Wittgenstein responds in his Notes on Logic to a discussion of Russell's Principles of Mathematics concerning assertion. Russell writes: "It is plain that, if I may be allowed to use the word assertion in a non-psychological sense, the proposition "p implies q" asserts an implication, though it does not assert p or q. The p and the q which enter into this proposition are not strictly the same as the p or the q which are separate propositions." (PoM p35) Wittgenstein (...) replies: "Assertion is merely psychological. In not-p, p is exactly the same as if it stands alone; this point is absolutely fundamental." (NB p95) Wittgenstein's response is intriguing, not least because of the centrality to his Tractatus of the idea that a proposition says something. This paper will examine that idea, distinguishing it from 'merely psychological' assertion, and explore in this context how we should understand the occurrence of a Tractarian proposition within another. (shrink)

Bertrand Russell was neither the first nor the last philosopher to engage in serious theorizing about propositions. But his work between 1903, when he published The Principles of Mathematics, and 1919, when his final lectures on logical atomism were published, remains among the most important on the subject. And its importance is not merely historical. Russell’s rapidly evolving treatment of propositions during this period was driven by his engagement with – and discovery of – puzzles that either continue to shape (...) contemporary theorizing about propositions, or ought to do so. Russell’s creative responses to these puzzles also laid the foundation for many later accounts (most obviously, contemporary ‘Russellian’ accounts of propositions). In this entry we provide an opinionated overview of Russell’s influential treatment of propositions, with a focus on the evolution of his views from 1903 to 1919. A growing secondary literature is dedicated to Russell’s changing views during this period, and their often complex or opaque motivations. We do not intervene overmuch in this ongoing scholarly discussion. Instead, our aim is to trace some of the central motivations for Russell’s evolving views, and highlight the extent to which these motivations remain relevant to contemporary theorizing about propositions. (shrink)

[Edited from Conclusion section:] We have looked at various challenging issues to do with getting connectionism to cope with high-level cognitive activities such a reasoning and natural language understanding. The issues are to do with various facets of generalization that are not commonly noted. We have been concerned in particular with the special forms these issues take in the arena of propositional attitude processing. The main problems we have looked at are: (1) The need to construct explicit representations of (...) generalizations, not just generalize correctly to individual cases; (2) The need to be able to match two or more complex short-term information structures, to enable rapid generalization from recent examples rather than from long-term memories; (3) The need to represent and reason with anomalous combinations of concepts; (4) The need to perform embedded reasoning. This presents special problems for systems using non-concatenative representations (as in mainstream connectionist approaches). We also touched on vague quantification in attitude report complements. Neither this topic nor that of analogies between short-term structures (point 2) has been adequately addressed in the symbolic framework, let alone in connectionism. -/- The opportunities and problems covered are put forward as things worth being optimistic about or pessimistic about, respectively. They are not put forward as decisive arguments for or against connectionism. The hope is that this chapter contributes to a greater understanding of the connectionist/symbolist gap by presenting some unusual issues and by throwing new light on some well known ones. (shrink)

The problem of approximating a propositional calculus is to find many-valued logics which are sound for the calculus (i.e., all theorems of the calculus are tautologies) with as few tautologies as possible. This has potential applications for representing (computationally complex) logics used in AI by (computationally easy) many-valued logics. It is investigated how far this method can be carried using (1) one or (2) an infinite sequence of many-valued logics. It is shown that the optimal candidate matrices for (1) (...) can be computed from the calculus. (shrink)

The folk Psychology frames propositional attitudes as fundamental theoretical entities for the construction of a model designed to predict the behavior of a subject. A trivial, such as grasping a pen and writing reveals - something complex - about the behavior. When I take a pen and start writing I do, trivially, because I believe that a certain object in front of me is a pen and who performs a specific function that is, in fact, that of writing. When (...) I believe that the object that stands before me is a pen, I am in relation to "believe" with the propositional content: that in front of me is a pen. Philosophers of the proposition, from Frege onwards, have dedicated their studies to the analysis of what kinds of entities are the propositional attitudes. Jerry Fodor says that now, the proper prediction of the psychology of common sense, can not be questioned and that the propositional attitudes represent the most effective way to describe our behavior. What Fodor says, however, is that propositional attitudes function, but not how they work. Most philosophers interested in the issue, we are dedicated to the search for a theory that can account consistently both a semantics for propositional attitudes, both of these entities that seem to cause the behavior of a rational subject. There are two main paradigms in the theory of the proposition that contributed to the discussion of the propositional attitudes. One is the one that begins with Gottlob Frege, the other with Bertrand Russell. Defenders of Frege argue that the paradigm scrub objects and properties can not be constituents of the propositional content which have a purely conceptual. In other words, the philosophers belonging to the paradigm of Frege, but not all, mean that you can test in a rigorous way the truth conditions of propositional attitudes. Who defends the russellian’s paradigm argues that the propositional content are made by the objects and properties on which propositional attitudes relate. The purpose of this article is not to rebuild - in detail - both paradigms, nor to reconstruct one but, in a sense, my work will be a completely partial objective is to demonstrate how the paradigm is more profitable russell not only to make a coherent semantic theory for propositional attitudes2 but also to predict the behavior of a rational subject thing, completely innovative, given the repeated objections in contemporary literature3. At the end of this paper will be drafted a proposal to build a consistent model to predict the behavior,of a rational agent, based on a referential theory of propositional attitudes. (shrink)

Propositional logics in general, considered as a set of sentences, can be undecidable even if they have “nice” representations, e.g., are given by a calculus. Even decidable propositional logics can be computationally complex (e.g., already intuitionistic logic is PSPACE-complete). On the other hand, finite-valued logics are computationally relatively simple—at worst NP. Moreover, finite-valued semantics are simple, and general methods for theorem proving exist. This raises the question to what extent and under what circumstances propositional logics represented in (...) various ways can be approximated by finite-valued logics. It is shown that the minimal m-valued logic for which a given calculus is strongly sound can be calculated. It is also investigated under which conditions propositional logics can be characterized as the intersection of (effectively given) sequences of finite-valued logics. (shrink)

This work presents a post-positivist research framework to explain any surprising fact in the evolutionary path of a complex, dynamic and contingent social phenomenon. Primarily, it reconciles the ontological and epistemological assumptions of Critical Realism with the principles of American Pragmatism. Then, the research approach is presented: theoretical propositions about a social structure are translated into a set of grammar rules that acknowledges a pattern of sequences of events of either individual action or social interaction between actors within a real (...) social system. The result is a discrete mathematical model for a concrete category of social process based on these rules. Finally, data-grounded refinement of the theory is possible by the comparison between cases belonging to the same category, but differing about some contingent pattern of sequences of event outcomes. Consequently, their grammars differ in some pairs of context-sensitive rules that can explain this surprising fact, such that the derivation of this alternative historical trajectory of event outcomes becomes an extension to the early category of social process. In this sense, the proposed framework suggests there is a hierarchy of classes of grammars for middle-range explanations based upon the ontological assumption of the generative nature of social reality. (shrink)

The basic principle of all realist theories of truth developed in the 13th and 14th centuries was that a proposition is true if and only if it tells us how things are in reality. Walter Burley (1275-1344) interpreted this principle in a more radical way than 13th-century realists did. Burley, in fact, proposed a strong correspondence theory, in which there is a strict biunique correspondence between linguistic and extra-linguistic elements. Now, if the principle of correspondence can be applied to Burley (...) unconditionally to all affirmative statements (both for accidental and essential predications), it cannot be applied in the case of negative propositions, since in reality there can be no negative state of affairs. In order to solve this problem, Burley uses the strategy of introducing a complex mental object or objective entity as the significatum adequatum of negative sentences. It is an object which, although it exists only in the mind, is completely independent of our mental operations and which ultimately refers to the extra-mental world, composed exclusively of positive objects and states of affairs. In fact, the truth of a negative sentence does not depend on it corresponding to some negative fact, but rather on the opposite affirmative sentence failing to correspond to some positive extramental fact. Thus, extramental reality, which is only composed of positive objects, recovers its role as a yardstick for verifying the truth or falsity of all particular sentences, both affirmative and negative. (shrink)

In the chapter “Information and Content” of their Impossible Worlds, Berto and Jago provide us with a semantic account of information in deductive reasoning such that we have an explanation for why some, but not all, logical deductions are informative. The framework Berto and Jago choose to make sense of the above-mentioned idea is a semantic interpretation of Sequent Calculus rules of inference for classical logic. I shall argue that although Berto and Jago’s idea and framework are hopeful, their definitions (...) do not capture what is intended. This is so because the definitions are solely based on the logical complexity of an argument and they fail to capture the richness of the non- logical content of that argument. Then I will suggest some amendments to address this problem. Finally, I will extend the application of the definitions to first-order logic. It shall be observed that in some classical deductions, applying contraction may lead to hiding some epistemic impossibilities. This happens when formulae which contribute different propositions to the proof get contracted at the quantified level. (shrink)

Deductive inference is usually regarded as being “tautological” or “analytical”: the information conveyed by the conclusion is contained in the information conveyed by the premises. This idea, however, clashes with the undecidability of first-order logic and with the (likely) intractability of Boolean logic. In this article, we address the problem both from the semantic and the proof-theoretical point of view. We propose a hierarchy of propositional logics that are all tractable (i.e. decidable in polynomial time), although by means of (...) growing computational resources, and converge towards classical propositional logic. The underlying claim is that this hierarchy can be used to represent increasing levels of “depth” or “informativeness” of Boolean reasoning. Special attention is paid to the most basic logic in this hierarchy, the pure “intelim logic”, which satisfies all the requirements of a natural deduction system (allowing both introduction and elimination rules for each logical operator) while admitting of a feasible (quadratic) decision procedure. We argue that this logic is “analytic” in a particularly strict sense, in that it rules out any use of “virtual information”, which is chiefly responsible for the combinatorial explosion of standard classical systems. As a result, analyticity and tractability are reconciled and growing degrees of computational complexity are associated with the depth at which the use of virtual information is allowed. (shrink)

Today decision-makers face surging increases in overall system complexity leading up to more unstable and unpredictable business environments. Leaders and decision-makers are confronted with volatility (dynamic and intense changes), uncertainty (lack of predictability), complexity (interconnection of parts which is sometimes overwhelmingly difficult to process), and ambiguity (unclear relationships), namely the VUCA-world. The implications of the VUCA-world for business and strategy can be applied to the rise of complex cyber-physical systems in Industry 4.0. There is an expressed need to (...) develop complexity management frameworks that integrate different individual measures of dealing with industrial system complexity into a synergetic strategic framework. In this regard new frameworks that reflect “real-life complexity” of industrial systems and their practitioners are being called for. It is therefore the core aim of the thesis to develop and apply a strategic complexity management framework (SCM) that fits in the individual reality of the decision-making practitioner by integrating different complexity dimensions of industrial systems in a holistic, synergetic, and strategic way. As a starting point for achieving this aim, an investigation and exploration of relevant theoretical frameworks is conducted and accumulates in the proposition of a set of hypotheses H1-H13 as an explanatory approach to achieve a multi-dimensional definition of industrial system complexity and to explore its impact on decision-making based on information growth in industrial systems. In a second step, H1-H13 are applied to develop a theoretical complexity space model for industrial systems. In the model the static and dynamic complexity of an industrial system are integrated in a complexity space modelling approach, where information complexity boundaries expand over time in a static compound space of a system and serve as an indicator for system instability in a static complexity space. The capabilities of the complexity space model are theoretically demonstrated, alongside a set of assumptions concerning the behavior of industrial system complexity. The developed complexity space model represents the core theoretical foundation for the establishment of the SCM in a third step. In the third step the complexity of an industrial system is captivated via the strategic complexity management framework (SCM) in the form of a strategic 8- quadrant matrix in adherence to the axioms of the paradigm of strategic complexity engineering which are to acknowledge, characterize, anticipate, and manage complexity. Definitions of static, dynamic and environmental conception of complexity of industrial systems are holistically integrated to capture the internal and external strategic management perspective in the SCM framework and the strategic capabilities of the SCM framework are theoretically demonstrated based on a set of generic norm strategies. In a fourth step the SCM is applied for strategic complexity management purposes to four different real-world cases of industrial manufacturing systems with the goal to test, explore and discuss the practical decision-aiding applicability of the framework via an interventionistic multi-case study based on qualitative document review. The individual results of the SCM application on the four different cases are described and discussed. Key-learnings across cases are identified and discussed as a conclusion. Finally, a research outlook is provided. (shrink)

Anyone familiar with Russell’s work on the multiple-relation theory of judgment will at some point have puzzled over the map of the five-term understanding complex at the end of Chapter 1, Part II of his Theory of Knowledge (1913). Russell presents the map with the intention of clarifying what goes on when a subject S understands the “proposition” that A and B are similar. But the map raises more questions than it answers. In this paper I present and develop some (...) of the central issues that arise from Russell’s map, and I offer an interpretation of it that reflects his evolving views in the manuscript. I argue that multiple lines in the map are not meant to represent many relations, but rather one comprehensive multiple relation of understanding. And I argue that such a relation relates in a complex way due to the distinctive nature of its relata. (shrink)

Abstract Introduction Logically valid deductive arguments are clear examples of abstract recursive computational proce‐ dures on propositions or on probabilities. However, it is not known if the cortical time‐consuming inferential pro‐ cesses in which logical arguments are eventually realized in the brain are in fact physically different from other kinds of inferential processes. Methods In order to determine whether an electrical EEG discernible pattern of logical deduction exists or not, a new experimental paradigm is proposed contrasting logically valid and invalid (...) inferences with exactly the same content (same premises and same relational variables) and distinct logical complexity (propositional truth‐functional operators). Electroencephalographic signals from 19 subjects (24.2 ± 3.3 years) were acquired in a two‐condition para‐ digm (100 trials for each condition). After the initial general analysis, a trial‐by‐trial approach in beta‐2 band allowed to uncover not only evoked but also phase asynchronous activity between trials. Results showed that (i) deductive inferences with the same content evoked the same response pattern in logically valid and invalid conditions, (ii) mean response time in logically valid inferences is 61.54% higher, (iii) logically valid inferences are subjected to an early (400 ms) and a late reprocessing (600 ms) verified by two distinct beta‐2 activa‐ tions (p‐value < 0,01, Wilcoxon signed rank test). Conclusion We found evidence of a subtle but measurable electrical trait of logical validity. Results put forward the hypothesis that some logically valid deductions are recursive or computational cortical events. Keywords Beta‐2 band, Evoked potentials, Induced potentials, Deductive inference, Logical validity, Cortical bases of logical reasoning. (shrink)

In this article, I explore the consequences of two commonsensical premises in semantics and epistemology: (1) natural language is a complex system rooted in the communal life of human beings within a given environment; and (2) linguistic knowledge is essentially dependent on natural language. These premises lead me to emphasize the process-socio-environmental character of linguistic meaning and knowledge, from which I proceed to analyse a number of long-standing philosophical problems, attempting to throw new light upon them on these grounds. In (...) particular, I criticize the use of expressions such as ‘absolute truth’, ‘absolute existence’ and ‘the thing in itself’, arguing that they lead to what I call ‘the ultralinguistic paradox’ (a fatal antinomy). In the same way, I review a number of mainstream topics in philosophical semantics, epistemology and metaphysics, reformulating them in terms much more naturalistic – and less mysterious – than usual. (shrink)

The aim of the paper is to sketch a principle of individuation that is intended to serve the Fregean notion of a proposition, a notion I take for granted. A salient feature of Fregean propositions, i.e. complexes of modes of presentation of objects, is that they are fine-grained items, so fine-grained that even synonymous sentences might express different Fregean propositions. My starting point is the principle labelled by Gareth Evans the Intuitive Criterion of Difference for Thoughts, which states that it (...) is impossible coherently to take different mental attitudes to the same proposition. As a logical truth, this is a synchronic principle, the application of which is restricted to attitudes held at a single time. I argue that such a restriction might be reasonably lifted and, on the basis of an adequate notion of attitude-retention, I propose an admissible diachronic extension of the principle. (shrink)

This paper provides a new approach to a family of outstanding logical and semantical puzzles, the most famous being Frege's puzzle. The three main reductionist theories of propositions (the possible-worlds theory, the propositional-function theory, the propositional-complex theory) are shown to be vulnerable to Benacerraf-style problems, difficulties involving modality, and other problems. The nonreductionist algebraic theory avoids these problems and allows us to identify the elusive nondescriptive, non-metalinguistic, necessary propositions responsible for the indicated family of puzzles. The algebraic approach (...) is also used to defend antiexistentialism against existentialist prejudices. The paper closes with a suggestion about how this theory of content might enable us to give purely semantic (as opposed to pragmatic) solutions to the puzzles based on a novel formulation of the principle of compositionality. (shrink)

I here discuss two problems facing Russellian act-type theories of propositions, and argue that Fregean act-type theories are better equipped to deal with them. The first relates to complex singular terms like '2+2', which turn out not to pose any special problem for Fregeans at all, whereas Soames' theory currently has no satisfactory way of dealing with them (particularly, with such "mixed" propositions as the proposition that 2+2 is greater than 3). Admittedly, one possibility stands out as the most promising (...) one, but it requires that the Russellian treat complex properties as constituents of propositions. This leads to the second major problem for Russellians: that of proliferating propositions. I show how the most direct solution to this problem, that of rejecting complex predicative propositional constituents is available to Fregeans but very implausible for Russellians, since this virtually means rejecting complex properties. (shrink)

In this paper, we outline an approach to giving extensional truth-theoretic semantics for what have traditionally been seen as opaque sentential contexts. We outline an approach to providing a compositional truth-theoretic semantics for opaque contexts which does not require quantifying over intensional entities of any kind, and meets standard objections to such accounts. The account we present aims to meet the following desiderata on a semantic theory T for opaque contexts: (D1) T can be formulated in a first-order extensional language; (...) (D2) T does not require quantification over intensional entities­i.e., meanings, propositions, properties, relations, or the like­in its treatment of opaque contexts; (D3) T captures the entailment relations that hold in virtue of form between sentences in the language for which it is a theory; (D4) T has a finite number of axioms. If the approach outlined here is correct, it resolves a longstanding complex of problems in metaphysics, the philosophy of mind and the philosophy of language. (shrink)

What is it to know someone? Epistemologists rarely take up this question, though recent developments make such inquiry possible and desirable. This paper advances an account of how such interpersonal knowledge goes beyond mere propositional and qualitative knowledge about someone, giving a central place to second-personal treatment. It examines what such knowledge requires, and what makes it distinctive within epistemology as well as socially. It assesses its theoretic value for several issues in moral psychology, epistemic injustice, and philosophy of (...) mind. And it offers an account of the complex content in play if interpersonal knowledge is to be understood in terms of its mental states and their functions. (shrink)

For sentences such as (1), "Columbus knows that the sea is unpredictable", there is a face-value theory, according to which ‘that’-clauses are singular terms denoting propositions. Famously, Prior raised an objection to the theory, but defenders of the face-value theory such as Forbes, King, Künne, Pietroski and Stanley urged that the objection could be met by maintaining that in (1) ‘to know’ designates a complex relation along the lines of being in a state of knowledge having as content. Is the (...) theory safe, then? The aim of this paper is to show that a new problem for the theory arises if we consider attributions of skills, knacks, propensities and abilities. (shrink)

This paper investigates Wittgenstein’s account of the relation between elementary and molecular propositions (and thus, also, the propositions of logic) in the Tractatus Logico-Philosophicus. I start by sketching a natural reading of that relation – which I call the “bipartite reading” – holding that the Tractatus gives an account of elementary propositions, based on the so-called picture theory, and a different account of molecular ones, based on the principle of truth- functionality. I then show that such a reading cannot be (...) attributed to Wittgenstein, because he holds the view that an explanation of logical complexity is already given by a correct account of the (pictorial) nature of elementary propositions; this is implied in his claim that “an elementary proposition contains all logical constants/operations in itself”. After clarifying Wittgenstein’s notion of an operation from the Notes on Logic to the Tractatus, I finally explain why Wittgenstein claims that an elementary proposition contains all logical operations in itself, and hence why he can be said to provide a unified (and thus not bipartite) account of language and logic. (shrink)

A central dispute in understanding Frege’s philosophy concerns how the sense of a complex expression relates to the senses of its component expressions. According to one reading, the sense of a complex expression is a whole built from the senses of the component expressions. On this interpretation, Frege is an early proponent of structured propositions. A rival reading says that senses compose by functional application: the sense of a complex expression is the value of the function denoted by its functional (...) component for the arguments denoted by its remaining components. I argue that two non-negotiable Fregean theses entail that senses compose by functional application. One thesis is that referents compose by functional application. The other thesis is that an expression in an indirect context refers to its customary sense. (shrink)

Complex constraints like conditionals ('If A, then B') and probabilistic constraints ('The probability that A is p') pose problems for Bayesian theories of learning. Since these propositions do not express constraints on outcomes, agents cannot simply conditionalize on the new information. Furthermore, a natural extension of conditionalization, relative information minimization, leads to many counterintuitive predictions, evidenced by the sundowners problem and the Judy Benjamin problem. Building on the notion of a `paradigm shift' and empirical research in psychology and economics, I (...) argue that the model of hypothesis testing can explain how people learn complex, theory-laden propositions like conditionals and probability constraints. Theories are formalized as probability distributions over a set of possible outcomes and theory change is triggered by a constraint which is incompatible with the initial theory. This leads agents to consult a higher order probability function, or a 'prior over priors,' to choose the most likely alternative theory which satisfies the constraint. The hypothesis testing model is applied to three examples: learning a simple probabilistic constraint involving coin bias, the sundowners problem for conditional learning, and the Judy Benjamin problem for learning conditional probability constraints. (shrink)

Complex human reasoning involves minimal abilities to extract conclusions implied in the available information. These abilities are considered “deductive” because they exemplify certain abstract relations among propositions or probabilities called deductive arguments. However, the electrophysiological dynamics which supports such complex cognitive pro- cesses has not been addressed yet. In this work we consider typically deductive logico- probabilistically valid inferences and aim to verify or refute their electrophysiological functional connectivity differences from invalid inferences with the same content (same relational variables, same (...) stimuli, same relevant and salient features). We recorded the brain electrophysiological activity of 20 participants (age 1⁄4 20.35 ± 3.23) by means of an MEG system during two consecutive reasoning tasks: a search task (invalid condition) without any specific deductive rules to follow, and a logically valid deductive task (valid condition) with explicit deductive rules as instructions. We calculated the functional connectivity (FC) for each condition and conducted a seed-based analysis in a set of cortical regions of interest. Finally, we used a cluster-based permutation test to compare the dif- ferences between logically valid and invalid conditions in terms of FC. As a first novel result we found higher FC for valid condition in beta band between regions of interest and left prefrontal, temporal, parietal, and cingulate structures. FC analysis allows a second novel result which is the definition of a propositional network with operculo-cingular, parietal and medial nodes, specifically including disputed medial deductive “core” areas. The experiment discloses measurable cortical processes which do not depend on content but on truth-functional propositional operators. These experimental novelties may contribute to understand the cortical bases of deductive processes. (shrink)

ABSTRACT: An introduction to Stoic logic. Stoic logic can in many respects be regarded as a fore-runner of modern propositional logic. I discuss: 1. the Stoic notion of sayables or meanings (lekta); the Stoic assertibles (axiomata) and their similarities and differences to modern propositions; the time-dependency of their truth; 2.-3. assertibles with demonstratives and quantified assertibles and their truth-conditions; truth-functionality of negations and conjunctions; non-truth-functionality of disjunctions and conditionals; language regimentation and ‘bracketing’ devices; Stoic basic principles of propositional (...) logic; 4. Stoic modal logic; 5. Stoic theory of arguments: two premisses requirement; validity and soundness; 6. Stoic syllogistic or theory of formally valid arguments: a reconstruction of the Stoic deductive system, which consisted of accounts of five types of indemonstrable syllogisms, which function as nullary argumental rules that identify indemonstrables or axioms of the system, and four deductive rules (themata) by which certain complex arguments can be reduced to indemonstrables and thus shown to be formally valid themselves; 7. arguments that were considered as non-syllogistically valid (subsyllogistic and unmethodically concluding arguments). Their validity was explained by recourse to formally valid arguments. (shrink)

Hilbert arithmetic in a wide sense, including Hilbert arithmetic in a narrow sense consisting by two dual and anti-isometric Peano arithmetics, on the one hand, and the qubit Hilbert space (originating for the standard separable complex Hilbert space of quantum mechanics), on the other hand, allows for an arithmetic version of Gentzen’s cut elimination and quantum measurement to be described uniformy as two processes occurring accordingly in those two branches. A philosophical reflection also justifying that unity by quantum neo-Pythagoreanism links (...) it to the opposition of propositional logic, to which Gentzen’s cut rule refers immediately, on the one hand, and the linguistic and mathematical theory of metaphor therefore sharing the same structure borrowed from Hilbert arithmetic in a wide sense. An example by hermeneutical circle modeled as a dual pair of a syllogism (accomplishable also by a Turing machine) and a relevant metaphor (being a formal and logical mistake and thus fundamentally inaccessible to any Turing machine) visualizes human understanding corresponding also to Gentzen’s cut elimination and the Gödel dichotomy about the relation of arithmetic to set theory: either incompleteness or contradiction. The metaphor as the complementing “half” of any understanding of hermeneutical circle is what allows for that Gödel-like incompleteness to be overcome in human thought. (shrink)

Donald Davidson and John Searle famously differ, among other things, on the issue of animal thoughts. Davidson seems to be a latter-day Cartesian, denying any propositional thought to subhuman animals, while Searle seems to follow Hume in claiming that if we have thoughts, then animals do, too. Davidson’s argument centers on the idea that language is necessary for thought, which Searle rejects. The paper argues two things. Firstly, Searle eventually argues that much of a more complex thought does depend (...) on language, which reduces a distance between himself and Davidson. Secondly, some of Davidson’s suggestions are promising – in particular the idea that we may lack a vocabulary to capture the contents of animal thoughts. Based on this insight, one might, pace Davidson, grant thoughts to animals. However, this does not mean, pace Searle, that it should be possible to construe even the simplest of such thoughts as propositional. Perhaps we need to move beyond Davidson and Searle by developing a theory of nonpropositional thought for animals. (shrink)

Abstract – The basic principle of all realist theories of truth developed in the 13th and 14th centuries was that a proposition is true if and only if it tells us how things are in reality. Walter Burley (1275-1344) interpreted this principle in a more radical way than 13th-century realists did. He proposed a correspondence theory in which there is a strict biunique correspondence between linguistic and extra-linguistic elements. If the principle of correspondence can be applied unconditionally to all affirmative (...) utterances about present entities, it cannot apply in the case of utterances concerning past entities, which no longer exist. In order to maintain the principle of correspondence, Burley argues that such utterances, in order to be true, must not correspond to an extra-mental object, but to a complex mental object or objective entity, a mental proposition with the verb in the present tense which, was true in a past moment. (shrink)

C.S. Peirce held what is nowadays called a “commitment view” of assertion. According to this type of view, assertion is a kind of act that is determined by its “normative effects”: by asserting a proposition one undertakes certain commitments, typically to be able to provide reason to believe what one is asserting, or, in Peirce’s words, one “takes responsibility” for the truth of the proposition one asserts. Despite being an early adopter of the view, if Peirce’s commitment view of assertion (...) is mentioned at all in contemporary discussions it is only in passing. His view is, however, far more complex and nuanced than he has been given credit for. My primary goal here, then, is to get a better understanding of Peirce’s version of a commitment view of assertion. I also argue that figuring out the details of Peirce’s theory of assertion can also provide us with a viable way to respond to problems that contemporary commitment views of assertion face. (shrink)

What does it mean to know how to do something? This book develops a comprehensive account of know-how, a crucial epistemic goal for all who care about getting things right, not only with respect to the facts, but also with respect to practice. It proposes a novel interpretation of the seminal work of Gilbert Ryle, according to which know-how is a competence, a complex ability to do well in an activity in virtue of guidance by an understanding of what it (...) takes to do so. This idea is developed into a full-fledged account, Rylean responsibilism, which understands know-how in terms of the normative guidance and responsible control of one's acts. Within the complex current debate about know-how, this view occupies a middle ground position between the intellectualist claim that know-how just is propositional or objectual knowledge and the anti-intellectualist claim that know-how just is ability. In genuine know-how, practical ability and guiding intellect are both necessary, but essentially intertwined. (shrink)

Non-cognitivists are known to face a problem in extending their account of straightforward predicative moral judgments to logically complex moral judgments. This paper presents a related problem concerning how non-cognitivists might extend their accounts of moral judgments to other kinds of moral attitudes, such as moral hopes and moral intuitions. Non-cognitivists must solve three separate challenges: they must explain the natures of these other attitudes, they must explain why they count as moral attitudes, and they must explain why the moral (...) attitudes are systematically correlated with ordinary propositional attitudes. After presenting the problem, this paper examines several contemporary theories with some initial promise for solving it, and argues that they are insufficient. (shrink)

My aim is to defend a peculiar epistemic version of the particularity thesis, which results from a sui generis combination of what I call the ‘singular relational view’ and what I call the ‘relativistic content view.’ Particulars are not represented as part of putative singular content. Instead, we are perceptually acquainted with them in the relevant sense that experience puts us in direct perceptual contact with them. And the content of experience is best modeled as a propositional function, that (...) is, the content of a complex predicate that is true or false only relative to some circumstances of evaluation. (shrink)

According to a classic but nowadays discarded philosophical theory, perceptual experience is a complex of nonconceptual sensory states and full-blown propositional beliefs. This classical dual-component theory of experience is often taken to be obsolete. In particular, there seem to be cases in which perceptual experience and belief conflict: cases of known illusions, wherein subjects have beliefs contrary to the contents of their experiences. Modern dual-component theories reject the belief requirement and instead hold that perceptual experience is a complex of (...) nonconceptual sensory states and some other sort of conceptual state. The most popular modern dual-component theory appeals to sui generis propositional attitudes called ‘perceptual seemings’. This article argues that the classical dual-component theory has the resources to explain known illusions without giving up the claim that the conceptual components of experience are beliefs. The classical dual-component view, though often viewed as outdated and implausible, should be regarded as a serious contender in contemporary debates about the nature of perceptual experience. (shrink)

Legal definitions will be examined from three perspectives: their pragmatic function, their propositional structure, and their argumentative role. In law, definitions can be used for different pragmatic purposes: they can be uttered to describe a concept, or to establish a new meaning for a term. The propositional content of definitional speech acts can be different. In law, like in ordinary conversation, there might be different types of definition: we can define by providing examples, or showing the fundamental characteristics (...) of the concept defined, or listing the constituent parts of the denotatum. All these definitions play different argumentative roles in legal discourse. At a third level, definitions can be thought of as premises in complex patterns of reasoning (for the subject of reasoning from definition in law, see Aarnio 1977; Moore 1980; Lindahl, 2004). They constitute the fundamental element of argument from classification, namely a pattern of inference in which a new property (or a name) is attributed to an entity on the basis of other properties. (shrink)

Expressivists have a problem with negation. The problem is that they have not, to date, been able to explain why ‘murdering is wrong’ and ‘murdering is not wrong’ are inconsistent sentences. In this paper, I explain the nature of the problem, and why the best efforts of Gibbard, Dreier, and Horgan and Timmons don’t solve it. Then I show how to diagnose where the problem comes from, and consequently how it is possible for expressivists to solve it. Expressivists should accept (...) this solution, I argue, because it is demonstrably the only way of avoiding the problem, and because it generalizes. Once we see how to solve the negation problem, I show, it becomes easy to state a constructive, compositional expressivist semantics for a purely normative language with the expressive power of propositional logic, in which we can for the first time give explanatory, formally adequate expressivist accounts of logical inconsistency, logical entailment, and logical validity. As a corollary, I give what I take to be the first real expressivist explanation of why Geach’s original moral modus ponens argument is genuinely logically valid. This proves that the problem with expressivism cannot be that it can’t account for the logical properties of complex normative sentences. But it does not show that the same solution can work for a language with both normative and descriptive predicates, let alone that expressivists are able to deal with more complex linguistic constructions like tense, modals, or even quantifiers. In the final section, I show what kind of constraints the solution offered here would place expressivists under, in answering these further questions. (shrink)

Logicism is the view that mathematical truths are logical truths. But a logical truth is commonly thought to be one with a universally valid form. The form of “7 > 5” would appear to be the same as “4 > 6”. Yet one is a mathematical truth, and the other not a truth at all. To preserve logicism, we must maintain that the two either are different subforms of the same generic form, or that their forms are not at all (...) what they appear. The historical record shows that Russell pursued both these options, but that the struggle with the logical paradoxes pushed him away from the first kind of response and toward the second. An object cannot itself have a kind of inner logical complexity that makes a proposition have a different logical form merely in virtue of being about it, nor can their representatives in logical forms be single things different for different forms, at least not without postulating too many such objects and thereby creating Cantorian diagonal paradoxes. There are only apparent objects which are actually fragments of logical forms, different in different cases. (shrink)

The standing tradition in theorizing about meaning, since at least Frege, identifies meaning with propositions, which are, or determine, the truth-conditions of a sentence in a context. But a recent trend has advocated a departure from this tradition: in particular, it has been argued that modal claims do not express standard propositional contents. This non-propositionalism has received different implementations in expressivist semantics and certain kinds of dynamic semantics. They maintain that the key aspect of interpretation of modal claims is (...) the characteristic dynamic effect they have on the context. I argue that pessimism about truth-conditions arises from an overly simplistic picture of content, context and their interaction. While I agree with the critics that an important aspect of modal meaning is the dynamic effect modals have on the context, I argue that they have mischaracterized the nature and the complexity of this effect. A more nuanced account of the interaction between modals and context shows that far from being incompatible with propositional meaning, the dynamic aspect of meaning is precisely what allows us to predict the correct propositional content of an utterance. (shrink)

A common view relating compositional semantics and the objects of assertion holds the following: Sentences φ and ψ expresses the same proposition iff φ and ψ have the same modal profile. Following Dummett, Evans, and Lewis, Stanley argues that this view is fundamentally mistaken. According to Dummett, we must distinguish the semantic contribution a sentence makes to more complex expressions in which it occurs from its assertoric content. Stojnić insists that views which distinguish the roles of content and semantic value (...) must nevertheless ensure a tight connection between the two. But, she contends, there is a crucial disanalogy between the views that follow Lewis and the views that follow Dummett. Stanley’s Dummettian view is argued to contain a fatal flaw: On such views, there is no way to secure an appropriate connection between semantic value and a theoretically motivated notion of assertoric content. I will review the background issues from Dummett, Evans, Lewis, and Stanley, and provide a principled way of bridging the gap between semantic value and a theoretically motivated notion of assertoric content. (shrink)

The epistemic modal auxiliaries must and might are vehicles for expressing the force with which a proposition follows from some body of evidence or information. Standard approaches model these operators using quantificational modal logic, but probabilistic approaches are becoming increasingly influential. According to a traditional view, must is a maximally strong epistemic operator and might is a bare possibility one. A competing account—popular amongst proponents of a probabilisitic turn—says that, given a body of evidence, must \ entails that \\) is (...) high but non-maximal and might \ that \\) is significantly greater than 0. Drawing on several observations concerning the behavior of must, might and similar epistemic operators in evidential contexts, deductive inferences, downplaying and retractions scenarios, and expressions of epistemic tension, I argue that those two influential accounts have systematic descriptive shortcomings. To better make sense of their complex behavior, I propose instead a broadly Kratzerian account according to which must \ entails that \ = 1\) and might \ that \ > 0\), given a body of evidence and a set of normality assumptions about the world. From this perspective, must and might are vehicles for expressing a common mode of reasoning whereby we draw inferences from specific bits of evidence against a rich set of background assumptions—some of which we represent as defeasible—which capture our general expectations about the world. I will show that the predictions of this Kratzerian account can be substantially refined once it is combined with a specific yet independently motivated ‘grammatical’ approach to the computation of scalar implicatures. Finally, I discuss some implications of these results for more general discussions concerning the empirical and theoretical motivation to adopt a probabilisitic semantic framework. (shrink)

I am presenting a sequent calculus that extends a nonmonotonic consequence relation over an atomic language to a logically complex language. The system is in line with two guiding philosophical ideas: (i) logical inferentialism and (ii) logical expressivism. The extension defined by the sequent rules is conservative. The conditional tracks the consequence relation and negation tracks incoherence. Besides the ordinary propositional connectives, the sequent calculus introduces a new kind of modal operator that marks implications that hold monotonically. Transitivity fails, (...) but for good reasons. Intuitionism and classical logic can easily be recovered from the system. (shrink)

This paper reconstructs Susan Stebbing’s account of intelligent dealing with a problem and defends this account against charges that it relies on a “censurable kind” of intellectualism. This charge was made in Stebbing’s own time by Laird and Wittgenstein. Michael Kremer has recently made the case that Stebbing is also a proximate target of Gilbert Ryle’s attack on intellectualism. This paper argues that Stebbing should indeed be counted as an intellectualist since she holds that intelligent dealing with a problem requires (...) propositional thought. Yet, for Stebbing, thinking is an activity of a whole person and is enabled and constrained by their dispositions. This complex picture of a thinker enables Stebbing’s account to resist arguments targeting certain forms of intellectualism such as Ryle’s regress argument. It also helps her to respond to the charge that she overemphasizes the importance of intellectual failures. On the picture that emerges, Stebbing offers a strikingly modern epistemology that incorporates the social features of a person as well as their purely intellectual features. (shrink)

Classical logic is usually interpreted as the logic of propositions. But from Boole's original development up to modern categorical logic, there has always been the alternative interpretation of classical logic as the logic of subsets of any given (nonempty) universe set. Partitions on a universe set are dual to subsets of a universe set in the sense of the reverse-the-arrows category-theoretic duality--which is reflected in the duality between quotient objects and subobjects throughout algebra. Hence the idea arises of a dual (...) logic of partitions. That dual logic is described here. Partition logic is at the same mathematical level as subset logic since models for both are constructed from (partitions on or subsets of) arbitrary unstructured sets with no ordering relations, compatibility or accessibility relations, or topologies on the sets. Just as Boole developed logical finite probability theory as a quantitative treatment of subset logic, applying the analogous mathematical steps to partition logic yields a logical notion of entropy so that information theory can be refounded on partition logic. But the biggest application is that when partition logic and the accompanying logical information theory are "lifted" to complex vector spaces, then the mathematical framework of quantum mechanics is obtained. Partition logic models indefiniteness (i.e., numerical attributes on a set become more definite as the inverse-image partition becomes more refined) while subset logic models the definiteness of classical physics (an entity either definitely has a property or definitely does not). Hence partition logic provides the backstory so the old idea of "objective indefiniteness" in QM can be fleshed out to a full interpretation of quantum mechanics. (shrink)

Husserl’s Logical Grammar is intended to explain how complex expressions can be constructed out of simple ones so that their meaning turns out to be determined by the meanings of their constituent parts and the way they are put together. Meanings are thus understood as structured contents and classified into formal categories to the effect that the logical properties of expressions reflect their grammatical properties. As long as linguistic meaning reduces to the intentional content of pre-linguistic representations, however, it is (...) not trivial to account for how semantics relates to syntax in this context. In this paper, I analyze Husserl’s Logical Grammar as a system of recursive rules operating on representations and suggest that the syntactic form of representations contributes to their semantics because it carries information about semantic role. I further discuss Husserl’s syntactic account of the unity of propositions and argue that, on this account, logical form supervenes on syntactic form. In the last section I draw some implications for the phenomenology of thought and conjecture that the structural features it displays are likely to convey the syntactic structures of an underlying language-like representational system. (shrink)

The paper proposes a way for adherents of Fregean, structured propositions to designate propositions and other complex senses/concepts using a special kind of functor. I consider some formulations from Peacocke's works and highlight certain problems that arise as we try to quantify over propositional constituents while referring to propositions using "that"-clauses. With the functor notation, by contrast, we can quantify over senses/concepts with objectual, first-order quantifiers and speak without further ado about their involvement in propositions. The functor notation also (...) turns out to come with an important kind of expressive strengthening, and is shown to be neutral on several controversial issues. (shrink)

My topic in this paper is the nature of faith. Much of the discussion concerning the nature of faith proceeds by focussing on the relationship between faith and belief. In this paper, I explore a different approach. I suggest that we approach the question of what faith involves by focussing on the relationship between faith and action. When we have faith, we generally manifest it in how we act; we perform acts of faith: we share our secrets, rely on other’s (...) judgment, refrain from going through our partner’s emails, let our children prepare for an important exam without our interference. Religious faith, too is manifested in acts of faith: attending worship, singing the liturgy, fasting, embarking on a pilgrimage. I argue that approaching faith by way of acts of faith, reveals that faith is a complex mental state whose elements go beyond doxastic states towards particular propositions. It also involves conative states and – perhaps more surprisingly – know how. This has consequences for the epistemology of faith: the role of testimony and experts, the importance of practices, and what we should make of Pascal’s advice for how to acquire faith. (shrink)

The syllogistic figures and moods can be taken to be argument schemata as can the rules of the Stoic propositional logic. Sentence schemata have been used in axiomatizations of logic only since the landmark 1927 von Neumann paper [31]. Modern philosophers know the role of schemata in explications of the semantic conception of truth through Tarski’s 1933 Convention T [42]. Mathematical logicians recognize the role of schemata in first-order number theory where Peano’s second-order Induction Axiom is approximated by Herbrand’s (...) Induction-Axiom Schema [23]. Similarly, in first-order set theory, Zermelo’s second-order Separation Axiom is approximated by Fraenkel’s first-order Separation Schema [17]. In some of several closely related senses, a schema is a complex system having multiple components one of which is a template-text or scheme-template, a syntactic string composed of one or more “blanks” and also possibly significant words and/or symbols. In accordance with a side condition the template-text of a schema is used as a “template” to specify a multitude, often infinite, of linguistic expressions such as phrases, sentences, or argument-texts, called instances of the schema. The side condition is a second component. The collection of instances may but need not be regarded as a third component. The instances are almost always considered to come from a previously identified language (whether formal or natural), which is often considered to be another component. This article reviews the often-conflicting uses of the expressions ‘schema’ and ‘scheme’ in the literature of logic. It discusses the different definitions presupposed by those uses. And it examines the ontological and epistemic presuppositions circumvented or mooted by the use of schemata, as well as the ontological and epistemic presuppositions engendered by their use. In short, this paper is an introduction to the history and philosophy of schemata. (shrink)

To justify inductive inference and vanquish classical skepticisms about human memory, external world realism, etc., Richard Fumerton proposes his “inferential internalism,” an epistemology whereby humans ‘see’ by Russellian acquaintance Keynesian probable relations (PRs) between propositions. PRs are a priori necessary relations of logical probability, akin to but not reducible to logical entailments, such that perceiving a PR between one’s evidence E and proposition P of unknown truth value justifies rational belief in P to an objective degree. A recent critic of (...) inferential internalism is Alan Rhoda, who questions its psychological plausibility. Rhoda argues that in order to see necessary relations between propositions E and P, one would need acquaintance with too many propositions at once, since our evidence E is often complex. In this paper, I criticize Rhoda’s implausibility objection as too quick. Referencing the causal status effect (CSE) from psychology, I argue that some of the complex features of evidence E contribute to our type-categorizing it as E-type, and thus we do not need to ‘see’ all of the complex features when we see the PR between E and P. My argument leaves unchanged Fumerton’s justificatory role for the PR, but enhances its psychological plausibility. (shrink)

The purpose of this paper is to show how micro-argumentation mechanisms of presumptive reasoning and reasoning from best explanation can be used for explaining some cases of presupposition cancellation. It will be shown how the relationship between presupposition triggers and pragmatic presuppositions can be analyzed in terms of presumptive and non-presumptive polyphonic articulation of an utterance, resulting in different types of commitments for the interlocutors. This approach is grounded on the two interconnected notions of presumptions and commitments. In some complex (...) cases of presupposition “suspension,” the speaker presumes the hearer’s acceptance of and commitment to propositions that cannot be presumed as such, namely that do not belong to the common ground, or that have been explicitly rejected as being commonly shared. This phenomenon triggers a complex type of reasoning that can be represented as an abductive pattern, grounded on hierarchies of presumptions and aimed at providing an interpretation that solves this conflict of presumptions. Several cases of suspension of presupposition will be investigated as resulting from non-presumptive polyphonic articulations, in which different voices responsible for distinct commitments are distinguished. By indirectly reporting an element of discourse, the speaker can refuse to take responsibility for the presupposed proposition, and correct the commitments that may result for him. This polyphonic treatment of utterances shows how and why a presupposition is suspended, and identifies the conflicting presumptions that can be further solved through reasoning from best explanation. This reasoning can result in a different reconstruction of the developed logical form of utterance or of its illocutionary force. (shrink)

A close reading of Peirce’s pragmatic maxim shows a correlation between meaning and purpose. If the meaning of a concept, proposition or hypothesis is clarified by formulating its practical effects, those also can be articulated as practical maxims. To the extent that the hypotheses or propositions upon which they are based are true, practical maxims recommend reliable courses of action. This can be translated into a broader claim of an integral relation between semiosis and goal-directed or teleological systems. Any goal-directed (...) system, to be propagating, must be capable of coordinating the information in its internal or endergonic processes with exergonic information found in its environment. Signs are critical links between these two sources of information and must also serve as steering mechanisms for that system as well. If signs detected or represented information in the environments without using that information to steer the system, it would have no practical effect on the system; conversely, if a system could steer itself, but had no representation of exergonic information, it would fail to be propagating. Obviously, to get food, it must not only find it, but must also use that information to direct its behavior in a manner that makes use of that food. Using concepts found in complex systems and modern information theory, it is argued that this analysis requires a distinction between information and meaning. The result of this investigation is the claim that meaning can be understood as the propagating work of information. The remainder of the paper follows some of the ramification of this analysis for Peirce’s semiotic theory. (shrink)

Failure of substitutivity of coreferential terms, one of the hallmarks of referential opacity, is standardly explained in terms of the presence of an expression (such as a verb of propositional attitude, a modal adverb or quotation marks) with opacity-inducing properties. It is thus assumed that any term in a complex expression for which substitutivity fails will be within the scope of an expression of one of these types, and that where there is an expression of one of these types (...) there will be failure of substitutivity for terms within its scope. I shall discuss a series of examples that have been thought to challenge this explanation by exhibiting failure of substitutivity of coreferential terms for positions not within the scope of any of the standard opacity-inducing expressions. If these examples are genuine, then the usual explanations of opacity are either incomplete – because there are sources of opacity other than those standardly identified, or completely mistaken – because the standardly identified expressions are not causes of opacity. I will argue, however, that the examples only exhibit failure of substitutivity of non-coreferential terms, and, hence, do not present a challenge to standard explanations of opacity. (shrink)