Mainstream economics has been accused of excessive mathematization, whereas the rejection of mathematical and other formal methods is often cited as a crucial trait of Austrian economics. Based on a systematic discussion of potential benefits and drawbacks of formalization, this paper corroborates legitimate concerns that predominant types of mathematization induce a shift of attention away from the key concepts of Austrian economics. Taking this shift to the extreme, predominant modes of mathematization tend to accompany a detachment from ‘reality’ incompatible (...) with Austrian pleas for realisticness. Contrary to popular prejudice however, the most prominent representatives of the Austrian School including Carl Menger, Ludwig Mises, Friedrich Hayek, Israel Kirzner, and Peter Boettke neither provide a justification for a wholesale rejection of formalization nor actually reject it. Adequate formalization can serve as a remedy for lacking logical and semantic rigor in standard mathematical economics as well as in murky verbal chains of reasoning. (shrink)

The dispute over the viability of various theories of relativistic, dissipative fluids is analyzed. The focus of the dispute is identified as the question of determining what it means for a theory to be applicable to a given type of physical system under given conditions. The idea of a physical theory's regime of propriety is introduced, in an attempt to clarify the issue, along with the construction of a formal model trying to make the idea precise. This construction involves a (...) novel generalization of the idea of a field on spacetime, as well as a novel method of approximating the solutions to partial-differential equations on relativistic spacetimes in a way that tries to account for the peculiar needs of the interface between the exact structures of mathematical physics and the inexact data of experimental physics in a relativistically invariant way. It is argued, on the basis of these constructions, that the idea of a regime of propriety plays a central role in attempts to understand the semantical relations between theoretical and experimental knowledge of the physical world in general, and in particular in attempts to explain what it may mean to claim that a physical theory models or represents a kind of physical system. This discussion necessitates an examination of the initial-value formulation of the partial-differential equations of mathematical physics, which suggests a natural set of conditions---by no means meant to be canonical or exhaustive---one may require a mathematical structure, in conjunction with a set of physical postulates, satisfy in order to count as a physical theory. Based on the novel approximating methods developed for solving partial-differential equations on a relativistic spacetime by finite-difference methods, a technical result concerning a peculiar form of theoretical under-determination is proved, along with a technical result purporting to demonstrate a necessary condition for the self-consistency of a physical theory. (shrink)

The class of points in a set-presented formal topology is a set, if all points are maximal. To prove this constructively a strengthening of the dependent choice principle to infinite well-founded trees is used.

Formal languages are widely regarded as being above all mathematical objects and as producing a greater level of precision and technical complexity in logical investigations because of this. Yet defining formal languages exclusively in this way offers only a partial and limited explanation of the impact which their use actually has. In this book, Catarina Dutilh Novaes adopts a much wider conception of formal languages so as to investigate more broadly what exactly is going on when theorists put these (...) tools to use. She looks at the history and philosophy of formal languages and focuses on the cognitive impact of formal languages on human reasoning, drawing on their historical development, psychology, cognitive science and philosophy. Her wide-ranging study will be valuable for both students and researchers in philosophy, logic, psychology and cognitive and computer science. (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)

In this thesis, we study the complexity of theorems that may be considered partially impredicative from the point of view of reverse mathematics and Weihrauch degrees.From the perspective of reverse mathematics and ordinal analysis, the axiomatic system $\mathsf {ATR}_0$ is known as the limit of predicativity, and $\Pi ^1_{1}\text {-}\mathsf {CA}_0$ is known as an impredicative system. In this thesis, we study the complexity of some theorems that are stronger than $\mathsf {ATR}_0$ and weaker than $\Pi ^1_{1}\text {-}\mathsf {CA}_0$ from (...) the point of view of reverse mathematics and Weihrauch degrees.In Chapter 3, we study some problems related to Knaster–Tarski’s theorem. Knaster–Tarski’s theorem states that any monotone operator on $2^{\omega }$ has a least fixed point. Avigad introduced a weaker variant, $\mathsf {FP}$, which asserts the existence of a fixed point instead of the least fixed point, and proved that $\mathsf {FP}$ for arithmetical operators is equivalent to $\mathsf {ATR}_0$ over $\mathsf {RCA}_0$. In this thesis, we show that $\mathsf {FP}$ for $\Sigma ^0_2$ -operators is strictly stronger than $\mathsf {ATR}_2$, a Weihrauch degree corresponding to $\mathsf {ATR}_0$, in terms of Weihrauch reduction. In addition, we study the bottom-up proof of Knaster–Tarski’s theorem. It is known that the least fixed point of a monotone operator is given by the $\omega _1$ -times iteration of the operator at the empty set. This implies that any monotone operator involves a hierarchy formed by the iterative applications of the operator, starting with the empty set and reaching the least fixed point. We prove that although the existence of a hierarchy is equivalent to $\mathsf {ATR}_0$ over $\mathsf {ACA}_0$, it is stronger than $\mathsf {C}_{\omega ^{\omega }}$ in the terms of Weirhauch reduction.In Chapter 5, we study the relative leftmost path principle in Weihrauch degrees. This principle was introduced by Towsner to study partial impredicativity in reverse mathematics. He gave a hierarchy between $\mathsf {ATR}_0$ and $\Pi ^1_1\text {-}\mathsf {CA}_0$ by this principle. We show that this principle also makes a hierarchy between $\mathsf {ATR}_2$ and $\mathsf {C}_{\omega ^{\omega }}$ in Weihrauch degrees. We also show that the relative leftmost path principle is, not the same as, but very close to a variant of $\beta $ -model reflection.In Chapter 6, we introduce a hierarchy dividing $\{\sigma \in \Pi ^1_2 : \Pi ^1_1\text {-}\mathsf {CA}_0 \vdash \sigma \}$. Then, we give some characterizations of this hierarchy using some principles equivalent to $\Pi ^1_1\text {-}\mathsf {CA}_0$ : leftmost path principle, Ramsey’s theorem for $\Sigma ^0_n$ classes of $[\mathbb {N}]^{\mathbb {N}}$ and the determinacy of Gale–Stewart game for $(\Sigma ^0_1)_n$ classes. As an application, our hierarchy explicitly shows that the number of applications of the hyperjump operator needed to prove $\Sigma ^0_n$ Ramsey’s theorem or $(\Sigma ^0_1)_n$ determinacy increases when the subscript n increases.Abstract prepared by Yudai Suzuki.E-mail: [email protected]. (shrink)

In this paper we propose a formal theory of metaphors called Constrained Semantic Transference [CST]. We start from the assumptions that metaphors are characterized by the description of one domain, called the target domain, in terms of another domain, called the source domain; and that a metaphor works by transferring a set of structural relationships from the source domain to the target domain coherently.Starting from these assumptions, we formally define the concept of T-MAPs which are partial coherent mappings from (...) the source domain to the target domain. We also define two operators, called Augmentation and Positing Structure that extend a given T-MAP by adding new structure to the target domain. (shrink)

This is a thesis in formal semantics. It consists of two parts corresponding to the distinction, due to Richard Montague, between universal grammar and specific semantic theories. The first part concerns universal grammar and is intended to provide a precise and unified conceptual framework within which different theories of formal semantics can be represented and compared. ;The second part of the thesis is concerned with intensional logic, i.e., with the logical analysis of discourse involving so called oblique contexts. These contexts (...) are characterized by the apparent failure of certain classically valid principles of substitutivity. Two kinds of reactions among logicians to the appearance of oblique contexts in natural languages are distinguished: (1) the intensional point of view, according to which oblique contexts are seen as genuine counterexamples to classical logic and to the related semantical principle of extensionality: the principle that the denotation of an expression is a function of the denotations of its parts; and (2) the extensional point of view, according to which the conflict between oblique contexts and classical logic is only apparent. The extensional point of view therefore calls for analyses of oblique contexts that preserve the laws of classical logic and the principle of extensionality. In this thesis, we are concerned with the precise formulation of and comparison between different programs for the formal semantic representation of oblique contexts. In Chapter 5, we are concerned with Church's program of representing oblique contexts within a formal language whose semantics is fully extensional and based on Frege's distinction between sense and denotation. The ambiguity between the "direct" and "indirect" denotation of an expression A is avoided by letting A be replaced in oblique contexts by an expression which denotes A's ordinary sense. We provide a possible-worlds semantics for a version of Church's formal language with the following features: (i) Objectual quantification into oblique constructions is accounted for. The treatment of quantification requires for each entity x an essence of x, by which we mean a sense which determines x in those worlds in which x exists and is undefined in all other worlds. (ii) The variables range over actually existing entities only. It is allowed that entities of certain types are contingent, i.e., the same entity may exist in one world and fail to exist in other worlds. (iii) In order to combine a proper treatment of the cross-world identification of functions with varying domains, partial functions are allowed. (iv) Senses are allowed to be partially defined. For example, the sense of a proper name is undefined in a world in which the denotation of the name does not exist. (v) Senses of functions from objects of type a to objects of type b are identified with functions from senses of objects of type a to senses of objects of type b. In Chapters 6 and 7, we pursue the Russellian Alternative in intensional semantics, where a sense/denotation distinction is avoided. Apparent failures of substitutivity principles for singular terms are explained along the lines of Russell's theory of definite descriptions. Failures of substitutivity of coextensional sentences and predicates are explained by Russell's doctrine that sentences and predicate denote propositions and propositional functions , respectively. Russellian semantics is fully extensional in the sense that the Russellian denotation of a designator is a function of the Russellian denotations of its parts. In Chapter 6, a theory of Russellian propositions is developed within set theory. This theory is then applied in Chapter 7 to the task of providing a set-theoretic semantics for Russellian type theory. (shrink)

One might identify two poles of thought about Kant’s Formula of Humanity. On the one hand, it provides the ‘matter’ of morality – a substantive value that animates moral concern. On the other hand, Kant argues that the different formulations of the Categorical Imperative are equivalent and that the Formula of Universal Law is a formal principle. Thus if one takes Kant’s claims about the equivalence of the formulas seriously, there must be a way to understand the Formula of Humanity (...) as a formal principle. This paper offers a partial list of desiderata for an interpretation of the Formula of Humanity and then suggests that a formal principle for Kant is a constitutive norm of some domain of cognition. I then consider two different interpretive approaches to the Formula of Humanity – one developed by Christine Korsgaard and David Velleman, the other by Stephen Engstrom – that can be seen to treat it as a formal principle of rational agency. (shrink)

We consider two formalisations of the notion of a compositionalsemantics for a language, and find some equivalent statements in termsof substitutions. We prove a theorem stating necessary and sufficientconditions for the existence of a canonical compositional semanticsextending a given partial semantics, after discussing what features onewould want such an extension to have. The theorem involves someassumptions about semantical categories in the spirit of Husserl andTarski.

Formal relationism in the philosophy of mind is the thesis that folk psychological states should be individuated, at least partially, in terms of the purely formal inference-licensing relations between underlying mental representations. It's supposed to provide a Russellian alternative to a Fregean theory of propositional attitudes. I argue that there's an inconsistency between the motivation for formal relationism and the use to which it's put in defense of Russellian propositions. Furthermore, I argue that formal relationism is committed to epiphenomenalism about (...) singular mental content. (shrink)

Three common strategies used by informal logicians are considered: (1) the appeal to standard cases, (2) the attempt to partially formalize so-called "informal fallacies," and (3) restatement of arguments in such a way as to make their logical character more perspicuous. All three strategies are found to be useful. Attention is drawn to several advantages of a "stock case" approach, a minimalist approach to formalization is recommended, and doubts are raised about the applicability, from a logical point of view, (...) of a principle of charitable construal in the reconstruction of arguments. (shrink)

This article connects certain writings of Raymond Smullyan on logic and formal systems with current research on constructive type theory. It also considers aspects of teaching logic to computer science students. Those students require logic in order to precisely define programming tasks and demonstrate that programs meet logical specifications of these tasks. Smullyan’s book First-Order Logic has been used for many years to teach logic to computer science students at Cornell. This article includes a brief account of an elegant result (...) from this book. It is based on an extension of a fourteen page technical report that analyzes two pages on Boolean valuations in chapter one of his classic book. The analysis and results are formulated in a formal system of type theory and proved using the Nuprl proof assistant. The article also briefly considers the role of partial types, showing how they provide a new way to prove unsolvability results, another topic on which Smullyan has written with remarkable clarity. Partial types also provide a simple and faithful semantics for Hoare’s partial correctness logic, widely used to reason about programs and taught in computer science as an important applied logic. They also make it possible to state a clean rule for defined functions in Hoare logic. (shrink)

I raise skeptical doubts about the prospects of Bayesian formal epistemology for providing an adequate general normative model of epistemic rationality. The notion of credence, I argue, embodies a very dubious psychological myth, viz., that for virtually any proposition p that one can entertain and understand, one has some quantitatively precise, 0-to-1 ratio-scale, doxastic attitude toward p. The concept of credence faces further serious problems as well—different ones depending on whether credence 1 is construed as full belief (the limit case (...) of so-called partial belief) or instead is construed as absolute certainty. I argue that the notion of an “ideal Bayesian reasoner” cannot serve as a normative ideal that actual human agents should seek to emulate as closely as they can, because different such reasoners who all have the same evidence as oneself—no single one them being uniquely psychologically most similar to oneself—will differ from one another in their credences (e.g., because they commence from different prior credences). I argue that epistemic probability, properly understood, is quantitative degree of evidential support relative to one’s evidence, and that principled epistemic probabilities arise only under quite special evidential circumstances—which means that epistemic probability is ill suited to figure centrally within general norms of human epistemic rationality. (shrink)

Given the collapse hypothesis (CH) of quantum measurement, EPR-type correlations along with the hypothesis of the impossibility of superluminal communication (ISC) have the effect of globalizing gross features of the quantum formalism making them universally true. In particular, these hypotheses imply that state transformations of density matrices must be linear and that evolution which preserves purity of states must also be linear. A gedanken experiment shows that Lorentz covariance along with the second law of thermodynamics imply a nonentropic version of (...) ISC. Partial results using quantum logic suggest, given ISC and a version of CH, a connection between Lorentz covariance and the covering law. These results show that standard quantum mechanics is structurally unstable, and suggest that viable relativistic alternatives must question CH. One may also speculate that some features of the Hilbert-space model of quantum mechanics have their origin in space time structure. (shrink)

The ramified legacy of Bernard Berenson’s writings within 20th century art historiography is both celebrated and maligned. In an effort to help reconcile this situation, this essay argues for the partial validity of Berenson’s peculiar version of art historical formalism by detailing its historical connections to the Pragmatist philosophy and psychology of William James and by analytically correlating Berenson’s arguments with recent work in aesthetics and the philosophy of perception. The essay examines the specific example of Berenson’s analysis of (...) Giotto’s paintings and leverages a Pragmatist interpretation of Berenson’s writings to frame Berenson’s known connections with other writers: including Adolf Hildebrand, Giovanni Morelli, and Walter Pater. In conclusion, the failure, potential, reception, and legacy of Berenson’s art historical scholarship are assessed in relation to Pragmatist ideas. Der vielfältige Einfluss von Bernard Berensons Schriften auf die Kunstgeschichte des 20. Jahrhunderts wird ebenso geschätzt wie verachtet. In dem Bestreben, diese Divergenzen zu berichtigen, versucht dieser Beitrag den Nachweis für die bedingte Gültigkeit von Berensons eigentümlicher Variante eines kunsthistorischen Formalismus zu erbringen, indem er einerseits seine historischen Verbindungen zur pragmatischen Philosophie und Psychologie von William James aufzeigt und indem er andererseits Berensons Argumentation ins Verhältnis zu aktuellen Debatten der wahrnehmungstheoretischen Ästhetik und Philosophie setzt. Am Beispiel von Berensons Interpretation der Gemälde Giottos führt dieser Essay eine pragmatische Analyse von Berensons Schriften durch und stellt diese ins Umfeld seiner Kontakte zu anderen Autoren: darunter Adolf Hildebrand, Giovanni Morelli und Walter Pater. Schließlich soll das Scheitern, das Potenzial, die Rezeption und das Erbe von Berensons kunsthistorischen Studien unter pragmatischen Gesichtspunkten bewertet werden. (shrink)

In this article, we propose an initial formal model of computationalism based on mathematical relations between cognition and computation. More specifically, based on a set of cognitive constituents as a domain, and a set of computational implementations as a range, we define two relations of transformation over these sets. Moreover, we define the principles of implementability, describability, and phenomena correspondence, and we conjecture that full computationalism does not hold since these principles are not fulfilled. Particularly, many cognitively-tied phenomena fail to (...) respect the describability principle which is necessary for representing a cognitive state by a computational state. (shrink)

The dissertation is an attempt to provide a formal semantics for occurrences of anaphoric pronouns and definite descriptions whose quantifier antecedents occur in sentences other than those in which the anaphoric pronouns and descriptions themselves occur, . The predominant view of anaphoric pronouns whose quantifier antecedents occur in the same sentence as they do is that they function as bound variables . Chapter 1 of this dissertation is constituted by a series of arguments against a bound variable treatment of q (...) - terms and the observation that the semantic behavior of q - terms is similar to that of certain singular terms in English arguments. Given the similarity of semantic behavior between the latter and q - terms, it seems plausible to suppose that a theory of the semantic behavior of these singular terms in English arguments would provide a model for the eventual production of a semantic theory of q - terms. In Chapter 2, a formal semantics for these singular terms in arguments is produced. In Chapter 3, a formal semantics for q - terms is produced, on the model of the semantics in Chapter 2. Finally, in Chapter 4 it is shown that the formal semantics of Chapter 3 can be extended to handle pronouns in discourses containing verbs of propositional attitudes such as 'wants', 'dreams' etc. It is also shown that some occurrences of sentences containing q - terms have truth conditions not expressible by any quantified first order sentence. One must use finite partially ordered quantifiers to express the truth conditions of such occurrences of sentences. ;The dissertation contains two appendices: the first is a technical discussion of the formal semantics of Hans Kamp which shows that his theory cannot accomodate the linguistic data mine is designed to handle. The second examines the views of Gareth Evans, Charles Chastain and Keith Donnellan on certain anaphoric pronouns. (shrink)

I draw lessons from experimental economics. I argue that the lack of mathematical formalism cannot be usefully thought as the cause of the underappreciation of contextual and generalizability considerations. Instead, this lack is problematic because it hinders a clear relationship between theory and quantitative predictions. I also advocate a pragmatic policy-focused approach as a partial remedy to the generalizability problem.

TRIZ (the Russian acronym for Theory of Resolution of Inventive Problems) is a methodology to guide the search for inventive solutions to one, or a few, difficult problems. Classic TRIZ is not well suited to the examination of complex situations composed of many problems, sub-problems and partial solutions, strongly interconnected. It has therefore been completed to give birth, among others, to the Inventive Design Methodology (IDM) framework.TRIZ and IDM share many similarities with Artificial Intelligence methods: they both propose to (...) solve a problem by reformulation in an abstract model. Generic solving patterns are applied to this abstract model to produce abstract solutions. The domain-specific knowledge is then used to get the final solution concept. However, neither TRIZ nor IDM's descriptions are formal enough to permit a reliable software implementation and rely mainly on the experts' manual work. Therefore this paper proposes an ontological formalization of TRIZ and IDM to overcome these difficulties and allow the development of software tools to assist TRIZ/idm experts in their work. (shrink)

The importance of contextual reasoning is emphasized by various researchers in AI. (A partial list includes John McCarthy and his group, R. V. Guha, Yoav Shoham, Giuseppe Attardi and Maria Simi, and Fausto Giunchiglia and his group.) Here, we survey the problem of formalizing context and explore what is needed for an acceptable account of this abstract notion.

The spread of formal constitutions during the last two and a half centuries worldwide is closely associated with the fact that armed conflict between (national) states has receded and that within each state, or at least in many of them, socioeconomic and cultural dynamics more conducive (in comparison to pre-modern times) to a peaceful resolution of political disputes have emerged. Vice versa, constitutions typically aim to contribute to a further internal pacification of a given human society and their ultimate measure (...) of success is the degree of their contribution towards that end. A formal constitution is a sort of a civil peace (in contrast to civil war) agreement between the various political forces or groups of a given human society, insofar as its drafting procedure was inclusive or, alternatively, as far as those forces have ex post facto accepted the constitutionally foreseen roadmap for political decision-making. Thus, pacification and constitutionalism are positively correlated and there is a partial mutual causation linking them. (shrink)

Hamblin’s Action-State Semantics provides a sound philosophical foundation for understanding the character of the imperative. Taking this as our inspiration, in this paper we present a logic of action, which we call ST, that captures the clear ontological distinction between being responsible for the achievement of a state of affairs and being responsible for the performance of an action. We argue that a relativised modal logic of type RT founded upon a ternary relation over possible worlds integrated with a basic (...) tense logic captures intuitions of the Hamblinian model of imperatives. The logic implements a direct mapping of each of Hamblin’s key concepts: strategies, partial strategies and wholehearted satisfaction. (shrink)

Computational dialectics is concerned with the formal representation of argument and dispute. The field emerged from developments in philosophy, artificial intelligence and legal theory. Its goal is to suggestalgorithms, procedures and protocols to investigate the tenability of logical claims, on the basis of information in the form of rules and cases. Currently, the field slowlyconverges to the opinion that dispute is the most fair and effective way to investigate claims. The basic assumption of this field is that dispute is the (...) most fair and effective way to investigate claims. The definition of a formal dispute varies throughout the literature, butis considered not to vary within one and the same logical system. In this paper it is shown that parts of the definition of a dispute may change within one logical system.To this end, the notion of partial protocol specification (PPS) is introduced. A PPS is a part of the definition of the protocol. A modification to the protocol, in the form of a PPS, can be put forward, disputed, established and incorporated as aneffective `point of order. The paper demonstrates the existence of self-undermining PPSs, it discusses the relevance of PPSs for dialectical models of legal argument and concludes with a description of how PPSs can be built into existing argumentation systems. (shrink)

Alongside the direct parallels and contrasts between traditional narrative fiction and games, there lie certain partial analogies that provide their own insights. This article begins by examining a direct parallel between narrative fiction and games—the role of fictional reliefs and reality checks in shaping aesthetic engagement—before arguing that from this a partial analogy can be developed stemming from a feature that distinguishes most games from most traditional fictions: the presence of rules. The relation between rules and fiction in (...) games has heretofore been acknowledged but not examined in detail, giving an impression of a tension that is constant. However, the paired concepts of formal reliefs and representation checks, once introduced, allow us to explain how rules and fiction interact to alter the ways in which players engage with games in a dynamic but limited way. (shrink)

A number of systems of logic, including formulations of the two-valued propositional logic, alethic modal propositional logics and deontic modal propositional logics, are described and discussed with the aim of utilizing some of these systems for the sociological analysis of normative structures. Evidence is adduced that certain normative concepts are explicated or partially explicated in these systems.--W.T.

In 1960, Eugene Wigner posed a question that has since become canonical in the philosophy of mathematics and physics: why do mathematical structures developed for purely formal reasons repeatedly turn out to describe physical reality with uncanny precision? Wigner declared this effectiveness "bordering on the mysterious" and offered no rational explanation. Subsequent responses — Hamming's partial accounts, Tegmark's Mathematical Universe Hypothesis, Wheeler's "It from Bit," Wolfram's computational universe, Penrose's three-worlds framework — each address aspects of the problem while remaining (...) captive to the presuppositions that generate it. -/- This paper advances a dissolution rather than a solution. The source of Wigner's puzzle is identified in a conflation of two fundamentally distinct descriptive modes: static description, characteristic of classical mathematics, which captures structural snapshots of reality; and dynamic description, the computational-algebraic mode, which captures reality as an ongoing operational process. The universe is not formalized by mathematical structures; it computes. Both mathematics and physical law are static projections of a single dynamic source: the minimal non-commutative algebra M3(C), whose necessity is derived from first principles within the Cognitional Mechanics (CM) framework rather than postulated. -/- Once the static/dynamic distinction is drawn, Wigner's question loses its force. Static mathematical descriptions are effective because they are cross-sections of a dynamic computational reality. The correspondence between mathematics and physics is not a contingent harmony; it is a structural inevitability. (shrink)

There is a duality in our everyday view of belief. On the one hand, we sometimes speak of credence as a matter of degree. We talk of having some level of confidence in a claim (that a certain course of action is safe, for example, or that a desired event will occur) and explain our actions by reference to these degrees of confidence – tacitly appealing, it seems, to a probabilistic calculus such as that formalized in Bayesian decision theory. On (...) the other hand, we also speak of belief as an unqualified, or flat-out, state (‘plain belief’ as it is sometimes called), which is either categorically present or categorically absent. We talk of simply believing or thinking that something is the case, and we cite these flat-out attitudes in explanation of our actions – appealing to classical practical reasoning of the sort formalized in the so-called ‘practical syllogism’.1 This tension in everyday discourse is reflected in the theoretical literature on belief. In formal epistemology there is a division between those in the Bayesian tradition, who treat credence as graded, and those who think of it as a categorical attitude of some kind. The Bayesian perspective also contrasts with the dominant view in philosophy of mind, where belief is widely regarded as a categorical state (a token sentence of a mental language, inscribed in a functionally defined ‘belief box’, according to one popular account). A parallel duality is present in our everyday view of desire. Sometimes we talk of having degrees of preference or desirability; sometimes we speak simply of wanting or desiring something tout court, and, again, this tension is reflected in the theoretical literature. What should we make of these dualities? Are there two different types of belief and desire – partial and flat-out, as they are sometimes called? If so, how are they related? And how could both have a role in guiding rational action, as the everyday view has it? The last question poses a particular challenge in relation to flat-out belief and desire.. (shrink)

This article uses the concept of partial organization to examine how organizing principles can facilitate the effective operation of networked forms of corruption. We analyze the case study of a corruption network in the South Korean maritime industry in terms of how it operated by selectively appropriating practices normally associated with formal bureaucratic organizations. Our findings show that organizational elements built into the corruption network enabled coordination of corruption activities and served to distort and override practices within member organizations. (...) The network was primarily organized through the hierarchical organization of a bounded and controlled set of members and, to a lesser extent, through processes of monitoring and sanctions. Given its clandestine nature, the network avoided the use of explicit rules to govern behavior, instead relying on habituated routines to ensure consistent and predictable action from members. We find that organizational elements were rescinded when the corruption network was exposed after the sinking of a passenger ferry, the Sewol. By rolling back its hierarchical organization and reverting to core relationships, the corruption network sought to preserve its center. The article illustrates the explanatory value of studying how the activities of corruption networks are enabled and adapt to existential challenges through partial organization. (shrink)

We design a method for solving natural language one-dimensional ordering problems by tightly integrating and co-developing a semantic parser with a logical inference module that deduces conclusions from the constraints stated in the premises. The semantic parser builds on Heim and Kratzer’s syntax-based compositional semantics with lambda calculus and introduces abstract types, templated rules, and a dynamic component for interpreting entities. It maps natural language into first-order logical forms defined in an axiom system and domain language that we develop for (...) one-dimensional ordering problems. These forms are evaluated by a logic-based inference module that we design and develop which enforces ordering constraints and determines whether candidate statements hold in all, some, or no possible worlds consistent with the premises, while addressing difficult constructs such as partial ordering and negation. The resulting system, the Formal Semantic Logic Inferer (FSLI), tightly integrates formal semantics with logic programming to provide a linguistically principled and logically sound framework for logical deduction problems stated in natural language. We demonstrate FSLI’s effectiveness on both synthetic and exam-style problems, achieving perfect performance in the controlled setting of the synthetic problems and high performance on the more linguistically and logically demanding exam-style ones. (shrink)

According to the received view formal semantics applies to natural language to some extent only. It is so because natural language is inherently indefinite, in particular, its expressions are ambiguous, vague and admits departures from syntactic rule. Moreover, intensional contexts occur in ordinary language—it results in limitations of the principle of compositionality. The ordinary conversation appeals to various principles, for instance, Grice’s maxims which exceed logical formalism. Thus, ordinary language cannot be fully formalized. On the other hand, if L is (...) a formal language, its metalanguage ML, must be partially informal—for instance, it contains, terms of ordinary mathematics, especially set theory. Even, if, for instance, due to the technique of aritmetization, ML can be represented in L, such a representation is only local. In fact, this view can be derived from some Tarski’s remarks on the role played by natural language. It is usually assumed that the universality of natural language, is the source of troubles associated with antinomies. It is so this circumstance requires a solution, for example by distinguishing levels of language. However, even if antinomies are excluded, what is informal is prior with respect to what is formal. It shows that formal semantics has limitations even with respect to formalized languages. (shrink)

This paper discusses one of the advantages of applying formal methods in ethics. First, an approach from democratic morality—which is a special case of contractualist ethics that brings together theories of legal and moral philosophy—will be adopted, in order to argue for the non-trivial thesis that moral norms are increasingly democratically motivated. To accept this thesis also as a desired way of justifying ethical principles raises some issues, such as the problem of providing adequate principles for moral opinion pooling. Secondly, (...) it is therefore shown how formal criteria of rationality provide at least a partial solution to such problems. In a broad context this results can be seen as formal preliminaries to contractualist ethics. (shrink)

We present a theory VF of partial truth over Peano arithmetic and we prove that VF and ID 1 have the same arithmetical content. The semantics of VF is inspired by van Fraassen's notion of supervaluation.

We are going to explain partial blocking as the result of diachronic processes based on what we will call associative learning. Especially, we argue that the task posed by partial blocking phenomena is to explain their emergence from unambiguous and fully expressive languages. This contrasts with approaches that presuppose underspecified semantic meanings or ineffability like Bidirectional Optimality Theory (Bi–OT) and some game theoretic explanations. We introduce a formal framework based on learning, speaker’s preferences and pure semantics for describing (...) diachronic strengthening of meaning. Moreover, we show how the diachronic development of systems of semantically co–extensive forms can be described in terms of a complete system of diachronic laws. (shrink)

In recent years, semantical partiality has emerged as an important explanatory concept in philosophical logic as well as in the study of natural language semantics. Despite the many applications, however, a number of mathematically intriguing questions associated with this concept have received only very limited attention. ;The present dissertation aims to present a systematic study of certain types of partiality in the area of basic model theory. Two types of issues are given special attention: Introducing partially defined models, there are (...) many ways to generalize the classical truth definition for sentences of a simple first order language relative to standard, complete models. Different interpretations of the formal framework motivate conflicting truth definitions between language and partial models: A partial model can be taken to represent a part of the world, or a partial information set. The truth of a sentence can be supported directly by a part of the world, but can also follow indirectly from an information set. These notions are related, and the relation motivates a comparison between various weaker and stronger alternative truth definitions. Results are obtained about the extent to which these truth definitions differ, and a number of characterization results are deduced. ;Among other conditions that are not expressible in the framework of standard, complete model theory, a condition of monotonicity or persistence of truth relative to partial models is argued to follow under both the given interpretations of the formal framework. The final chapter investigates the relation between such conditions and expressibility properties in general. These discussions culminate with a combined Lindstrom and persistence characterization theorem. (shrink)

Partial functions are ubiquitous in both mathematics and computer science. Therefore, it is imperative that the underlying logical formalism for a general-purpose mechanized mathematics system provide strong support for reasoning about partial functions. Unfortunately, the common logical formalisms — first-order logic, type theory, and set theory — are usually only adequate for reasoning about partial functionsin theory. However, the approach to partial functions traditionally employed by mathematicians is quite adequatein practice. This paper shows how the traditional (...) approach to partial functions can be formalized in a range of formalisms that includes first-order logic, simple type theory, and Von-Neumann—Bernays—Gödel set theory. It argues that these new formalisms allow one to directly reason about partial functions; are based on natural, well-understood, familiar principles; and can be effectively implemented in mechanized mathematics systems. (shrink)

Logics in which a relation R is semantically incomplete in a particular universe E, i.e. the union of the extension of R with its anti-extension does not exhaust the whole universe E, have been studied quite extensively in the last years. (Cf. van Benthem (1985), Blamey (1986), and Langholm (1988), for partial predicate logic; Muskens (1996), for the applications of partial predicates to formal semantics, and Doherty (1996) for applications to modal logic.) This is not so with semantically (...) incomplete generalized quantifiers which constitute the subject of the present paper. The only systematic study of these quantifiers from a purely logical point of view, is, to the best of my knowledge, that by van Eijck (1995). We shall take here a different approach than that of van Eijck and mention some of the abstract properties of the resulting logic. Finally we shall prove that the two approaches are interdefinable. (shrink)

Three claims about what makes a theory “physically complete” are (1) Shimony's assertion that a complete theory says “all there is to say” about nature; (2) EPR's requirement that a complete theory describe all “elements of reality”; and (3) Ballentine and Jarrett's claim that a “predictively complete” theory must obey a condition used in Bell deviations. After introducing “statistical completeness” as a partial formalization of (1), we explore the logical and motivational relationships connecting these completeness conditions. We find (...) that statistical completeness motivates but does not imply Jarrett's completeness condition, because Jarrett's condition encodes further intuitions about locality and causality. We also dispute Ballentine and Jarrett's claim that EPR-completeness implies Jarrett's completeness condition. (shrink)

The paper surveys some recent work on formal aspects of the logic of theory change. It begins with a general discussion of the intuitive processes of contraction and revision of a theory, and of differing strategies for their formal study. Specific work is then described, notably Gärdenfors'' postulates for contraction and revision, maxichoice contraction and revision functions and the condition of orderliness, partial meet contraction and revision functions and the condition of relationality, and finally the operations of safe contraction (...) and revision. Verifications and proofs are omitted, with references given to the literature, but definitions and principal results are presented with rigour, along with discussion of their significance. (shrink)

It is a remarkable fact that Hilbert's programmatic papers from the 1920s still shape, almost exclusively, the standard contemporary perspective of his views concerning (the foundations of) mathematics; even his own, quite different work on the foundations of geometry and arithmetic from the late 1890s is often understood from that vantage point. My essay pursues one main goal, namely, to contrast Hilbert's formal axiomatic method from the early 1920s with his existential axiomatic approach from the 1890s. Such a contrast illuminates (...) the circuitous beginnings of the finitist consistency program and connects the complex emergence of existential axiomatics with transformations in mathematics and philosophy during the 19th century; the sheer complexity and methodological difficulties of the latter development are partially reflected in the well known, but not well understood correspondence between Frege and Hilbert. Taking seriously the goal of formalizing mathematics in an effective logical framework leads also to contemporary tasks, not just historical and systematic insights; those are briefly described as “one direction” for fascinating work. (shrink)

This paper introduces a stratified non-normal modal logic, denoted R0, designed to formalize tran- sitions between epistemic regimes with partially ordered constraint structures. Unlike standard modal systems, R0 rejects normality and duality, allowing a finer articulation of local validity and inter-regime tension. The logic features regime-indexed modal operators, a stratified admissibility function, and a stability condition that governs modal transitions. We provide a formal Kripke-style semantics based on partial inclusion of constraint sets, and prove a completeness theorem relative to (...) this semantics. The system is self-sufficient within its minimal formal setting, yet explicitly avoids ontological or epistemic closure, making it suitable for applications in pluralist philosophy of science, model-theoretic relativism, and the formal analysis of conceptual change. This work lays the groundwork for a general theory of modal reasoning under heterogeneous and dynamically shifting regimes of validity. Open to feedback. (shrink)