Thirteen meanings of 'implication' are described and compared. Among them are relations that have been called: logical implication, material implication,deductive implication, formal implication, enthymemic implication, and factual implication. In a given context, implication is the homogeneous two-place relation expressed by the relation verb 'implies'. For heuristic and expository reasons this article skirts many crucial issues including use-mention, the nature of the entities that imply and are implied, and the processes by which (...) knowledge of these relations are achieved. This paper is better thought of as an early stage of a dialogue than as a definitive treatise. (shrink)

Formal views of autonomy rule out substantive rational capacities (reasons-responsiveness) as a condition of autonomous agency. I argue that such views face a number of underappreciated problems: they have trouble making sense of how autonomous agents could be robustly responsible for their choices, face the burden of explaining why there should be a stark distinction between the importance of factual and evaluative information within autonomous agency, and leave it mysterious why autonomy is the sort of thing that has value (...) and ought to be promoted. Moreover, I argue that the alternative view that includes substantive rational capacities need not have the unacceptable political implications it is sometimes thought to have. (shrink)

What are the implications for human society, and for our institutions of higher learning, of the discovery of a sophisticated extraterrestrial intelligence (ETI) operating on and around Earth? This book explores this timely question from a multidisciplinary perspective. It considers scientific, philosophical, theological, and interdisciplinary ways of thinking about the question, and it represents all viewpoints on how likely it is that an ETI is already operating here on Earth. The book’s contributors represent a wide range of academic disciplines in (...) their formal training and later vocations, and, upon reflection on the book’s topic, they articulate a diverse range of insights into how ETI will impact humankind. It is safe to say that any contact or communication with ETI will not be merely a game changer for human society, but it also will be a paradigm changer. It makes sense for human beings to prepare themselves now for this important transition. (shrink)

I was quite excited when I first read Restall and Russell’s (2010) paper. For two reasons. First, because the paper provides rigorous formulations and formal proofs of implication barrier theses, namely “theses [which] deny that one can derive sentences of one type from sentences of another”. Second (and primarily), because the paper proves a general theorem, the Barrier Construction Theorem, which unifies implication barrier theses concerning four topics: generality, necessity, time, and normativity. After thinking about the paper, (...) I am satisfied with its treatment of the first three topics, namely generality, necessity, and time. But I am not satisfied with its treatment of normativity, so my comments are exclusively on that topic. (shrink)

Joshua Greene has argued that the empirical findings of cognitive science have implications for ethics. In particular, he has argued (1) that people’s deontological judgments in response to trolley problems are strongly influenced by at least one morally irrelevant factor, personal force, and are therefore at least somewhat unreliable, and (2) that we ought to trust our consequentialist judgments more than our deontological judgments when making decisions about unfamiliar moral problems. While many cognitive scientists have rejected Greene’s dual-process theory of (...) moral judgment on empirical grounds, philosophers have mostly taken issue with his normative assertions. For the most part, these two discussions have occurred separately. The current analysis aims to remedy this situation by philosophically analyzing the implications of moral dilemma research using the CNI model of moral decision-making – a formalized, mathematical model that decomposes three distinct aspects of moral-dilemma judgments. In particular, we show how research guided by the CNI model reveals significant conceptual, empirical, and theoretical problems with Greene’s dual-process theory, thereby questioning the foundations of his normative conclusions. (shrink)

Whether Trinitarianism is coherent depends not only on whether some account of the Trinity is coherent, but on which accounts of the Trinity count as "Trinitarian." After all, Arianism and Modalism are both accounts of the Trinity, but neither counts as Trinitarian (which is why defenses of Arianism or Modalism don’t count as defenses of Trinitarianism). This raises the question, if not just any account of the Trinity counts as Trinitarian, which do? Dale Tuggy is one of very few philosophers (...) to give explicit definitions of Trinitarian (versus Unitarian) theology. But they are no mere formalities. They are essential to his central criticisms of both historical and contemporary forms of Trinitarianism. In this paper, I offer my own definitions of Trinitarian and Unitarian theology, contrast them with Tuggy’s, and argue for the superiority of my definitions to Tuggy’s. If Trinitarianism and Unitarianism are what Tuggy says they are, the outlook for Trinitarianism is bleak indeed. If they are what I say they are, Tuggy’s central objection to Trinitarianism fails. To show what is at stake in these pairs of definitions, I examine a doctrine much neglected in Analytic Theology, but central to Nicene Trinitarianism—the Monarchy of the Father. (shrink)

It is a received view that Kant’s formal logic (or what he calls “pure general logic”) is thoroughly intensional. On this view, even the notion of logical extension must be understood solely in terms of the concepts that are subordinate to a given concept. I grant that the subordination relation among concepts is an important theme in Kant’s logical doctrine of concepts. But I argue that it is both possible and important to ascribe to Kant an objectual notion of (...) logical extension according to which the extension of a concept is the multitude of objects falling under it. I begin by defending this ascription in response to three reasons that are commonly invoked against it. First, I explain that this ascription is compatible with Kant’s philosophical reflections on the nature and boundary of a formal logic. Second, I show that the objectual notion of extension I ascribe to Kant can be traced back to many of the early modern works of logic with which he was more or less familiar. Third, I argue that such a notion of extension makes perfect sense of a pivotal principle in Kant’s logic, namely the principle that the quantity of a concept’s extension is inversely proportional to that of its intension. In the process, I tease out two important features of the Kantian objectual notion of logical extension in terms of which it markedly differs from the modern one. First, on the modern notion the extension of a concept is the sum of the objects actually falling under it; on the Kantian notion, by contrast, the extension of a concept consists of the multitude of possible objects—not in the metaphysical sense of possibility, though—to which a concept applies in virtue of being a general representation. While the quantity of the former extension is finite, that of the latter is infinite—as is reflected in Kant’s use of a plane-geometrical figure (e.g., circle, square), which is continuum as opposed to discretum, to represent the extension in question. Second, on the modern notion of extension, a concept that signifies exactly one object has a one-member extension; on the Kantian notion, however, such a concept has no extension at all—for a concept is taken to have extension only if it signifies a multitude of things. This feature of logical extension is manifested in Kant’s claim that a singular concept (or a concept in its singular use) can, for lack of extension, be figuratively represented only by a point—as opposed to an extended figure like circle, which is reserved for a general concept (or a concept in its general use). Precisely on account of these two features, the Kantian objectual extension proves vital to Kant’s theory of logical quantification (in universal, particular and singular judgments, respectively) and to his view regarding the formal truth of analytic judgments. (shrink)

In this study, I intend to show how and why, in the Port-Royal Logic, a singular term can reveal the nature of the logical judgment in the handbook. As I argue, the treatment given to one of thee singular terms, namely, the defined descriptions, in the terminology introduced by Russell, leads to an opening to langage that sounds unexpected and unjustified. Considering the privilege of thinking over langage and also that judgment is the mental act that defines logic, however, we (...) may understand how the authors regard langage, in relation to the epistemic constituents, namely, the mental acts within the terms. In doing so we are compelled to recognize the implications of this step towards pragmatism in fixing the meaning of defined descriptions to the nature of judgment in the handbook. This opening to langage reveals the conception of judgment as a twofold mental act: a formal and a practical (moral and theological) one. (shrink)

I was quite excited when I first read Restall and Russell’s (2010) paper. For two reasons. First, because the paper provides rigorous formulations and formal proofs of implication barrier the- ses, namely “theses [which] deny that one can derive sentences of one type from sentences of another”. Second (and primarily), because the paper proves a general theorem, the Barrier Con- struction Theorem, which unifies implication barrier theses concerning four topics: generality, necessity, time, and normativity. After thinking about (...) the paper, I am satisfied with its treatment of the first three topics, namely generality, necessity, and time. But I am not satisfied with its treatment of normativity, so my comments are exclusively on that topic. (shrink)

Ontology has been proposed as a solution to the 'Tower of Babel' problem that threatens the semantic interoperability of information systems constructed independently for the same domain. In information systems research and applications, ontologies are often implemented by formalizing the meanings of words from natural languages. However, words in different natural languages sometimes subdivide the same domain of reality in terms of different conceptual categories. If the words and their associated concepts in two natural languages, or even in two terminological (...) traditions within the same language, do not have common referents in the real world, an ontology based on word meanings will inherit the 'Tower of Babel' problem from the languages involved, rather than solve it. In this paper we present evidence from a preliminary comparison of landscape terms in English with those in the Yindjibarndi language of northwestern Australia demonstrating that this problem is not just hypothetical. Some possible solutions are suggested. (shrink)

Seminal work intended to found a new field of integrative Noetic Science is summarized. Until now the philosophy of Biological Mechanism has ruled medicine and psychology. Penrose claims, AA scientific world-view which does not profoundly come to terms with the problem of conscious mind can have no serious pretensions of completeness@. A noetic action principle synonymous with the historic concept of élan vital is introduced as the basis of a Continuous State Conscious Universe (CSCU). The least unit of CSCU superspace (...) defines Awareness as a fundamental physical quantity like charge in electrodynamics. This cosmological context reveals the origin of complexity in self-organized living-systems wherein the physical basis of qualia is formalized. The dynamics of this teleological action principle, mediated by a unitary noetic field pervading all biochemical species, optimizes the state of well-being through homeostasis and provides the fundamental basis for developing a Moral Psychology. (shrink)

There is a profound, but frequently ignored relationship between logical consequence (formal implication) and material implication. The first repeats the patterns of the latter, but with a wider modal reach. It is argued that this kinship between formal and material implication simply means that they express the same kind of implication, but differ in scope. Formal implication is unrestricted material implication. This apparently innocuous observation has some significant corollaries: (1) conditionals are (...) not connectives, but arguments; (2) the traditional examples of valid argumentative forms are metalogical principles that express the properties of logical consequence; (3) formal logic is not a useful guide to detect valid arguments in the real world; (4) it is incoherent to propose alternatives to the material implication while accepting the classical properties of formal implication; (5) some of the counter-examples to classical argumentative forms and known conditional puzzles are unsound. (shrink)

In the article I deal with some paradoxes and errors caused by improper usage of logical and philosophical terms appearing in the arguments for existence of god and other philosophical issues. I point at rst some paradoxes coming om improper usage of propositional calculus as an instrument for analysis of a natural language. this language is actually not using simple sentences but rather propositional functions, their logical connections, and some replacements for variables in them. We still have to deal with (...) so called paradox of material implication. the second paragraph provides formal and metatheoretical critics of Charles Sanders Peirce’s theory of deduction, induction and abduction. I argue that what Peirce and his followers call abduction is actually deduction or some reasoning unable to describe in terms of the logic used by them. Both syllogistic and inferential theory of abduction generate some paradoxes and contradictions. In the last paragraph also some paradoxes and contradictions resulting om the theory of causation by Jan Łukasiewicz are presented. the central issue of the article is erroneous usage of the implication: in logical paraphrases of a natural language, in description of the scienti c reasoning, and in description of causality. However, my objective is not to solve all problems mentioned above but rather to open a discussion over them. (shrink)

This paper presents a formalization of the classical proof of completeness in Henkin-style developed by Troelstra and van Dalen for intuitionistic logic with respect to Kripke models. The completeness proof incorporates their insights in a fresh and elegant manner that is better suited for mechanization. We discuss details of our implementation in the Lean theorem prover with emphasis on the prime extension lemma and construction of the canonical model. Our implementation is restricted to a system of intuitionistic propositional logic with (...) implication, conjunction, disjunction, and falsity given in terms of a Hilbert-style axiomatization. As far as we know, our implementation is the first verified Henkin-style proof of completeness for intuitionistic logic following Troelstra and van Dalen's method in the literature. (shrink)

Formal criteria of theoretical equivalence are mathematical mappings between specific sorts of mathematical objects, notably including those objects used in mathematical physics. Proponents of formal criteria claim that results involving these criteria have implications that extend beyond pure mathematics. For instance, they claim that formal criteria bear on the project of using our best mathematical physics as a guide to what the world is like, and also have deflationary implications for various debates in the metaphysics of physics. (...) In this paper, I investigate whether there is a defensible view according to which formal criteria have significant non-mathematical implications, of these sorts or any other, reaching a chiefly negative verdict. Along the way, I discuss various foundational issues concerning how we use mathematical objects to describe the world when doing physics, and how this practice should inform metaphysics. I diagnose the prominence of formal criteria as stemming from contentious views on these foundational issues, and endeavor to motivate some alternative views in their stead. (shrink)

Information-theoretic approaches to formal logic analyze the "common intuitive" concepts of implication, consequence, and validity in terms of information content of propositions and sets of propositions: one given proposition implies a second if the former contains all of the information contained by the latter; one given proposition is a consequence of a second if the latter contains all of the information contained by the former; an argument is valid if the conclusion contains no information beyond that of the (...) premise-set. This paper locates information-theoretic approaches historically, philosophically, and pragmatically. Advantages and disadvantages are identified by examining such approaches in themselves and by contrasting them with standard transformation-theoretic approaches. Transformation-theoretic approaches analyze validity (and thus implication) in terms of transformations that map one argument onto another: a given argument is valid if no transformation carries it onto an argument with all true premises and false conclusion. Model-theoretic, set-theoretic, and substitution-theoretic approaches, which dominate current literature, can be construed as transformation-theoretic, as can the so-called possible-worlds approaches. Ontic and epistemic presuppositions of both types of approaches are considered. Attention is given to the question of whether our historically cumulative experience applying logic is better explained from a purely information-theoretic perspective or from a purely transformation-theoretic perspective or whether apparent conflicts between the two types of approaches need to be reconciled in order to forge a new type of approach that recognizes their basic complementarity. (shrink)

This paper presents a recent formalization of a Henkin-style completeness proof for the propositional modal logic S5 using the Lean theorem prover. The proof formalized is close to that of Hughes and Cresswell, but the system, based on a different choice of axioms, is better described as a Mendelson system augmented with axiom schemes for K, T, S4, and B, and the necessitation rule as a rule of inference. The language has the false and implication as the only primitive (...) logical connectives and necessity as the only primitive modal operator. The full source code is available online and has been typechecked with Lean 3.4.2. (shrink)

This paper defends a view of the Gene Ontology (GO) and of Basic Formal Ontology (BFO) as examples of what the manufacturing industry calls product-service systems. This means that they are products (the ontologies) bundled with a range of ontology services such as updates, training, help desk, and permanent identifiers. The paper argues that GO and BFO are contrasted in this respect with DOLCE, which approximates more closely to a scientific theory or a scientific publication. The paper provides a (...) detailed overview of ontology services and concludes with a discussion of some implications of the product-service system approach for the understanding of the nature of applied ontology. Ontology developer communities are compared in this respect with developers of scientific theories and of standards (such as W3C). For each of these we can ask: what kinds of products do they develop and what kinds of services do they provide for the users of these products? (shrink)

Este artículo presenta una aproximación lógico-filosófica al problema de las medidas sin interacción (ifm, por sus siglas en inglés) presentes en ciertos experimentos físicos mecánico-cuánticos. Se explicitarán tanto las posibles vías para abordar el estudio de las IFM desde una perspectiva formal, como algunos de los principales retos a la hora de llevar a cabo dicha aproximación.

Advances in neuroscience implicate reentrant signaling as the predominant form of communication between brain areas. This principle was used in a series of masking experiments that defy explanation by feed-forward theories. The masking occurs when a brief display of target plus mask is continued with the mask alone. Two masking processes were found: an early process affected by physical factors such as adapting luminance and a later process affected by attentional factors such as set size. This later process is called (...) masking by object substitution, because it occurs whenever there is a mismatch between the reentrant visual representation and the ongoing lower level activity. Iterative reentrant processing was formalized in a computational model that provides an excellent fit to the data. The model provides a more comprehensive account of all forms of visual masking than do the long-held feed-forward views based on inhibitory contour interactions. (shrink)

The Generalized Quantifiers Theory, I will argue, in the second half of last Century has led to an important rapprochement, relevant both in logic and in linguistics, between logical quantification theories and the semantic analysis of quantification in natural languages. In this paper I concisely illustrate the formal aspects and the theoretical implications of this rapprochement.

Recent work in formal semantics suggests that the language system includes not only a structure building device, as standardly assumed, but also a natural deductive system which can determine when expressions have trivial truth-conditions (e.g., are logically true/false) and mark them as unacceptable. This hypothesis, called the `logicality of language', accounts for many acceptability patterns, including systematic restrictions on the distribution of quantifiers. To deal with apparent counter-examples consisting of acceptable tautologies and contradictions, the logicality of language is often (...) paired with an additional assumption according to which logical forms are radically underspecified: i.e., the language system can see functional terms but is `blind' to open class terms to the extent that different tokens of the same term are treated as if independent. This conception of logical form has profound implications: it suggests an extreme version of the modularity of language, and can only be paired with non-classical---indeed quite exotic---kinds of deductive systems. The aim of this paper is to show that we can pair the logicality of language with a different and ultimately more traditional account of logical form. This framework accounts for the basic acceptability patterns which motivated the logicality of language, can explain why some tautologies and contradictions are acceptable, and makes better predictions in key cases. As a result, we can pursue versions of the logicality of language in frameworks compatible with the view that the language system is not radically modular vis-a-vis its open class terms and employs a deductive system that is basically classical. (shrink)

Various results show the ‘formal equivalence’ of kin and group selectionist methodologies, but this does not preclude there being a real and useful distinction between kin and group selection processes. I distinguish individual- and population-centred approaches to drawing such a distinction, and I proceed to develop the latter. On the account I advance, the differences between kin and group selection are differences of degree in the structural properties of populations. A spatial metaphor provides a useful framework for thinking about (...) these differences: kin and group selection may be conceptualized as large, overlapping regions of K - G space. I then consider some implications of the account, defend it from possible objections, and further argue that the structural features characteristic of both kin and group selection may recur at multiple levels of biological organization. (shrink)

The question of how we come to accept new theories is a central area of inquiry in scientonomic discourse. However, there has yet to be a formal discussion of the subjective reasons an agent may have for accepting theories. This paper explores these epistemic reasons and constructs a historically sensitive definition of reason. This formulation takes an abstractionist stance towards the ontology of reasons and makes use of a composite basing relation. The descriptive and normative components of reasons are (...) fully formulated in scientonomic terms through the application of the newly introduced notion of implication, and its separation from the notion of inference. In addition, the paper provides scientonomic definitions for sufficient reason, support, and normative inference. The fruitfulness of this formulation of reasons is illustrated by a few examples. (shrink)

What does it look like when a group of scientists set out to re-envision an entire field of biology in symbolic and formal terms? I analyze the founding and articulation of Numerical Taxonomy between 1950 and 1970, the period when it set out a radical new approach to classification and founded a tradition of mathematics in systematic biology. I argue that introducing mathematics in a comprehensive way also requires re-organizing the daily work of scientists in the field. Numerical taxonomists (...) sought to establish a mathematical method for classification that was universal to every type of organism, and I argue this intrinsically implicated them in a qualitative re-organization of the work of all systematists. I also discuss how Numerical Taxonomy’s re-organization of practice became entrenched across systematic biology even as opposing schools produced their own competing mathematical methods. In this way, the structure of the work process became more fundamental than the methodological theories that motivated it. (shrink)

In this paper I will develop a lambda-term calculus, lambda-2Int, for a bi-intuitionistic logic and discuss its implications for the notions of sense and denotation of derivations in a bilateralist setting. Thus, I will use the Curry-Howard correspondence, which has been well-established between the simply typed lambda-calculus and natural deduction systems for intuitionistic logic, and apply it to a bilateralist proof system displaying two derivability relations, one for proving and one for refuting. The basis will be the natural deduction system (...) of Wansing's bi-intuitionistic logic 2Int, which I will turn into a term-annotated form. Therefore, we need a type theory that extends to a two-sorted typed lambda-calculus. I will present such a term-annotated proof system for 2Int and prove a Dualization Theorem relating proofs and refutations in this system. On the basis of these formal results I will argue that this gives us interesting insights into questions about sense and denotation as well as synonymy and identity of proofs from a bilateralist point of view. (shrink)

Recent work in formal semantics suggests that the language system includes not only a structure building device, as standardly assumed, but also a natural deductive system which can determine when expressions have trivial truth‐conditions (e.g., are logically true/false) and mark them as unacceptable. This hypothesis, called the ‘logicality of language’, accounts for many acceptability patterns, including systematic restrictions on the distribution of quantifiers. To deal with apparent counter‐examples consisting of acceptable tautologies and contradictions, the logicality of language is often (...) paired with an additional assumption according to which logical forms are radically underspecified: i.e., the language system can see functional terms but is ‘blind’ to open class terms to the extent that different tokens of the same term are treated as if independent. This conception of logical form has profound implications: it suggests an extreme version of the modularity of language, and can only be paired with non‐classical—indeed quite exotic—kinds of deductive systems. The aim of this paper is to show that we can pair the logicality of language with a different and ultimately more traditional account of logical form. This framework accounts for the basic acceptability patterns which motivated the logicality of language, can explain why some tautologies and contradictions are acceptable, and makes better predictions in key cases. As a result, we can pursue versions of the logicality of language in frameworks compatible with the view that the language system is not radically modular vis‐á‐vis its open class terms and employs a deductive system that is basically classical. (shrink)

Information-theoretic approaches to formal logic analyse the "common intuitive" concept of propositional implication (or argumental validity) in terms of information content of propositions and sets of propositions: one given proposition implies a second if the former contains all of the information contained by the latter; an argument is valid if the conclusion contains no information beyond that of the premise-set. This paper locates information-theoretic approaches historically, philosophically and pragmatically. Advantages and disadvantages are identified by examining such approaches in (...) themselves and by contrasting them with standard transformation-theoretic approaches. Transformation-theoretic approaches analyse validity (and thus implication) in terms of transformations that map one argument onto another: a given argument is valid if no transformation carries it onto an argument with all true premises and false conclusion. Model-theoretic, set-theoretic, and substitution-theoretic approaches, which dominate current literature, can be construed as transformation-theoretic, as can the so-called possible-worlds approaches. Ontic and epistemic presuppositions of both types of approaches are considered. Attention is given to the question of whether our historically cumulative experience applying logic is better explained from a purely information-theoretic perspective or from a purely transformation-theoretic perspective or whether apparent conflicts between the two types of approaches need to be reconciled in order to forge a new type of approach that recognizes their basic complementarity. (shrink)

If the goal of statistical analysis is to form justified credences based on data, then an account of the foundations of statistics should explain what makes credences justified. I present a new account called statistical reliabilism (SR), on which credences resulting from a statistical analysis are justified (relative to alternatives) when they are in a sense closest, on average, to the corresponding objective probabilities. This places (SR) in the same vein as recent work on the reliabilist justification of credences generally (...) [Dunn, 2015, Tang, 2016, Pettigrew, 2018], but it has the advantage of being action-guiding in that knowledge of objective probabilities is not required to identify the best-justified available credences. The price is that justification is relativized to a specific class of candidate objective probabilities, and to a particular choice of reliability measure. On the other hand, I show that (SR) has welcome implications for frequentist-Bayesian reconciliation, including a clarification of the use of priors; complemen- tarity between probabilist and fallibilist [Gelman and Shalizi, 2013, Mayo, 2018] approaches towards statistical foundations; and the justification of credences outside of formal statistical settings. Regarding the latter, I demonstrate how the insights of statistics may be used to amend other reliabilist accounts so as to render them action-guiding. I close by discussing new possible research directions for epistemologists and statisticians (and other applied users of probability) raised by the (SR) framework. (shrink)

In the latter half of the twentieth century, philosophers of science have argued (implicitly and explicitly) that epistemically rational individuals might compose epistemically irrational groups and that, conversely, epistemically rational groups might be composed of epistemically irrational individuals. We call the conjunction of these two claims the Independence Thesis, as they together imply that methodological prescriptions for scientific communities and those for individual scientists might be logically independent of one another. We develop a formal model of scientific inquiry, define (...) four criteria for individual and group epistemic rationality, and then prove that the four definitions diverge, in the sense that individuals will be judged rational when groups are not and vice versa. We conclude by explaining implications of the inconsistency thesis for (i) descriptive history and sociology of science and (ii) normative prescriptions for scientific communities. (shrink)

We discuss the philosophical implications of formal results showing the con- sequences of adding the epsilon operator to intuitionistic predicate logic. These results are related to Diaconescu’s theorem, a result originating in topos theory that, translated to constructive set theory, says that the axiom of choice (an “existence principle”) implies the law of excluded middle (which purports to be a logical principle). As a logical choice principle, epsilon allows us to translate that result to a logical setting, where one (...) can get an analogue of Diaconescu’s result, but also can disentangle the roles of certain other assumptions that are hidden in mathematical presentations. It is our view that these results have not received the attention they deserve: logicians are unlikely to read a discussion because the results considered are “already well known,” while the results are simultaneously unknown to philosophers who do not specialize in what most philosophers will regard as esoteric logics. This is a problem, since these results have important implications for and promise signif i cant illumination of contem- porary debates in metaphysics. The point of this paper is to make the nature of the results clear in a way accessible to philosophers who do not specialize in logic, and in a way that makes clear their implications for contemporary philo- sophical discussions. To make the latter point, we will focus on Dummettian discussions of realism and anti-realism. Keywords: epsilon, axiom of choice, metaphysics, intuitionistic logic, Dummett, realism, antirealism. (shrink)

This chapter offers an opinionated introduction to higher-order formal languages with an eye towards their applications in metaphysics. A simply relationally typed higher-order language is introduced in four stages: starting with first-order logic, adding first-order predicate abstraction, generalizing to higher-order predicate abstraction, and finally adding higher-order quantification. It is argued that both β-conversion and Universal Instantiation are valid on the intended interpretation of this language. Given these two principles, it is then shown how we can use pure higher-order logic (...) to ask, and begin to answer, metaphysical questions with non-trivial implications. In particular, while we must reject the popular idea that structural differences between sentences correspond to parallel distinctions in the logical structure of extra-linguistic reality, it may still be possible to give a purely logical characterization of objectual aboutness and related notions. (shrink)

It is plausible that there are epistemic reasons bearing on a distinctively epistemic standard of correctness for belief. It is also plausible that there are a range of practical reasons bearing on what to believe. These theses are often thought to be in tension with each other. Most significantly for our purposes, it is obscure how epistemic reasons and practical reasons might interact in the explanation of what one ought to believe. We draw an analogy with a similar distinction between (...) types of reasons for actions in the context of activities. The analogy motivates a two-level account of the structure of normativity that explains the interaction of correctness-based and other reasons. This account relies upon a distinction between normative reasons and authoritatively normative reasons. Only the latter play the reasons role in explaining what state one ought to be in. All and only practical reasons are authoritative reasons. Hence, in one important sense, all reasons for belief are practical reasons. But this account also preserves the autonomy and importance of epistemic reasons. Given the importance of having true beliefs about the world, our epistemic standard typically plays a key role in many cases in explaining what we ought to believe. In addition to reconciling (versions of) evidentialism and pragmatism, this two-level account has implications for a range of important debates in normative theory, including the interaction of right and wrong reasons for actions and other attitudes, the significance of reasons in understanding normativity and authoritative normativity, the distinction between ‘formal’ and ‘substantive’ normativity, and whether there is a unified source of authoritative normativity. (shrink)

The assignment of truth values assigned bivalent logic to conditional in tabular standard definition, is based on epistemological nature categories, which are incompatible with the formal and abstract nature of logical structures. The logic is intended to qualify with epistemological categories, non-epistemological formal structures. This assignment evades the rigor of logicality that demand any formal structure and therefore it lacks rational necessity.

We reconsider the pragmatic interpretation of intuitionistic logic [21] regarded as a logic of assertions and their justi cations and its relations with classical logic. We recall an extension of this approach to a logic dealing with assertions and obligations, related by a notion of causal implication [14, 45]. We focus on the extension to co-intuitionistic logic, seen as a logic of hypotheses [8, 9, 13] and on polarized bi-intuitionistic logic as a logic of assertions and conjectures: looking at (...) the S4 modal translation, we give a de nition of a system AHL of bi-intuitionistic logic that correctly represents the duality between intuitionistic and co-intuitionistic logic, correcting a mistake in previous work [7, 10]. A computational interpretation of cointuitionism as a distributed calculus of coroutines is then used to give an operational interpretation of subtraction.Work on linear co-intuitionism is then recalled, a linear calculus of co-intuitionistic coroutines is de ned and a probabilistic interpretation of linear co-intuitionism is given as in [9]. Also we remark that by extending the language of intuitionistic logic we can express the notion of expectation, an assertion that in all situations the truth of p is possible and that in a logic of expectations the law of double negation holds. Similarly, extending co-intuitionistic logic, we can express the notion of conjecture that p, de ned as a hypothesis that in some situation the truth of p is epistemically necessary. (shrink)

Urban spaces, often emerging outside formal, recognized boundaries, underscore the pivotal role women play in shaping these environments. Despite the enduring influence of patriarchal and hierarchical structures that render these spaces overtly gendered, it is within these contexts that women’s actions become particularly transformative. Drawing from feminist urban theories of the global south, this paper investigates informal placemaking, feminist urban activism, revolutionary placemaking, online protest movements, and the networks that support women’s solidarity groups. Employing a mixed-methods approach that includes (...) case studies, interviews with activists, and social media analysis, this research focuses on Iran, with a specific emphasis on the recent ‘Women, Life, Freedom’ movement. This study not only highlights how women navigate, contest, and reshape urban spaces through feminist urban activism and informal revolutionary placemaking but also anticipates the broader implications of these actions for urban planning and policy. By analyzing and comparing these case studies, we aim to uncover the commonalities, differences, challenges, and opportunities between informal/formal, state-led/bottom-up, and revolutionary feminist placemaking practices in Iran. The findings of this paper are expected to contribute valuable insights into the dynamics of feminist urbanism and suggest avenues for future research in enhancing the inclusivity and responsiveness of urban spaces to gendered needs and activism. (shrink)

This paper generalises the classical Condorcet jury theorem from majority voting over two options to plurality voting over multiple options. The paper further discusses the debate between epistemic and procedural democracy and situates its formal results in that debate. The paper finally compares a number of different social choice procedures for many-option choices in terms of their epistemic merits. An appendix explores the implications of some of the present mathematical results for the question of how probable majority cycles (as (...) in Condorcet's paradox) are in large electorates. (shrink)

I develop and defend a truthmaker semantics for the relevant logic R. The approach begins with a simple philosophical idea and develops it in various directions, so as to build a technically adequate relevant semantics. The central philosophical idea is that truths are true in virtue of specific states. Developing the idea formally results in a semantics on which truthmakers are relevant to what they make true. A very natural notion of conditionality is added, giving us relevant implication. I (...) then investigate ways to add conjunction, disjunction, and negation; and I discuss how to justify contraposition and excluded middle within a truthmaker semantics. (shrink)

This volume offers very selected papers from the 2014 conference of the “International Association for Computing and Philosophy” (IACAP) - a conference tradition of 28 years. - - - Table of Contents - 0 Vincent C. Müller: - Editorial - 1) Philosophy of computing - 1 Çem Bozsahin: - What is a computational constraint? - 2 Joe Dewhurst: - Computing Mechanisms and Autopoietic Systems - 3 Vincenzo Fano, Pierluigi Graziani, Roberto Macrelli and Gino Tarozzi: - Are Gandy Machines really local? (...) - 4 Doukas Kapantais: - A refutation of the Church-Turing thesis according to some interpretation of what the thesis says - 5 Paul Schweizer: - In What Sense Does the Brain Compute? - 2) Philosophy of computer science & discovery - 6 Mark Addis, Peter Sozou, Peter C R Lane and Fernand Gobet: - Computational Scientific Discovery and Cognitive Science Theories - 7 Nicola Angius and Petros Stefaneas: - Discovering Empirical Theories of Modular Software Systems. An Algebraic Approach. - 8 Selmer Bringsjord, John Licato, Daniel Arista, Naveen Sundar Govindarajulu and Paul Bello: - Introducing the Doxastically Centered Approach to Formalizing Relevance Bonds in Conditionals - 9 Orly Stettiner: - From Silico to Vitro: - Computational Models of Complex Biological Systems Reveal Real-world Emergent Phenomena - 3) Philosophy of cognition & intelligence - 10 Douglas Campbell: - Why We Shouldn’t Reason Classically, and the Implications for Artificial Intelligence - 11 Stefano Franchi: - Cognition as Higher Order Regulation - 12 Marcello Guarini: - Eliminativisms, Languages of Thought, & the Philosophy of Computational Cognitive Modeling - 13 Marcin Miłkowski: - A Mechanistic Account of Computational Explanation in Cognitive Science and Computational Neuroscience - 14 Alex Tillas: - Internal supervision & clustering: - A new lesson from ‘old’ findings? - 4) Computing & society - 15 Vasileios Galanos: - Floridi/Flusser: - Parallel Lives in Hyper/Posthistory - 16 Paul Bello: - Machine Ethics and Modal Psychology - 17 Marty J. Wolf and Nir Fresco: - My Liver Is Broken, Can You Print Me a New One? - 18 Marty J. Wolf, Frances Grodzinsky and Keith W. Miller: - Robots, Ethics and Software – FOSS vs. Proprietary Licenses. (shrink)

In recent years, the e ffort to formalize erotetic inferences (i.e., inferences to and from questions) has become a central concern for those working in erotetic logic. However, few have sought to formulate a proof theory for these inferences. To fill this lacuna, we construct a calculus for (classes of) sequents that are sound and complete for two species of erotetic inferences studied by Inferential Erotetic Logic (IEL): erotetic evocation and regular erotetic implication. While an attempt has been made (...) to axiomatize the former in a sequent system, there is currently no proof theory for the latter. Moreover, the extant axiomatization of erotetic evocation fails to capture its defeasible character and provides no rules for introducing or eliminating question-forming operators. In contrast, our calculus encodes defeasibility conditions on sequents and provides rules governing the introduction and elimination of erotetic formulas. We demonstrate that an elimination theorem holds for a version of the cut rule that applies to both declarative and erotetic formulas and that the rules for the axiomatic account of question evocation in IEL are admissible in our system. (shrink)

This paper is concerned with a propositional modal logic with operators for necessity, actuality and apriority. The logic is characterized by a class of relational structures defined according to ideas of epistemic two-dimensional semantics, and can therefore be seen as formalizing the relations between necessity, actuality and apriority according to epistemic two-dimensional semantics. We can ask whether this logic is correct, in the sense that its theorems are all and only the informally valid formulas. This paper gives outlines of two (...) arguments that jointly show that this is the case. The first is intended to show that the logic is informally sound, in the sense that all of its theorems are informally valid. The second is intended to show that it is informally complete, in the sense that all informal validities are among its theorems. In order to give these arguments, a number of independently interesting results concerning the logic are proven. In particular, the soundness and completeness of two proof systems with respect to the semantics is proven (Theorems 2.11 and 2.15), as well as a normal form theorem (Theorem 3.2), an elimination theorem for the actuality operator (Corollary 3.6), and the decidability of the logic (Corollary 3.7). It turns out that the logic invalidates a plausible principle concerning the interaction of apriority and necessity; consequently, a variant semantics is briefly explored on which this principle is valid. The paper concludes by assessing the implications of these results for epistemic two-dimensional semantics. (shrink)

In this paper, we identify a new and mathematically well-defined sense in which the coherence of a set of hypotheses can be truth-conducive. Our focus is not, as usual, on the probability but on the confirmation of a coherent set and its members. We show that, if evidence confirms a hypothesis, confirmation is “transmitted” to any hypotheses that are sufficiently coherent with the former hypothesis, according to some appropriate probabilistic coherence measure such as Olsson’s or Fitelson’s measure. Our findings have (...) implications for scientific methodology, as they provide a formal rationale for the method of indirect confirmation and the method of confirming theories by confirming their parts. (shrink)

One of the hottest philosophical debates in recent years concerns the nature of the semantics/pragmatics divide. Some writers have expressed the reserve that this might be merely terminological, but in my view it ultimately concerns a substantive issue with empirical implications: the scope and limits of a serious scientific undertaking, formal semantics. In this critical note I discuss two arguments by Recanati: his main methodological argument --viz. that the contents posited by what he calls 'literalists' play no relevant role (...) in communication--, and some phenomenological considerations regarding the "Availability Principle" that he appeals to in order to buttress that main argument. /// Uno de los más encarnizados debates filosóficos recientes atañe a la naturaleza de la distinción entre semántica y pragmática. Aunque algunos autores han expresado reservas en el sentido de que èste pudiera ser sólo terminológico, en mi opinión tiene que ver con una cuestión sustantiva con implicaciones empíricas: el alcance y los límites de una empresa científica seria, la semántica formal. En este texto discuto dos argumentos de Recanati: su principal argumento metodológico, que los contenidos postulados por los autores que él denomina "literalistas" no desempeñan ningùn papel relevante en la comunicación, y, en segundo lugar, ciertas consideraciones fenomenológicas en torno a su "Principio de Accesibilidad", a las cuales apela para apoyar el argumento metodológico. (shrink)

In ‘The normative role of knowledge’ (2012), Declan Smithies defends a ‘JK-rule’ for belief: One has justification to believe that P iff one has justification to believe that one is in a position to know that P. Similar claims have been defended by others (Huemer, 2007, Reynolds, forthcoming). In this paper, I shall argue that the JK-rule is false. The standard and familiar way of arguing against putative rules for belief or assertion is, of course, to describe putative counterexamples. My (...) argument, though, won’t be like this – indeed I doubt that there are any intuitively compelling counterexamples to the JK-rule. Nevertheless, the claim that there are counterexamples to the JK-rule can, I think, be given something approaching a formal proof. My primary aim here is to sketch this proof. I will briefly consider some broader implications for how we ought to think about the epistemic standards governing belief and assertion. (shrink)

It is a widespread intuition that the coherence of independent reports provides a powerful reason to believe that the reports are true. Formal results by Huemer, M. 1997. “Probability and Coherence Justification.” Southern Journal of Philosophy 35: 463–72, Olsson, E. 2002. “What is the Problem of Coherence and Truth?” Journal of Philosophy XCIX : 246–72, Olsson, E. 2005. Against Coherence: Truth, Probability, and Justification. Oxford University Press., Bovens, L., and S. Hartmann. 2003. Bayesian Epistemology. Oxford University Press, prove that, (...) under certain conditions, coherence cannot increase the probability of the target claim. These formal results, known as ‘the impossibility theorems’ have been widely discussed in the literature. They are taken to have significant epistemic upshot. In particular, they are taken to show that reports must first individually confirm the target claim before the coherence of multiple reports offers any positive confirmation. In this paper, I dispute this epistemic interpretation. The impossibility theorems are consistent with the idea that the coherence of independent reports provides a powerful reason to believe that the reports are true even if the reports do not individually confirm prior to coherence. Once we see that the formal discoveries do not have this implication, we can recover a model of coherence justification consistent with Bayesianism and these results. This paper, thus, seeks to turn the tide of the negative findings for coherence reasoning by defending coherence as a unique source of confirmation. (shrink)

My paper addresses a topic--the implications of Rawls's justice as fairness for affirmative action--that has received remarkably little attention from Rawls's major interpreters. The only extended treatments of it that are in print are over a quarter-century old, and they bear scarcely any relationship to Rawls's own nonideal theorizing. Following Christine Korsgaard's lead, I work through the implications of Rawls's nonideal theory and show what it entails for affirmative action: viz. that under nonideal conditions, aggressive forms of formal equality (...) of opportunity (e.g., sensitivity training, outreach efforts, external monitoring and enforcement) and compensating support (e.g., special fellowship programs, childcare facilities, mentoring, co-op opportunities, etc.) can be justified, but that "hard" and even "soft" quotas are difficult to defend under any conditions. I conclude the paper by exploring the implications of these surprising results for contemporary liberalism more broadly and for constitutional law and public policy. (shrink)

Attempts to ‘naturalize’ phenomenology challenge both traditional phenomenology and traditional approaches to cognitive science. They challenge Edmund Husserl’s rejection of naturalism and his attempt to establish phenomenology as a foundational transcendental discipline, and they challenge efforts to explain cognition through mainstream science. While appearing to be a retreat from the bold claims made for phenomenology, it is really its triumph. Naturalized phenomenology is spearheading a successful challenge to the heritage of Cartesian dualism. This converges with the reaction against Cartesian thought (...) within science itself. Descartes divided the universe between res cogitans, thinking substances, and res extensa, the mechanical world. The latter won with Newton and we have, in most of objective science since, literally lost our mind, hence our humanity. Despite Darwin, biologists remain children of Newton, and dream of a grand theory that is epistemologically complete and would allow lawful entailment of the evolution of the biosphere. This dream is no longer tenable. We now have to recognize that science and scientists are within and part of the world we are striving to comprehend, as proponents of endophysics have argued, and that physics, biology and mathematics have to be reconceived accordingly. Interpreting quantum mechanics from this perspective is shown to both illuminate conscious experience and reveal new paths for its further development. In biology we must now justify the use of the word “function”. As we shall see, we cannot prestate the ever new biological functions that arise and constitute the very phase space of evolution. Hence, we cannot mathematize the detailed becoming of the biosphere, nor write differential equations for functional variables we do not know ahead of time, nor integrate those equations, so no laws “entail” evolution. The dream of a grand theory fails. In place of entailing laws, a post-entailing law explanatory framework is proposed in which Actuals arise in evolution that constitute new boundary conditions that are enabling constraints that create new, typically unprestatable, Adjacent Possible opportunities for further evolution, in which new Actuals arise, in a persistent becoming. Evolution flows into a typically unprestatable succession of Adjacent Possibles. Given the concept of function, the concept of functional closure of an organism making a living in its world, becomes central. Implications for patterns in evolution include historical reconstruction, and statistical laws such as the distribution of extinction events, or species per genus, and the use of formal cause, not efficient cause, laws. (shrink)

At the core of republican thought, on Philip Pettit’s account, lies the conception of freedom as non-domination, as opposed to freedom as noninterference in the liberal sense. I revisit the distinction between liberal and republican freedom and argue that republican freedom incorporates a particular rule-of-law requirement, whereas liberal freedom does not. Liberals may also endorse such a requirement, but not as part of their conception of freedom itself. I offer a formal analysis of this rule-of-law requirement and compare liberal (...) and republican freedom on its basis. While I agree with Pettit that republican freedom has broader implications than liberal freedom, I conclude that we face a trade-off between two dimensions of freedom (scope and robustness) and that it is harder for republicans to solve that trade-off than it is for liberals. Key Words: freedom • republicanism • liberalism • noninterference • non-domination • rule of law • robustness • liberal paradox. (shrink)

This paper has three main objectives: (a) Discuss the formal analogy between some important symmetry-invariance arguments used in physics, probability and statistics. Specifically, we will focus on Noether’s theorem in physics, the maximum entropy principle in probability theory, and de Finetti-type theorems in Bayesian statistics; (b) Discuss the epistemological and ontological implications of these theorems, as they are interpreted in physics and statistics. Specifically, we will focus on the positivist (in physics) or subjective (in statistics) interpretations vs. objective interpretations (...) that are suggested by symmetry and invariance arguments; (c) Introduce the cognitive constructivism epistemological framework as a solution that overcomes the realism-subjectivism dilemma and its pitfalls. The work of the physicist and philosopher Max Born will be particularly important in our discussion. (shrink)

What method should we use to determine the nature of perceptual experience? My focus here is the Kantian thought that transcendental arguments can be used to determine the nature of perceptual experience. I set out a dilemma for the use of transcendental arguments in the philosophy of perception, one which turns on a comparison ofthe transcendental method with the first-personal method of early analytic philosophy, and with the empirical methods of much contemporary philosophy of mind. The transcendental method can avoid (...) this dilemma only if it commits to our possessing a capacity for imaginative reflection, one which is capable of identifying certain formal properties of experience.This result indicates some of the commitments which must be made if transcendental arguments are to be used in the philosophy of perception, and it has implications for those views that take the philosophy of perception to be autonomous of the empirical science of perception. (shrink)