This paper explores the scientific viability of the concept of causality—by questioning a central element of the distinction between “fundamental” and non-fundamental physics. It will be argued that the prevalent emphasis on fundamental physics involves formalistic and idealized partial models of physical regularities abstracting from and idealizing the causal evolution of physical systems. The accepted roles of partial models and of the special sciences in the growth of knowledge help demonstrate proper limitations of the concept of (...) fundamental physics. We expect that a cause precedes its effect. But in some tension with this point, fundamental physical law is often held to be symmetrical and all-encompassing. Physical time, however, has not only measurable extension, as with spatial dimensions, it also has a direction—from the past through the present into the future. This preferred direction is time’s arrow. In spite of this standard contrast of time with space, if all the fundamental laws of physics are symmetrical, they are indifferent to time’s arrow. In consequence, excessive emphasis on the ideal of symmetrical, fundamental laws of physics generates skepticism regarding the common-sense and scientific uses of the concept of causality. The expectation has been that all physical phenomena are capable of explanation and prediction by reference to fundamental physicals laws—so that the laws and phenomena of statistical thermodynam- ics —and of the special sciences—must be derivative and/or secondary. The most important and oft repeated explanation of time’s arrow, however, is provided by the second law of thermodynamics. This paper explores the prospects for time’s arrow based on the second law. The concept of causality employed here is empirically based, though acknowledging practical scientific interests, and is linked to time’s arrow and to the thesis that there can be no causal change, in any domain of inquiry, without physical interaction. (shrink)

I show that the partial truth of a sentence in a partial structure is equivalent to the truth of that sentence in an expansion of a structure that corresponds naturally to the partial structure. Further, a mapping is a partial homomorphism/partial isomorphism between two partial structures if and only if it is a homomorphism/isomorphism between their corresponding structures. It is a corollary that the partial truth of a sentence in a partial structure (...) is equivalent to the truth of a specific Ramsey sentence in a corresponding structure. Hence the partial structures approach can be expressed in standard first or second-order model theory, and it can be captured in the received view on scientific theories as developed by Carnap and Hempel. (shrink)

Partial models of the theory New Foundations (NF) introduced by Quine have already appeared in the literature, but in every model the membership set of NF is missing. On the other hand, Jensen showed that "NF + Urelements" is consistent with respect to ZF and, in the model built there, the membership set of the theory exists. Here we build a partial model of NF from the one of Jensen in which the membership set exists.

The theory New Foundations of Quine was introduced in [14]. This theory is finitely axiomatizable as it has been proved in [9]. A similar result is shown in [8] using a system called K. Particular subsystems of NF, inspired by [8] and [9], have models in ZF. Very little is known about subsystems of NF satisfying typical properties of ZF; for example in [11] it is shown that the existence of some sets which appear naturally in ZF is an (...) axiom independent from NF . Here we discuss a model of subsystems of NF in which there is a set which is a model of ZF. MSC: 03E70. (shrink)

A paper by Beneš, published in 1954, was an attempt to prove the consistency of $\mathsf{NF}$ via a partial model of Hailperin’s finite axiomatization of $\mathsf{NF}$. Here, I offer an analysis of Beneš’s proof in a De Giorgi-style setting for set theory. This approach leads to an abstract version of Beneš’s theorem that emphasizes the monotone and invariant content of the axioms proved to be consistent, in a sense of monotony and invariance that this paper intends to state rigorously (...) and to help clarify. Moreover, some tentative speculation will be made about possible developments of the topic in the following two directions: which set theories can be proved to be consistent via Beneš-like constructions, and how can we elaborate on Beneš’s model to get a consistency proof for full $\mathsf{NF}$? (shrink)

This paper explores the scientific viability of the concept of causality—by questioning a central element of the distinction between “fundamental” and non-fundamental physics. It will be argued that the prevalent emphasis on fundamental physics involves formalistic and idealized partial models of physical regularities abstracting from and idealizing the causal evolution of physical systems. The accepted roles of partial models and of the special sciences in the growth of knowledge help demonstrate proper limitations of the concept of (...) fundamental physics. We expect that a cause precedes its effect. But in some tension with this point, fundamental physical law is often held to be symmetrical and all-encompassing. Physical time, however, has not only measurable extension, as with spatial dimensions, it also has a direction—from the past through the present into the future. This preferred direction is time’s arrow. In spite of this standard contrast of time with space, if all the fundamental laws of physics are symmetrical, they are indifferent to time’s arrow. In consequence, excessive emphasis on the ideal of symmetrical, fundamental laws of physics generates skepticism regarding the common-sense and scientific uses of the concept of causality. The expectation has been that all physical phenomena are capable of explanation and prediction by reference to fundamental physicals laws—so that the laws and phenomena of statistical thermodynamics—and of the special sciences—must be derivative and/or secondary. The most important and oft repeated explanation of time’s arrow, however, is provided by the second law of thermodynamics. This paper explores the prospects for time’s arrow based on the second law. The concept of causality employed here is empirically based, though acknowledging practical scientific interests, and is linked to time’s arrow and to the thesis that there can be no causal change, in any domain of inquiry, without physical interaction. (shrink)

We investigate first order sentences valid in completions of a given partial algebraic structure - a partial model. We give semantic and syntactic description of the set of all sentences valid in every completion of the given partial model - first order theory of this model.

Clausal complements of different kinds of attitude verbs such as believe, doubt, be surprised, wonder, say, and whisper behave differently semantically in a number of respects. For example, they differ in the inference patterns they display. This paper develops a semantic account of clausal complements using partial logic which accounts for such semantic differences on the basis of a uniform meaning of clauses. It focuses on explaining the heterogeneous inference patterns associated with different kinds of attitude verbs, but it (...) contributes also to explaining differences among clausal complements of attitude verbs regarding the possibility of de re reference, anaphora support, presupposition satisfaction, and the distribution of subjunctive in certain languages. Moreover, it gives a new account of factivity. The point of departure of this paper is the general observation that the failure of inferences from attitude reports is relative in that it depends both on the general type of attitude and on the particular instance of the attitude described. Thus, from John is surprised that P and Q one cannot infer John is surprised that P and John is surprised that Q, though this is possible with believe. Conversely, one can infer from John believes that P and John believes that Q, to John believes that P and Q, but only as long as the same belief state of John is involved. In order to capture this dependency of inferences from attitude reports on a particular mental state or act, I propose an account on which clausal complements of attitude verbs (as well as independent sentences) characterize the intentional state or act described by the attitude verb in question, rather than referring to independent propositions. The semantic account of attitude reports of this paper can hence be called an 'event-based account' of clauses. Formally, the denotation of any sentence, both independent and embedded, is construed as a function mapping an intentional state or act to a function from situations (which form the content of the state or act) to truth values.. (shrink)

In this paper we show that any reasoning process in which conclusions can be both fallible and corrigible can be formalized in terms of two approaches: (i) syntactically, with the use of defeasible reasoning, according to which reasoning consists in the construction and assessment of arguments for and against a given claim, and (ii) semantically, with the use of partial structures, which allow for the representation of less than conclusive information. We are particularly interested in the formalization of scientific (...) reasoning, along the lines traced by Lakatos’ methodology of scientific research programs. We show how current debates in cosmology could be put into this framework, shedding light on a very controversial topic. (shrink)

The article by Ron Wallace 'proposes the deployment of partial modelling, utilising Boolean networks (BNs), as an inductive discovery procedure for the development of economic theory'. The central argument in favour of partial models is well-made, and while I agree with this aspect of the paper, and the conclusion that models should serve as 'cognitive instruments in a regime of exploration,' I have a number of comments about the proposed strategy and the example of BNs......

Economics is currently experiencing a climate of uncertainty regarding the soundness of its theoretical framework and even its status as a science. Much of the criticism is within the discipline, and emphasises the alleged failure of the neoclassical viewpoint. This article proposes the deployment of partial modelling, utilising Boolean networks (BNs), as an inductive discovery procedure for the development of economic theory. The method is presented in detail and then linked to the Semantic View of Theories (SVT), closely identified (...) with Bas van Fraassen and Patrick Suppes, in which models are construed as mediators creatively negotiating between theory and reality. It is suggested that this approach may be appropriate for economics and, by implication, for any science in which there is no consensus theory, and a wide range of viewpoints compete for acceptance. (shrink)

Over the years, two models of freedom have emerged as competitors: the alternative-possibilities model and the actual-sequence model. This paper is a partial defense of the actual-sequence model. My defense relies on two strategies. The first strategy consists in de-emphasizing the role of examples in arguing for a model of freedom. Imagine that, as some people think, Frankfurt-style cases fail to undermine the alternative-possibilities model. What follows from this? Not much, I argue. In particular, I note that the (...) counterparts of Frankfurt-style cases also fail to undermine the actual-sequence model. My second strategy of defense consists in revitalizing the original motivation for the actual-sequence model, by revamping it, isolating it from claims that do not fully capture the same idea, and arguing that it can be developed in a successful way. (shrink)

In reliability engineering and lifetime analysis, many units of the product fail with different causes of failure, and some tests require stress higher than normal stress. Also, we need to design the life experiments which present methodology for formulating scientific and engineering problems using statistical models. So, in this paper, we adopted a partially constant stress accelerated life test model to present times to failure in a small period of time for Gompertz life products. Also, considering that, units are (...) failing with the only two independent causes of failure and tested under type-I generalized hybrid censoring scheme the data built. Obtained data are analyzed with two methods of estimations, maximum likelihood and Bayes methods. These two methods are used to construct the point and interval estimators with the help of the MCMC method. The developed results are measured and compared under Monte Carlo studying. Also, a data set is analyzed for illustration purposes. Finally, some comments are presented to describe the numerical results. (shrink)

In a recent paper, Suárez and Cartwright return to the example of London and London's construction of a model for superconductivity and raise a number of concerns against the account of this construction presented in French and Ladyman and elsewhere. In this discussion note, we examine the challenge they raised and offer our responses.

We state the consistency problem of extensional partial set theory and prove two complementary results toward a definitive solution. The proof of one of our results makes use of an extension of the topological construction that was originally applied in the paraconsistent case.

For any n, we construct a model of in which each formula is equivalent to an formula.

As they are conventionally formulated, Boolean games assume that players make their choices in ignorance of the choices being made by other players – they are games of simultaneous moves. For many settings, this is clearly unrealistic. In this paper, we show how Boolean games can be enriched by dependency graphs which explicitly represent the informational dependencies between variables in a game. More precisely, dependency graphs play two roles. First, when we say that variable x depends on variable y, then (...) we mean that when a strategy assigns a value to variable x, it can be informed by the value that has been assigned to y. Second, and as a consequence of the first property, they capture a richer and more plausible model of concurrency than the simultaneous-action model implicit in conventional Boolean games. Dependency graphs implicitly define a partial ordering of the run-time events in a game: if x is dependent on y, then the assignment of a value to y must precede the assignment of a value to x; if x and y are independent, however, then we can say nothing about the ordering of assignments to these variables—the assignments may occur concurrently. We refer to Boolean games with dependency graphs as partial-order Boolean games. After motivating and presenting the partial-order Boolean games model, we explore its properties. We show that while some problems associated with our new games have the same complexity as in conventional Boolean games, for others the complexity blows up dramatically. We also show that the concurrency in partial-order Boolean games can be modelled using a closure-operator semantics, and conclude by considering the relationship of our model to Independence-Friendly logic. (shrink)

In this paper we address the modelling of reasoning processes in natural agents. We focus on a very basic kind of non-monotonic inference for which we identify a simple and plausible underlying process, and we develop a family of logical models that allow to match this process. Partial worlds models, as we call them, are a variant of Kraus, Lehmann and Magidor’s cumulative models. We show that the inference relations they induce form a strict subclass of (...) cumulative relations and tackle the issue of providing sound and complete sets of rules to characterise them. Taking inspiration from the work of Gabbay and Schlechta, we analyse the question in terms of definable sets of partial worlds and conclude that completeness is probably unreachable using a standard propositional language. This brings us to enrich our language with an additional connective, which makes it possible to distinguish between two kinds of disjunction in the partial worlds context. Within this renewed framework, we provide two representation theorems: one for inference relations induced by precisification-free smooth models, and the other for inference relations induced by precisification-free ranked models. Finally we give an aperçu of how partial worlds models lend themselves to the modelling of learning. (shrink)

Da Costa and French explore the consequences of adopting a 'pragmatic' notion of truth in the philosophy of science. Their framework sheds new light on issues to do with belief, theory acceptance, and the realism-antirealism debate, as well as the nature of scientific models and their heuristic development.

In the past thirty years, two fundamental issues have emerged in the philosophy of science. One concerns the appropriate attitude we should take towards scientific theories--whether we should regard them as true or merely empirically adequate, for example. The other concerns the nature of scientific theories and models and how these might best be represented. In this ambitious book, da Costa and French bring these two issues together by arguing that theories and models should be regarded as partially (...) rather than wholly true. They adopt a framework that sheds new light on issues to do with belief, theory acceptance, and the realism-antirealism debate. The new machinery of "partial structures" that they develop offers a new perspective from which to view the nature of scientific models and their heuristic development. Their conclusions will be of wide interest to philosophers and historians of science. (shrink)

The aim of the paper is to develop the notion of partial probability distributions as being more realistic models of belief systems than the standard accounts. We formulate the theory of partial probability functions independently of any classical semantic notions. We use the partial probability distributions to develop a formal semantics for partial propositional calculi, with extensions to predicate logic and higher order languages. We give a proof theory for the partial logics and obtain (...) soundness and completeness results. (shrink)

This paper is an attempt to put forward a new kind of partial model for representing belief states. I first introduce some philosophical motivations for working with partial models. Then, I present the standard (total) model proposed by Hintikka, and the partial models studied by Humberstone and Holliday. I then show how to reduce Hintikka’s semantics in order to obtain a partial model which, however, differs from Humberstone’s and Holliday’s. The nature of such differences (...) is assessed, and I provide motivations for using the newly proposed semantics rather than the existing ones. Finally, I review some promising philosophical applications of the ideas developed throughout the discussion. (shrink)

The work is an attempt to transfer a structure from Euclidean plane (pure geometrical) under the physical observation limit (resolving power) to a physical space (observable space). The transformation from the mathematical space to physical space passes through the observation condition. The mathematical modelling is adopted. The project is based on two stapes: (1) Looking for a simple mathematical model satisfies the definition of Euclidian plane; (2)That model is examined against three observation resolution conditions (resolved, unresolved and partially resolved). The (...) simplest mechanical model satisfies the definition of Euclidian plane is a planetary gear. The interesting examination of the mechanical model is that is under partial resolution. That examination shows analogous equation for Euler’s formula. The derived complex formula contains the resolved (observable) quantities of the mechanical system and satisfies the linear wave equation. The interpretation of this complex formula is: it is a function related to the position vector of a point in the small wheel of the partially resolved planetary gear system. The function is in terms of the observable quantities only. The work shows the possibility of transformation from real to complex space. The work is purely classical but the result of the partial resolution shows a function similar to the Quantum mechanics wave function. (shrink)

The paper builds on both a simply typed term system ${\cal PR}^\omega$ and a computation model on Scott domains via so-called parallel typed while programs (PTWP). The former provides a notion of partial primitive recursive functional on Scott domains $D_\rho$ supporting a suitable concept of parallelism. Computability on Scott domains seems to entail that Kleene's schema of higher type simultaneous course-of-values recursion (scvr) is not reducible to partial primitive recursion. So extensions ${\cal PR}^{\omega e}$ and PTWP $^e$ are (...) studied that are closed under scvr. The twist are certain type 1 Gödel recursors ${\cal R}_k$ for simultaneous partial primitive recursion. Formally, ${\cal R}_k\vec{g}\vec{H}xi$ denotes a function $f_i \in D_{\iota\to\iota}$ , however, ${\cal R}_k$ is modelled such that $f_i$ is finite, or in other words, a partial sequence. As for PTWP $^e$ , the concept of type $\iota\to\iota$ writable variables is introduced, providing the possibility of creating and manipulating partial sequences. It is shown that the PTWP $^e$ -computable functionals coincide with those definable in ${\cal PR}^{\omega e}$ plus a constant for sequential minimisation. In particular, the functionals definable in ${\cal PR}^{\omega e}$ denoted ${\cal R}^{\omega e}$ can be characterised by a subclass of PTWP $^e$ -computable functionals denoted ${\rm PPR}^{\omega e}$ . Moreover, hierarchies of strictly increasing classes ${\cal R}^{\omega e}_n$ in the style of Heinermann and complexity classes ${\rm PPR}^{\omega e}_n$ are introduced such that $\forall n\ge 0. {\cal R}^{\omega e}_n ={\rm PPR}^{\omega e}_n$ . These results extend those for ${\cal PR}^\omega$ and PTWP [Nig94]. Finally, scvr is employed to define for each type $\sigma$ the enumeration functional $E^\sigma$ of all finite elements of $D_\sigma$. (shrink)

This article investigates models of axiomatizations related to the semantic conception of truth presented by Kripke (J Philos 72(19):690–716, 1975), the so-called _fixed-point semantics_. Among the various proof systems devised as a proof-theoretic characterization of the fixed-point semantics, in recent years two alternatives have received particular attention: _classical systems_ (i.e., systems based on classical logic) and _nonclassical systems_ (i.e., systems based on some nonclassical logic). The present article, building on Halbach and Nicolai (J Philos Log 47(2):227–257, 2018), shows that (...) there is a sense in which classical and nonclassical theories (in suitable variants) have the same models. (shrink)

A persuasion dialogue is a dialogue in which a conflict between agents with respect to their points of view arises at the beginning of the talk and the agents have the shared, global goal of resolving the conflict and at least one agent has the persuasive aim to convince the other party to accept an opposing point of view. I argue that the persuasive force of argument may have not only extreme values but also intermediate strength. That is, I wish (...) to introduce two additional types of the effects of persuasion in addition to successful and unsuccessful ones (cf. Van Eemeren and Houtlosser in Argumentation 14(3):293–305, 2000; Advances in pragma-dialectics. Sic Sat, Amsterdam, 2002; Walton in A pragmatic theory of fallacy. University of Alabama Press, Tuscaloosa, 1995; Walton and Krabbe in Commitment in dialogue: basic concepts of interpersonal reasoning. State University of New York Press, Albany, New York, 1995). I propose a model which provides for modified versions of the standpoint of an agent needed in order to bring about two possible outcomes of a persuasion dialogue. These two outcomes I label partially-successful and over-successful. I call the potential, not yet verbalised, standpoint of an agent here the original topic t. Based on some aspects of relevance theory (Sperber and Wilson in Relevance: communication and cognition. Blackwell, Oxford, 1986; Wilson and Sperber in The handbook of pragmatics. Blackwell Publishing, Malden, 2006), I explain that the modified version of the original topic t is an implicature created from the original topic t and from a specific mental topic which belongs to, what I call the beneficial cognitive model (hence BCM). I define BCMi,t as a set of topics which are within the area of agent i’s interest of persuasion with respect to t. (shrink)

The partial structures program of da Costa, French and others offers a unified framework within which to handle a wide range of issues central to contemporary philosophy of science. I argue that the program is inadequately equipped to account for simple cases where idealizations are used to construct abstract, mathematical models of physical systems. These problems show that da Costa and French have not overcome the objections raised by Cartwright and Suárez to using model‐theoretic techniques in the philosophy (...) of science. However, my concerns arise independently of the more controversial assumptions that Cartwright and Suárez have employed. (shrink)

Following a proposal of Humberstone, this paper studies a semantics for modal logic based on partial “possibilities” rather than total “worlds.” There are a number of reasons, philosophical and mathematical, to find this alternative semantics attractive. Here we focus on the construction of possibility models with a finitary flavor. Our main completeness result shows that for a number of standard modal logics, we can build a canonical possibility model, wherein every logically consistent formula is satisfied, by simply taking (...) each individual finite formula (modulo equivalence) to be a possibility, rather than each infinite maximally consistent set of formulas as in the usual canonical world models. Constructing these locally finite canonical models involves solving a problem in general modal logic of independent interest, related to the study of adjoint pairs of modal operators: for a given modal logic L, can we find for every formula phi a formula f(phi) such that for every formula psi, phi -> BOX psi is provable in L if and only if f(phi) -> psi is provable in L? We answer this question for a number of standard modal logics, using model-theoretic arguments with world semantics. This second main result allows us to build for each logic a canonical possibility model out of the lattice of formulas related by provable implication in the logic. (shrink)

Based on a mixed-methods study involving triad tasks and ethnobiological models, we analyze local categories and knowledge of key ethnospecies of fish exploring partial overlaps between artisanal fishers’ and academic knowledge in a fishing community in northeast Brazil. We argue that fishers’ and academic knowledge overlaps may provide common ground for transdisciplinary collaboration, while their partiality requires reflection on epistemological and ontological differences. Here, we show how knowledge of artisanal fishers can complement academic knowledge and bring about tensions (...) that need to be addressed through intercultural dialogue. By integrating a general philosophical framework of partial overlaps with a mixed-methods study on fishers’ knowledge, we show how ethnobiology can contribute to reflective and empirically-grounded transdisciplinary practices. (shrink)

This is the first of a series of papers devoted to the thorough investigation of refinement based on an underlying partial relational model. In this paper we restrict attention to operation refinement. We explore four theories of refinement based on an underlying partial relation model for specifications, and we show that they are all equivalent. This, in particular, sheds some light on the relational completion operator due to Woodcock which underlies data refinement in, for example, the specification language (...) Z. It further leads to two simple alternative models which are also equivalent to the others. (shrink)

The partial structures program of da Costa, French and others offers a unified framework within which to handle a wide range of issues central to contemporary philosophy of science. I argue that the program is inadequately equipped to account for simple cases where idealizations are used to construct abstract, mathematical models of physical systems. These problems show that da Costa and French have not overcome the objections raised by Cartwright and Suárez to using model-theoretic techniques in the philosophy (...) of science. However, my concerns arise independently of the more controversial assumptions that Cartwright and Suárez have employed. (shrink)

The Trek Separation Theorem states necessary and sufficient conditions for a linear directed acyclic graphical model to entail for all possible values of its linear coefficients that the rank of various sub-matrices of the covariance matrix is less than or equal to n, for any given n. In this paper, I extend the Trek Separation Theorem in two ways: I prove that the same necessary and sufficient conditions apply even when the generating model is partially non-linear and contains some cycles. (...) This justifies application of constraint-based causal search algorithms to data generated by a wider class of causal models that may contain non-linear and cyclic relations among the latent variables. (shrink)

It has been shown in Spirtes(1995) that X and Y are d-separated given Z in a directed graph associated with a recursive or non-recursive linear model without correlated errors if and only if the model entails that ρXY.Z = 0. This result cannot be directly applied to a linear model with correlated errors, however, because the standard graphical representation of a linear model with correlated errors is not a directed graph. The main result of this paper is to show how (...) to associate a directed graph with a linear model L with correlated errors, and then use d-separation in the associated directed graph to determine whether L entails that a particular partial correlation is zero. (shrink)

In this brief commentary of Kamila Debowska-Kozlowska’s insightful analysis of persuasive outcomes (Processing topics from the Beneficial Cognitive Model in partially and over-successful persuasion dialogues. Argumentation, 2014), I articulate some suggestions for future development of her ideas. My main claim is that, while instances of partially and over-successful persuasion are indeed worthy of further theoretical inquiry, the topical analysis proposed by Debowska-Kozlowska may benefit from integration with other approaches.