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)

A general mathematical framework, based on countable partitions of Natural Numbers [1], is presented, that allows to provide a Semantics to propositional languages. It has the particularity of allowing both the valuations and the interpretation Sets for the connectives to discriminate complexity of the formulas. This allows different adequacy criteria to be used to assess formulas associated with the same connective, but that differ in their complexity. The presented method can be adapted potentially infinite number of connectives (...) and truth values, therefore, it can be considered a general framework to provide semantics to several of the known logic systems (eg, LC, L3 LP, FDE). The presented semantics allow to converge to different standard semantics if the separation complexity procedure is annulled. Therefore, it can be understood as a framework that allows greater precision (in complexity terms) with respect to formula satisfaction. Naturally, because of how it is built, it can be incorporated into non-deterministic semantics. The presented procedure also allows generating valuations that grant a different truth value to each formula of propositional language. As a positive side effect, our method allows a constructive proof of the equipotence between N and N^n for all Natural n. (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)

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)

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)

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)

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)

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)

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)

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)

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)

The depth-bounded approach seeks to provide realistic models of reasoners. Recognizing that most useful logics are idealizations in that they are either undecidable or likely to be intractable, the approach accounts for how they can be approximated in practice by resource-bounded agents. The approach has been applied to Classical Propositional Logic (CPL), yielding a hierarchy of tractable depth-bounded approximations to that logic, which in turn has been based on a KE/KI system. -/- This Thesis shows that the approach can (...) be naturally extended to useful nonclassical logics such as First-Degree Entailment (FDE), the Logic of Paradox (LP), Strong Kleene Logic (K3 ) and Intuitionistic Propositional Logic (IPL). To do this, we introduce a KE/KI-style system for each of those logics such that: is formulated via signed formulae, consist of linear operational rules and branching structural rule(s), can be used as a direct-proof and a refutation method, and is interesting independently of the approach in that it has an exponential speed-up on its tableau system counterpart. The latter given that we introduce a new class of examples which we prove to be hard for all tableau systems sharing the V/& rules with the classical one, but easy for their analogous KE-style systems. Then we focus on showing that each of our KE/KI-style systems naturally yields a hierarchy of tractable depth-bounded approximations to the respective logic, in terms of the maximum number of allowed nested applications of the branching rule(s). The rule(s) express(es) a generalized rule of bivalence, is (are) essentially cut rule(s) and govern(s) the manipulation of virtual information, which is information that an agent does not hold but she temporarily assumes as if she held it. Intuitively, the more virtual information needs to be invoked via the branching rule(s), the harder the inference is for the agent. So, the nested application the branching rule(s) provides a sensible measure of inferential depth. We also show that each hierarchy approximating FDE, LP, and K3 , admits of a 5-valued non-deterministic semantics; whereas, paving the way for a semantical characterization of the hierarchy approximating IPL, we provide a 3-valued non-deterministic semantics for the full logic that fixes the meaning of the connectives without appealing to “structural” conditions. -/- Moreover, we show a super-polynomial lower bound for the strongest possible version of clausal tableaux on the well-known class of “truly fat” expressions (which are easy for KE), settling a problem left open in the literature. Further, we investigate a hierarchy of tractable depth-bounded approximations to CPL based only on KE. Finally, we propose a refinement of the p-simulation relation which is adequate to establish positive results about the superiority of a system over another with respect to proof-search. (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)

This paper investigates the necessary functional architecture underlying complex cognitive states such as belief, desire, hope, and fear, specifically those characterized as Meaningful Propositional Attitudes About Something Not Itself (MPAASNI). MPAASNI are defined as states possessing directed propositional content, susceptibility to systematic processing, and an internal stance conferring functional significance within a system. We identify three fundamental functional capacities required for such states: Reference (R), providing directed content; Inference (I), providing systematic processing and relation of contents; and Preference (...) (P), providing the internal stance, weighting, and functional significance. The core contribution of this paper is the articulation and defense of the Trialectics, defined as the specific functional mode of operation characterized by systematic and constitutive mutual conditioning among R, I, and P. Through rigorous, descriptive conceptual analysis, we argue that this Trialectic functioning—this deep functional integration where each capacity's state and operation conditions and is conditioned by the others—is not merely one possible arrangement but constitutes a necessary condition for the possibility of any system exhibiting MPAASNI. The necessity is demonstrated by showing that the functional integration inherently required by the definition of MPAASNI logically entails the mutual conditioning described by the Trialectics. This framework, derived non-empirically, applies to attitudes directed towards both tangible and non-tangible domains and posits a fundamental structure necessary for intentionality, rationality, and other sophisticated cognitive phenomena dependent on meaningful propositional attitudes. (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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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 – 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)

The aim of this thesis is to confront the crisis in art and argument over whether it has lost its way. According to Friedrich Schelling, the ‘modern mythology’, bolstered by the onset of Christianity, is responsible for generating ‘aesthetic privation’ producing a joint crisis of meaning for humanity and art. Their artificial historicising, at the root of this, began with overturning the ‘ancient mythology’ in which art was a unified principle integrally linked to both Nature and History via the Person. (...) Extending this argument, drawing on other Radical Enlightenment thinkers, I show why this corrupted the essential link between aesthetics, ethics, and logic (exacerbated by Kant’s re-definition of aesthetics). And subsequently how the human habitus and telos globally transformed under an evolving modern ‘positivistic materialism’, characterised by an ideological, reflective standpoint, ‘worlding’ humanity toward posthumanism and possible extinction. Addressing the underlying problem of modern ‘mythologising’ and ‘aesthetic privation’ is proposed as essential to mending the associated historicised disjunctures between Art and Society, Nature, and the Person connecting both meaning crises. Early chapters examine why reassociating art ontologically with the normative discipline of aesthetics rather than theoretical ‘aesthetics’ is necessary for this. Reconceiving art as complexity science (Wissenschaft), as Schelling’s ‘process metaphysics’; ‘naturalising’ it to restore habitual primary attendance to bearers of higher meaning (‘internal’ goods) is proposed. This requires understanding ‘ethical value’ in the phenomenology of this ‘science of admiring’. A method for which, and for returning virtue ethics (firstly to the arts ecology), is suggested as a meaningful, practical way to reunite ethics with morals in modern society. Naturalising Art is thus argued as necessary for developing a new mythology and genuine political community needed to reorient humanity. The procedure followed is to firstly examine the posited underlying problem’s significance and causes. Deterioration of the Principle of Art (and essential link between Art and the Person, via corruption of the normative disciplines) emerges as a key reason for why art and humanity’s meaning crises developed together, peaking in contemporary ‘modernity’. This central claim and corresponding remedial propositions (reconnecting Art with normative aesthetics) centre on four main arguments for addressing five suggested historical ‘modifications’ (identified by Raymond Williams, and others) producing the above disjunctures. Re-establishing an ontological conception of Art, restoring dialectical normativity to our modes of admiring (‘idealising’), is thus proposed as essential for confronting deep assumptions inherent in modern mythologising. A methodology for assessing ‘ethical’ meaning-value directionality in any artwork, by combining Peircian semiotics with Max Scheler’s hierarchy of values to revive Schelling’s principle of Art, is then developed to suggest a practical approach for restoring virtue ethics to the human telos. (shrink)

Emotions Caused by Untrue Propositions: A Broader View of the Paradox of Fiction Ever since Colin Radford wrote his article ‘How Can We Be Moved by the Fate of Anna Karenina?’ in 1975, philosophers have tried to solve the so-called paradox of fiction, or the question how we can be moved by objects of which we know they don’t really exist. What is striking about discussions on the paradox of fiction is that they often present fictional works as collections of (...) untrue statements and focus on the content of these works, without regard for their form or mode of presentation. In this paper, I argue for a re-examination of the paradox of fiction, in which the work of fiction is treated as a complex of form and content. In this regard, I propose to expand Peter Lamarque’s thought theory, which he explicitly formulated to solve the paradox of fiction, with his later developed concept of opacity, which states that the content of the imaginings we form when reading fiction are fundamentally connected to the specific descriptions within the fictional work. (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)

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)

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)

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)

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)

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)

Substantial facts are not well-understood entities. Many philosophers object to their existence on this basis. Yet facts, if they can be understood, promise to do a lot of philosophical work: they can be used to construct theories of property possession and truthmaking, for example. Here, I give a formal theory of facts, including negative and logically complex facts. I provide a theory of reduction similar to that of the typed λ -calculus and use it to provide identity conditions for facts. (...) This theory validates truthmaker maximalism : it provides truthmakers for all truths. I then show how the usual truth-in-a-model relation can be replaced by two relations: one between models and facts, saying that a given fact obtains relative to the model, and the other between facts and propositions: the truthmaking relation. (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)

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)

In The Philosophy of Logical Atomism Russell held the view that facts in the world are formally structured complexes, the structure of which matches the logical structure of correspondent propositions. Russell also seems to have denied that there are facts of identity and of diversity. This paper argues that Identity and Diversity can be understood as purely formal structures in Russellian facts. It considers Russell’s possible reasons for denying the existence of facts of identity and diversity and shows how problematic (...) these reasons are. In particular, I argue that identity statements are not tautologies, and their denial does not result into a contradiction. An important consequence of this thesis is that Metaphysics and Logic are not as tied up as Russell took them to be, but nevertheless these are good news for the old formal program for Metaphysics that lies at the very heart of what he called philosophical logic. (shrink)

Dreams are not real, so when we recount them we prefix an intensional operator like “I dreamed that…”. Linguists will analyze this construction in terms of clausal complementation syntax and possible worlds semantics. But talking about a dream is often more like telling a story, with a potentially complex discourse structure (involving propositional discourse units connected by coherence relations like NARRATION, BACKGROUND, and EXPLANATION) that is hard to fit inside a single syntactically embedded that-clause (or a sequence of independently (...) embedded clauses). I show how we can analyze actual, complex dream report stories using a formal discourse semantics framework. I then explore how to extend this discourse framework to visual dream reporting, like in movies and comics, where it’s not immediately clear that we even have any intensional operators or embeddings to begin with. (shrink)

The relationship between the One and the Multiple in mystic philosophy is a profound and central theme that explores the nature of existence, the cosmos, and the divine. This theme is present in various mystical traditions, including those of the East and West, and it addresses the paradoxical coexistence of the unity and multiplicity of all things. -/- In mystic philosophy, the **One** often represents the ultimate reality, the source from which all things emanate and to which all things return. (...) It is the absolute, the infinite, and the unchanging. The One is beyond all attributes and is often associated with the divine or the absolute truth. -/- The **Multiple**, on the other hand, represents the manifest world, the diversity of forms, and the realm of change and plurality. It is the world we experience through our senses, the domain of time and space, where differentiation and individuality are apparent. -/- The relationship between the One and the Multiple is not one of opposition but of emanation and unity. The Multiple is seen as a reflection, expression, or manifestation of the One. In this sense, the diversity of the world doesn’t contradict the unity of the One but rather demonstrates it in a myriad of forms. -/- Mystics seek to understand and experience this relationship through various practices and insights. They aim to transcend the illusion of separation and duality to experience the non-dual reality where the One and the Multiple are recognized as inseparable. -/- This concept can be illustrated by the metaphor of the ocean and its waves. The ocean represents the One—vast, deep, and all-encompassing—while the waves represent the Multiple—distinct, diverse, and ever-changing. Each wave is unique, yet it is not separate from the ocean. The wave’s existence is dependent on and made of the same substance as the ocean. In the same way, each individual entity in the Multiple is an expression of the One. -/- In summary, the relationship between the One and the Multiple in mystic philosophy is a dynamic interplay that challenges the conventional understanding of separation. It invites a deeper exploration of reality, where the apparent multiplicity of the world is a direct expression of the singular, underlying essence of all that is. -/- The relationship between the One and the Multiple in the context of mathematical philosophy is a profound topic that touches upon the very foundations of existence and knowledge. It’s a theme that has been explored by philosophers and mathematicians alike, often leading to the contemplation of unity and diversity within the structures of reality. -/- In mathematics, the concept of the One can be seen as the basis of unity from which all numbers derive. It’s the identity element in multiplication, the starting point in counting, and the foundation of dimension in geometry. The One is often associated with the concept of monism in philosophy, which posits that there is a single, underlying substance or principle that constitutes reality. -/- On the other hand, the Multiple represents the infinite variety and diversity of forms and numbers that arise from the One. It’s the embodiment of plurality and the complex interplay of different entities that mathematics seeks to understand and describe. This reflects the philosophical stance of pluralism, which acknowledges the existence of multiple realities or truths. -/- The interplay between the One and the Multiple can be seen in the mathematical concept of sets. A set can be thought of as a unity, a whole composed of distinct elements. Yet, each element within the set also retains its individuality, contributing to the diversity of the set’s composition. This duality is mirrored in the philosophical exploration of the universal and the particular, where the universal represents the One, and the particulars represent the Multiple. -/- In the realm of mathematical philosophy, this relationship often leads to questions about the nature of mathematical objects: Are they discovered as part of an objective reality (the One), or are they constructed by the human mind from a multitude of experiences (the Multiple)? This debate resonates with the philosophical inquiry into the nature of truth and reality. -/- Reflecting on the One and the Multiple can also lead to a deeper understanding of the self and the cosmos. Just as the number one is integral to the existence of all other numbers, the individual self can be seen as a unique expression of the universal whole. Similarly, the cosmos can be viewed as a grand unity composed of a multiplicity of forms and phenomena. -/- Gödel’s incompleteness theorems have a fascinating connection to the philosophical concepts of the One and the Multiple. These theorems, which are pivotal in mathematical logic and philosophy of mathematics, articulate the inherent limitations of formal axiomatic systems, particularly those sufficient to express the arithmetic of natural numbers. -/- Gödel’s incompleteness theorems have a fascinating connection to the philosophical concepts of the One and the Multiple. These theorems, which are pivotal in mathematical logic and philosophy of mathematics, articulate the inherent limitations of formal axiomatic systems, particularly those sufficient to express the arithmetic of natural numbers⁴. -/- The **first incompleteness theorem** reveals that within any such consistent system, there are propositions that are true but cannot be proven within the system itself. This reflects the idea of the Multiple in that there is an abundance of mathematical truths, a multiplicity that exceeds the unifying framework of any one system. It suggests that the realm of mathematical truth is more extensive than any single formal system can fully capture. -/- The **second incompleteness theorem** extends this by showing that a system cannot prove its own consistency. This relates to the concept of the One, as it implies that a system’s complete self-understanding, its unity and coherence, is unattainable from within. It must look beyond itself, to an external vantage point, to ascertain its consistency. -/- In the context of the One and the Multiple, Gödel’s theorems imply that the One (a consistent formal system) is inherently incomplete and cannot encompass the Multiple (the totality of mathematical truths). This resonates with philosophical discussions about the relationship between unity and plurality. Just as a single philosophical system cannot capture the entirety of truth, a single formal mathematical system cannot encapsulate all mathematical truths. -/- Moreover, Gödel’s work suggests that the pursuit of a single, unified theory of everything in mathematics—a One that encompasses all Multiples—is an inherently Sisyphean task. There will always be more truths (Multiples) than can be derived from any given set of axioms (the One). -/- In essence, Gödel’s incompleteness theorems provide a formal underpinning to the philosophical notion that the One cannot exist without the Multiple, and vice versa. They are interdependent, with the One giving rise to the Multiple, and the Multiple necessitating the One for its expression and comprehension. This interplay is a dance of limitations and possibilities, where the boundaries of logic, mathematics, and philosophy blur into one another. -/- The relationship between the One and the Multiple in the context of the mathematics of zero is a deeply philosophical inquiry that bridges the abstract world of numbers with the existential questions of being and non-being. -/- Zero, in mathematics, is a symbol of absence, a representation of nothingness, yet it holds a pivotal position as a number. It is the void from which all things emerge and to which they return. In the philosophy of mathematics, zero is the paradoxical junction where the One and the Multiple converge and diverge. -/- From the perspective of the One, zero can be seen as the origin—the singular point that precedes the existence of numbers. It is the empty set, the foundation upon which the edifice of mathematics is constructed. As the identity element in addition, zero maintains the integrity of numbers, for adding zero to any number leaves it unchanged, reflecting the immutable nature of the One. -/- Conversely, when we consider the Multiple, zero represents the infinite potentiality of creation. It is the canvas upon which the integers, both positive and negative, express their multitude. Zero is the balance point, the fulcrum around which the symphony of numbers dances. It embodies the plurality of possibilities, the beginning of the number line that stretches infinitely in both directions. -/- Philosophically, zero challenges our understanding of existence. It is both something and nothing—a number that quantifies the absence of quantity. This duality echoes the philosophical struggle to comprehend how the One gives rise to the Multiple. How does the unity of being manifest the diversity of the cosmos? Zero offers a mathematical metaphor for this mystery, as it encapsulates the transition from non-existence to existence, from the undifferentiated One to the differentiated Multiple. -/- In the realm of set theory, zero corresponds to the empty set—a set with no elements. This set is unique in that it is the only set that contains nothing, yet it is the foundation upon which all other sets are built. The empty set is the mathematical embodiment of the One, and all other sets, containing multiple elements, arise from it. -/- Reflecting on zero in the context of Gödel’s incompleteness theorems, we find a resonance with the idea that the One (a consistent formal system) cannot capture the entirety of the Multiple (the totality of mathematical truths). Zero, as the foundation of numbers, similarly suggests that from the nothingness of the One, the infinite complexity of the Multiple emerges—yet it can never be fully encompassed or expressed by any single system. -/- In conclusion, the mathematics of zero offers a profound reflection on the relationship between the One and the Multiple. It serves as a bridge between the abstract and the concrete, the known and the unknowable, challenging us to ponder the origins of existence and the nature of reality itself. -/- . (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)

Despite some notable similarities between the scientific realisms of Sellars and Peirce (such as both being anti-representationalist, and future-directed), in his mature work Science and Metaphysics Sellars explicitly critiqued Peirce’s account of truth, as lacking “an intelligible foundation” (Sellars 1968: vii). In this paper, I explore Sellars’ proposed remedy to Peirce’s purported lack, in his complex and enigmatic account of picturing – a non-discursive ‘mapping’ of the world. I argue that although Sellars’ development of this idea is largely sound, much (...) of what he charges Peirce’s philosophy with missing is actually present there. By means of his semiotic icon / index / symbol distinction, Peirce manages to develop a philosophy of language which effectively coordinates the real order and the order of signification within the very structure of the proposition as he understands it, by contrast to Sellars’ claim that the two orders are merely connected by ‘analogy’. I also argue that in between Sellars’ ambitious account of veridicality, which appears to anticipate a form of scientific self-mensuration, and the dismissive ‘anti-truth’ quietism of neopragmatists such as Rorty, Peirce’s “contrite fallibilism” (Peirce CP 1.14) charts a wise middle path. (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)

Event concepts are unstructured atomic concepts that apply to event types. A paradigm example of such an event type would be that of diaper changing, and so a putative example of an atomic event concept would be DADDY'S-CHANGING-MY-DIAPER.1 I will defend two claims about such concepts. First, the conceptual claim that it is in principle possible to possess a concept such as DADDY'S-CHANGING-MY-DIAPER without possessing the concept DIAPER. Second, the empirical claim that we actually possess such concepts and that they (...) play an important role in our cognitive lives. The argument for the empirical claim has the form of an inference to the best explanation and is aimed at those who are already willing to attribute concepts and beliefs to infants and nonhuman animals. Many animals and prelinguistic infants seem capable of re-identifying event-types in the world, and they seem to store information about things happening at particular times and places. My account offers a plausible model of how such organisms are able to do this without attributing linguistically structured mental states to them. And although language allows adults to form linguistically structured mental representations of the world, there is no good reason to think that such structured representations necessarily replace the unstructured ones. There is also no good reason for a philosopher who is willing to explain the behavior of an organism by appealing to atomic concepts of individuals or kinds to not use a similar form of explanation when explaining the organism's capacity to recognize events. -/- We can form empirical concepts of individuals, kinds, properties, event-types, and states of affairs, among other things, and I assume that such concepts function like what François Recanati calls ‘mental files’ or what Ruth Millikan calls ‘substance concepts’ (Recanati 2012; Millikan 1999, 2000, 2017). To possess such a concept one must have a reliable capacity to re-identify the object in question, but this capacity of re-identification does not fix the reference of the concept. Such concepts allow us to collect and utilize useful information about things that we re-encounter in our environment. We can distinguish between a perception-action system and a perception-belief system, and I will argue that empirical concepts, including atomic event concepts, can play a role in both systems. The perception-action system involves the application of concepts in the service of (often skilled) action. We can think of the concept as a mental file containing motor-plans that can be activated once the individual recognizes that they are in a certain situation. In this way, recognizing something (whether an object or an event) as a token of a type, plays a role in guiding immediate action. The perception-belief system, in contrast, allows for the formation of beliefs that can play a role in deliberation and planning and in the formation of expectations. I distinguish between two particular types of belief which I call where-beliefs and when-beliefs, and I argue that we can model the formation of such perceptual beliefs in nonlinguistic animals and human infants in terms of the formation of a link between an empirical concept and a position on a cognitive map. According to the account offered, seemingly complex beliefs, such as a baby's belief that Daddy changed her diaper in the kitchen earlier, will not be linguistically structured. If we think that prelinguistic infants possess such concepts and are able to form such beliefs, it is likely that adults do too. The ability to form such beliefs does not require the capacity for public language, and we can model them in nonlinguistic terms; thus, we have no good reason to think of such beliefs as propositional attitudes. Of course, we can use sentences to refer to such beliefs, and thus it is possible to think of such beliefs as somehow relations to propositions. But it is not clear to me what is gained by this as we have a perfectly good way to think about the structure of such beliefs that does not involve any appeal to language. (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)