This paper explores the relation between natural modality and our modelling practices. It will be argued that some modelling practices such as abstraction and idealization should be understood as presupposing empirical claims about objective modal features of the behavior of target systems. To establish the connection between natural modality on the one hand and modelling practices on the other an analysis of natural modality in terms of empirically accessible invariance relations will be provided.

Let us sum up. We began with the question, “What is the interest of a model-theoretic definition of validity?” Model theoretic validity consists in truth under all reinterpretations of non-logical constants. In this paper, we have described for each necessity concept a corresponding modal invariance property. Exemplification of that property by the logical constants of a language leads to an explanation of the necessity, in the corresponding sense, of its valid sentences. I have fixed upon the epistemic modalities in (...) characterizing the logical constants: to be a logical constant in the language of a population is to be invariant over a modality describing complete possible epistemic states of that population (or an idealized analogue thereof). The grounds for this characterization are these: (1) It leads, I believe, to an extensionally reasonable demarcation of the logical constants, including clear cases and excluding clear non-cases. It gives a principled criterion for deciding unclear cases. (2) It provides an analysis of the topic-neutrality of logic. (3) It leads to an explanation of the epistemic necessity of the logical truths in terms of the topic-neutrality of the logical constants.All the same, it is reasonable to ask, even if the suggested demarcation of logic is extensionally correct, whether it can reasonably be expected to be fundamental. The epistemic invariance of an expression is a rather striking property, one which we should want to explain. What is missing, then, is an explanation of the distinguishing epistemic properties of the constants in terms of more fundamental properties involving their understanding and use. It would be these that properly define the nature, not just the extent, of logic. (shrink)

There are few, perhaps no known, exact, true, general laws. Some of the work of generalization is carried by ceteris paribus generalizations. I suggest that many models continue such work in more complex form, with the idea of ceteris paribus conditions thought of as extended to more general conditions of application. I use the term regularity guide to refer collectively to cp‐generalizations and such regularity‐purveying models. Laws in the traditional sense can then be thought of as idealizations, which idealize away (...) from the conditions of application of regularity guides. If we keep clearly in mind the status of laws as such idealizations, problems surrounding traditional topics—such as lawlikeness, corresponding counterfactuals and modality—no longer look to be intractable. (shrink)

In most Western countries, health law bioethics are strongly intertwined. This strong connection is the result of some specific factors that, in the early years of these disciplines, facilitated a rapid development of both. In this paper, I analyse these factors and construe a development theory existing of three phases, or ideal‐typical models. In the moralistic‐paternalistic model, there is almost no health law of explicit medical ethics and the little law there is is usually based on traditional morality, combined with (...) paternalist motives, the objections to this modal are that its paternalism and moralism are unacceptable, that it is too static and knows no external control mechanisms. In the liberal model, which is now dominant on most Western countries, law and ethics closely cooperate and converge, both disciplines use the same framework for analysis: they are product‐oriented rather than practice‐oriented; they use the same conceptual categories, they focus on the minimally decent rather than the ideal, and they are committed to the same substantive normative theory in which patient autonomy and patient rights are central. However, each of these four characteristics also result in a certain one‐sidedness. In some countries, a third model is emerging. In this postliberal model, health law is more modest and acknowledges its inherent and normative limits, whereas ethics takes a richer and most ambitious self image. As a result health law and ethics will partly diverge again. (shrink)

I first give a brief summary of a critique of the traditional theories of approximation and idealization; and after identifying one of the major roles of idealization as detaching component processes or systems from their joints, a detailed analysis is given of idealized laws – which are discoverable and/or applicable – in such processes and systems (i.e., idealized model systems). Then, I argue that dispositional properties should be regarded as admissible properties for laws and that such an inclusion supplies the (...) much needed connection between idealized models and the laws they `produce'' or `accommodate''. And I then argue that idealized law-statements so produced or accommodated in the models may be either true simpliciter or true approximately, but the latter is not because of the idealizations involved. I argue that the kind of limiting-case idealizations that produce approximate truth is best regarded as approximation; and finally I compare my theory with some existing theories of laws of nature.We seem to trace [in KingLear] ... the tendency of imagination toanalyse and abstract, to decomposehuman nature into its constituentfactors, and then to construct beings in whomone or more of these factors isabsent or atrophied or only incipient. (shrink)

Interpretations of Nietzsche as a virtue theorist have proliferated in recent years as commentators have sought to read him as a modern eudaimonistic philosopher while also attempting to show what makes his contribution to this tradition valuable and distinctive.1While some commentators still contend that interpreting Nietzsche as a eudaimonist is antithetical to his overtly-stated philosophical aims,2 over the last decade there has been a upsurge of support for such readings, especially from commentators who emphasise what they claim is the pervasive (...) influence of the Hellenistic tradition on his work. Keith Ansell-Pearson has argued that Epicurus was a key influence on Nietzsche’s middle period, for example; whereas Michael Ure has claimed that the Stoic thought of Seneca and Epictetus was also highly influential.3 Nevertheless, even those commentators who agree that Nietzsche can be informatively situated, or is even best situated, within the Hellenistic tradition cannot agree on two seemingly-intractable puzzles which any virtue-theoretical reading must solve in order to give a full account of his moral philosophy. The puzzles can be stated as follows: Puzzle 1: Which character traits does Nietzsche endorse as virtues? Puzzle 2: What is Nietzsche’s ethical ideal? This article offers an exegetical strategy to shed light on both puzzles, especially the first one regarding which character traits Nietzsche endorses as virtues which, as we shall see, is tougher to answer by a straightforward appeal to his texts. To elucidate this puzzle, I will propose that his approving comments regarding excellence-based moral philosophy indicate that his own ethics is also structured in terms of an ethical ideal with a requisite set of virtues which, following his ancient philosophical influences, he views as fundamentally connected. As Julia Annas notes, one the most distinctive ‘assumptions which ancient theories make [is] the relationship of [our] virtues to our final end’,4 and given Nietzsche’s interest in, and apparent endorsement of, ancient eudaimonism – especially compared to his invariably scathing remarks on the modern deontological and utilitarian traditions – we have reason to think that he shares this view.5 What is significant for this article, however, is that Nietzsche’s commitment to a kind of eudaimonism modelled on the ancient world offers a potential way to solve both puzzles. If his virtues and ethical ideal are connected in a similar way to ancient eudaimonistic theories, then understanding his ethical ideal allows us to infer which character traits he endorses as virtues, and vice versa. Although it might be objected that a method tackling both puzzles in tandem would be unworkable if their solutions were contained in each other, in what follows I will show that Nietzsche’s extensive comments on his ethical ideal of ‘becoming what one is’ positions us in a strong position to infer which character traits he prizes most highly. I will call these character traits ‘virtues of self-cultivation’. (shrink)

_Grounding_ is meant to be a metaphysically explanatory relation of non-causal constitutive determination. Recently there has been significant interest in the idea that there might be ‘laws of metaphysics’ for grounding, analogous to the laws of nature for causation. In this paper I argue that current accounts of the structure of law-based grounding (focusing on Jonathan Schaffer’s structural equation modeling account) do not capture grounding’s directionality—a central feature. The formal account must be supplemented to satisfy this demand and give a (...) successful general account of directed grounding relations. I thus propose two alternative supplements: Priority-Inextricable Grounding and Priority-Extricable Grounding (itself divided into two alternatives—Priority by Absolute Fundamentality and Priority by Relative Fundamentality). Each supplement offers a distinct image of grounding—most illustratively, modally: for each, the structure of grounding contrastingly constrains the metaphysical compossibility of worlds that share facts or grounding relations. As such, I conclude that the supplements offer incompatible strategies for sourcing grounding directionality and grounding theorists ought to decide between them. (shrink)

Substantive counterlegal discourse poses a problem for those according to whom the laws of nature are metaphysically necessary. I discern two types of necessitarianism about laws: dispositional essentialism and modal necessitarianism. I argue that Toby Handfield’s response to the problem of counterlegals cannot help the modal necessitarian, according to whom all possible worlds are identical with respect to the laws. I thus propose a fictionalist treatment of counterlegals. Fictions are not limited by metaphysical possibility; hence, fictionalism affords the modal necessitarian (...) the means to account for the apparent substance of counterlegals even granting the metaphysical necessity of the laws. (shrink)

In formal theories of measurement meaningfulness is usually formulated in terms of numerical statements that are invariant under admissible transformations of the numerical representation. This is equivalent to qualitative relations that are invariant under automorphisms of the measurement structure. This concept of meaningfulness, appropriately generalized, is studied in spaces constructed from a number of conjoint and extensive structures some of which are suitably interrelated by distribution laws. Such spaces model the dimensional structures of classical physics. It is shown that this (...) qualitative concept corresponds exactly with the numerical concept of dimensionally invariant laws of physics. (shrink)

Fictional models in science -- The hypothetical versus the fictional -- What is wrong with the new fictionalism of scientific models? -- Re-inflating the conception of scientific representation -- Idealization, confirmation, and scientific realism -- Laws and models in a theory of idealization -- Approximation and its measures -- Approximation, idealization, and the laws of nature -- Coordination of space and unity of science -- Gauge gravity and the unification of natural forces -- Models and theories II: issues and applications (...) -- Models and theories I: the semantic view revisited -- Explaining quantum spontaneous symmetry breaking -- Review: symmetries in physics: philosophical reflections -- Classical spontaneous symmetry breaking -- Spontaneous symmetry breaking and chance in a classical world -- Approximations, idealizations, and models in statistical mechanics -- Infinite systems in SM explanations: thermodynamic limit, renormalization (semi-) groups, and irreversibility -- Explaining the emergence of cooperative phenomena -- A possible unified understanding of probabilistic objects -- Particularism and holism revisited -- Potential, propensity and categorical realism -- The Aharonov-Bohm effect and the reality of wave packets -- Realism and spacetime: of arguments against metaphysical realism and manifold realism -- Gauge invariance, Cauchy problem, indeterminism, and symmetry breaking -- Is there a relativistic thermodynamics? a case study of the meaning of special relativity. (shrink)

Eugene Wigner's several general discussions of symmetry and invariance principles are among the canonical texts of contemporary philosophy of physics. Wigner spoke from a position of authority, having pioneered for recognition of the importance of symmetry principles from nuclear to molecular physics. But perhaps recent commentators have not sufficiently stressed that Wigner always took care to situate the notion of invariance principles with respect to two others, initial conditions and laws of nature. Wigner's first such general consideration of (...) invariance principles, an address presented at Einstein's 70th birthday celebration, held in Princeton on 19 March 1949, began by laying out just this distinction, and in a way that seems to suggest that the three notions arise through abstraction in an analysis of the general problem of cognition in the natural sciences: The world is very complicated and it is clearly impossible for the human mind to understand it completely. Man has therefore devised an artifice which permits the complicated nature of the world to be blamed on something which is called accidental and thus permits him to abstract a domain in which simple laws can be found. The complications are called initial conditions; the domain of regularities, laws of nature. the underlying abstraction is probably one of the most fruitful the human mind has made. It has made the natural sciences possible. (shrink)

When is a law too idealized to be usefully applied to a specific situation? To answer this question, this essay considers a law in hydrogeology called Darcy''s Law, both as it is used in what is called the symmetric-cone model, and as it is used in equations to determine a well''s groundwater velocity and hydraulic conductivity. After discussing Darcy''s law and its applications, the essay concludes that this idealized law, as well as associated models and equations in hydrogeology, are not (...) realistic in the sense required by the D-N account. They exhibit what McMullin calls mathematical idealization, construct idealization, empirical-causal idealization, and subjunctive-causal idealization. Yet this lack of realism in hydrogeology is problematic for reasons unrelated to the status of the D-N account. These idealizations are also problematic in applied situations. Their problems require developing two supplemental criteria, necessary for their productive application. (shrink)

Standard philosophical accounts attempt to understand physical modality either in terms of special metaphysical entities and relationships or in terms of the organization of non-modal information, as in Best Systems Analysis. This paper defends an alternative to both these approaches in which invariance and various independence conditions play a central role. The methodological importance of separating law-claims from claims about initial and boundary conditions is highlighted.

The remarkable successes of the physical sciences have been built on highly general quantitative laws, which serve as the basis for understanding an enormous variety of specific physical systems. How far is it possible to construct universal principles in the cognitive sciences, in terms of which specific aspects of perception, memory, or decision making might be modelled? Following Shepard (e.g., ), it is argued that some universal principles may be attainable in cognitive science. Here, 2 examples are proposed: the simplicity (...) principle (which states that the cognitive system prefers patterns that provide simpler explanations of available data); and the scale‐invariance principle, which states that many cognitive phenomena are independent of the scale of relevant underlying physical variables, such as time, space, luminance, or sound pressure. This article illustrates how principles may be combined to explain specific cognitive processes by using these principles to derive SIMPLE, a formal model of memory for serial order (), and briefly mentions some extensions to models of identification and categorization. This article also considers the scope and limitations of universal laws in cognitive science. (shrink)

There exists a widespread consensus amongst contemporary jurisprudents, positivists and non-positivists alike, that the meaning of ‘obligation’ should not radically shift from law to morality, or any of the other domains of practical reason. Yet there is limited effort in contemporary discussions of legal obligation to engage with the metaphysics of normativity with an eye to a well-founded account of those elements that deliver its non-conditional character. On a recent occasion I discussed the shortcomings of a prominent positivist account of (...) legal obligation, that of Jules Coleman. In this chapter I turn to a prominent non-positivist account, the model of principle, and argue that, even though it identifies key elements or conditions of normativity simpliciter, it stops short of delivering a conclusive account of unconditional legal obligation, an account that would place legal obligation in the same continuum with all other types of obligation. Taking up from where the model of principle halts, I propose a complementary—if more fundamental—account of normativity simpliciter, which I dub the model of norms. I make a case for it, by looking into universal conditions of normativity and, in conclusion, offer some more specific remarks about the advantages of the model of norms over other competing models. Part 2 looks into the account of legal obligation tendered by the model of principle. According to it, law is an instance of action-directing action or action that purports to get other agents to comply with the ends it sets out to attain. The idea here is that the very logic of action-direction draws moral reasons—principles—into the picture of legal obligation, as the one item that can explain how and whether the facts of a social practice, which purports to direct action, come to acquire the status of reasons for action for the subjects of law. Subsequently, this model is contrasted with an alternative model of obligation that takes facts of authority to constitute reasons of action in virtue solely of their structure. In conclusion it is argued that, in contrast to the second model, the model of principle manages to capture what is distinctive about action-directing action in the domain of law—that is, the special normative significance of the possibility to coerce others under a scheme of public institutions. Part 3 opens by pointing to a more widespread worry that needs to be addressed before the model of principle can be deemed fit for the role it is employed—the worry relates to the ability of principles to constitute genuine reasons for action. In particular, the enquiry investigates the nature of principles and their ability to avoid certain flaws that might pertain to reasons for action in general. In taking up this line of enquiry the paper looks into the more general debate on normativity with a view to specifying requirements that anything which purports to be a reason ought to meet. I employ a rationalist analysis of normativity, which brings the idea that intentional thought is normative to bear on the analysis of the meaning of normative terms, such as ‘ought’, ‘obligation’, ‘duty’. In conclusion, I argue that the content of normativity consists in normative facts—ie norms—which purport to model the content of ideal—or counterfactual—states of the will. Such norms give exhaustively the content of normativity. In light of the above, part 4 advances a two-layered model of norms, with the higher level being populated by norms simpliciter, and the lower by norms in a domain. When considered jointly the two layers ground the possibility of non-conditional obligation without evoking moral realism and the concomitant suspicion of scepticism. On the face of it some key advantages of the model of norms are discussed over the two other models of legal obligation, that of principle and that of authority. On the one hand norms resist the ‘talking past each other objection’ which is commonly levelled against principles. On the other, norms are much better suited to account for the moral limits of action-directing action than either principles or facts of authority, for they illustrate cogently that the grounds of any reason for action already include a concern for others’ autonomy. (shrink)

The tangle modality is a propositional connective that extends basic modal logic to a language that is expressively equivalent over certain classes of finite frames to the bisimulation-invariant fragments of both first-order and monadic second-order logic. This paper axiomatises several logics with tangle, including some that have the universal modality, and shows that they have the finite model property for Kripke frame semantics. The logics are specified by a variety of conditions on their validating frames, including local and global connectedness (...) properties. Some of the results have been used to obtain completeness theorems for interpretations of tangled modal logics in topological spaces. (shrink)

This paper has three aims: first, to present in a clear way Newton da Costa’s argument against the necessity of logical laws. In order to do so, we need to clearly advance his views on the idea that logic is context-relative, and not known a priori. Doing so, however, requires that we present his methodology for the development of counter-examples to logical laws: the use of hypothetical models in logic. Given that this method has been overlooked in most discussions on (...) the epistemology of logic, our second goal is to present da Costa’s views on it carefully. The discussion of some tensions resulting from the relation of a system of logic and the context it governs, in da Costa’s approach, is our third goal. Basically, da Costa seems to swing between two incompatible views on such relation, requiring sometimes that a logic is dependent on a context, and in other cases, that the nature of the context is dependent on a logic. Bringing this to light may also benefit current discussions on logical relativism. (shrink)

The paper tries to provide an alternative to Hempel’s approach to scientific laws and scientific explanation as given in his D-N model. It starts with a brief exposition of the main characteristics of Hempel’s approach to deductive explanations based on universal scientific laws and analyzes the problems and paradoxes inherent in this approach. By way of solution, it analyzes the scientific laws and explanations in classical mechanics and then reconstructs the corresponding models of explanation, as well as the types of (...) scientific laws appearing in it. Finally, it compares this reconstruction with the approaches of J. Woodward and C. Hitchcock, C. Liu and with the views of M. Thalos on analytic mechanics. (shrink)

Since the 1930’s, several attempts have been made to develop a general theory of technical systems or objects and their evolution: in France, Jacques Lafitte, André Leroi-Gourhan, Bertrand Gille, Yves Deforge, and Gilbert Simondon are the main representatives of this trend. In this paper, we focus on the work of Simondon: his analysis of technical progress is based on the hypothesis that technology has its own laws and that customer demand has no paramount influence upon the evolution of technical systems. (...) We first describe the process Simondon called “concretization” and compare it with the process of “idealization” as defined by Genrich Altshuller. We then explain how the progress of technical lineages can be characterized as following a specific rhythm of relaxation and how it thus obeys a “law” of evolution in the industrial context. Simondon’s theoretical approach, although similar to some aspects of methodologies of conception, emphasized a more accurate understanding of technical progress over possible operational applications. Simondon never intended to optimize the engineer’s tasks from an economic point of view and, in fact, his conception of technical progress can be considered as independent from the capitalistic trend of innovation. However, the philosophy of Simondon provides a better understanding of what is at stake theoretically in the modeling of laws of technical evolution. (shrink)

In this paper we define and examine frame constructions for the family of manyvalued modal logics introduced by M. Fitting in the '90s. Every language of this family is built on an underlying space of truth values, a Heyting algebra H. We generalize Fitting's original work by considering complete Heyting algebras as truth spaces and proceed to define a suitable notion of H-indexed families of generated subframes, disjoint unions and bounded morphisms. Then, we provide an algebraic generalization of the canonical (...) extension of a frame and model, and prove a preservation result inspired from Fitting's canonical model argument in [FIT 92a]. The analog of a complex algebra and of a principal ultrafilter is defined and the embedding of a frame into its canonical extension is presented. (shrink)

Adding certain cardinality quantifiers into first-order language will give substantially more expressive languages. Thus, many mathematical concepts beyond first-order logic can be handled. Since basic modal logic can be seen as the bisimular invariant fragment of first-order logic on the level of models, it has no ability to handle modally these mathematical concepts beyond first-order logic. By adding modalities regarding the cardinalities of successor states, we can, in principle, investigate modal logics of all cardinalities. Thus ways of exploring model-theoretic logics (...) can be transferred to modal logics. (shrink)

This article demonstrates that non-mechanistic, dynamical explanations are a viable approach to explanation in the special sciences. The claim that dynamical models can be explanatory without reference to mechanisms has previously been met with three lines of criticism from mechanists: the causal relevance concern, the genuine laws concern, and the charge of predictivism. I argue, however, that these mechanist criticisms fail to defeat non-mechanistic, dynamical explanation. Using the examples of Haken et al.’s model of bimanual coordination, and Thelen et al.’s (...) dynamical field model of infant perseverative reaching, I show how each mechanist criticism fails once the standards of Woodward’s interventionist framework are applied to dynamical models. An even-handed application of Woodwardian interventionism reveals that dynamical models are capable of producing genuine explanations without appealing to underlying mechanistic details. 1Introduction2Interventionism and Mechanistic Explanation 2.1Causal relevance and ideal interventions2.2Invariance2.3Explanation3Covering-Laws and Dynamical Explanation 3.1Dynamical models3.2Covering-law explanation3.3Prediction4Causal Relevance 4.1The causal relevance concern4.2Intervening on dynamical models4.3Test case I: The Haken–Kelso–Bunz model4.4Test case II: Dynamical field model5Genuine Laws 5.1The genuine laws concern5.2Using invariance in place of laws5.3Test case I: The Haken–Kelso–Bunz model5.4Test case II: Dynamical field model6Prediction 6.1Predictivism6.2Crude and invariant prediction7Interventionist Criticism of the Haken–Kelso–Bunz Model8Dynamical Explanation8Conclusion. (shrink)

Scientific models invariably involve some degree of idealization, abstraction, or nationalization of their target system. Nonetheless, I argue that there are circumstances under which such false models can offer genuine scientific explanations. After reviewing three different proposals in the literature for how models can explain, I shall introduce a more general account of what I call model explanations, which specify the conditions under which models can be counted as explanatory. I shall illustrate this new framework by applying it to the (...) case of Bohr's model of the atom, and conclude by drawing some distinctions between phenomenological models, explanatory models, and fictional models. (shrink)

In this article, we aim at presenting a thorough and comprehensive explanation of the mathematical and theoretical relation between all the aspects of Ptolemaic planetary models and their counterparts which are built according to Kepler’s first two laws. Our article also analyzes the predictive differences which arise from comparing Ptolemaic and these ideal Keplerian models, making clear distinctions between those differences which must be attributed to the structural variations between the models, and those which are due to the specific parameters (...) Ptolemy determined in the Almagest. We expect that our work will be a contribution for a better understanding not only of the Ptolemaic theories for planetary longitudes through a clearer perception of the way in which Keplerian features are present—or absent—in Ptolemy’s models, but also for a more balanced judgement of different aspects of the contribution of the first two laws of Kepler to the modern astronomical revolution. (shrink)

Adding certain cardinality quantifiers into first-order language will give substantially more expressive languages. Thus, many mathematical concepts beyond first-order logic can be handled. Since basic modal logic can be seen as the bisimular invariant fragment of first-order logic on the level of models, it has no ability to handle modally these mathematical concepts beyond first-order logic. By adding modalities regarding the cardinalities of successor states, we can, in principle, investigate modal logics of all cardinalities. Thus ways of exploring model-theoretic logics (...) can be transferred to modal logics. (shrink)

This book provides both an introduction to the philosophy of scientific modeling and a contribution to the discussion and clarification of two recent philosophical conceptions of models: artifactualism and fictionalism. These can be viewed as different stances concerning the standard representationalist account of scientific models. By better understanding these two alternative views, readers will gain a deeper insight into what a model is as well as how models function in different sciences. Fictionalism has been a traditional epistemological stance related to (...) antirealist construals of laws and theories, such as instrumentalism and inferentialism. By contrast, the more recent fictional view of models holds that scientific models must be conceived of as the same kind of entities as literary characters and places. This approach is essentially an answer to the ontological question concerning the nature of models, which in principle is not incompatible with a representationalist account of the function of models. The artifactual view of models is an approach according to which scientific models are epistemic artifacts, whose main function is not to represent the phenomena but rather to provide epistemic access to them. It can be conceived of as a non-representationalist and pragmatic account of modeling, which does not intend to focus on the ontology of models but rather on the ways they are built and used for different purposes. The different essays address questions such as the artifactual view of idealization, the use of information theory to elucidate the concepts of abstraction and idealization, the deidealization of models, the nature of scientific fictions, the structural account of representation and the ontological status of structures, the role of surrogative reasoning with models, and the use of models for explaining and predicting physical phenomena. (shrink)

In 2012, a law against hiring models with a BMI below 18.5 was passed in Israel. In addition, every photoshopped advertisement must have a visible subtitle that indicates that the picture was photoshopped. Dr. Rachel Adatto, the initiator of the law, states that the law is “a beginning of a revolution against the anorectic beauty model ideal,” and that its aim is to prevent eating disorders that may lead to death in the aspiration to lose weight, especially among the general (...) population of teenagers and young adults who are exposed to the thin role models in the media. Adi Barkan, a photographer and models’ agent, who was also involved in promoting the legislation, viewed it from a different angle.... (shrink)

. We prove new Lindström theorems for the basic modal propositional language, and for some related fragments of first-order logic. We find difficulties with such results for modal languages without a finite-depth property, high-lighting the difference between abstract model theory for fragments and for extensions of first-order logic. In addition we discuss new connections with interpolation properties, and the modal invariance theorem.

The paper presents an infinite hierarchy PR m [ m = 1, 2, . . . ] of sound and complete axiomatic systems for modal logic with graded probabilistic modalities , which are to reflect what I have elsewhere called the Bolding-Ekelöf degrees of evidential strength as applied to the establishment of matters of fact in law-courts. Our present approach is seen to differ from earlier work by the author in that it treats the logic of these graded modalities not (...) only from a semantical or model-theoretic viewpoint but from a prooftheoretical and axiomatic stance as well. A paramount feature of the approach is its use of so-called systematic frame constants as labels of diverse grades of probability. Apart from this novel feature our approach can be seen to go back to pioneering work by Lou Goble in 1970. (shrink)

What is the origin of the concept of a law of nature? How much does it owe to theology and metaphysics? To what extent do the laws of nature permit contingency? Are there exceptions to the laws of nature? Is it possible to give a reductive analysis of lawhood, or is it a primitive? -/- Twelve brand-new essays by an international team of leading philosophers take up these and other central questions on the laws of nature, whilst also examining some (...) of the most important intuitions and assumptions that have guided the debate over laws of nature since the concept's invention in the seventeenth century. -/- Laws of Nature spans the history of philosophy and of science, contemporary metaphysics, and contemporary philosophy of science. Contents: 1. Intuitions and Assumptions in the Debate over Laws of Nature, Walter Ott and Lydia Patton 2. Early Modern Roots of the Philosophical Concept of a Law of Nature, Helen Hattab 3. Laws of Nature and the Divine Order of Things: Descartes and Newton on Truth in Natural Philosophy, Mary Domski 4. Leges sive natura: Bacon, Spinoza, and a Forgotten Concept of Law, Walter Ott 5. Laws and Powers in the Frame of Nature, Stathis Psillos 6. Laws and Ideal Unity, Angela Breitenbach 7. Becoming Humean, John W. Carroll 8. A Perspectivalist Better Best System Account of Lawhood, Michela Massimi 9. Laws: An Invariance Based Account, James Woodward 10. How the Explanations of Natural Laws Make Some Reducible Physical Properties Natural and Explanatorily Powerful, Marc Lange 11. Laws and their Exceptions, Stephen Mumford 12. Are laws of nature consistent with contingency?, Nancy Cartwright and Pedro Merlussi. (shrink)

This paper considers the method of idealization and factualization as the main method of all advanced empirical science. The procedure is as follows. Some idealizing conditions are assumed: the vanishing of factors $(p_{i}=0)$ which never vanish in the real world. An idealization law is formulated -- a law which is exactly (non-vacuously) fulfilled only in an ideal model, not in any real system. Then the idealizing assumptions are abrogated one by one-it is a process of gradual factualization, of the transition (...) to the factual laws which are fulfilled in real systems. These laws may be directly applied and tested by experience. (shrink)

One puzzle concerning highly idealized models is whether they explain. Some suggest they provide so-called ‘how-possibly explanations’. However, this raises an important question about the nature of how-possibly explanations, namely what distinguishes them from ‘normal’, or how-actually, explanations? I provide an account of how-possibly explanations that clarifies their nature in the context of solving the puzzle of model-based explanation. I argue that the modal notions of actuality and possibility provide the relevant dividing lines between how-possibly and how-actually explanations. Whereas how-possibly (...) explanations establish claims of possible explanations, how-actually explanations establish claims of actual ones. Models, in turn, simply provide evidence for these claims. (shrink)

Models are of central importance in many scientific contexts. The centrality of models such as the billiard ball model of a gas, the Bohr model of the atom, the MIT bag model of the nucleon, the Gaussian-chain model of a polymer, the Lorenz model of the atmosphere, the Lotka-Volterra model of predator-prey interaction, the double helix model of DNA, agent-based and evolutionary models in the social sciences, or general equilibrium models of markets in their respective domains are cases in point. (...) Scientists spend a great deal of time building, testing, comparing and revising models, and much journal space is dedicated to introducing, applying and interpreting these valuable tools. In short, models are one of the principal instruments of modern science. -/- Philosophers are acknowledging the importance of models with increasing attention and are probing the assorted roles that models play in scientific practice. The result has been an incredible proliferation of model-types in the philosophical literature. Probing models, phenomenological models, computational models, developmental models, explanatory models, impoverished models, testing models, idealized models, theoretical models, scale models, heuristic models, caricature models, didactic models, fantasy models, toy models, imaginary models, mathematical models, substitute models, iconic models, formal models, analogue models and instrumental models are but some of the notions that are used to categorize models. While at first glance this abundance is overwhelming, it can quickly be brought under control by recognizing that these notions pertain to different problems that arise in connection with models. For example, models raise questions in semantics (what is the representational function that models perform?), ontology (what kind of things are models?), epistemology (how do we learn with models?), and, of course, in philosophy of science (how do models relate to theory?; what are the implications of a model based approach to science for the debates over scientific realism, reductionism, explanation and laws of nature?). (shrink)

The main purpose of this paper is to explore the role played by logic in the legal domain. In the traditional conception which underlies the movement of codification, judges are able to find in the legal system (the Master System) a unique answer for every legal problem. This entails its completeness, consistency and the possibility of deriving from it the contents of all judicial decisions. Although the ideal model of this conception is supported by important theoretical and political ideals, it (...) has significant shortcomings. The elements of normative systems (Master Systems) are “norms” and not mere “norm-formulations.” A “norm” is the meaning attributed to normative linguistic expressions. The set of all normative expressions, such as statutes, codes, etc. forms what is called the Master Book. One of the main problems for the ideal model is the identification of a normative system behind the Master Book. Interpretative arguments are the tools designed to solve these problems. Although the requirements of the model are not totally fulfilled in actual practice, it remains as an effective ideal rational goal behind legal activities linked to adjudication and most theoretical approaches to law. (shrink)

Lewis proposed to test the validity of a modal thesis by checking whether its possible-world translation is a theorem of counterpart theory. However, that criterion fails to validate many standard modal laws, thus raising doubts about the logical adequacy of the Lewisian framework. The present paper considers systems of counterpart theory of increasing strength and shows how each can be motivated by exhibiting a suitable intended model. In particular, perfect counterpart theory validates all the desired modal laws and therefore provides (...) a way out of the logical objection. Finally, a weakening of perfect counterpart theory is put forward as a response to some metaphysical objections. (shrink)

There are many different approaches to the logic of truth. We could agree with Tarski, that the appropriate way to formalise a truth predicate is in a hierarchy, in which the truth predicate in one language can apply only to sentences from another language. Or, we could attempt to do without type restrictions on the truth predicate. Bradwardine’s theory of truth takes the second of these options: it is type-free, and admits sentences which say of themselves that they are not (...) true to be well-formed. We could take the behaviour of the paradoxes such as the liar to motivate a revision of the basic logic of propositional inference, to allow for truth-value gaps or gluts [9, 11, 15]. On the other hand, we could take it that the paradoxes are no reason to revise our account of the basic laws of logic: a novel account of the behaviour of the truth predicate is what is required. Bradwardine’s account, as elaborated by Read, takes this second option.1 Finally. (shrink)

What are logical notions? According to a very popular proposal, a logical notion is something invariant under some “transformation” of objects, usually permutations or isomorphisms. The first chapter is about extending “invariance” accounts of logicality to intensional notions, by asking for invariance under arbitrary permutations of both possible worlds and objects. I discuss the results one gets in this extended theory of invariance, and how to fix many technical issues. The second chapter is about setting out a (...) better theory of logicality. I discuss the limits of invariance frameworks, and the need for a theory of logicality with a more solid philosophical ground. I believe that the concept of information can play a major role in defining what logic is and what logical notions are. I spell out this intuition, by designing a new test for logicality. A notion is logical iff it behaves in a certain way, by checking only “structural aspects of information”, and it does so under arbitrary transformations of its “informational inputs”. In the last chapter I explore some interesting features of my theory. I show how, contrary to standard invariance, in mine logical notions tend to stay persistent across different models of information. I also spell out an intermediate notion of quasi-logicality to make sense of the formality of “world-sensitive” notions: notions whose behaviour changes across worlds. I finally propose a case study: deontic modals. I discuss how one can argue for their quasi-logicality, in my framework. The dissertation is concluded with a technical appendix, in which I prove that my theory is a restriction of standard permutation invariance when we model the space of information in a certain way: as a set of complete powersets of some sets. (shrink)

Properties and relations in general have a certain degree of invariance, and some types of properties/relations have a stronger degree of invariance than others. In this paper I will show how the degrees of invariance of different types of properties are associated with, and explain, the modal force of the laws governing them. This explains differences in the modal force of laws/principles of different disciplines, starting with logic and mathematics and proceeding to physics and biology.

Idealizations are ubiquitous in physics. They are distortions or falsities that enter into theories, laws, models, and scientific representations. Various questions suggest themselves: What are idealizations? Why do we appeal to idealizations and how do we justify them? Are idealizations essential to physics and, if so, in what sense and for which purpose? How can idealizations provide genuine understanding? If our motivation for believing in the existence of unobservable entities like electrons and quarks is that they are indispensable to our (...) best theories, should we also believe in the existence of indispensable idealizations? This Element will tackle such questions and offer an opinionated and selective introduction to philosophical issues concerning idealizations in physics. Topics to be covered include the concept of and reasons for introducing idealization, abstraction, and approximation, possible taxonomy and justification, and application to issues of mathematical Platonism, scientific realism, and scientific understanding. (shrink)

The paper examines the invariance principles proposed by the analytical and phenomenological traditions for demarcating the boundaries of formal and regional ontologies. The principle of invariance with respect to isomorphic transformations, generalizing Alfred Tarski’s criterion for logical concepts, is extended to formal ontology as the theory of manifolds in its phenomenological interpretation. Isomorphism types, which are abstract individuals of the highest order, hypostases of forms of all possible ontologies, are considered as model-theoretical analogs of manifolds. The correlativity of (...) the phenomenological principles of demarcation of ontological regions and the criterion of invariance with respect to isomorphic transformations is demonstrated, leading to the convergence of logic and formal mathematics in both traditions and, at the same time, to the exclusion of geometry from formal ontology. Particular attention is paid to the discussion of the analytical and phenomenological traditions of the synthetic (material) a priori and the contribution that Wittgenstein’s doctrine on internal relations at different stages of its evolution makes to this discussion. The paper reveals the basis for later Wittgenstein’s criticism of his earlier project of creating a phenomenological language for expressing internal regional relations (such as the colours exclusion). The paper shows how Wittgenstein’s doubts about the possibility of an ideal notation based on the dichotomy of the logical and phenomenological led him to the study of invariants arising in language games. These invariants are not determined by the special properties of the categorical objects of formal ontology or the structures of regional subject matter, but are stable equilibria generated by the “consensus of actions.” New perspectives are outlined that are opened for logic and phenomenology by switching focus from the invariants of ontological structures to the invariants of structured interactions of various agents. (shrink)

Maxwell accounted for the apparent elastic behavior of the electromagnetic field by augmenting Ampere’s law with the so-called displacement current, in much the same way that he treated the viscoelasticity of gases. Maxwell’s original constitutive relations for both electrodynamics and fluid dynamics were not material invariant. In the theory of viscoelastic fluids, the situation was later corrected by Oldroyd, who introduced the upper-convective derivative. Assuming that the electromagnetic field should follow the general requirements for a material field, we show that (...) if the upper convected derivative is used in place of the partial time derivative in the displacement current term, Maxwell’s electrodynamics becomes material invariant. Note, that the material invariance of Faraday’s law is automatically established if the Lorentz force is admitted as an integral part of the model. The new formulation ensures that the equation for conservation of charge is also material invariant in vacuo. The viscoelastic medium whose apparent manifestation are the known phenomena of electrodynamics is called here the metacontinuum. (shrink)

The use of idealized models in science is by now well-documented. Such models are typically constructed in a “top-down” fashion: starting with an intractable theory or law and working down toward the phenomenon. This view of model-building has motivated a family of confirmation schemes based on the convergence of prediction and observation. This paper considers how chaotic dynamics blocks the convergence view of confirmation and has forced experimentalists to take a different approach to model-building. A method known as “phase space (...) reconstruction” not only reveals a lacuna in the philosophical literature on models, it also fails to conform to conventional views about how models are used to confirm a theory. (shrink)

Metaphysicians speak of laws of nature in terms of necessity and universality; scientists, in terms of symmetry and invariance. In this book van Fraassen argues that no metaphysical account of laws can succeed. He analyzes and rejects the arguments that there are laws of nature, or that we must believe there are, and argues that we should disregard the idea of law as an adequate clue to science. After exploring what this means for general epistemology, the author develops the (...) empiricist view of science as a construction of models to represent the phenomena. (shrink)

This paper examines the ‘deep-end’ of the international justice process—the incarceration of persons convicted in specially constituted international criminal tribunals and courts for gross violations of human rights, genocide, crimes against humanity and war crimes with a focus on language rights of such prisoners who are commonly serving sentences in foreign prisons. The punishment phase of the international justice process and its effects are not easily quantifiable and have been largely hidden from view. Although international criminal law asserts that equal (...) treatment before the law requires that there be no significant disparity in punishment regimes from one sentence-enforcing country to another, comparative penology shows that there are considerable differences in the conditions of confinement and the nature of correctional services in the prison systems of different countries. This has a direct impact on post-sentence procedural and rehabilitation rights of which language rights from a key part. In this specific context, and drawing from existing literature, the paper therefore examines the extent to which enforcement practice conforms to the ideal of equal treatment espoused by the tribunals. (shrink)

Idealization is a necessity. Stripping away levels of complexity makes questions tractable, focuses our attention, and lets us develop comprehensible, testable models. Applying such models, however, requires care and attention to how the idealizations incorporated into their development affect their predictions. In epistemology, we tend to focus on idealizations concerning individual agents' capacities, such as memory, mathematical ability, and so on, when addressing this concern. By contrast, this dissertation focuses on social idealizations, particularly those pertaining to salient social categories like (...) race, sex, and gender. In Chapter II, Privilege and Superiority, we begin with standpoint epistemology, one of the earliest efforts to grapple with the ways that social structures affect our epistemic lives. I argue that, if we interpret standpoint epistemologists' claims as hypotheses about the ways that our social positions affect access to evidence, we can fruitfully employ recent developments in evidence logic to study the consequences. I lay the groundwork for this project, developing a model based on neighborhood semantics for modal logic. Adapting this framework to standpoint epistemology helps to clarify the meaning of terms like "epistemic privilege" and "superior knowledge" and to elucidate the differences between various accounts of standpoint epistemology. I also address a longstanding criticism of these views: Longino's (1990) bias paradox, which suggests that there is no objective position from which to judge the goodness of a particular standpoint. Chapter III, Evidence in a Non-Ideal World, turns to the broader social context, looking at how ideology affects the availability of evidence. Throughout the chapter, I take the formation, justification, and maintenance of racist, sexist, and otherwise oppressive beliefs as a central case. I argue that these beliefs are, at least sometimes, formed as a result of evidential distortion, a structural feature of our epistemic contexts that skews readily available evidence in favor of dominant ideologies. Because they are formed this way, such beliefs will appear justified on prominent accounts of justification, both internalist and externalist. As a result, epistemic norms that fail to account for such non-ideal conditions will deliver verdicts that are not only counter-intuitive, but also morally unpalatable. This, I argue, reveals a kind of structural epistemic injustice, especially where oppressive ideology is involved and suggests the need for epistemic norms that are sensitive to agents' social contexts. Much of the discussion in Chapters II and III depends on social categories like race and gender, arguing that they have a distinctive influence on our epistemic lives. In Chapter IV, I Know You Are, But What Am I?, my co-author and I focus on social categories themselves, distinguishing between self-identity, social identity, and social role. We self-identify as gay or straight, men or women, couch-potatoes or gym rats. Sometimes, these identities affect our social roles---the way we are perceived and treated by others---and sometimes they do not. This relationship between our internal identities and our preferred public perceptions begs for explanation. On our account, this relationship is captured by what we refer to as 'social identity'---roughly, internal identities made available to others. We argue that this account of social identity plays an illuminating role in structural explanation of discrimination and individual behavior, dissolves puzzles surrounding the phenomenon of 'passing', and explains certain moral and political obligations toward individuals. (shrink)

This work analyses the speech-act of arguing as proposed by Linguistic Normative Model of Argumentation (LNMA) with the help of diagrams, examples and basic formalization techniques. The focus is set on one of the most novel issues of LNMA, modal qualification, and the distinction between epistemic and ontological modals. The first conclusion is that employing LNMA in order to analyse and evaluate actual argumentation as it is proposed is too complex to be applied as is. The second conclusion, at a (...) theoretical level, is that the distinction between ontological and epistemic modals is highly problematic in LNMA. (shrink)

Laws through which we explain particular events need not be laws which describe uniform sequences of events; they may be laws stating uniform connections between two types of factor contained within a complex event. Hempel's apparent insistence that laws state the conditions invariably accompanying a type of complex event, that the event be an instance of the laws "covering" it, results from the Humean analysis in which causation obtains between types of events and "the cause" means necessary conditions. But historians (...) often depict sufficient conditions. On the other hand, some knowledge of general laws is a presupposition of Dray's "continuous series" model of historical explanation. (shrink)

Let [Formula: see text] be a monster model of an arbitrary theory [Formula: see text], let [Formula: see text] be any tuple of bounded length of elements of [Formula: see text], and let [Formula: see text] be an enumeration of all elements of [Formula: see text]. By [Formula: see text] we denote the compact space of all complete types over [Formula: see text] extending [Formula: see text], and [Formula: see text] is defined analogously. Then [Formula: see text] and [Formula: see (...) text] are naturally [Formula: see text]-flows. We show that the Ellis groups of both these flows are of bounded size, providing an explicit bound on this size. Next, we prove that these Ellis groups do not depend on the choice of the monster model [Formula: see text]; thus, we say that these Ellis groups are absolute. We also study minimal left ideals of the Ellis semigroups of the flows [Formula: see text] and [Formula: see text]. We give an example of a NIP theory in which the minimal left ideals are of unbounded size. Then we show that in each of these two cases, boundedness of a minimal left ideal is an absolute property and that whenever such an ideal is bounded, then in some sense its isomorphism type is also absolute. Under the assumption that [Formula: see text] has NIP, we give characterizations of when a minimal left ideal of the Ellis semigroup of [Formula: see text] is bounded. Then we adapt the proof of Theorem 5.7 in Definably amenable NIP groups, J. Amer. Math. Soc. 31 609–641 to show that whenever such an ideal is bounded, a certain natural epimorphism 863–932]) from the Ellis group of the flow [Formula: see text] to the Kim–Pillay Galois group [Formula: see text] is an isomorphism. We also obtain some variants of these results, formulate some questions, and explain differences which occur when the flow [Formula: see text] is replaced by [Formula: see text]. (shrink)