A formal model of metaphor is introduced. It models metaphor, first, as an interaction of “frames” according to the frame semantics, and then, as a wave function in Hilbert space. The practical way for a probability distribution and a corresponding wave function to be assigned to a given metaphor in a given language is considered. A series of formal definitions is deduced from this for: “representation”, “reality”, “language”, “ontology”, etc. All are based on Hilbert space. A few statements (...) about a quantum computer are implied: The sodefined reality is inherent and internal to it. It can report a result only “metaphorically”. It will demolish transmitting the result “literally”, i.e. absolutely exactly. A new and different formal definition of metaphor is introduced as a few entangled wave functions corresponding to different “signs” in different language formally defined as above. The change of frames as the change from the one to the other formal definition of metaphor is interpreted as a formal definition of thought. Four areas of cognition are unified as different but isomorphic interpretations of the mathematical model based on Hilbert space. These are: quantum mechanics, frame semantics, formal semantics by means of quantum computer, and the theory of metaphor in linguistics. (shrink)

In the past few years, social epistemologists have developed several formal models of the social organisation of science. While their robustness and representational adequacy has been analysed at length, the function of these models has begun to be discussed in more general terms only recently. In this article, I will interpret many of the current formal models of the scientific community as representing the latest development of what I will call the ‘Kuhnian project’. These models share with Kuhn (...) a number of questions about the relation between individuals and communities. At the same time, they also inherit some of Kuhn’s problematic characterisations of the scientific community. In particular, current models of the social organisation of science represent the scientific community as essentially value-free. This may put into question both their representational adequacy and their normative ambitions. In the end, it will be shown that the discussion on the formal models of the scientific community may contribute in fruitful ways to the ongoing debates on value judgements in science. (shrink)

The standard model of precedential constraint holds that a court is equally free to modify a precedent of its own and a precedent of a superior court—overruling aside, it does not differentiate horizontal and vertical precedents. This paper shows that no model can capture the U.S. doctrine of precedent without making that distinction. A precise model is then developed that does just that. This requires situating precedent cases in a formal representation of a hierarchical legal structure, and adjusting the (...) constraint that a precedent imposes based on the relationship of the precedent court and the instant court. The paper closes with suggestions for further improvements of the model. (shrink)

Reflective equilibrium (RE) is often regarded as a powerful method in ethics, logic, and even philosophy in general. Despite this popularity, characterizations of the method have been fairly vague and unspecific so far. It thus may be doubted whether RE is more than a jumble of appealing but ultimately sketchy ideas that cannot be spelled out consistently. In this paper, we dispel such doubts by devising a formal model of RE. The model contains as components the agent’s commitments and (...) a theory that tries to systematize the commitments. It yields a precise picture of how the commitments and the theory are adjusted to each other. The model differentiates between equilibrium as a target state and the dynamic equilibration process. First solutions to the model, obtained by computer simulation, show that the method allows for consistent specification and that the model’s implications are plausible in view of expectations on RE. In particular, the mutual adjustment of commitments and theory can improve one’s commitments, as proponents of RE have suggested. We argue that our model is fruitful not only because it points to issues that need to be dealt with for a better understanding of RE, but also because it provides the means to address these issues. (shrink)

Each of us is not just a set of actions, experiences, and plans but also a set of traits, capacities, and attitudes; we are as much our character as our life. And while story form can help unify a messy life, when it comes to a messy character, we may need something like the form of a poem. Could we model our self-conception, then, on a work like Sonnet 35? In finding deep-going unity—and even bittersweet beauty—beneath surface-level ambivalence, Sonnet 35 (...) arguably offers a perfect formal model, pointing the way to a transfiguration, through art, of intractable internal conflict. (shrink)

I argue that normative formal epistemology (NFE) is best understood as modelling, in the sense that this is the reconstruction of its methodology on which NFE is doing best. I focus on Bayesianism and show that it has the characteristics of modelling. But modelling is a scientific enterprise, while NFE is normative. I thus develop an account of normative models on which they are idealised representations put to normative purposes. Normative assumptions, such as the transitivity of (...) comparative credence, are characterised as modelling idealisations motivated normatively. I then survey the landscape of methodological options: what might formal epistemologists be up to? I argue the choice is essentially binary: modelling or theorising. If NFE is theorising it is doing very poorly: generating false claims with no clear methodology for separating out what is to be taken seriously. Modelling, by contrast, is a successful methodology precisely suited to the management of useful falsehoods. Regarding NFE as modelling is not costless, however. First, our normative inferences are less direct and are muddied by the presence of descriptive idealisations. Second, our models are purpose-specific and limited in their scope. I close with suggestions for how to adapt our practice. (shrink)

This chapter presents the core challenge before Hamlet as that of achieving authenticity in the face of inner multiplicity. Authenticity—which this chapter will take to mean (1) acting on the (2) knowledge of (3) what one truly is, beneath one’s various masks and social roles—becomes a particularly pressing need under conditions of (early) modernity, when traditional forms of action-guidance are at least halfway off the table. But authenticity is highly problematic when the self that is discovered turns out to be (...) multiple. Which self, exactly, should one be true to? Hamlet’s solution, this chapter suggests, is an “actor’s ethos,” in which each of his aspects is given its day in the sun, granted full commitment by means of what we now call “method acting.” That is what Hamlet learns from the players—and that too is what we stand to learn from _Hamlet_: not an idea but a method. (shrink)

Logics based on weak Kleene algebra (WKA) and related structures have been recently proposed as a tool for reasoning about flaws in computer programs. The key element of this proposal is the presence, in WKA and related structures, of a non-classical truth-value that is “contaminating” in the sense that whenever the value is assigned to a formula ϕ, any complex formula in which ϕ appears is assigned that value as well. Under such interpretations, the contaminating states represent occurrences of a (...) flaw. However, since different programs and machines can interact with (or be nested into) one another, we need to account for different kind of errors, and this calls for an evaluation of systems with multiple contaminating values. In this paper, we make steps toward these evaluation systems by considering two logics, HYB1 and HYB2, whose semantic interpretations account for two contaminating values beside classical values 0 and 1. In particular, we provide two main formal contributions. First, we give a characterization of their relations of (multiple-conclusion) logical consequence—that is, necessary and sufficient conditions for a set Δ of formulas to logically follow from a set Γ of formulas in HYB1 or HYB2 . Second, we provide sound and complete sequent calculi for the two logics. (shrink)

Although formal thought disorder (FTD) has been for long a clinical label in the assessment of some psychiatric disorders, in particular of schizophrenia, it remains a source of controversy, mostly because it is hard to say what exactly the “formal” in FTD refers to. We see anomalous processing of terminological knowledge, a core construct of human knowledge in general, behind FTD symptoms and we approach this anomaly from a strictly formal perspective. More specifically, we present here a (...) symbolic computational model of storage in, and activation of, a human semantic network, or semantic memory, whose core element is logical form; this is normalized by description logic (DL), namely by CL, a DL-based language – Conception Language – designed to formalize conceptualization from the viewpoint of individual cognitive agency. In this model, disruptions in the rule-based implementation of the logical form account for the apparently semantic anomalies symptomatic of FTD, which are detected by means of a CL-based algorithmic assessment. (shrink)

The present Yearbook (which is the fourth in the series) is subtitled Trends & Cycles. Already ancient historians (see, e.g., the second Chapter of Book VI of Polybius' Histories) described rather well the cyclical component of historical dynamics, whereas new interesting analyses of such dynamics also appeared in the Medieval and Early Modern periods (see, e.g., Ibn Khaldūn 1958 [1377], or Machiavelli 1996 [1531] 1). This is not surprising as the cyclical dynamics was dominant in the agrarian social systems. With (...) modernization, the trend dynamics became much more pronounced and these are trends to which the students of modern societies pay more attention. Note that the term trend – as regards its contents and application – is tightly connected with a formal mathematical analysis. Trends may be described by various equations – linear, exponential, power-law, etc. On the other hand, the cliodynamic research has demonstrated that the cyclical historical dynamics can be also modeled mathematically in a rather effective way (see, e.g., Usher 1989; Chu and Lee 1994; Turchin 2003, 2005a, 2005b; Turchin and Korotayev 2006; Turchin and Nefedov 2009; Nefedov 2004; Korotayev and Komarova 2004; Korotayev, Malkov, and Khaltourina 2006; Korotayev and Khaltourina 2006; Korotayev 2007; Grinin 2007), whereas the trend and cycle components of historical dynamics turn out to be of equal importance. (shrink)

In (Gebharter 2014) I suggested a framework for modeling the hierarchical organization of mechanisms. In this short addendum I want to highlight some connections of my approach to the statistics and machine learning literature and some of its limitations not mentioned in the paper.

Formal thought disorder (FTD) is a clinical mental condition that is typically diagnosable by the speech productions of patients. However, this has been a vexing condition for the clinical community, as it is not at all easy to determine what “formal” means in the plethora of symptoms exhibited. We present a logic-based model for the syntax–semantics interface in semantic networking that can not only explain, but also diagnose, FTD. Our model is based on description logic (DL), which is (...) well known for its adequacy to model terminological knowledge. More specifically, we show how faulty logical form as defined in DL-based Conception Language (CL) impacts the semantic content of linguistic productions that are characteristic of FTD. We accordingly call this the dyssyntax model. (shrink)

An important part of the Unified Medical Language System (UMLS) is its Semantic Network, consisting of 134 Semantic Types connected to each other by edges formed by one or more of 54 distinct Relation Types. This Network is however for many purposes overcomplex, and various groups have thus made attempts at simplification. Here we take this work further by simplifying the relations which involve the three Semantic Types – Diagnostic Procedure, Laboratory Procedure and Therapeutic or Preventive Procedure. We define operators (...) which can be used to generate terms instantiating types from this selected set when applied to terms designating certain other Semantic Types, including almost all the terms specifying clinical tasks. Usage of such operators thus provides a useful and economical way of specifying clinical tasks. The operators allow us to define a mapping between those types within the UMLS which do not represent clinical tasks and those which do. This mapping then provides a basis for an ontology of clinical tasks that can be used in the formulation of computer-interpretable clinical guideline models. (shrink)

Because formal systems of symbolic logic inherently express and represent the deductive inference model formal proofs to theorem consequences can be understood to represent sound deductive inference to deductive conclusions without any need for other representations.

One of the main motivations for having a compositional semantics is the account of the productivity of natural languages. Formal languages are often part of the account of productivity, i.e., of how beings with finite capaci- ties are able to produce and understand a potentially infinite number of sen- tences, by offering a model of this process. This account of productivity con- sists in the generation of proofs in a formal system, that is taken to represent the way (...) speakers grasp the meaning of an indefinite number of sentences. The informational basis is restricted to what is represented in the lexicon. This constraint is considered as a requirement for the account of productivity, or at least of an important feature of productivity, namely, that we can grasp auto- matically the meaning of a huge number of complex expressions, far beyond what can be memorized. However, empirical results in psycholinguistics, and especially particular patterns of ERP, show that the brain integrates informa- tion of different sources very fast, without any felt effort on the part of the speaker. This shows that formal procedures do not explain productivity. How- ever, formal models are still useful in the account of how we get at the seman- tic value of a complex expression, once we have the meanings of its parts, even if there is no formal explanation of how we get at those meanings. A practice-oriented view of modeling gives an adequate interpretation of this re- sult: formal compositional semantics may be a useful model for some ex- planatory purposes concerning natural languages, without being a good model for dealing with other explananda. (shrink)

There has recently been an explosion of formal models of signalling, which have been developed to learn about different aspects of meaning. This paper discusses whether that success can also be used to provide an original naturalistic theory of meaning in terms of information or some related notion. In particular, it argues that, although these models can teach us a lot about different aspects of content, at the moment they fail to support the idea that meaning just is some (...) kind of information. As an alternative, I suggest a more modest approach to the relationship between informational notions used in models and semantic properties in the natural world. (shrink)

The introspective devices framework proposed by Kammerer and Frankish (this issue) offers an attractive conceptual tool for evaluating and developing accounts of introspection. However, the framework assumes that different views about the nature of introspection can be easily evaluated against a set of common criteria. In this paper, I set out to test this assumption by analysing two formal models of introspection using the introspective device framework. The question I aim to answer is not only whether models developed outside (...) of philosophy can be successfully evaluated against the set of conceptual criteria proposed by Kammerer and Frankish, but also whether this kind of evaluation can reveal some limitations inherent to the framework. (shrink)

How does being a woman affect one’s epistemic life? What about being Black? Or queer? Standpoint theorists argue that such social positions can give rise to otherwise unavailable epistemic privilege. “Epistemic privilege” is a murky concept, however. Critics of standpoint theory argue that the view is offered without a clear explanation of how standpoints confer their benefits, what those benefits are, or why social positions are particularly apt to produce them. For this reason, many regard standpoint theory as being out (...) of step with epistemology more broadly. But this need not be so. This article articulates a minimal version of standpoint epistemology that avoids these criticisms and supports the normative goals of its feminist forerunners. This account serves as the foundation for developing a formal model in which to explore standpoint epistemology using neighborhood semantics for modal logic. (shrink)

How does one formalize the structure of structures necessary for the foundations of physics? This work is an attempt at conceptualizing the metaphysics of pregeometric structures, upon which new and existing notions of quantum geometry may find a foundation. We discuss the philosophy of pregeometric structures due to Wheeler, Leibniz as well as modern manifestations in topos theory. We draw attention to evidence suggesting that the framework of formal language, in particular, homotopy type theory, provides the conceptual building blocks (...) for a theory of pregeometry. This work is largely a synthesis of ideas that serve as a precursor for conceptualizing the notion of space in physical theories. In particular, the approach we espouse is based on a constructivist philosophy, wherein ``structureless structures'' are syntactic types realizing formal proofs and programs. Spaces and algebras relevant to physical theories are modeled as type-theoretic routines constructed from compositional rules of a formal language. This offers the remarkable possibility of taxonomizing distinct notions of geometry using a common theoretical framework. In particular, this perspective addresses the crucial issue of how spatiality may be realized in models that link formal computation to physics, such as the Wolfram model. (shrink)

In this article, I present a formal semantic framework that renders explicit how to reconcile the condition that a proposition about a contingent future event is true at a moment t0 with the idea that at t0, this proposition is ‘truth-maker indeterminate’: a state of affairs making it true will obtain later on, though no such state of affairs obtains at t0. The semantics I formulate employs ‘open temporal models’. They represent the passage of time by a specific component (...) termed time-resource, which acts on durations construed as model-external inputs. A model does not by itself specify which course of events gets actualized in a given duration depending on the latest moment that has already got actualized. A time-resource merely represents schematically the dependence between a moment t and a course of events that gets actualized in a time-span of a given length counted from t; until that much time has indeed passed, it is not fixed which course of events actually extends t. Further, I introduce evaluations as a fine-grained tool for studying truth-conditions of tensed formulas, and I use this tool to define the notion of truth-maker. I define what it means that a truth-maker will obtain but does not, and what it means for a truth-maker to be determinate. It is proven that my semantic analysis retains the desirable link between determinacy and historical necessity—namely, a truth-maker of a proposition being determinate entails that the proposition is historically necessary. (shrink)

Two types of formal models - landscape search tasks and two-armed bandit models - are often used to study the effects that various social factors have on epistemic performance. I argue that they can be understood within a single framework. In this unified framework, I develop a model that may be used to understand the effects of functional and demographic diversity and their interaction. Using the unified model, I find that the benefit of demographic diversity is most pronounced in (...) a functionally homogeneous group, and decreases with the increase of functional diversity. (shrink)

A speculative exploration of the distinction between a relational formal ontology and a classical formal ontology for modelling phenomena in nature that exhibit relationally-mediated wholism, such as phenomena from quantum physics and biosemiotics. Whereas a classical formal ontology is based on mathematical objects and classes, a relational formal ontology is based on mathematical signs and categories. A relational formal ontology involves nodal networks (systems of constrained iterative processes) that are dynamically sustained through signalling. The (...) nodal networks are hierarchically ordered and exhibit characteristics of deep learning. (shrink)

The problem of demarcating between what is scientific and what is pseudoscientific or merely unscientific - in other words, the problem of defining scientificity - remains open. The modern debate was firstly structured around Karl Popper's falsificationist epistemology from the 1930's, before diversifying a few decades later. His central idea is that what makes something scientific is not so much how adequate it is with data, but rather to what extent it might not have been so. Since the second half (...) of the century, and in the wake of criticisms, such as the Duhem-Quine thesis, that were raised against falsificationism(s), most approaches to the problem of scientific demarcation are now multicriteria and holistic. However, the approach presented in this paper does not follow the same guideline. The present work can be seen as an attempt to adapt Popper's (sophisticated) falsificationism to a model-based view of scientific knowledge. Using formalization and focusing on a particular epistemic unit of analysis (namely, empirical models) allows to properly define the popperian corroboration degree and to view scientificity as the maximization of this degree of corroboration over all available models and data. We eventually recover, in a natural way, well-accepted scientificity criteria: empirical adequacy, Lakatos' progressive problemshifts, balance between strength and simplicity, parsimony, and coherence as special cases of this general scientificity principle. From this viewpoint, the language dependency of our empirical knowledge no longer appears as a limitation of falsificationism but as one more reason to take it as a good epistemological framework. (shrink)

This paper provides a general introduction to the use of causal models in the metaphysics of causation, specifically structural equation models and directed acyclic graphs. It reviews the formal framework, lays out a method of interpretation capable of representing different underlying metaphysical relations, and describes the use of these models in analyzing causation.

Based on the Aristotelian dynamis-energeia-differentiation, a concept issuing dynamic coherence providers as the sub-level of individual realizations. This logical sub-level is given for any kind of realizations. Based on this two-level approach, to some degree similar to the two-level approach developed by Polanyi, model of biopsychosocial interaction is established. It is suggested as the theoretical basis for a person-centered approach in healthcare, integrating science and humanitites.

In the context of pluralization, sophistication, and combination of formal models, it is becoming difficult to propose uniform – or even comparable – model comparison practices. This paper outlines a broad and classificatory comparative epistemology of models. The aim of this epistemology is to propose applicable, and if necessary rectifiable, conceptual tools that can be useful to modellers as well as to historians and epistemologists. The notion of model characteristic vector – incorporating concepts of function, nature, principle and use (...) of the model – is introduced for this end. This proposal has been developed to serve a better-equipped writing of a comparative and interdisciplinary history of models and simulations. (shrink)

In formal epistemology, we use mathematical methods to explore the questions of epistemology and rational choice. What can we know? What should we believe and how strongly? How should we act based on our beliefs and values? We begin by modelling phenomena like knowledge, belief, and desire using mathematical machinery, just as a biologist might model the fluctuations of a pair of competing populations, or a physicist might model the turbulence of a fluid passing through a small aperture. (...) Then, we explore, discover, and justify the laws governing those phenomena, using the precision that mathematical machinery affords. For example, we might represent a person by the strengths of their beliefs, and we might measure these using real numbers, which we call credences. Having done this, we might ask what the norms are that govern that person when we represent them in that way. How should those credences hang together? How should the credences change in response to evidence? And how should those credences guide the person’s actions? This is the approach of the first six chapters of this handbook. In the second half, we consider different representations—the set of propositions a person believes; their ranking of propositions by their plausibility. And in each case we ask again what the norms are that govern a person so represented. Or, we might represent them as having both credences and full beliefs, and then ask how those two representations should interact with one another. This handbook is incomplete, as such ventures often are. Formal epistemology is a much wider topic than we present here. One omission, for instance, is social epistemology, where we consider not only individual believers but also the epistemic aspects of their place in a social world. Michael Caie’s entry on doxastic logic touches on one part of this topic, but there is much more. Relatedly, there is no entry on epistemic logic, nor any on knowledge more generally. There are still more gaps. These omissions should not be taken as ideological choices. This material is missing, not because it is any less valuable or interesting, but because we v failed to secure it in time. Rather than delay publication further, we chose to go ahead with what is already a substantial collection. We anticipate a further volume in the future that will cover more ground. Why an open access handbook on this topic? A number of reasons. The topics covered here are large and complex and need the space allowed by the sort of 50 page treatment that many of the authors give. We also wanted to show that, using free and open software, one can overcome a major hurdle facing open access publishing, even on topics with complex typesetting needs. With the right software, one can produce attractive, clear publications at reasonably low cost. Indeed this handbook was created on a budget of exactly £0 (≈ $0). Our thanks to PhilPapers for serving as publisher, and to the authors: we are enormously grateful for the effort they put into their entries. (shrink)

Conceptual models as representations of real-world systems are based on diverse techniques in various disciplines but lack a framework that provides multidisciplinary ontological understanding of real-world phenomena. Concurrently, systems’ complexity has intensified, leading to a rise in developing models using different formalisms and diverse representations even within a single domain. Conceptual models have become larger; languages tend to acquire more features, and it is not unusual to use different modeling languages for different components. This diversity has caused problems with consistency (...) between models and incompatibly with designed systems. Two main solutions have been adopted over the last few years: (1) A currently dominant technology-based solution tries “to harmonize or unify” models, e.g., unifies EER and UML. This solution would solidify modeling achievements, reaping benefits from huge investments over the last thirty years. (2) A less prevalent solution is to pursuit deeper roots that reveal unifying modeling principles and apparatuses. An example of the second method is a “category theory”-based approach that utilizes the strengths of the graph and set theory, along with other topological tools. This manuscript is a sequel in a research venture that belongs to the second approach and uses a model called thinging machines (TMs) founded on Stoic ontology and Lupascian logic. TM modeling contests the thesis that there is no universal approach that covers all aspects of an application, and the paper demonstrates that pursuing such universality is anything but a dead-end method. This paper continues in this direction, with emphasis on TM foundation (e.g., existence and subsistence of things) and exemplifies this pursuit by proposing an alternative representation of set theory. (shrink)

This paper takes up Huw Price׳s challenge to develop a retrocausal toy model of the Bell-EPR experiment. I develop three such models which show that a consistent, local, hidden-variables interpretation of the EPR experiment is indeed possible, and which give a feel for the kind of retrocausation involved. The first of the models also makes clear a problematic feature of retrocausation: it seems that we cannot interpret the hidden elements of reality in a retrocausal model as possessing determinate dispositions to (...) affect the outcome of experiments. This is a feature which Price has embraced, but Gordon Belot has argued that this feature renders retrocausal interpretations “unsuitable for formal development”, and the lack of such determinate dispositions threatens to undermine the motivation for hidden-variables interpretations in the first place. But Price and Belot are both too quick in their assessment. I show that determinate dispositions are indeed consistent with retrocausation. What is more, I show that the ontological economy allowed by retrocausation holds out the promise of a classical understanding of spin and polarization. (shrink)

We propose a typology of representational artifacts for health care and life sciences domains and associate this typology with different kinds of formal ontology and logic, drawing conclusions as to the strengths and limitations for ontology in a description logics framework. The four types of domain representation we consider are: (i) lexico-semantic representation, (ii) representation of types of entities, (iii) representations of background knowledge, and (iv) representation of individuals. We advocate a clear distinction of the four kinds of representation (...) in order to provide a more rational basis for using ontologies and related artifacts to advance integration of data and enhance interoperability of associated reasoning systems. We highlight the fact that only a minor portion of scientifically relevant facts in a domain such as biomedicine can be adequately represented by formal ontologies as long as the latter are conceived as representations of entity types. In particular, the attempt to encode default or probabilistic knowledge using ontologies so conceived is prone to produce unintended, erroneous models. (shrink)

his paper is an excerpt from a larger project that aims to open a new pathway into Spinoza's Ethics by formally reconstructing an initial fragment of this text. The semantic backbone of the project is a custom-made Spinozian model theory that lays out some of the formal prerequisites for more ne-grained investigations into Spinoza's fundamental ontology and modal metaphysics. We implement Spinoza's theory of attributes using many-sorted models with a rich system of identity that allows us to clarify the (...) puzzling status of such logical principles as the Substitution of Identicals and Transitivity of Identity in Spinoza's thought. The intensional structure of our Spinozian models also captures his proposal that states of a airs can be necessitated or excluded by the essences of particular things, an essence-relative modality that should be of interest to philosophers who have sought to rehabilitate the concept of essence in contemporary analytic metaphysics. (shrink)

I defend the thesis that Kantian analytic judgments are about objects (as opposed to concepts) against two challenges raised by recent scholars. First, can it accommodate cases like “A two-sided polygon is two-sided”, where no object really falls under the subject-concept as Kant sees it? Second, is it compatible with Kant’s view that analytic judgments make no claims about objects in the world and that we can know them to be true without going beyond the given concepts? I address these (...) challenges in two steps. First, given Kant’s distinction between an object in general = x from an object of sensible intuition, I argue that analytic judgments are about objects in the former sense, no matter whether the purported objects can be given in our intuition. Second, using Kant’s method of representing certain logical relations of concepts with such figures as circles, I construct a model to show that analytic truths are truths about objects in general = x and yet can be determined solely by the intensional relation between the given concepts plus certain Kantian-logical laws. Analytic truths are thus shown as formal in the Kantian sense that they do not presuppose the purported objects as givable in our intuition. This account of the formality of analytic truths captures Kant’s diagnosis of the Leibnizian illusion that we can make material claims about the world by analytically true judgments. (shrink)

The following considerations concern modelling Belief Dynamics (BD) not just in the sense of a formalization, but rather in the sense of building a computational model and implementing the corresponding data structures and algorithms of recomputing beliefs. The purpose of such a project is to illustrate some ideas about belief changes in a Web of Beliefs (WoB) to explore and deepen one's understanding of belief changes by trying to implement or improve corresponding algorithms.

The objective of this article is to analyse definitions of culture gathered by Alfred L. Kroeber and Clyde Kluckhohn and published in Culture. A Critical Review of Concepts and Definitions in 1952. This article emphasizes a possibility of re-analysing the material collected by these researchers (Kroeber–Kluckhohn Culture Classification, hereinafter referred to as KKCC). The article shows that the KKCC material constitutes a coherent conceptual and theoretical paradigm. This paradigm was subject to contextual, frequential and conceptual (Formal Conceptual Analysis, hereinafter (...) referred to as FCA) analyses. The obtained research results enabled the author to develop a formal concept of culture of KKCC, which could be used as a model for further analysis. The final conclusions are as follows: (1) the notion of "culture" is definable only within the frameworks of a conceptually coherent paradigm; (2) determination of a paradigm requires material repository (resp. text corpus); (3) contextual and frequential analyses enable one to index that kind of repository in order to determine general categories which will be used to develop a formal concept; (4) the formal concept of culture of KKCC constitutes the framework of all possible theoretical analyses concerning the meaning of the notion of "culture" in anthropology; (5) KKCC constitutes a representation of one theory of culture. (shrink)

Levins and Lewontin have contributed significantly to our philosophical understanding of the structures, processes, and purposes of biological mathematical theorizing and modeling. Here I explore their separate and joint pleas to avoid making abstract and ideal scientific models ontologically independent by confusing or conflating our scientific models and the world. I differentiate two views of theorizing and modeling, orthodox and dialectical, in order to examine Levins and Lewontin’s, among others, advocacy of the latter view. I compare the positions of these (...) two views with respect to four points regarding ontological assumptions: (1) the origin of ontological assumptions, (2) the relation of such assumptions to the formal models of the same theory, (3) their use in integrating and negotiating different formal models of distinct theories, and (4) their employment in explanatory activity. Dialectical is here used in both its Hegelian–Marxist sense of opposition and tension between alternative positions and in its Platonic sense of dialogue between advocates of distinct theories. I investigate three case studies, from Levins and Lewontin as well as from a recent paper of mine, that show the relevance and power of the dialectical understanding of theorizing and modeling. (shrink)

This paper compares several models of formalization. It articulates criteria of correct formalization and identifies their problems. All of the discussed criteria are so called “semantic” criteria, which refer to the interpretation of logical formulas. However, as will be shown, different versions of an implicitly applied or explicitly stated criterion of correctness depend on different understandings of “interpretation” in this context.

I am arguing that it is only by concentrating on the role of models in theory construction, interpretation and change, that one can study the progress of science sensibly. I define the level at which these models operate as a level above the purely empirical (consisting of various systems in reality) but also indeed below that of the fundamental formal theories (expressed linguistically). The essentially multi-interpretability of the theory at the general, abstract linguistic level, implies that it can potentially (...) make claims about systems in reality, other than the particular one which originally induced it. Any so-called correspondence relation between (systems in) reality and the entities and relations in some scientific theory, thus consists of two jumps or interpretations: from the theory (linguistic level) to some model of it (constructural level); and from there to some system in reality. Clearly then the level of fundamental theories cannot be ignored la Nancy Cartwright - in studying the relations between a theory and reality, because the particular features of the theory (the various systems in reality onto which the theory can be mapped) cannot be studied without the underlying knowledge that these systems have one common feature, namely that each of them is the range (or other pole) of a mapping of a context-specific model of the theory - which in itself, is a mapping, or more specifically, an interpretation of the theory. I am also claiming that the nature of these levels and the relations between them necessitate an epistemological rather than an ontological notion of truth criteria, and a referential rather than a representational link between science and reality. (shrink)

Over the last decade, multi-agent systems have come to form one of the key tech- nologies for software development. The Formal Approaches to Multi-Agent Systems (FAMAS) workshop series brings together researchers from the fields of logic, theoreti- cal computer science and multi-agent systems in order to discuss formal techniques for specifying and verifying multi-agent systems. FAMAS addresses the issues of logics for multi-agent systems, formal methods for verification, for example model check- ing, and formal approaches to (...) cooperation, multi-agent planning, communication, coordination, negotiation, games, and reasoning under uncertainty in a distributed environment. In 2007, the third FAMAS workshop, FAMAS'007, was one of the agent workshops gathered together under the umbrella of Multi-Agent Logics, Languages, and Organ- isations - Federated Workshops, MALLOW'007, taking place from 3 to 7 September 2007 in Durham. This current special issue of the Logic Journal of the IGPL gathers together the revised and updated versions of the five best FAMAS'007 contributions. (shrink)

Reasons-based accounts of our normative conclusions face difficulties in distinguishing between what ought to be done and what is required. This article addresses this problem from a formal perspective. I introduce a rudimentary formalization of a reasons-based account and demonstrate that that the model faces difficulties in accounting for the distinction between oughts and requirements. I briefly critique attempts to distinguish between oughts and requirements by appealing to a difference in strength or weight of reasons. I then present a (...) formalized reasons-based account of permissions, oughts and requirements. The model exploits Joshua Gert (2004; 2007) and Patricia Greenspan’s (2005; 2007; 2010) suggestion that some reasons perform a purely justificatory function. I show that the model preserves the standard entailment relationships between requirements, oughts and permissions. (shrink)

A generative grammar for a language L generates one or more syntactic structures for each sentence of L and interprets those structures both phonologically and semantically. A widely accepted assumption in generative linguistics dating from the mid-60s, the Generative Grammar Hypothesis , is that the ability of a speaker to understand sentences of her language requires her to have tacit knowledge of a generative grammar of it, and the task of linguistic semantics in those early days was taken to be (...) that of specifying the form that the semantic component of a generative grammar must take. Then in the 70s linguistic semantics took a curious turn. Without rejecting GGH, linguists turned away from the task of characterizing the semantic component of a generative grammar to pursue instead the Montague-inspired project of providing for natural languages the same kind of model-theoretic semantics that logicians devise for the artificial languages of formal systems of logic, and “formal semantics” continues to dominate semantics in linguistics. This essay argues that the sort of compositional meaning theory that would verify GGH would not only be quite different from the theories formal semanticists construct, but would be a more fundamental theory that supersedes those theories in that it would explain why they are true when they are true, but their truth wouldn’t explain its truth. Formal semantics has undoubtedly made important contributions to our understanding of such phenomena as anaphora and quantification, but semantics in linguistics is supposed to be the study of meaning. This means that the formal semanticist can’t be unconcerned that the kind of semantic theory for a natural language that interests her has no place in a theory of linguistic competence; for if GGH is correct, then the more fundamental semantic theory is the compositional meaning theory that is the semantic component of the internally represented generative grammar, and if that is so, then linguistic semantics has so far ignored what really ought to be its primary concern. (shrink)

Under the independence and competence assumptions of Condorcet’s classical jury model, the probability of a correct majority decision converges to certainty as the jury size increases, a seemingly unrealistic result. Using Bayesian networks, we argue that the model’s independence assumption requires that the state of the world (guilty or not guilty) is the latest common cause of all jurors’ votes. But often – arguably in all courtroom cases and in many expert panels – the latest such common cause is a (...) shared ‘body of evidence’ observed by the jurors. In the corresponding Bayesian network, the votes are direct descendants not of the state of the world, but of the body of evidence, which in turn is a direct descendant of the state of the world. We develop a model of jury decisions based on this Bayesian network. Our model permits the possibility of misleading evidence, even for a maximally competent observer, which cannot easily be accommodated in the classical model. We prove that (i) the probability of a correct majority verdict converges to the probability that the body of evidence is not misleading, a value typically below 1; (ii) depending on the required threshold of ‘no reasonable doubt’, it may be impossible, even in an arbitrarily large jury, to establish guilt of a defendant ‘beyond any reasonable doubt’. (shrink)

The formal and empirical-generative perspectives of computation are demonstrated to be inadequate to secure the goals of simulation in the social sciences. Simulation does not resemble formal demonstrations or generative mechanisms that deductively explain how certain models are sufficient to generate emergent macrostructures of interest. The description of scientific practice implies additional epistemic conceptions of scientific knowledge. Three kinds of knowledge that account for a comprehensive description of the discipline were identified: formal, empirical and intentional knowledge. The (...) use of formal conceptions of computation for describing simulation is refuted; the roles of programming languages according to intentional accounts of computation are identified; and the roles of iconographic programming languages and aesthetic machines in simulation are characterized. The roles that simulation and intentional decision making may be able to play in a participative information society are also discussed. (shrink)

This article presents a simple derivation of optimization models for reaction networks leading to a generalized form of the mass-action law, and compares the formal structure of Minimum Information Divergence, Quadratic Programming and Kirchhoff type network models. These optimization models are used in related articles to develop and illustrate the operation of ontology alignment algorithms and to discuss closely connected issues concerning the epistemological and statistical significance of sharp or precise hypotheses in empirical science.

In this article, after presenting the basic idea of causal accounts of implementation and the problems they are supposed to solve, I sketch the model of computation preferred by Chalmers and argue that it is too limited to do full justice to computational theories in cognitive science. I also argue that it does not suffice to replace Chalmers’ favorite model with a better abstract model of computation; it is necessary to acknowledge the causal structure of physical computers that is not (...) accommodated by the models used in computability theory. Additionally, an alternative mechanistic proposal is outlined. (shrink)

The appearance of openly accessible Artificial Intelligence Applications such as Large Language Models, nowadays capable of almost human-level performances in complex reasoning tasks had a tremendous impact on public opinion. Are we going to be "replaced" by the machines? Or - even worse - "ruled" by them? The behavior of these systems is so advanced they might almost appear "alive" to end users, and there have been claims about these programs being "sentient". Since many of our relationships of power and (...) social dominance are apparently based on intelligence, where the "smarter" seems to prevail on the "dumber" (as we see for example with livestock farming, or with the distribution of salaries according to formal and intellectual qualifications etc.) the emergence of programs and AI applications of this level of sophistication brings us to the question "what will AI do to us?". Our error is to frame Artificial Intelligence in the same way we frame Natural Intelligence and mistakenly address it as we would do with biological life, even applying to it the same biopolitical categories. We here try to reverse the common arguments in relationship between life and intelligence and show that our progresses in Artificial Intelligence might have no immediate consequence for the topic of life as such, as life and intelligence are well separated issues, and - even when we would like to somehow fuse them together, we are very far away from having an "Artificial Life" to the degree of complexity and effectiveness we have with "Artificial Intelligence". (shrink)

A dialectical contradiction can be appropriately described within the framework of classical formal logic. It is in harmony with the law of noncontradiction. According to our definition, two theories make up a dialectical contradiction if each of them is consistent and their union is inconsistent. It can happen that each of these two theories has an intended model. Plenty of examples are to be found in the history of science.

Boolean-valued models of set theory were independently introduced by Scott, Solovay and Vopěnka in 1965, offering a natural and rich alternative for describing forcing. The original method was adapted by Takeuti, Titani, Kozawa and Ozawa to lattice-valued models of set theory. After this, Löwe and Tarafder proposed a class of algebras based on a certain kind of implication which satisfy several axioms of ZF. From this class, they found a specific 3-valued model called PS3 which satisfies all the axioms of (...) ZF, and can be expanded with a paraconsistent negation *, thus obtaining a paraconsistent model of ZF. The logic (PS3 ,*) coincides (up to language) with da Costa and D'Ottaviano logic J3, a 3-valued paraconsistent logic that have been proposed independently in the literature by several authors and with different motivations such as CluNs, LFI1 and MPT. We propose in this paper a family of algebraic models of ZFC based on LPT0, another linguistic variant of J3 introduced by us in 2016. The semantics of LPT0, as well as of its first-order version QLPT0, is given by twist structures defined over Boolean agebras. From this, it is possible to adapt the standard Boolean-valued models of (classical) ZFC to twist-valued models of an expansion of ZFC by adding a paraconsistent negation. We argue that the implication operator of LPT0 is more suitable for a paraconsistent set theory than the implication of PS3, since it allows for genuinely inconsistent sets w such that [(w = w)] = 1/2 . This implication is not a 'reasonable implication' as defined by Löwe and Tarafder. This suggests that 'reasonable implication algebras' are just one way to define a paraconsistent set theory. Our twist-valued models are adapted to provide a class of twist-valued models for (PS3,*), thus generalizing Löwe and Tarafder result. It is shown that they are in fact models of ZFC (not only of ZF). (shrink)

The terms “model” and “model-building” have been used to characterize the field of formal philosophy, to evaluate philosophy’s and philosophical logic’s progress and to define philosophical logic itself. A model is an idealization, in the sense of being a deliberate simplification of something relatively complex in which several important aspects are left aside, but also in the sense of being a view too perfect or excellent, not found in reality, of this thing. Paraconsistent logic is a branch of philosophical (...) logic. It is however not clear how paraconsistent logic can be seen as model-building. What exactly is modeled? In this paper I adopt the perspective of looking at a particular instance of paraconsistent logic—paranormal modal logic—which might be seen as a model of a specific kind of agent: inductive agents. After ntroducing what I call the highlevel and low-level models of inductive agents, I analyze the extent to which the above-mentioned idealizing features of model-building appear in paranormal modal logic and how they affect its philosophical significance. (shrink)

It is here proposed an analysis of symbolic and sub-symbolic models for studying cognitive processes, centered on emergence and logical openness notions. The Theory of logical openness connects the Physics of system/environment relationships to the system informational structure. In this theory, cognitive models can be ordered according to a hierarchy of complexity depending on their logical openness degree, and their descriptive limits are correlated to Gödel-Turing Theorems on formal systems. The symbolic models with low logical openness describe cognition by (...) means of semantics which fix the system/environment relationship, while the sub-symbolic ones with high logical openness tends to seize its evolutive dynamics. An observer is defined as a system with high logical openness. In conclusion, the characteristic processes of intrinsic emergence typical of “bio-logic” - emerging of new codes-require an alternative model to Turing- computation, the natural or bio-morphic computation, whose essential features we are going here to outline. (shrink)

I propose to explain Kant’s novel claim, in the Critique of Pure Reason, that all judgments have a formal modality. I begin by distinguishing the modality of a judgment’s form from the modality of its content, and I suggest that the former is peculiar in merely affecting the subject’s understanding of his own act of judging. I then contrast the modal account of such an understanding (in terms of the possibility and actuality of a judgment) with the traditional, non-modal (...) understanding of it (in terms of the giving and withholding of assent). I conclude by suggesting that Kant prefers the former because he conceives of knowledge on Aristotle’s model: as a progress in the mind from capacity to act. (shrink)