This chapter contains sections titled: Validity in the Finite Model Theory in the Finite? Definability and Complexity First‐Order Definability Second‐Order Definability Inductive Definability Infinitary Logics Random Graphs and 0–1 Laws.

Alternative models of idealized scientific inquiry are investigated and compared. Particular attention is devoted to paradigms in which a scientist is required to determine the truth of a given sentence in the structure giving rise to his data.

The presence of nonobservational vocabulary is shown to be necessary for wide application of a conservative principle of theory revision.

A model of idealized scientific inquiry is presented in which scientists are required to infer the nature of the structure that makes true the data they examine. A necessary and sufficient condition is presented for scientific success within this paradigm.

We provide a new interpretation of Zeno’s Paradox of Measure that begins by giving a substantive account, drawn from Aristotle’s text, of the fact that points lack magnitude. The main elements of this account are (1) the Axiom of Archimedes which states that there are no infinitesimal magnitudes, and (2) the principle that all assignments of magnitude, or lack thereof, must be grounded in the magnitude of line segments, the primary objects to which the notion of linear magnitude applies. Armed (...) with this account, we are ineluctably driven to introduce a highly constructive notion of (outer) measure based exclusively on the total magnitude of potentially infinite collections of line segments. The Paradox of Measure then consists in the proof that every finite or potentially infinite collection of points lacks magnitude with respect to this notion of measure. We observe that the Paradox of Measure, thus understood, troubled analysts into the 1880’s, despite their knowledge that the linear continuum is uncountable. The Paradox was ultimately resolved by Borel in his thesis of 1893, as a corollary to his celebrated result that every countable open cover of a closed line segment has a finite sub-cover, a result he later called the “First Fundamental Theorem of Measure Theory.” This achievement of Borel has not been sufficiently appreciated. We conclude with a metamathematical analysis of the resolution of the paradox made possible by recent results in reverse mathematics. (shrink)

We consider drawbacks to scientific methods that prefer simple hypotheses to complex ones that cover the same data. The discussion proceeds in the context of a precise model of scientific inquiry.

Criteria of approximate scientific success are defined within a formal paradigm of empirical inquiry. One consequence of aiming for less than perfect truth is examined.

We describe a logic of preference in which modal connectives reflect reasons to desire that a sentence be true. Various conditions on models are introduced and analyzed.

This paper provides a mathematical model of scientific discovery. It is shown in the context of this model that any discovery problem that can be solved by a computable scientist can be solved by a computable scientist all of whose conjectures are finitely axiomatizable theories.

A criterion of adequacy is proposed for theories of relevant consequence. According to the criterion, scientists whose deductive reasoning is limited to some proposed subset of the standard consequence relation must not thereby suffer a reduction in scientific competence. A simple theory of relevant consequence is introduced and shown to satisfy the criterion with respect to a formally defined paradigm of empirical inquiry.

A paradigm of scientific discovery is defined within a first-order logical framework. It is shown that within this paradigm there exists a formal scientist that is Turing computable and universal in the sense that it solves every problem that any scientist can solve. It is also shown that universal scientists exist for no regular logics that extend first-order logic and satisfy the Löwenheim-Skolem condition.

This note investigates the class of finite initial segments of the cumulative hierarchy of pure sets. We show that this class is first-order definable over the class of finite directed graphs and that this class admits a first-order definable global linear order. We apply this last result to show that FO = FO.

This book gives a comprehensive overview of central themes of finite model theory – expressive power, descriptive complexity, and zero-one laws – together with selected applications relating to database theory and artificial intelligence, especially constraint databases and constraint satisfaction problems. The final chapter provides a concise modern introduction to modal logic, emphasizing the continuity in spirit and technique with finite model theory. This underlying spirit involves the use of various fragments of and hierarchies within first-order, second-order, fixed-point, and infinitary logics (...) to gain insight into phenomena in complexity theory and combinatorics. The book emphasizes the use of combinatorial games, such as extensions and refinements of the Ehrenfeucht-Fraissé pebble game, as a powerful way to analyze the expressive power of such logics, and illustrates how deep notions from model theory and combinatorics, such as o-minimality and treewidth, arise naturally in the application of finite model theory to database theory and AI. Students of logic and computer science will find here the tools necessary to embark on research into finite model theory, and all readers will experience the excitement of a vibrant area of the application of logic to computer science. (shrink)

This is a review of the film Big Eyes. Adapted from a true story about artist Margaret Keane, the overarching theme of the movie is plagiarism. While most people think of written works such as books and articles being plagiarized, Big Eyes gives viewers insight into the world of stolen works of visual art, namely paintings. The victim finds moral courage through religion, while the thief lives in denial until death. Anyone with an interest in art, law, or psychiatry will (...) enjoy what Big Eyes has to offer. (shrink)

ON DECEMBER 10, 1991 Charles Shonubi, a Nigerian citizen but a resident of the USA, was arrested at John F. Kennedy International Airport for the importation of heroin into the United States.1 Shonubi's modus operandi was ``balloon swallowing.'' That is, heroin was mixed with another substance to form a paste and this paste was sealed in balloons which were then swallowed. The idea was that once the illegal substance was safely inside the USA, the smuggler would pass the balloons and (...) recover the heroin. On the date of his arrest, Shonubi was found to have swallowed 103 balloons containing a total of 427.4 grams of heroin. There was little doubt about Shonubi's guilt. In fact, there was considerable evidence that he had made at least seven prior heroin-smuggling trips to the USA (although he was not tried for these). In October 1992 Shonubi was convicted in a United States District Court for possessing and importing heroin. Although the conviction was only for crimes associated with Shonubi's arrest date of December 10, 1991, the sentencing judge, Jack B. Weinstein, also made a ®nding that Shonubi had indeed made seven prior drug-smuggling trips to the USA. The interesting part of this case was in the sentencing. According to the federal sentencing guidelines, the sentence in cases such as this should depend on the total quantity of heroin involved. This instruction was interpreted rather broadly.. (shrink)

Academic dishonesty is a persistent problem in the American educational system. The present investigation examined how reports of academic cheating related to students' emphasis on their moral identities and their sensitivity to social evaluation. Seventy college students at a large southeastern university completed a battery of surveys. Symptoms of social anxiety were positively correlated with recall of academic cheating. Additionally, relative to students who placed less importance on their moral identities, students who placed more importance on their moral identities recalled (...) significantly fewer instances of cheating. In summary, these findings suggest that students are less likely to cheat on their school work when they place greater emphasis on their moral identity and are less sensitive to social evaluation. Practical interventions to rampant cheating in American schools are discussed. (shrink)

What sorts of things are there in the world? Clearly enough, there are concrete, material things; but are there other things too, perhaps nonconcrete or non-material things? Some people believe that there are such things, which are often called abstract ; purported examples of such objects include numbers, properties, possible but non-actual states of affairs, propositions, and sets. Following a long-standing tradition, I shall describe persons who believe that there are abstract objects as ‘platonists’. In this paper, I shall not (...) directly address the plausibility of platonism, as compared with its rivals; instead, I shall confine my attention to one way in which some people have tried to combine platonism and theism. More specifically, I shall concentrate upon the claim that abstract objects depend upon God ontologically ; I shall argue that platonistic theists should reject DEP in favour of the claim that abstract objects exist independently of God . In order to evaluate the relative merits of DEP versus IND, it will be helpful to examine in some detail a particular articulation of DEP. When it comes to recent work on DEP, we can do no better in this regard than to examine the recent work of Thomas V. Morris and Christopher H. Menzel. According Morris and Menzel, there is a sense in which God literally creates such abstracta through engaging in intellective activities. (shrink)

There are few participants in academic or policy debates over prostitution who would disagree that steps should be taken to improve conditions for those working in prostitution; so Moen1 is in good and plentiful company with respect to his recommendations.I will focus here on the analysis leading up to his conclusions, and with whether it helps us understand why prostitution is so commonly harmful and what it would take to mitigate those harms.i On these matters I am dubious. The question (...) of whether or not prostitution is harmful would seem, manifestly, to be an empirical question, rather than a philosophical issue. I take it that Moen's aim is to clarify the evaluative task, and then to evaluate the arguments that can be made to show prostitution is harmful—tasks which philosophers can responsibly engage in. But I would suggest that Moen's approach to this particular subject oversimplifies it by abstracting away from key facts about the context in which prostitution takes place, and thus that it does not offer as strong a case for normalising prostitution as he hopes.The basic thesis of Moen's essay is that if casual sex is harmless , then the sale of casual sexual services for money is also harmless, or at …. (shrink)

The consideration of ‘mutual benefits’ and partner cooperation have long been the accepted standpoint from which to draw inference about the onset, maintenance and breakdown of the coral‐algae endosymbiosis. In this paper, I review recent research into the climate‐induced breakdown of this important symbiosis (namely ‘coral bleaching’) that challenges the validity of this long‐standing belief. Indeed, I introduce a more parsimonious explanation, in which the coral host exerts a ‘controlled parasitism’ over its algal symbionts that is akin to an enforced (...) domestication arrangement. Far from being pathogenic, a range of well‐established cellular processes are reviewed that support the role of the coral host as an active ‘farmer’ of the energy‐rich photoassimilates from its captive symbionts. Importantly, this new paradigm reposes the deleterious bleaching response in terms of an envelope of environmental conditions in which the exploitative and captive measures of the coral host are severely restricted. The ramification of this new paradigm for developing management strategies that may assist the evolution of bleaching resistance in corals is discussed. (shrink)

From the perspective of nonlinear science, it is argued that one may accept physicalism and reject substance dualism without being forced into reductionism. This permits a property dualism under which biological and mental phenomena may emerge from intricate positive feedback networks, involving many levels of both the biological and cognitive hierarchies.

Volume 19, Issue 9, September 2019, Page 39-41.

The law of gravitational attraction is a window on three formal approaches to laws of nature based on Lorentz-invariance: Poincaré’s four-dimensional vector space (1906), Minkowski’s matrix calculus and spacetime geometry (1908), and Sommerfeld’s 4-vector algebra (1910). In virtue of a common appeal to 4-vectors for the characterization of gravitational attraction, these three contributions track the emergence and early development of four-dimensional physics.

American football is played in a chaotic visual environment filled with relevant and distracting information. We investigated the hypothesis that collegiate football players show exceptional skill at shielding their response execution from the interfering effects of distraction ( interference control ). The performances of 280 football players from National Collegiate Athletic Association Division I football programs were compared to age-matched controls in a variant of the Eriksen flanker task ( Eriksen and Eriksen, 1974 ). This task quantifies the magnitude of (...) interference produced by visual distraction on split-second response execution. Overall, football athletes and age controls showed similar mean reaction times (RTs) and accuracy rates. However, football athletes were more proficient at shielding their response execution speed from the interfering effects of distraction (i.e., smaller flanker effect costs on RT). Offensive and defensive players showed smaller interference costs compared to controls, but defensive players showed the smallest costs. All defensive positions and one offensive position showed statistically smaller interference effects when compared directly to age controls. These data reveal a clear cognitive advantage among football athletes at executing motor responses in the face of distraction, the existence and magnitude of which vary by position. Individual differences in cognitive control may have important implications for both player selection and development to improve interference control capabilities during play. (shrink)

I argue that a well-known argument concerning moral luck supports something like the Principle of Alternate Possibilities (PAP), despite the attacks on PAP by Harry Frankfurt and John Martin Fischer.

In the early 1880s, Henri Poincaré discovered an equilibrium figure for uniformly-rotating fluid masses—the pear, or piriform figure—and speculated that in certain circumstances the pear splits into two unequal parts, and provides thereby a model for the origin of binary stars. The contemporary emergence of photometric and spectroscopic studies of variable stars fueled the first models of eclipsing binaries, and provided empirical support for a realist view of equilibrium figures—including the pear—in the cosmic realm. The paper reviews astrophysical interpretation of (...) the Poincaré pear and the Poincaré-Darwin fission hypothesis with respect to research on variable stars from 1885 to 1901. (shrink)

: The rights to liberty championed by classical liberal and libertarian theorists may be supported as products of practical reason. The foundations for these rights rest initially on the idea that the separateness of persons is embedded in the circumstances of life that make justice a meaningful concept. We can discover the duties justice imposes […].

In “Molinism, Meticulous Providence, and Luck,” Steven Cowan argues that the doctrine of meticulous providence creates a damaging dilemma for Molinists. I argue that Molinists can overcome this dilemma without giving up the doctrine of meticulous providence.

Research programmes are sets of problems preferred on epistemic grounds and including preferred heuristics for inquiry. Charles Lyell's research programme for biogeograpy includes the problem of explaining the distribution of species constrained by laws governing locomotion and containment of species. Included in the programme are laws governing the supernatural introduction of replacement species. Wallace and Darwin derected arguments against the putative intelligibility of this aspect of Lyell's programme before discovering natural selection, and their defence, at this time of natural laws (...) governing the introduction of new species is interesting as a defence of a noval programme of research, not a defence of a proposed theroy. These arguments are presented and an epistemological foundation is offered for them. 1 The author is indebted to a referee for helpful comments on an earlier draft of this paper. (shrink)

This chapter contains sections titled: The Present Moment Sterner on Returning to the Present Clock Time and Experienced Time Notes.

In the past three decades there has been a rapid development of the formal machinery for modal logic. Quantified modal logic has developed along with a semantics and model theory that is appropriate to it. With this technical development there has been relatively little discussion of what modality is all about. There are two fundamental questions that have gone unanswered. First, to what does necessity amount? Is this a new logical notion, or is it something that can be further analyzed (...) in terms of other notions that we already have at our disposal? The second question is what makes truths involving necessity true? What is their ontological grounding in the world? This essay is directed at the first of these questions. ;There are three possible reductions of metaphysical modality. First, there is the reduction suggested by the semantics for modal logic: a reduction in terms of possible worlds. Second, there is the reduction in terms of cognition. What is possible is what is conceivable. Third, there is the reduction in terms of language. Necessities arise from the structures of language and/or language use. ;I argue that none of these is successful. All of them suffer either from presupposing some form of metaphysical necessity in the reductive base, rendering them circular and not truly reductive, or they do not do justice to the modality being reduced. ;Since necessity is not reducible to any non-modal features of the world, we need to determine whether we ought to reject it as unacceptable on this basis, or whether we ought to retain it, but treat is as a new primitive that is introduced into a philosophical or logical theory. I urge the latter course is the one that we ought to take because without it too many things will likewise be deemed unacceptable. Causal necessity and explanation, normally accepted theories or knowledge and perception, logic and logical validity, and one common manner of distinguishing sets from properties will be deemed unacceptable if de re necessity is unacceptable. All of these presuppose de re metaphysical necessity in some way. I conclude that de re metaphysical necessity ought to be retained in our theory as primitive, unanalyzable notion. (shrink)

This collection was inspired by the observation that film remakes offer us the opportunity to revisit important issues, stories, themes, and topics in a manner that is especially relevant and meaningful to contemporary audiences. Like mythic stories that are told again and again in differing ways, film remakes present us with updated perspectives on timeless ideas. While some remakes succeed and others fail aesthetically, they always say something about the culture in which_and for which_they are produced. Contributors explore the ways (...) in which the fears of death, loss of self, and bodily violence have been expressed and then reinterpreted in such films and remakes as Invasion of the Body Snatchers, Night of the Living Dead, and Dawn of the Dead. Films such as Rollerball, The Ring, The Grudge, The Great Yokai Wars, and Insomnia are discussed as well because of their ability to give voice to collective anxieties concerning cultural change, nihilism, and globalization. While opening on a note that emphasizes the compulsion of filmmakers to revisit issues concerning fear and anxiety, this collection ends by using films like Solaris, King Kong, Star Trek, Doom, and Van Helsing to suggest that repeated confrontation with these issues allows the opportunity for creative and positive transformation. (shrink)

We address two major limitations of Schyns et al. First, we clarify their concept of “features” by postulating several levels for processing. The composition of the feature set at each level determines the set at the next higher level, following simple structural guidelines. Second, we show that our proposed framework reconciles feature-creation and fixed-feature approaches.