The recovery of Aristotle’s logic during the twelfth century was a great stimulus to medieval thinkers. Among their own theories developed to explain Aristotle’s theories of valid and invalid reasoning was a theory of consequence, of what arguments were valid, and why. By the fourteenth century, two main lines of thought had developed, one at Oxford, the other at Paris. Both schools distinguished formal from material consequence, but in very different ways. In Buridan and his (...) followers in Paris, formal consequence was that preserved under uniform substitution. In Oxford, in contrast, formal consequence included analytic consequences such as ‘If it’s a man, then it’s an animal’. Aristotle’s notion of syllogistic consequence was subsumed under the treatment of formal consequence. Buridan developed a general theory embracing the assertoric syllogism, the modal syllogism and syllogisms with oblique terms. The result was a thoroughly systematic and extensive treatment of logical theory and logical consequence which repays investigation. (shrink)

This paper deals with Tarski's first axiomatic presentations of the syntax of deductive system. Andrzej Grzegorczyk's significant results which laid the foundations for the formalization of metalogic, are touched upon briefly. The results relate to Tarski's theory of concatenation, also called the theory of strings, and to Tarski's ideas on the formalization of metamathematics. There is a short mention of author's research in the field. The main part of the paper surveys research on the theory of deductive systems initiated by (...) Tarski, in particular research on the axiomatization of the general notion of consequence operation, axiom systems for the theories of classic consequence and for some equivalent theories, and axiom systems for the theories of nonclassic consequence. In this paper the results of Jerzy Supecki's research are taken into account, and also the author's and other people belonging to his circle of scientific research. Particular study is made of his dual characterization of deductive systems, both as systems in regard to acceptance and systems in regard to rejection . Comparison is made, therefore, with axiomatizations of the theories of rejection and dual consequence, and the theory of the usual consequence operation. (shrink)

We introduce -ranked preferential structures and combine them with an accessibility relation. -ranked preferential structures are intermediate between simple preferential structures and ranked structures. The additional accessibility relation allows us to consider only parts of the overall -ranked structure. This framework allows us to formalize contrary to duty obligations, and other pictures where we have a hierarchy of situations, and maybe not all are accessible to all possible worlds. Representation results are proved.

The aim of the paper is to present and evaluate Bolzano's theory of grounding, that is, his theory of the concept expressed and the relation brought into play by 'because'. In the first part of the paper (Sections 1-4) the concept of grounding is distinguished from and related to three other concepts: the concept of an epistemic reason}, the concept of causality, and the concept of deducibility (i.e., logical consequence). In its second part (Sections 5-7) Bolzano's positive account of (...) grounding is reconstructed in axiomatic form and critically discussed. (shrink)

There is little doubt that a second-order axiomatization of Zermelo-Fraenkel set theory plus the axiom of choice (ZFC) is desirable. One advantage of such an axiomatization is that it permits us to express the principles underlying the first-order schemata of separation and replacement. Another is its almost-categoricity: M is a model of second-order ZFC if and only if it is isomorphic to a model of the form Vκ, ∈ ∩ (Vκ × Vκ) , for κ a strongly inaccessible ordinal.

This article argues that Habermas’s formal-pragmatics are better understood as a set of weak-universal dispositions susceptible to erosion over the course of a lifetime, if exposed to continual “disappointing” communicative experiences. Habermas’s rational-reconstructive project to explicate the intuitive rule-consciousness held by competent speakers retains immense theoretical value for analyzing both partisan and mass political discourse, if his emphasis on isolated speech situations is supplemented with a logic of communicative memory better accounting for how disagreement antecedes discourse on the (...) class='Hi'>formal-pragmatic register. I argue that Habermas’s concept of the “lifeworld” contains untapped theoretical resources for thinking about the formal-pragmatic consequences of accumulated partisan experiences; namely, how such experiences lead inter-partisan actors to jettison mutual imputations of communicative accountability. I conclude by offering revisions to Habermas’s discourse ethics. Rapport-building intended to alleviate the negative effects of prior accumulated partisan experiences is first necessary if a norm is to enjoy real justification. (shrink)

We here present explicit relational theories of a class of geometrical systems (namely, inner product spaces) which includes Euclidean space and Minkowski spacetime. Using an embedding approach suggested by the theory of measurement, we prove formally that our theories express the entire empirical content of the corresponding geometric theory in terms of empirical relations among a finite set of elements (idealized point-particles or events) thought of as embedded in the space. This result is of interest within the general (...) phenomenalist tradition as well as the theory of space and time, since it seems to be the first example of an explicit phenomenalist reconstruction of a realist theory which is provably equivalent to it in observational consequences. The interesting paper "On the Space-Time Ontology of Physical Theories" by Ken Manders, Philosophy of Science, vol. 49, number 4, December 1982, p. 575-590, has significant affinities to this one. We both, in a sense, try to formally vindicate Leibniz's notion of a relational theory of space, by constructing theories of spatial relations among physical objects which are provably equivalent to the standard absolutist theories. The essential difference between our approaches is that Manders retains Leibniz's explicitly modal framework, whereas I do not. Manders constructs a spacetime theory which explicitly characterizes the totality of possible configurations of physical objects, using a modal language in which the notion of a possible configuration occurs as a primitive. There is no doubt that this is a more accurate realization of Leibniz's own conception of space than the embedding-based approach developed here. However, it also remains open to objections (such as those cited here from Sklar) on account of the special appeal to modal notions. Our approach here, by contrast, aims to avoid the special appeal to modal notions by giving directly a set of laws which are satisfied by a configuration individually, if and only if it is one of the allowable ones. One thus avoids the need for reference to possible but not actual configurations or objects, in the statement of the spacetime laws. We may then take this alternative set of laws as the actual geometric theory, and do away with the hypothetical entity called 'space'. Yet at the same time there is no invocation of modality, except in the ordinary sense in which every physical theory constrains what is possible. So that a relationalist is not forced to utilize a modal language (though Leibniz certainly does.). (shrink)

According to one tradition, uttering an indicative conditional involves performing a special sort of speech act: a conditional assertion. We introduce a formal framework that models this speech act. Using this framework, we show that any theory of conditional assertion validates several inferences in the logic of conditionals, including the False Antecedent inference. Next, we determine the space of truth-conditional semantics for conditionals consistent with conditional assertion. The truth value of any such conditional is settled whenever the antecedent is (...) false, and whenever the antecedent is true and the consequent is false. Then, we consider the space of dynamic meanings consistent with the theory of conditional assertion. We develop a new family of dynamic conditional-assertion operators that combine a traditional test operator with an update operation. (shrink)

It is accepted that certain mereological concepts and phenomenological conceptualisations presented in Carl Stumpf’s Über den psychologischen Ursprung der Raumvorstellung and Tonpsychologie played an important role in the development of the Husserlian formal ontology. In the third Logical Investigation, which displays the formal relations between part and whole and among parts that make out a whole, one of the main concepts of contemporary formal ontology and metaphysics is settled: ontological dependence or foundation (Fundierung). My main objective is (...) to display Stumpf’s concepts of partial content, independent content, spatial wholes, sound wholes, and the different kinds of connection among parts, in particular, fusion (Verschmelzung). Second, I will show how Husserl improved this background, in particular with regards to the exact nature of the theory of manifolds (Mannigfaltigkeitslehre), in discussion with Georg Cantor, the father of set theory. Third, I will focus on Ingarden’s use of formal ontology and on the different modes of being that can be justified by appealing to the concept of ontological dependence in its Ingardenian variations. If my interpretation is adequate, it should be inferred that formal ontology is the operative theory of phenomenological philosophy, and this must be acknowledged in its full significance with respect to the supposed independence of the phenomenological method since 1913. A further consequence, not developed in this essay, is that formal ontology can be mathematised. (shrink)

The idea of rejection of some sentences on the basis of others comes from Aristotle, as Jan Łukasiewicz states in his studies on Aristotle's syllogistic [1939, 1951], concerning rejection of the false syllogistic form and those on certain calculus of propositions. Short historical remarks on the origin and development of the notion of a rejected sentence, introduced into logic by Jan Łukasiewicz, are contained in the Introduction of this paper. This paper is to a considerable extent a summary of papers (...) which are not easily available, even to the Polish reader: (1) J. Słupecki, Funkcja Łukasiewicza (Łukasiewicz’s function), Zeszyty Naukowe Uniwersytetu Wrocławskiego, Seria B, nr 3 (1959), 33-40; (2) U. Wybraniec-Skardowska, Teoria zdań odrzuconych (Theory of Rejected Sentences), (doctoral dissertation under the supervision of Jerzy Słupecki, published as a monograph), Zeszyty Naukowe Wyższej Szkoły Pedagogicznej w Opolu, Studia i Monografie, Nr 22 (1969), 5-131; (3) G. Bryll, Kilka uzupełnień teorii zdań odrzuconych (Some supplements to the theory of rejcted sentences), Zeszyty Naukowe Wyższej Szkoły Pedagogicznej w Opolu, Studia i Mnografie, Nr 22 (1969), 153-154. The paper also contains a good number of results which have not been published yet. Chapter I contains results presented in the papers (1)-(3). It provides an extension of Alfred Tarski’s theory of deductive systems presented by him in the papers [1930]: Fundamentale Begriffe der Methodologie der deduktiven Wssenschaften, I and Über einige fundamentale Begriffe der Metamathematik. The enriched theory is marked with T. The most essential new concept in T is the function Cn-1, whose definition was given by Słupecki in (1) on the basis of the so-called Tarski’s general theory of deductive systems. It has the form: y e Cn-1X iff Ex e X (x e Cn {y}), where Cn is Tarski’s consequence operation. In accordance with the definition: A sentence y is rejected on the basis of the sentences of the set X iff at least one of sentences of X is a consequence of y (is deducible from y). The intuitive meaning of the rejection function Cn-1: on the basis of false sentences we can reject false sentences only (while by means of the consequence operation Cn on the basis of true sentences we can deduce true sentences only). The function Cn-1 is a generalization of the notion of rejected sentences which was introduced into logic by Łukasiewicz. The essential property of the rejection function Cn-1 is that it satisfies the axioms of general Tarski’s consequence Cn, so it is a consequence operation, called the rejection consequence. In addition, it is an additive and normal operation. In Chapter I, there are given notions analogous to those of the theory of deductive systems, but they are written down by means of the symbol ‘Cn-1’ and not ‘Cn’. There are established the properties of introduced notions and differences and analogies taking place between them and properties of respective notions of the theory T. There are also given generalizations of the notions of ‘decidable system’ and ‘consistent system’ used by Łukasiewicz. The short Chapter II contains axioms of the system T’ which is equivalent to the system T. The only difference between sets of primitive notions of these systems consists in the appearance of the function Cn-1 in the system T’ instead of the function Cn. This chapter reproduces the results given in (2), but they are partially simplified. (shrink)

_ Source: _Volume 56, Issue 3-4, pp 292 - 319 With William of Ockham and John Buridan, Walter Burley is often listed as one of the most significant logicians of the medieval period. Nevertheless, Burley’s contributions to medieval logic have received notably less attention than those of either Ockham or Buridan. To help rectify this situation, the author here provides a comprehensive examination of Burley’s account of consequences, first recounting Burley’s enumeration, organization, and division of consequences, with particular attention to (...) the shift from natural and accidental to formal and material consequence, and then locating Burley’s contribution to the theory of consequences in the context of fourteenth-century work on the subject, detailing its relation to the earliest treatises on consequences, then to Ockham and Buridan. (shrink)

Logical consequence in first-order predicate logic is defined substitutionally in set theory augmented with a primitive satisfaction predicate: an argument is defined to be logically valid if and only if there is no substitution instance with true premises and a false conclusion. Substitution instances are permitted to contain parameters. Variants of this definition of logical consequence are given: logical validity can be defined with or without identity as a logical constant, and quantifiers can be relativized in substitution instances (...) or not. It is shown that the resulting notions of logical consequence are extensionally equivalent to versions of first-order provability and model-theoretic consequence. Every model-theoretic interpretation has a substitutional counterpart, but not vice versa. In particular, in contrast to the model-theoretic account, there is a trivial intended interpretation on the substitutional account, namely, the homophonic interpretation that does not substitute anything. Applications to free logic, and theories and languages other than set theory are sketched. (shrink)

This book presents novel formalizations of three of the most important medieval logical theories: supposition, consequence and obligations. In an additional fourth part, an in-depth analysis of the concept of formalization is presented - a crucial concept in the current logical panorama, which as such receives surprisingly little attention.Although formalizations of medieval logical theories have been proposed earlier in the literature, the formalizations presented here are all based on innovative vantage points: supposition theories as algorithmic hermeneutics, (...) theories of consequence analyzed with tools borrowed from model-theory and two-dimensional semantics, and obligations as logical games. For this reason, this is perhaps the first time that these medieval logical theories are made fully accessible to the modern philosopher and logician who wishes to obtain a better grasp of them, but who has always been held back by the lack of appropriate ‘translations' into modern terms.Moreover, the book offers a reflection on the very nature of logic, a reflection that is prompted by the comparisons between medieval and modern logic, their similarities and dissimilarities. It is thus a contribution not only to the history of logic, but also to the philosophy of logic, the philosophy of language and semantics.The analysis of medieval logic is also relevant for the modern philosopher and logician in that, being the unifying methodology used across all disciplines at that time, logic really provided unity to science. It thus presents a unified model of scientific investigation, where logic plays the aggregating role. (shrink)

The aim of this paper is to trace in Leibniz’s drafts the sketched outline of a conceptual framework he organized around the key concept of ‘requisite’. We are faced with the project of a semi-formal theory of conditions, whose logical skeleton can have a lot of different interpretations. In particular, it is well suited to capture some crucial relations of ontological dependence. Firstly the area of ‘mediate requisites’ is explored - where causal and temporal relations are dealt with on (...) the basis of a general theory of ‘consequence’.Then the study of ‘immediate requisites’ is taken into account - a true sample of mereological inquiry, where Leibniz strives for a unitary treatment of part-whole relation, conceptual inclusion and inherence. Far from simply conflating these relations one with another and with causality, therefore, Leibniz tried to spell them out, while at the same time understanding them within a single conceptual framework. (shrink)

The aim of this paper is to trace in Leibniz’s drafts the sketched outline of a conceptual framework he organized around the key concept of ‘requisite’. We are faced with the project of a semi-formal theory of conditions, whose logical skeleton can have a lot of different interpretations. In particular, it is well suited to capture some crucial relations of ontological dependence. Firstly the area of ‘mediate requisites’ is explored - where causal and temporal relations are dealt with on (...) the basis of a general theory of ‘consequence’.Then the study of ‘immediate requisites’ is taken into account - a true sample of mereological inquiry, where Leibniz strives for a unitary treatment of part-whole relation, conceptual inclusion and inherence. Far from simply conflating these relations one with another and with causality, therefore, Leibniz tried to spell them out, while at the same time understanding them within a single conceptual framework. (shrink)

Two of Aristotle’s major legacies, namely, the theory of scientific syllogism and teleology seem to conflict on several planes. Indeed, an array of formal limitations prevents him from formalizing teleological explanations into scientific syllogisms, which are entirely absent from his works. To achieve this, Aristotle resorts to a different tool, the logic of ‘consequence’. This governs both the teleological relation between an end and a means that underlies necessity ‘from a hypothesis’—which is the necessity proper to living things—and (...) a different form of syllogisms, namely, syllogisms ‘from a hypothesis’. His guidelines in the first chapter of his Parts of Animals on the proper form of demonstration to be adopted in biology should be read as laying out the rules of inference for translating teleological explanations into syllogisms ‘from a hypothesis’. (shrink)

The current paper studies the formal properties of the Global Reflection Principle, to wit the assertion “All theorems of$\mathrm {Th}$are true,” where$\mathrm {Th}$is a theory in the language of arithmetic and the truth predicate satisfies the usual Tarskian inductive conditions for formulae in the language of arithmetic. We fix the gap in Kotlarski’s proof from [15], showing that the Global Reflection Principle for Peano Arithmetic is provable in the theory of compositional truth with bounded induction only ($\mathrm {CT}_0$). Furthermore, (...) we extend the above result showing that$\Sigma _1$-uniform reflection over a theory of uniform Tarski biconditionals ($\mathrm {UTB}^-$) is provable in$\mathrm {CT}_0$, thus answering the question of Beklemishev and Pakhomov [2]. Finally, we introduce the notion of a prolongable satisfaction class and use it to study the structure of models of$\mathrm {CT}_0$. In particular, we provide a new model-theoretical characterization of theories of finite iterations of uniform reflection and present a new proof characterizing the arithmetical consequences of$\mathrm {CT}_0$. (shrink)

Without directly addressing the Demarcation Problem for logic—the problem of distinguishing logical vocabulary from others—we focus on distinctive aspects of logical vocabulary in pursuit of a second goal in the philosophy of logic, namely, proposing criteria for the justification of logical rules. Our preferred approach has three components. Two of these are effectively Belnap’s, but with a twist. We agree with Belnap’s response to Prior’s challenge to inferentialist characterisations of the meanings of logical constants. Belnap argued that for a logical (...) constant to exist, its rules must be conservative over a previously given consequence relation and guarantee the uniqueness of the constant. The twist is that we require logical vocabulary to be provably conservative, not over a previously given formal consequence relation, but over a previously given meaningful vocabulary of a language. Uniqueness is also a feature defined in terms of provability: if two syntactically distinguished expressions are governed by the same rules, then formulas with them as main operators are interderivable. Belnap’s criteria are not only those for the existence of a logical constant, but more: they are what distinguishes logical vocabulary from all other expressions. It is the defining mark of a logical constant that it is provably conservative over the fragment of the language which excludes it and that its rules guarantee its uniqueness. The third component is the topic neutrality of logic. The provable conservativeness of logic over a previously given vocabulary of a language is motivated, in part, by appeal to molecularism in the theory of meaning. Molecularity is a feature endorsed by the theory of meaning as a whole, so it does not distinguish logical constants from other expressions. The same is true for conservativeness. We argue that molecularity, and hence conservativeness, are implicit presuppositions of speakers’ use of language: the addition of new vocabulary to a language is presupposed to be conservative. But this presupposition is one that we should be able reflectively to endorse (such as when attempting a rational reconstruction of the use of the vocabulary). Thus, where conservativeness is found to fail, this defect should be remedied and the use of the vocabulary corrected (as in classical negation) or excised altogether (as in pejoratives). We go on to characterise a notion of topic neutrality, which we argue applies to logical vocabulary. We then note that reflective endorsement of the conservativeness of a topic neutral vocabulary requires a proof that the vocabulary is conservative relative to any base vocabulary. Thus we require that logical vocabulary be demonstrably conservative. Allying this requirement, distinctive of logic, to a general consideration about the commitments of assertion yields a mode of justification for logical constants akin to some conceptions of Harmony, i.e., to the idea that the consequences of assertion of a logical complex need to be warranted by the grounds and ought to be the strongest consequences warranted by the grounds. Intuitionistic logic acquires a somewhat familiar justification but emanating from a new motivation. (shrink)

From Hobbes to Weber, discussions of power increasingly made a modern concept of "will" their pivotal category. Although sometimes tinged with other concerns, this tendency continues today. Focusing through the lens of the "will" displays an image of power that reasserts untenable conceptions of the person and obscures the fact that power is a relation and not a property, a faculty, or a thing-in-itself. The dissertation tackles this fundamental problem. ;To begin, "dependence" is given the centering position. "Dependence," unlike "will," (...) is a necessarily relational concept. A distinction is introduced between dependence-from-things and dependence-from-persons. The interrelation between these is considered in terms of non-formal anthropological conceptions of reciprocity. This complex reciprocity is contrasted to reciprocity understood as "equality." ;Paradoxically, the theoretical move to contextually determined reciprocity forces reconsideration of the "will," for the background normative institutional patterns of reciprocity in liberal societies are delineated in terms of the "will." This is a virtuous, not a vicious, circle. Once the "will" has been forced from its central position in the theory of power, a critical perspective is gained by viewing "will" through "dependence." ;An analysis of the ways people rationalize or appropriate to their own advantage the unintended consequences of action illuminates the link between "will" and "dependence." The emergence of dependence itself provides a general example of an "unintended consequence of action." People seeking to gain advantage assert their independence from the unintended, even while appropriating the "unintended consequences of action." Cultural patterns for denying dependence play an important part in asserting advantage. ;Disruptions of practical relations of reciprocity cannot be determined a priori; rather, they follow from speech and action. These disruptions lead to contention. Two notoriously vague notions, public and private, have long been terms for playing out such contentions. Theorists often assume that public/private indicates two distinct "spheres" . By contrast, the present theory provides an approach to the analysis of the transformation of private into public. This is a necessary condition for the emergence and control of power. (shrink)

The aim of this dissertation is to offer and defend a correspondence theory of truth. I begin by critically examining the coherence, pragmatic, simple, redundancy, disquotational, minimal, and prosentential theories of truth. Special attention is paid to several versions of disquotationalism, whose plausibility has led to its fairly constant support since the pioneering work of Alfred Tarski, through that by W. V. Quine, and recently in the work of Paul Horwich. I argue that none of these theories meets (...) the correspondence intuition---that a true sentence or proposition in some way corresponds to reality---despite the explicit claims by each to capture this intuition. I distinguish six versions of the correspondence theory, and defend two against traditional objections, standardly taken as decisive against them, and show, plainly, that these two theories capture the correspondence intuition. Due to the importance of meeting this intuition, only these two theories stands a chance of being a satisfactory theory of truth. I argue that the version of the correspondence theory incorporating a simple semantic representation relation is preferable to its rival, for which the representation relation is complex. I present and argue for a novel version of this correspondence theory according to which truth is a correspondence property sensitive to semantic context. One consequence of this context-sensitivity is that an ungrounded sentence does not express a proposition. In addition to accounting for the similarity between the Liar and Truth-Teller sentences, this theory of truth is immune to the Liar Paradox, including empirical versions. It is argued that the Liar Paradox is devastating to all of the other theories above, and even formal theories of truth designed to solve it, such as the revision and vagueness theories. Customized versions of the Liar Paradox besetting this theory are handled by its context-sensitivity, and by enforcing the distinction between truth and truth value. This same pair of considerations also yields solutions to Lob's Paradox and Grelling's Paradox. Arguments similar to those given to defend this correspondence theory show that with one minor alteration, Kripke's fixed point theory may be used to model this correspondence notion of truth. (shrink)

Frege's theory of real numbers has undeservedly received almost no attention, in part because what we have is only a fragment. Yet his theory is interesting for the light it throws on logicism, and it is quite different from standard modern approaches. Frege polemicizes vigorously against his contemporaries, sketches the main features of his own radical alternative, and begins the formal development. This paper summarizes and expounds what he has to say, and goes on to reconstruct the most important (...) steps which he is likely to have subsequently taken. The various difficulties facing his theory in this reconstruction are outlined, and some surprising consequences drawn about the nature of his logicism. (shrink)

Three leading philosopher-logicians present a clear and concise overview of formal theories of truth, explaining key logical techniques. Truth is as central topic in philosophy: formal theories study the connections between truth and logic, including the intriguing challenges presented by paradoxes like the Liar.

Husserl’s notion of definiteness, i.e., completeness is crucial to understanding Husserl’s view of logic, and consequently several related philosophical views, such as his argument against psychologism, his notion of ideality, and his view of formal ontology. Initially Husserl developed the notion of definiteness to clarify Hermann Hankel’s ‘principle of permanence’. One of the first attempts at formulating definiteness can be found in the Philosophy of Arithmetic, where definiteness serves the purpose of the modern notion of ‘soundness’ and leads Husserl (...) to a ‘computational’ view of logic. Inspired by Gauss and Grassmann Husserl then undertakes a further investigation of theories of manifolds. When Husserl subsequently renounces psychologism and changes his view of logic, his idea of definiteness also develops. The notion of definiteness is discussed most extensively in the pair of lectures Husserl gave in front of the mathematical society in Göttingen (1901). A detailed analysis of the lectures, together with an elaboration of Husserl’s lectures on logic beginning in 1895, shows that Husserl meant by definiteness what is today called ‘categoricity’. In so doing Husserl was not doing anything particularly original; since Dedekind’s ‘Was sind und sollen die Zahlen’ (1888) the notion was ‘in the air’. It also characterizes Hilbert’s (1900) notion of completeness. In the end, Husserl’s view of definiteness is discussed in light of Gödel’s (1931) incompleteness results. (shrink)

Formal theories, as in logic and mathematics, are sets of sentences closed under logical consequence. Philosophical theories, like scientific theories, are often far less formal. There are many axiomatic theories of the truth predicate for certain formal languages; on analogy with these, some philosophers (most notably Paul Horwich) have proposed axiomatic theories of the property of truth. Though in many ways similar to logical theories, axiomatic theories of truth must (...) be different in several nontrivial ways. I explore what an axiomatic theory of truth would look like. Because Horwich’s is the most prominent, I examine his theory and argue that it fails as a theory of truth. Such a theory is adequate if, given a suitable base theory, every fact about truth is a consequence of the axioms of the theory. I show, using an argument analogous to Gödel’s incompleteness proofs, that no axiomatic theory of truth could ever be adequate. I also argue that a certain class of generalizations cannot be consequences of the theory. (shrink)

In various publications over the past years, Floridi has developed a theory of semantic information as well-formed, meaningful, and truthful data. This theory is more or less orthogonal to the standard entropy-based notions of information known from physics, information theory, and computer science that all define the amount of information in a certain system as a scalar value without any direct semantic implication. In this context the question rises what the exact relation between these various conceptions of information is and (...) whether there is a real need to enrich these mathematically more or less rigid definitions with a less formal notion of semantic information. I investigate various philosophical aspects of the more formal definitions of information in the light of Floridi’s theory. The position I defend is that the formal treatment of the notion of information as a general theory of entropy is one of the fundamental achievements of modern science that in itself is a rich source for new philosophical reflection. This makes information theory a competitor of classical epistemology rather than a servant. In this light Floridi’s philosophy of information is more a reprise of classical epistemology that only pays lip service to information theory but fails to address the important central questions of philosophy of information. Specifically, I will defend the view that notions that are associated with truth, knowledge, and meaning all can adequately be reconstructed in the context of modern information theory and that consequently there is no need to introduce a concept of semantic information. (shrink)

n various publications over the past years, Floridi has developed a theory of semantic information as well-formed, meaningful, and truthful data. This theory is more or less orthogonal to the standard entropy-based notions of information known from physics, information theory, and computer science that all define the amount of information in a certain system as a scalar value without any direct semantic implication. In this context the question rises what the exact relation between these various conceptions of information is and (...) whether there is a real need to enrich these mathematically more or less rigid definitions with a less formal notion of semantic information. I investigate various philosophical aspects of the more formal definitions of information in the light of Floridi’s theory. The position I defend is that the formal treatment of the notion of information as a general theory of entropy is one of the fundamental achievements of modern science that in itself is a rich source for new philosophical reflection. This makes information theory a competitor of classical epistemology rather than a servant. In this light Floridi’s philosophy of information is more a reprise of classical epistemology that only pays lip service to information theory but fails to address the important central questions of philosophy of information. Specifically, I will defend the view that notions that are associated with truth, knowledge, and meaning all can adequately be reconstructed in the context of modern information theory and that consequently there is no need to introduce a concept of semantic information. (shrink)

Disease transmission is a fruitful domain in which to examine how scientific and folk theories interrelate, given laypeople’s access to multiple sources of information to explain events of personal significance. The current paper reports an in-depth survey of U.S. adults’ causal reasoning about two viral illnesses: a novel, deadly disease that has massively disrupted everyone’s lives, and a familiar, innocuous disease that has essentially no serious consequences. Participants received a series of closed-ended and open-ended questions probing their reasoning about (...) disease transmission, with a focus on causal mechanisms underlying disease contraction, transmission, treatment, and prevention; non-visible biological processes; and ontological frameworks regarding what kinds of entities viruses are. We also assessed participants’ attitudes, such as their trust in scientific experts and willingness to be vaccinated. Results indicated complexity in people’s reasoning, consistent with the co-existence of multiple explanatory frameworks. An understanding of viral transmission and viral replication existed alongside folk theories, placeholder beliefs, and lack of differentiation between viral and non-viral disease. For example, roughly 40% of participants who explained illness in terms of the transmission of viruses also endorsed a non-viral folk theory, such as exposure to cold weather or special foods as curative. Additionally, participants made use of competing modes of construal when explaining how viruses operate, such as framing the immune system response as cells trying to fight off the virus. Indeed, participants who displayed greater knowledge about viral transmission were significantly more likely to anthropomorphize bodily processes. Although comparisons of COVID-19 and the common cold revealed relatively few differences, the latter, more familiar disease elicited consistently lower levels of accuracy and greater reliance on folk theories. Moreover, for COVID-19 in particular, accuracy positively correlated with attitudes, self-protective behaviors, and willingness to be vaccinated. For both diseases, self-assessed knowledge about the disease negatively predicted accuracy. The results are discussed in relation to challenges for formal models of explanatory reasoning. (shrink)

In recent years we may observe increasing interest in the development of social innovation both regarding theory as well as the practice of responding to social problems and challenges. One of the crucial challenges at the beginning of the 21st century is population ageing. Various new and innovative initiatives, programs, schemes, and projects to respond to negative consequences of this demographic process are emerging around the world. However, social theories related to ageing are still insufficiently combined with these new (...) practices, social movements, organisational models, and institutions. Many scholars are still using notions and tools from classical theories of social gerontology or the sociology of ageing such as disengagement theory, activity theory, and successful and productive ageing. Such theories do not sufficiently explain ageing in the context of, for example, a broad use of the information and communications technologies including robotics and automation, new healthcare and long-term care models, advancements in the development and governance of age-friendly environments, and public engagement of older adults into co-production of services delivered by public, private, non-governmental as well as non-formal entities. (shrink)

Giulio Tononi's integrated information theory (IIT) proposes explaining consciousness by directly identifying it with integrated information. We examine the construct validity of IIT's measure of consciousness,phi(Φ), by analyzing its formal properties, its relation to key aspects of consciousness, and its co-variation with relevant empirical circumstances. Our analysis shows that IIT's identification of consciousness with the causal efficacy with which differentiated networks accomplish global information transfer (which is what Φ in fact measures) is mistaken. This misidentification has the consequence (...) of requiring the attribution of consciousness to a range of natural systems and artifacts that include, but are not limited to, large-scale electrical power grids, gene-regulation networks, some electronic circuit boards, and social networks. Instead of treating this consequence of the theory as a disconfirmation, IIT embraces it. By regarding these systems as bearers of consciousnessex hypothesi, IIT is led toward the orbit of panpsychist ideation. This departure from science as we know it can be avoided by recognizing the functional misattribution at the heart of IIT's identity claim. We show, for example, what function is actually performed, at least in the human case, by the cortical combination of differentiation with integration that IIT identifies with consciousness. Finally, we examine what lessons may be drawn from IIT's failure to provide a credible account of consciousness for progress in the very active field of research concerned with exploring the phenomenon from formal and neural points of view. (shrink)

We prove that a variant of Robinson arithmetic $\mathsf{Q}$ with nontotal operations is interpretable in the theory of concatenation $\mathsf{TC}$ introduced by A. Grzegorczyk. Since $\mathsf{Q}$ is known to be interpretable in that nontotal variant, our result gives a positive answer to the problem whether $\mathsf{Q}$ is interpretable in $\mathsf{TC}$. An immediate consequence is essential undecidability of $\mathsf{TC}$.

The resemblance of the theory of formal consequence first offered by the fourteenth-century logician John Buridan to that later offered by Alfred Tarski has long been remarked upon. But it has not yet been subjected to sustained analysis. In this paper, I provide just such an analysis. I begin by reviewing today’s classical understanding of formal consequence, then highlighting its differences from Tarski’s 1936 account. Following this, I introduce Buridan’s account, detailing its philosophical underpinnings, then its (...) content. This then allows us to separate those aspects of Tarski’s account representing genuine historical advances, unavailable to Buridan, from others merely differing from—and occasionally explicitly rejected by—Buridan’s account. (shrink)

An analysis of the role of language in basic and applied science from the semantics of science and the theory of reference requires several steps. First, to specify the field of analysis in the light of several factors: the semantic problems of science; the reference in its triple dimension of relation between language and reality, of referent and of transmission in science; and the link between meaning and reference in science.Second, to consider the central approach to the semantics of science, (...) which forks into two main directions: the semantic line and the pragmatic path. De facto, they lead to different interpretations of the role of language in basic science and in applied science. The semantic line focuses on the content expressed through terms, statements and theories, which has been influential in important philosophical trends and still is prominent in some versions of scientific realism. Meanwhile, the pragmatic path emphasizes the meaning as use, which has influenced philosophers of science of diverse tendencies, such as S. Toulmin, Th. Kuhn, American pragmatists and supporters of the methodological pluralism.Third, to make explicit the leading conceptions regarding the theory of reference, both for the formal sciences and for the empirical sciences. There are a number of options, four of which are analyzed here. The view associated with the semantic role and the semantic value, which connects semantic, epistemological and ontological realms in basic science and in applied science. The causal theory of reference, which has shifted towards internal realism. Anti-realistic semantics, where truth is replaced by proof and the reference is the use made by someone of a term in a context. Kuhn’s approach in his linguistic period, where he rethinks the scientific revolutions taking into account the causal theory of reference.Fourth, to be aware of the consequences of these analyses for basic science and applied science in two ways: on the one hand, for the semantic differences between them, and, on the other, for the perspective of reference. (shrink)

This volume is a collection of original contributions about the core knowledge in fundamental domains. It includes work on naive physics, such as formal specifications of intuitive theories of spatial relations, time causality, substance and physical objects, and on naive psychology.

Inspired by impossibility theorems of social choice theory, many democratic theorists have argued that aggregative forms of democracy cannot lend full democratic justification for the collective decisions reached. Hence, democratic theorists have turned their attention to deliberative democracy, according to which “outcomes are democratically legitimate if and only if they could be the object of a free and reasoned agreement among equals” (Cohen 1997a, 73). However, relatively little work has been done to offer a formal theory of democratic deliberation. (...) This article helps fill that gap by offering a formal theory of three different modes of democratic deliberation: myopic discussion, constructive discussion, and debate. We show that myopic discussion suffers from indeterminacy of long run outcomes, while constructive discussion and debate are conclusive. Finally, unlike the other two modes of deliberation, debate is path independent and converges to a unique compromise position, irrespective of the initial status quo. (shrink)

The knowledge representation and reasoning of both humans and artificial systems often involves conditionals. A conditional connects a consequence which holds given a precondition. It can be easily recognized in natural languages with certain key words, like “if” in English. A vast amount of literature in both fields, both artificial intelligence and psychology, deals with the questions of how such conditionals can be best represented and how these conditionals can model human reasoning. On the other hand, findings in the (...) psychology of reasoning, such as those in the Suppression Task, have led to a paradigm shift from the monotonicity assumptions in human inferences towards nonmonotonic reasoning. Nonmonotonic reasoning is sensitive for information change, that is, inferences are drawn cautiously such that retraction of previous information is not required with the addition of new information. While many formalisms of nonmonotonic reasoning have been proposed in the field of Artificial Intelligence, their capability to model properties of human reasoning has not yet been extensively investigated. In this paper, we analyzed systematically from both a formal and an empirical perspective the power of formal nonmonotonic systems to model possible explicit defeaters, as in the Suppression Task, and more implicit conditional rules that trigger nonmonotonic reasoning by the keywords in such rules. The results indicated that the classical evaluation for the correctness of inferences has to be extended in the three major aspects regarding the inference system, the knowledge base, and possible assumed exceptions for the rule. (shrink)

In this paper, I introduce an intrinsic account of the quantum state. This account contains three desirable features that the standard platonistic account lacks: (1) it does not refer to any abstract mathematical objects such as complex numbers, (2) it is independent of the usual arbitrary conventions in the wave function representation, and (3) it explains why the quantum state has its amplitude and phase degrees of freedom. -/- Consequently, this account extends Hartry Field’s program outlined in Science Without Numbers (...) (1980), responds to David Malament’s long-standing impossibility conjecture (1982), and establishes an important first step towards a genuinely intrinsic and nominalistic account of quantum mechanics. I will also compare the present account to Mark Balaguer’s (1996) nominalization of quantum mechanics and discuss how it might bear on the debate about “wave function realism.” In closing, I will suggest some possible ways to extend this account to accommodate spinorial degrees of freedom and a variable number of particles (e.g. for particle creation and annihilation). -/- Along the way, I axiomatize the quantum phase structure as what I shall call a “periodic difference structure” and prove a representation theorem as well as a uniqueness theorem. These formal results could prove fruitful for further investigation into the metaphysics of phase and theoretical structure. -/- (For a more recent version of this paper, please see "The Intrinsic Structure of Quantum Mechanics" available on PhilPapers.). (shrink)

The aim of this paper is to introduce a formal system STW of self-referential truth, which extends the classical first-order theory of pure combinators with a truth predicate and certain approximation axioms. STW naturally embodies the mechanisms of general predicate application/abstraction on a par with function application/abstraction; in addition, it allows non-trivial constructions, inspired by generalized recursion theory. As a consequence, STW provides a smooth inner model for Myhill's systems with levels of implication.

In The Dynamics of Meaning , Gennaro Chierchia tackles central issues in dynamic semantics and extends the general framework. Chapter 1 introduces the notion of dynamic semantics and discusses in detail the phenomena that have been used to motivate it, such as "donkey" sentences and adverbs of quantification. The second chapter explores in greater depth the interpretation of indefinites and issues related to presuppositions of uniqueness and the "E-type strategy." In Chapter 3, Chierchia extends the dynamic approach to the domain (...) of syntactic theory, considering a range of empirical problems that includes backwards anaphora, reconstruction effects, and weak crossover. The final chapter develops the formal system of dynamic semantics to deal with central issues of definites and presupposition. Chierchia shows that an approach based on a principled enrichment of the mechanisms dealing with meaning is to be preferred on empirical grounds over approaches that depend on an enrichment of the syntactic apparatus. Dynamics of Meaning illustrates how seemingly abstract stances on the nature of meaning can have significant and far-reaching linguistic consequences, leading to the detection of new facts and influencing our understanding of the syntax/semantics/pragmatics interface. (shrink)

In this article I want to investigate the concept of reliability employed in process reliabilist theories of justification and knowledge. What is essential to process reliabilist theories of justification is that there is a sense of the word ”justifi- cation” (a strong or an objective concept of justification) such that a belief is justified only if it is produced by a reliable process. Different versions of reliabilism may add different sufficient conditions to this to get a complete definition (...) of justification or knowledge, and disagree about whether there are other interesting concepts of justification, but all agree that reliability (global or local) is necessary for both justification (in some sense) and knowlede. This of course, raises the question of what reliability is. Reliabilist theories of justification cannot be said to have a very secure foundation if they do not address this question. However, reliabilists have not done very much to answer it as has of course been often pointed out by their opponents. The most famous reliabilist, Alvin Goldman, has in one place [6, page 63] suggested that the concept of reliability he uses should be understood so that reliability is a propensity; however, he does not formulate this idea very exactly nor develop it very far. However, I think that his suggestion is correct, and important; in this article I will try to clarify it by linking it to formal analyses of propensities that are found in the literature (as well as the whole discussion about interpretations of probability) and explore its consequences. (shrink)

We present an approach to combining three areas of research which we claim are all based on information theory: knowledge representation in Artificial Intelligence and Cognitive Science using prototypes, plans, or schemata; formal semantics in natural language, especially the semantics of the `if-then' conditional construct; and the logic of subjunctive conditionals first developed using a possible worlds semantics by Stalnaker and Lewis. The basic premise of the paper is that both schema-based inference and the semantics of conditionals are based (...) on Dretske's notion of information flow and Barwise and Perry's notion of a constraint in situation semantics. That is, the connection between antecedent and consequent of a conditional `if were the case then would be the case' is an informational relation holding with respect to a pragmatically determined utterance situation. The bridge between AI and conditional logic is that a prototype or planning schema represents a situation type, and the background assumptions underlying the application of a schema in a situation correspond to channel conditions on the flow of information. Adapting the work of Stalnaker and Lewis, the semantics of conditionals is modeled by a refinement ordering on situations: a conditional `if then ' holds with respect to a situation if all the minimal refinements of the situation that support also support . We present new logics of situations, information flow, and subjunctive conditionals based on three-valued partial logic that formalizes our approach, and conclude with a discussion of the resulting theory of conditionals, including the "paradoxes" of conditional implication, the difference between truth conditions and assertability conditions for subjunctive conditionals, and the relationship between subjunctive and indicative conditionals. (shrink)

One of the tasks of ontology in information science is to support the classification of entities according to their kinds and qualities. We hold that to realize this task as far as entities such as material objects are concerned we need to distinguish four kinds of entities: substance particulars, quality particulars, substance universals, and quality universals. These form, so to speak, an ontological square. We present a formal theory of classification based on this idea, including both a semantics for (...) the theory and a provably sound axiomatization. (shrink)

One of the traditional pragmatic approaches to vagueness suggests that there needs to be a significant gap between individuals or objects that can be described using a vague adjective like tall and those that cannot. In contrast, intuitively, an explicit comparative like taller does not require fulfillment of the gap requirement. Our starting point for this paper is the consideration that people cannot make precise measures under time pressure and their ability to discriminate approximate heights obeys Weber’s law. We formulate (...) and experimentally test three hypotheses relating to the difference between positive and comparative forms of the vague adjectives, gap requirement, and Weber’s law. In two experiments, participants judged appropriateness of usage of positive and comparative forms of vague adjectives in a sentence-picture verification task. Consequently, we review formal analysis of vagueness using weak orders and semi-orders and suggest adjustments based on the experimental results and properties of Weber’s law. (shrink)

Philosophers of science as divergent as the inductivist Carnap and the deductivist Popper share the notion that the (logical) content of a proposition is given by its consequence class. I claim that this notion of content is (a) unintuitive and (b) inappropriate for many of the formal needs of philosophers of science. The basic problem is that given this notion of content, for any arbitrary p and q, [(p ∨ q)] will count as part of the content of (...) both p and q. In other words, any arbitrary p and q share some common content. This notion of content has disastrous effects on, for instance, Carnap's attempts to explicate the notion of confirmation in terms of probabilistic favorable relevance, and Popper's attempts to define verisimilitude. After briefly reviewing some of the problems of the traditional notion of content I present an alternative notion of (basic) content which (a) better fits our intuitions about content and (b) better serves the formal needs of philosophers of science. (shrink)

In this article we strive to provide a detailed and principled analysis of the role of beliefs in goal processing—that is, the cognitive transition that leads from a mere desire to a proper intention. The resulting model of belief-based goal processing has also relevant consequences for the analysis of intentions, and constitutes the necessary core of a constructive theory of intentions, i.e. a framework that not only analyzes what an intention is, but also explains how it becomes what it is. (...) We discuss similarities and differences between our approach and other standard accounts of intention, in particular Bratman’s planning theory. The aim here is to question and refine the conceptual foundations of many theories of intentional action: as a consequence, although our analysis is not formal in itself, it is ultimately meant to have deep consequences for formal models of intentional agency. (shrink)

The author presents a relatively formal theory of the rule of law which includes three basic components: conceptual, institutional and axiological. He then emphasizes the differences between a formal and a substantive theory of the rule of law and highlights the advantages and limits of the former. Finally, the author indicates the importance of this type of theory, namely the values it implies such as predictability, justified reliance, autonomous choice, minimization of disputes and legitimacy.**.

I consider the geometrical structure of the apparent visual field. Although the optics of vision is well understood, the nature of visual awareness remains largely in the dark. A famous attempt at a formal description of the apparent visual field was by Helmholtz, in the late nineteenth century. It purportedly explains the phenomenon of the subjective curvatures often reported when viewing objectively straight lines of great extent. I consider the general problem, and suggest an alternative formal account. On (...) phenomenological grounds the very existence of a coherent geometry may be doubted. Yet, although seemingly an academic question, the issue has very real consequences. The two models I consider here may approximately apply to certain visual modes. The nature of such visual modes is discussed. (shrink)

The doctrine of double effect is an ethical principle that can account for human judgment in moral dilemmas: situations in which all available options have large good and bad consequences. We have previously formalized \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {{DDE}}$$\end{document} in a computational logic that can be implemented in robots. \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {{DDE}}$$\end{document}, as an ethical principle for robots, is attractive for a number of reasons: Empirical studies (...) have found that \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {{DDE}}$$\end{document} is used by untrained humans; many legal systems use \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {{DDE}}$$\end{document}; and finally, the doctrine is a hybrid of the two major opposing families of ethical theories. In spite of all its attractive features, we have found that \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {{DDE}}$$\end{document} does not fully account for human behavior in many ethically challenging situations. Specifically, standard \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {{DDE}}$$\end{document} fails in situations wherein humans have the option of self-sacrifice. Accordingly, we present an enhancement of our \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {{DDE}}$$\end{document}-formalism to handle self-sacrifice; we end by looking ahead to future work. (shrink)