this way, the humanoid robot as depicted these television series represents a continuing effort to define and describe the essence of humanity in a society where the boundaries between machines and humans are becomingly increasingly blurred. (shrink)

The Halpern–Läuchli theorem, a combinatorial result about trees, admits an elegant proof due to Harrington using ideas from forcing. In an attempt to distill the combinatorial essence of this proof, we isolate various partition principles about products of perfect Polish spaces. These principles yield straightforward proofs of the Halpern–Läuchli theorem, and the same forcing from Harrington’s proof can force their consistency. We also show that these principles are not ZFC theorems by showing that they put lower bounds on the size (...) of the continuum. (shrink)

We have been discussing some of the fundamental features of the classical calculus of probability. The equiprobability of rival events was seen to be a major assumption of the calculus. Moreover, it is an assumption which the pure mathematician need not bother to justify. He need only present his formal system as follows.

Motivated by a characterization of weakly compact cardinals due to Todorcevic, we introduce a new cardinal characteristic, the C-sequence number, which can be seen as a measure of the compactness of a regular uncountable cardinal. We prove a number of ZFC and independence results about the C-sequence number and its relationship with large cardinals, stationary reflection, and square principles. We then introduce and study the more general C-sequence spectrum and uncover some tight connections between the C-sequence spectrum and the strong (...) coloring principle U(. . .), introduced in Part I of this series. (shrink)