Logic has been a—disputed—ingredient in the emergence and development of the now very large field known as knowledge representation and reasoning. In this book (in progress), I select some central topics in this highly fruitful, albeit controversial, association (e.g., non-monotonic reasoning, implicit belief, logical omniscience, closed world assumption), identifying their sources and analyzing/explaining their elaboration in highly influential published work.

Intermediary metabolism molecules are orchestrated into logical pathways stemming from history (L-amino acids, D-sugars) and dynamic constraints (hydrolysis of pyrophosphate or amide groups is the driving force of anabolism). Beside essential metabolites, numerous variants derive from programmed or accidental changes. Broken down, variants enter standard pathways, producing further variants. Macromolecule modification alters enzyme reactions specificity. Metabolism conform thermodynamic laws, precluding strict accuracy. Hence, for each regular pathway, a wealth of variants inputs and produces metabolites that are similar to but (...) not the exact replicas of core metabolites. As corollary, a shadow, paralogous metabolism, is associated to standard metabolism. We focus on a logic of paralogous metabolism based on diversion of the core metabolic mimics into pathways where they are modified to minimize their input in the core pathways where they create havoc. We propose that a significant proportion of paralogues of well-characterized enzymes have evolved as the natural way to cope with paralogous metabolites. A second type of denouement uses a process where protecting/deprotecting unwanted metabolites - conceptually similar to the procedure used in the laboratory of an organic chemist - is used to enter a completely new catabolic pathway. (shrink)

My real position is that logic is a mere sub-branch of rhetoric, but in this paper I only try to show an area of overlap. Certain usages in logical work are metaphorical, and I argue that this has pernicious effects in a discipline assumed strictly literal. Among these pernicious effects are the bizarre and fruitless focus of philosophy of mathematics on the pseudo-problems of foundations and objects. I mostly examine the locution 'logical construction' and a range of associated (...) metaphors. Some sketchy remarks on the history of rhetoric are offered in explanation. (shrink)

Many philosophers take purportedly logical cases of ground ) to be obvious cases, and indeed such cases have been used to motivate the existence of and importance of ground. I argue against this. I do so by motivating two kinds of semantic determination relations. Intuitions of logical ground track these semantic relations. Moreover, our knowledge of semantics for first order logic can explain why we have such intuitions. And, I argue, neither semantic relation can be a species of (...) ground even on a quite broad conception of what ground is. Hence, without a positive argument for taking so-called ‘logical ground’ to be something distinct from a semantic determination relation, we should cease treating logical cases as cases of ground. (shrink)

This article introduces some concepts that help exploring the ontological import of universal logic. It studies the notions of an antilogic and counterlogic associated to each logic and shows some of their properties. It presents the notion of galaxy, as the class of possible worlds compatible with a given logic.We explore some consequences of these developments.

The overwhelming majority of those who theorize about implicit biases posit that these biases are caused by some sort of association. However, what exactly this claim amounts to is rarely specified. In this paper, I distinguish between different understandings of association, and I argue that the crucial senses of association for elucidating implicit bias are the cognitive structure and mental process senses. A hypothesis is subsequently derived: if associations really underpin implicit biases, then implicit biases should be modulated by counterconditioning (...) or extinction but should not be modulated by rational argumentation or logical interventions. This hypothesis is false; implicit biases are not predicated on any associative structures or associative processes but instead arise because of unconscious propositionally structured beliefs. I conclude by discussing how the case study of implicit bias illuminates problems with popular dual-process models of cognitive architecture. (shrink)

Bilattices, introduced by Ginsberg as a uniform framework for inference in artificial intelligence, are algebraic structures that proved useful in many fields. In recent years, Arieli and Avron developed a logical system based on a class of bilattice-based matrices, called logical bilattices, and provided a Gentzen-style calculus for it. This logic is essentially an expansion of the well-known Belnap–Dunn four-valued logic to the standard language of bilattices. Our aim is to study Arieli and Avron’s logic from the perspective (...) of abstract algebraic logic . We introduce a Hilbert-style axiomatization in order to investigate the properties of the algebraic models of this logic, proving that every formula can be reduced to an equivalent normal form and that our axiomatization is complete w.r.t. Arieli and Avron’s semantics. In this way, we are able to classify this logic according to the criteria of AAL. We show, for instance, that it is non-protoalgebraic and non-self-extensional. We also characterize its Tarski congruence and the class of algebraic reducts of its reduced generalized models, which in the general theory of AAL is usually taken to be the algebraic counterpart of a sentential logic. This class turns out to be the variety generated by the smallest non-trivial bilattice, which is strictly contained in the class of algebraic reducts of logical bilattices. On the other hand, we prove that the class of algebraic reducts of reduced models of our logic is strictly included in the class of algebraic reducts of its reduced generalized models. Another interesting result obtained is that, as happens with some implicationless fragments of well-known logics, we can associate with our logic a Gentzen calculus which is algebraizable in the sense of Rebagliato and Verdú . We also prove some purely algebraic results concerning bilattices, for instance that the variety of distributive bilattices is generated by the smallest non-trivial bilattice. This result is based on an improvement of a theorem by Avron stating that every bounded interlaced bilattice is isomorphic to a certain product of two bounded lattices. We generalize it to the case of unbounded interlaced bilattices. (shrink)

It would be good to have a Bayesian decision theory that assesses our decisions and thinking according to everyday standards of rationality — standards that do not require logical omniscience (Garber 1983, Hacking 1967). To that end we develop a “fragmented” decision theory in which a single state of mind is represented by a family of credence functions, each associated with a distinct choice condition (Lewis 1982, Stalnaker 1984). The theory imposes a local coherence assumption guaranteeing that as an (...) agent's attention shifts, successive batches of "obvious" logical information become available to her. A rule of expected utility maximization can then be applied to the decision of what to attend to next during a train of thought. On the resulting theory, rationality requires ordinary agents to be logically competent and to often engage in trains of thought that increase the unification of their states of mind. But rationality does not require ordinary agents to be logically omniscient. (shrink)

The classical theory of computation does not represent an adequate model of reality for simulation in the social sciences. The aim of this paper is to construct a methodological perspective that is able to conciliate the formal and empirical logic of program verification in computer science, with the interpretative and multiparadigmatic logic of the social sciences. We attempt to evaluate whether social simulation implies an additional perspective about the way one can understand the concepts of program and computation. We demonstrate (...) that the logic of social simulation implies at least two distinct types of program verifications that reflect an epistemological distinction in the kind of knowledge one can have about programs. Computer programs seem to possess a causal capability (Fetzer, 1999) and an intentional capability that scientific theories seem not to possess. This distinction is associated with two types of program verification, which we call empirical and intentional verification. We demonstrate, by this means, that computational phenomena are also intentional phenomena, and that such is particularly manifest in agent-based social simulation. Ascertaining the credibility of results in social simulation requires a focus on the identification of a new category of knowledge we can have about computer programs. This knowledge should be considered an outcome of an experimental exercise, albeit not empirical, acquired within a context of limited consensus. The perspective of intentional computation seems to be the only one possible to reflect the multiparadigmatic character of social science in terms of agent-based computational social science. We contribute, additionally, to the clarification of several questions that are found in the methodological perspectives of the discipline, such as the computational nature, the logic of program scalability, and the multiparadigmatic character of agent-based simulation in the social sciences. (shrink)

We begin with an introductory overview of contributions made by more than twenty scholars associated with the Philosophy Department at the University of Buffalo during the last half-century to our understanding and evaluation of Aristotle's logic. More well-known developments are merely mentioned in..

We generalize, by a progressive procedure, the notions of conjunction and disjunction of two conditional events to the case of n conditional events. In our coherence-based approach, conjunctions and disjunctions are suitable conditional random quantities. We define the notion of negation, by verifying De Morgan’s Laws. We also show that conjunction and disjunction satisfy the associative and commutative properties, and a monotonicity property. Then, we give some results on coherence of prevision assessments for some families of compounded conditionals; in particular (...) we examine the Fréchet-Hoeffding bounds. Moreover, we study the reverse probabilistic inference from the conjunction Cn+1 of n + 1 conditional events to the family {Cn,En+1|Hn+1}. We consider the relation with the notion of quasi-conjunction and we examine in detail the coherence of the prevision assessments related with the conjunction of three conditional events. Based on conjunction, we also give a characterization of p-consistency and of p-entailment, with applications to several inference rules in probabilistic nonmonotonic reasoning. Finally, we examine some non p-valid inference rules; then, we illustrate by an example two methods which allow to suitably modify non p-valid inference rules in order to get inferences which are p-valid. (shrink)

Darwiche and Pearl’s seminal 1997 article outlined a number of baseline principles for a logic of iterated belief revision. These principles, the DP postulates, have been supplemented in a number of alternative ways. Most suggestions have resulted in a form of ‘reductionism’ that identifies belief states with orderings of worlds. However, this position has recently been criticised as being unacceptably strong. Other proposals, such as the popular principle (P), aka ‘Independence’, characteristic of ‘admissible’ operators, remain commendably more modest. In this (...) paper, we supplement the DP postulates and (P) with a number of novel conditions. While the DP postulates constrain the relation between a prior and a posterior conditional belief set, our new principles notably govern the relation between two posterior conditional belief sets obtained from a common prior by different revisions. We show that operators from the resulting family, which subsumes both lexicographic and restrained revision, can be represented as relating belief states associated with a ‘proper ordinal interval’ (POI) assignment, a structure more fine-grained than a simple ordering of worlds. We close the paper by noting that these operators satisfy iterated versions of many AGM era postulates, including Superexpansion, that are not sound for admissible operators in general. (shrink)

This paper contributes to explaining the rise of logical empiricism in mid-twentieth century (North) America and to a better understanding of American philosophy of science before the dominance of logical empiricism. We show that, contrary to a number of existing histories, philosophy of science was already a distinct subfield of philosophy, one with its own approaches and issues, even before logical empiricists arrived in America. It was a form of speculative philosophy with a concern for speculative metaphysics, (...) normative issues relating to science and society and issues which later were associated with logical empiricist philosophy of science, issues such as confirmation, scientific explanation, reductionism and laws of nature. Further, philosophy of science was not primarily pragmatist in orientation. We also show, with the help of our historical characterization, that a recent account of the emergence of analytic philosophy applies to the rise of logical empiricism. It has been argued that the emergence of American analytic philosophy is partly explained by analytic philosophers’ use of key institutions, including of journals, to marginalize speculative philosophy and promote analytic philosophy. We argue that this use of institutions included the marginalization of speculative and value-laden philosophy of science and the promotion of logical empiricism. (shrink)

The starting point of this paper concerns the apparent difference between what we might call absolute truth and truth in a model, following Donald Davidson. The notion of absolute truth is the one familiar from Tarski’s T-schema: ‘Snow is white’ is true if and only if snow is white. Instead of being a property of sentences as absolute truth appears to be, truth in a model, that is relative truth, is evaluated in terms of the relation between sentences and models. (...) I wish to examine the apparent dual nature of logical truth (without dwelling on Davidson), and suggest that we are dealing with a distinction between a metaphysical and a linguistic interpretation of truth. I take my cue from John Etchemendy, who suggests that absolute truth could be considered as being equivalent to truth in the ‘right model’, i.e., the model that corresponds with the world. However, the notion of ‘model’ is not entirely appropriate here as it is closely associated with relative truth. Instead, I propose that the metaphysical interpretation of truth may be illustrated in modal terms, by metaphysical modality in particular. One of the tasks that I will undertake in this paper is to develop this modal interpretation, partly building on my previous work on the metaphysical interpretation of the law of non-contradiction (Tahko 2009). After an explication of the metaphysical interpretation of logical truth, a brief study of how this interpretation connects with some recent important themes in philosophical logic follows. In particular, I discuss logical pluralism and propose an understanding of pluralism from the point of view of the metaphysical interpretation. (shrink)

Unconscious logical inference seems to rely on the syntactic structures of mental representations (Quilty-Dunn & Mandelbaum 2018). Other transitions, such as transitions using iconic representations and associative transitions, are harder to assimilate to syntax-based theories. Here we tackle these difficulties head on in the interest of a fuller taxonomy of mental transitions. Along the way we discuss how icons can be compositional without having constituent structure, and expand and defend the “symmetry condition” on Associationism (the idea that associative links (...) and transitions are perfectly symmetric). In the end, we show how a BIT (“bare inferential transition”) theory can cohabitate with these other non-inferential mental transitions. (shrink)

Since the pioneering work of Birkhoff and von Neumann, quantum logic has been interpreted as the logic of (closed) subspaces of a Hilbert space. There is a progression from the usual Boolean logic of subsets to the "quantum logic" of subspaces of a general vector space--which is then specialized to the closed subspaces of a Hilbert space. But there is a "dual" progression. The notion of a partition (or quotient set or equivalence relation) is dual (in a category-theoretic sense) to (...) the notion of a subset. Hence the Boolean logic of subsets has a dual logic of partitions. Then the dual progression is from that logic of partitions to the quantum logic of direct-sum decompositions (i.e., the vector space version of a set partition) of a general vector space--which can then be specialized to the direct-sum decompositions of a Hilbert space. This allows the logic to express measurement by any self-adjoint operators rather than just the projection operators associated with subspaces. In this introductory paper, the focus is on the quantum logic of direct-sum decompositions of a finite-dimensional vector space (including such a Hilbert space). The primary special case examined is finite vector spaces over ℤ₂ where the pedagogical model of quantum mechanics over sets (QM/Sets) is formulated. In the Appendix, the combinatorics of direct-sum decompositions of finite vector spaces over GF(q) is analyzed with computations for the case of QM/Sets where q=2. (shrink)

The classic analytic tradition associated the philosophy of George Berkeley with idealism. Yet in terms of the German Idealismus, Berkeley was no idealist. Rather, he described himself as an “immaterialist”. In the classic analytic tradition we find a misunderstanding of the German Idealismus. This paper will suggest, through reference to the work of Paul Redding, that Hegel’s Phenomenology of Spirit presents Idealismus as that which reconciles objectivity and subjectivity in the experience of consciousness. Hegel’s Phenomenology develops this idea in the (...) elaboration of a remarkably novel theory of consciousness. For Hegel, the conditions of the possibility of the objects of experience are a dialectical movement between consciousness and the object, or immediacy and mediacy. In the whole movement of consciousness we have the logic of contradiction working at the back of phenomenological experience that Hegel will make explicit in the Science of Logic, a logic that involves the thinker becoming consciously aware of their own thought processes. Yet Hegel’s Logic is different from the common meaning of ‘logic’. His Logic is not a formal approach to valid inference but captures the method and the moments and movement of logic. For Hegel, the great problem of classical logic is the immobility of the categories. This paper proposes that Hegel’s ‘holism’ entails the description wherein Logic, Nature, and Spirit are articulated as a whole in dialectical movement. (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)

The aim of this paper is to introduce a system of dynamic deontic logic in which the main problems related to the de finition of deontic concepts, especially those emerging from a standard analysis of permission in terms of possibility of doing an action without incurring in a violation of the law, are solved. The basic idea is to introduce two crucial distinctions allowing us to differentiate (i) what is ideal with respect to a given code, which fixes the types (...) of action that are abstractly prescribed, and what is ideal with respect to the specific situation in which the agent acts, and (ii) the transitions associated with actions and the results of actions, which can obtain even without the action being performed. (shrink)

A fascinating recent turn in epistemology focuses on inquiring attitudes like wondering and being curious. Many have argued that these attitudes are governed by norms similar to those that govern our doxastic attitudes. Yet, to date, this work has only considered norms that might *prohibit* having certain inquiring attitudes (``norms of restriction''), while ignoring those that might *require* having them (``norms of expansion''). We aim to address that omission by offering a framework that generates norms of expansion for inquiring attitudes. (...) The framework draws on inferential erotetic logic, which we explain and augment with some theorems. We explore several of the norms that it yields - some sympathetically, others unsympathetically. (shrink)

You ask if metaphysics is possible after modernity, or after Barth and Wittgenstein and Derrida and the critique of foundationalism? May I invite you, by way of response, to listen in on a conversation? It is a dialogue between what I will call a postcritical philosopher ("P") and a postcritical scriptural theologian —— I'll label the latter a "textualist" ("T"). What I mean by "postcritical" would be displayed as the pattern of inquiry traced by this dialogue. I take the term (...) "postcritical" from George Lindbeck, whose theological work is described by his commentators as more properly "textualist" rather than "philosophic." I believe my usage is, however, true to Lindbeck's discourse. This means that one of the arguments of this essay is that there is a mode of philosophic inquiry proper to the postcritical orientation in theology that we may associate with such Christian theologians as Hans Frei, etc., as well as Lindbeck. A second argument, offered indirectly, is that there is a family of Jewish thinkers whose work may also be labeled "postcritical" on the model of these Christian thinkers, and that this Jewish postcritical theology would also be displayed in dialogues between philosophic and textualist tendencies. A third argument is that, if we listen in on the philosophic side of any of these dialogues, we will hear a postcritical philosophy. By philosophy, I mean primarily logic, defined as an inquiry that examines problematic rules of reasoning and recommends testable ways of correcting them. Secondarily, philosophy includes metaphysics, defined as an inquiry that, for the sake of assuring people about the reliability of a given logic, constructs pictures of the world whose existence would warrant this logic. We need not assume either that logic and metaphysics can be conducted only in the manner of modern and scholastic foundationalism, or that non-foundationalist theology must be "textualist" in a manner that excludes any philosophic generalization. I will argue that there are, indeed, non-foundationalist ways of conceiving of both logical and metaphysical inquiry and that these ways contribute to the dialogic activity of postcritical inquiry. (shrink)

This paper introduces two languages and associated logics designed to afford perspicuous representations of a range of natural language arguments involving adverbs and the like: first-order logic with basic adverbs (FOL-BA) and first-order logic with scoped adverbs (FOL-SA). The guiding logical idea is that an adverb can come between a term and the rest of the statement it is a part of, resulting in a logically stronger statement. I explain various interesting challenges that arise in the attempt to implement (...) the guiding idea, and provide solutions for some but not all of them. I conclude by outlining some directions for further research. (shrink)

This paper focuses on order-preserving logics defined from varieties of distributive lattices with negation, and in particular on the problem of whether these can be axiomatized by means Hilbert-style calculi that are finite. On the negative side, we provide a syntactic condition on the equational presentation of a variety that entails failure of finite axiomatizability for the corresponding logic. An application of this result is that the logic of all distributive lattices with negation is not finitely axiomatizable; we likewise establish (...) that the order-preserving logic of the variety of all Ockham algebras is also not finitely axiomatizable. On the positive side, we show that an arbitrary subvariety of semi-De Morgan algebras is axiomatized by a finite number of equations if and only if the corresponding order-preserving logic is axiomatized by a finite Hilbert-style calculus. This equivalence also holds for every subvariety of a Berman variety of Ockham algebras. We obtain, as a corollary, a new proof that the implication-free fragment of intuitionistic logic is finitely axiomatizable, as well as a new corresponding Hilbert-style calculus. Our proofs are constructive in that they allow us to effectively convert an equational presentation of a variety of algebras into a Hilbert-style calculus for the corresponding order-preserving logic, and vice versa. We also consider the assertional logics associated to the above-mentioned varieties, showing in particular that the assertional logics of finitely axiomatizable subvarieties of semi-De Morgan algebras are finitely axiomatizable as well. (shrink)

[[[ (Here only the chapters 3 – 8, see *** ) First I argue that the prohibition of linguistic self-reference as a solution to the antinomy problem contains a pragmatic contradiction and is thus not only too restrictive, but just inconsistent (chap.1). Furthermore, the possibilities of non-restrictive strategies for antinomy avoidance are discussed, whereby the explicit inclusion of the – pragmatically presuposed – consistency requirement proves to be the optimal strategy (chap.2). ]]] The central question here is that about the (...) actual reason for antinomic structures. It turns out to be a form of negative self-conditioning (chap.3). This makes it necessary to clarify the status of negative concepts (chap.4). The generalization of these considerations (chap.5) leads to the actual analysis of the antinomic basic structure (chap.6): Decisively for the pragmatics of the concept is that it positively owns a meaning, so that positivity is always constituted by the concept qua concept. Thus a negative concept is characterized by a fundamental ambivalence: From a semantic point of view it has negative character, in its pragmatic status as a concept, however, it has positive character. If the meaning is especially that of a negative self-reference, the ambivalence leads to the antinomic constellation of a negative self-condition – that is the crux of the matter here! The concept thus possesses the property defined by it exactly when it does not possess it and vice versa. A closer analysis shows that the function of reflective structures for the occurrence of antinomies has to be judged much more differentiated than previous opinions suggest. Not only are four forms of reflectivity to be distinguished in this context – ontic, semantic, pragmatic reflectivity, and especially the form of negative self-condition; but it is also apparent that these are intertwined with each other in a way that is difficult to be understood. The astonishing variety of relationships associated with this makes the irritation that has always emanated from the antinomy problem appear more comprehensible. In the developed pragmatic perspective furtheron parallels to the structure of self-consciousness become visible (chap.7). I conclude with considerations about the significance of the antinomic structure for the problem of dialectics, especially for the synthesis formation of mutually exclusive terms (chap.8). (shrink)

We introduce translations between display calculus proofs and labeled calculus proofs in the context of tense logics. First, we show that every derivation in the display calculus for the minimal tense logic Kt extended with general path axioms can be effectively transformed into a derivation in the corresponding labeled calculus. Concerning the converse translation, we show that for Kt extended with path axioms, every derivation in the corresponding labeled calculus can be put into a special form that is translatable to (...) a derivation in the associated display calculus. A key insight in this converse translation is a canonical representation of display sequents as labeled polytrees. Labeled polytrees, which represent equivalence classes of display sequents modulo display postulates, also shed light on related correspondence results for tense logics. (shrink)

In this article, we discuss some issues concerning magical thinking—forms of thought and association mechanisms characteristic of early stages of mental development. We also examine good reasons for having an ambivalent attitude concerning the later permanence in life of these archaic forms of association, and the coexistence of such intuitive but informal thinking with logical and rigorous reasoning. At the one hand, magical thinking seems to serve the creative mind, working as a natural vehicle for new ideas and innovative (...) insights, and giving form to heuristic arguments. At the other hand, it is inherently difficult to control, lacking effective mechanisms needed for rigorous manipulation. Our discussion is illustrated with many examples from the Hebrew Bible, and some final examples from modern science. (shrink)

I argue against the skeptical epistemological view exemplified by the Groarkes that “all theories of informal argument must face the regress problem.” It is true that in our theoretical representations of reasoning, infinite regresses of self-justification regularly and inadvertently arise with respect to each of the RSA criteria for argument cogency (the premises are to be relevant, sufficient, and acceptable). But they arise needlessly, by confusing an RSA criterion with argument content, usually premise material.

In this article, we discuss some issues concerning magical thinking—forms of thought and association mechanisms characteristic of early stages of mental development. We also examine good reasons for having an ambivalent attitude concerning the later permanence in life of these archaic forms of association, and the coexistence of such intuitive but informal thinking with logical and rigorous reasoning. At the one hand, magical thinking seems to serve the creative mind, working as a natural vehicle for new ideas and innovative (...) insights, and giving form to heuristic arguments. At the other hand, it is inherently difficult to control, lacking effective mechanisms needed for rigorous manipulation. Our discussion is illustrated with many examples from the Hebrew Bible, and some final examples from modern science. (shrink)

In this work Husserl makes the distinction between expressions and indications that Derrida will later plant the bomb of Husserl's own Phenomenology of Internal Time Consciousness underneath it in order to undermine the dream for presence and inaugurate Deconstruction. Logic, as Husserl sees it, is concerned in the first place with meanings (propositions, concepts) and with associated meaning-instantiating acts. Most importantly, it is concerned with that sort of deductively closed collection of meanings which constitutes a scientific theory. For Husserl, as (...) for Bolzano, logic is a theory of science. Only where we have an appropriate unity and organization also on the side of the objects (states of affairs, properties) to which the relevant acts refer, however, will we have a scientific theory, so that the unity which is characteristic of the latter must involve both (1) an interconnection of truths (or of propositional meanings in general), and (2) an interconnection of the things to which these truths (and the associated cognitive acts) are directed. Where formal logic relates in the first place to meaning categories such as proposition, concept, subject and predicate, its sister discipline of formal ontology relates to object categories such as object and property, relation and relatum, manifold, part, whole, state of affairs, existence and so on. Logic in a broader sense therefore seeks to delimit the concepts which belong to the idea of a unity of theory in relation to both meanings and objects, and the truths of logic are all the necessary truths relating to those categories of constituents, on the side of both meanings and objects, from out of which science as such is necessarily constituted (including what we might think of as bridge-categories such as identity and truth which span the division between meanings and objects). The best way to deal with Husserl's theory of formal ontology, therefore, is to explicate both the connections between the formal and material, and those between the ontological and the logical. In introducing his distinction between formal and material ontology, Husserl asserts that the former is descriptive and involves analytic a priori judgements, and that the latter involves synthetic a priori judgements. In its most general sense formal ontology concerns itself with characterizing the simple 'something'. The sphere of material ontology in this sense are the laws of non-independence (2) which delimit the ontological regions. For the genetic interpretation, material ontology precedes formal ontology; for the descriptive interpretation it is the other way round (1913, art. 10). Here emerges 'the fundamental distinction between formal and material ontology': namely, the distinction between analytic a priori and synthetic a priori (Introduction to Formale und transzendentale Logik, 1929). (shrink)

We are concerned in this paper to establish the rationality of American legal realism by adopting a theory of reconstruction. American realism is plagued with dichotomies in relating theory and practice; and the need to broach these dichotomies involves transcendence of experience and transference of consciousness. In doing this, we have both to excavate and to justify its philosophy, logic and science. American legal realism has its root in the philosophy of pragmatism and a logic that sets out the essential (...) elements associated with the making and determination of the law through instrumentality of the court. The validity of this category of legal theory tends to lie on the extent of immediate use to which law can be put or the benefits it can afford the American society. Believing in the possibility of a realistic theory of law that is purely American precludes belief in universal understanding of human legal experience distinct from the understanding gained through the cultural lenses of the American people. Although American realists differ remarkably even within a single paradigm, nevertheless three areas of logical unity among them are that: They bear a cross relevance, a complementing and interlocking of results, and a similar faith in attacking legal problems. A completely empirical understanding of American legal realism seems nebulous, because causality presupposes the interaction of American liberal and legalistic political attitudes. Legalism is the life wire of American culture and this makes distribution of rights and legal predictability possible: incidentally language is an important instrument for making this happens. Countries seeking to adopt the American model of legal order or something similar to it should be capable of an equivalent orientation in terms of formulating their philosophy, logic and science of adjudication. (shrink)

Contemporary research offers a more compelling account on the complex emotion of envy than the traditional view of envy as simply something bad. This essay explains how Logic-Based Therapy can use this account to coach individuals struggling with negative species of envy. Given that jealousy and envy are often equated, the essay differentiates the two; explains the conditions that make the four species of envy possible; identifies cardinal fallacies associated with negative species of envy; proposes counteractive virtues, and describes ways (...) to help people struggling with negative species of envy acquire these virtues. (shrink)

This paper accomplishes two tasks. First, I examine in detail Edmund Husserl’s earliest philosophy of surrogates, as it is found in his 1890 “On the Logic of Signs ”. I analyze his psychological and logical investigations of surrogates, where the former is concerned with explaining how these signs function and the latter with how they do so reliably. His differentiation of surrogates on the basis of their genetic origins and degrees of necessity is discussed. Second, the historical importance of (...) this text is disclosed by showing how Semiotic serves as both the inspiration for, and the foil to, Husserl’s 1901 First Logical Investigation. Husserl not only adopts the idea that linguistic signs can function via association, but also maintains that such signs can motivate me to execute one of two experiences. The key difference between the texts is that Husserl abandons his theory of surrogates in 1901, instead holding that I can experience absent objects by means of empty intentions. The reasons why Husserl found it necessary to transform this tenet of his philosophy are discussed at length. (shrink)

Firstly I characterize Simple Partial Logic (SPL) as the generalization and extension of a certain two-valued logic. Based on the characterization I present two definitions of validity in SPL. Finally I show that given my characterization these two definitions are more appropriate than other definitions that have been prevalent, since both have some desirable semantic properties that the others lack.

The assumption that known physical laws are sufficient for explaining mental phenomena is flawed from the outset. Qualities such as phenomenal redness do not exist within the known physical laws so by definition they are incomplete. Now assuming a new law was added that could explain how some physical property or vibration causes or is associated with phenomenal redness it would not be enough because it still wouldn’t explain how different qualities are bound together into a subjective unity. Assuming more (...) additional laws could now explain the popping into existence of subjective selves this also would still not be enough because a subjective self that cannot be directly observed nor indirectly observed via its effects vanishes into non-existence. This implies that subjective selves must have causal efficacy. But this would require still additional physical laws or perhaps an accommodated interpretation of quantum physics because there is no current understanding of how a mind can change the probability distribution of matter. But even if an expanded quantum physics was understood this would still not be enough because no general law can determine the indexical fact that I am me and you are you. -/- Then the hard problem of consciousness is real, non-trivial and when taken seriously appears to be actually separate problems. 1. How are qualia generated from purely physical activity? This appears to be a strictly deterministic process. 2. The so called binding problem. That is how is that I hear a sound and see a visual scene and feel a bodily sensation, all separate modalities that are unrelated, and yet I experience them all at the same time? 3. Can it be that I am causally efficacious? It certainly seems that the actual feelings of pain and pleasure serve some real purpose. Since conscious entities can never be directly observed and are only known through their effects, if they have no effects they disappear altogether. 4. The so called problem of indexicality. That is why I am me and not you. This seems to be a real fact above and beyond any objective fact. Eliminative materialism ignores the empirical evidence that phenomenal qualities exist and in doing so attains logical consistency. Other forms of emergence that try to explain qualia and give it a meaning while being restricted to physical closure are illogical. I explore these hard problems and arrive at a justification for a panpsychic interactive dualism. (shrink)

This article provides the foundation for a new predictive theory of animal learning that is based upon a simple logical model. The knowledge of experimental subjects at a given time is described using logical equations. These logical equations are then used to predict a subject’s response when presented with a known or a previously unknown situation. This new theory suc- cessfully anticipates phenomena that existing theories predict, as well as phenomena that they cannot. It provides a theoretical (...) account for phenomena that are beyond the domain of existing models, such as extinction and the detection of novelty, from which “external inhibition” can be explained. Examples of the methods applied to make predictions are given using previously published results. The present theory proposes a new way to envision the minimal functions of the nervous system, and provides possible new insights into the way that brains ultimately create and use knowledge about the world. (shrink)

Consider the concept combination ‘pet human’. In word association experiments, human subjects produce the associate ‘slave’ in relation to this combination. The striking aspect of this associate is that it is not produced as an associate of ‘pet’, or ‘human’ in isolation. In other words, the associate ‘slave’ seems to be emergent. Such emergent associations sometimes have a creative character and cognitive science is largely silent about how we produce them. Departing from a dimensional model of human conceptual space, this (...) article will explore concept combinations, and will argue that emergent associations are a result of abductive reasoning within conceptual space, that is, below the symbolic level of cognition. A tensor-based approach is used to model concept combinations allowing such combinations to be formalized as interacting quantum systems. Free association norm data is used to motivate the underlying basis of the conceptual space. It is shown by analogy how some concept combinations may behave like quantum-entangled particles. Two methods of analysis were presented for empirically validating the presence of non-separable concept combinations in human cognition. One method is based on quantum theory and another based on comparing a joint probability distribution with another distribution based on a separability assumption using a chi-square goodness-of-fit test. Although these methods were inconclusive in relation to an empirical study of bi-ambiguous concept combinations, avenues for further refinement of these methods are identified. (shrink)

This paper studies the relationship between labelled and nested calculi for propositional intuitionistic logic, first-order intuitionistic logic with non-constant domains and first-order intuitionistic logic with constant domains. It is shown that Fitting’s nested calculi naturally arise from their corresponding labelled calculi—for each of the aforementioned logics—via the elimination of structural rules in labelled derivations. The translational correspondence between the two types of systems is leveraged to show that the nested calculi inherit proof-theoretic properties from their associated labelled calculi, such as (...) completeness, invertibility of rules and cut admissibility. Since labelled calculi are easily obtained via a logic’s semantics, the method presented in this paper can be seen as one whereby refined versions of labelled calculi (containing nested calculi as fragments) with favourable properties are derived directly from a logic’s semantics. (shrink)

For Meinong, familiarly, fictional entities are not created, but rather merely discovered (or picked out) from the inexhaustible realm of Aussersein (beyond being and non-being). The phenomenologist Roman Ingarden, in contrast, offers in his Literary Work of Art of 1931 a constructive ontology of fiction, which views fictional objects as entities which are created by the acts of an author (as laws, for example, are created by acts of parliament). We outline the logic of fiction which is implied by Ingarden’s (...) approach, showing how it distinguishes the properties possessed by fictional objects (for instance of having been created by such and such an author in such and such a work) from characteristics (for instance of smoking a pipe, of living in Baker Street) which are merely associated with such objects. (shrink)

This thesis introduces the "method of structural refinement", which serves as a means of transforming the relational semantics of a modal and/or constructive logic into an 'economical' proof system by connecting two proof-theoretic paradigms: labelled and nested sequent calculi. The formalism of labelled sequents has been successful in that cut-free calculi in possession of desirable proof-theoretic properties can be automatically generated for large classes of logics. Despite these qualities, labelled systems make use of a complicated syntax that explicitly incorporates the (...) semantics of the associated logic, and such systems typically violate the subformula property to a high degree. By contrast, nested sequent calculi employ a simpler syntax and adhere to a strict reading of the subformula property, making such systems useful in the design of automated reasoning algorithms. However, the downside of the nested sequent paradigm is that a general theory concerning the automated construction of such calculi (as in the labelled setting) is essentially absent, meaning that the construction of nested systems and the confirmation of their properties is usually done on a case-by-case basis. The refinement method connects both paradigms in a fruitful way, by transforming labelled systems into nested (or, refined labelled) systems with the properties of the former preserved throughout the transformation process. To demonstrate the method of refinement and some of its applications, we consider grammar logics, first-order intuitionistic logics, and deontic STIT logics. The introduced refined labelled calculi will be used to provide the first proof-search algorithms for deontic STIT logics. Furthermore, we employ our refined labelled calculi for grammar logics to show that every logic in the class possesses the effective Lyndon interpolation property. (shrink)

This paper shows how to derive nested calculi from labelled calculi for propositional intuitionistic logic and first-order intuitionistic logic with constant domains, thus connecting the general results for labelled calculi with the more refined formalism of nested sequents. The extraction of nested calculi from labelled calculi obtains via considerations pertaining to the elimination of structural rules in labelled derivations. Each aspect of the extraction process is motivated and detailed, showing that each nested calculus inherits favorable proof-theoretic properties from its associated (...) labelled calculus. (shrink)

Abstract for Descent and Logic in Biosystematics: An Essay AUTHOR: THOMAS MCCABE PUBLISHER: PERSEVERANT PUBLISHING Descent and Logic in Biosystematics: An Essay is a short book about biological systematics and taxonomy. Some of the subjects con- sidered in it are philosophical: taxonomic theory, species concepts, speciation models, and evolutionary theories. Yet the book also covers matters not philosophical, such as taxonomic operations, experi- mental taxonomy, and a new suggested taxonomic method with worked examples. The author finds relationships among these topics. (...) The book is addressed to biosystematists, practicing biological tax- onomists, and philosophers of biology. It will also interest others who draw on biological taxonomy and biosystematics in their work. Descent and Logic in Biosystematics: An Essay goes into some old topics such as traditional biological identifying, classifying, and nomenclature; some recent, such as cladistic analysis, phylogenetics, and phylogenomics; and a few new, such as the logic of mutually exclusive taxon definitions, and techniques for using directly obser- ved reproductive events and pedigree analysis to untangle certain taxonomic dilemmas. There is a chapter about minimizing am- biguities when defining biological taxa, a chapter on the relevance of human biology to biosystematics, chapters addressing some biosys- tematic problems associated with the phenomenon of hybridization, a chapter on the relationship of biological taxonomy to conservation biology, and a chapter about the scientificity of evolutionary theories. Descent and Logic in Biosystematics: An Essay is published with a glossary, twelve black and white line figures, a dynamic table of contents, linked cross references, linked bibliographic citations, and a detailed index in the print and PDF versions. Descent and Logic in Biosystematics: An Essay, is available from the publisher in print and PDF formats, and from distributors and retailers as an ebook. It should be considered for academic libraries, research libraries, natural history museum libraries, the libraries of conservation organizations, and some private libraries. (shrink)

Part 1 [Hodes, 2021] “looked under the hood” of the familiar versions of the classical propositional modal logic K and its intuitionistic counterpart. This paper continues that project, addressing some familiar classical strengthenings of K and GL), and their intuitionistic counterparts. Section 9 associates two intuitionistic one-step proof-theoretic systems to each of the just mentioned intuitionistic logics, this by adding for each a new rule to those which generated IK in Part 1. For the systems associated with the intuitionistic counterparts (...) of D and T, these rules are “pure one-step”: their schematic formulations does not use □ or ♢. For the systems associated with the intuitionistic counterparts of K4, etc., these rules meet these conditions: neither □ nor ♢ is iterated; none use both □ and ♢. The join of the two systems associated with each of these familiar logics is the full one-step system for that intuitionistic logic. And further “blended” intuitionistic systems arise from joining these systems in various ways. Adding the 0-version of Excluded Middle to their intuitionistic counterparts yields the one-step systems corresponding to the familiar classical logics. Each proof-theoretic system defines a consequence relation in the obvious way. Section 10 examines inclusions between these consequence relations. Section 11 associates each of the above consequence relations with an appropriate class of models, and proves them sound with respect to their appropriate class. This allows proofs of some failures of inclusion between consequence relations. Section 12 proves that the each consequence relation is complete or weakly complete, that relative to its appropriate class of models. The Appendix presents three further results about some of the intuitionistic consequence relations discussed in the body of the paper. For Keywords, see Part 1. (shrink)

: For Meinong, familiarly, fictional entities are not created, but rather merely discovered (or picked out) from the inexhaustible realm of Aussersein (beyond being and non-being). The phenomenologist Roman Ingarden, in contrast, offers in his Literary Work of Art of 1931 a constructive ontology of fiction, which views fictional objects as entities which are created by the acts of an author (as laws, for example, are created by acts of parliament). We outline the logic of fiction which is implied by (...) Ingarden’s approach, showing how it distinguishes the properties possessed by fictional objects (for instance of having been created by such and such an author in such and such a work) from characteristics (for instance of smoking a pipe, of living in Baker Street) which are merely associated with such objects. (shrink)

Learning mathematics through distance education can be challenging, with the “logical” and “rewarding” nature proving difficult to measure. This article aimed to articulate an argument explaining the “logical” and “rewarding” nature of online mathematics learning, elucidating their causal factors. Existing data from the literature that involving students at Visayas State University, Philippines, were utilized in this study. The study used statistical measures to capture descriptions from the data, and quantile regression analysis was employed to forecast the predictors of (...) the logicality and rewarding nature of learning mathematics at a distance. Results indicate that learning mathematics in the new normal is perceived as “logical” and moderately “rewarding”. The regression and correlation analyses revealed a significant positive association between the perceived “logical” nature and the rewarding experience of learning mathematics. The constructed statistical models depicted that the determinants of logicality in learning mathematics include family income, money spent on the internet, learning environment, household size, social status, and health. Moreover, causal factors such as family income, money spent on the internet, learning environment, leisure activities, social status, and health significantly determine the rewarding nature of learning mathematics online. Conclusively, institution must support college students with their online learning needs. Furthermore, mathematics instructors should create lively and exciting online discussions that boost their logical thinking. Providing problem-solving task that are intrinsically rewarding can contribute to a more fulfilling learning experience. (shrink)

I construct a quantum-logical model of the type of situation that seems to be at the root of the problem of interpreting the projection postulate (Luders' rule) as a criterion of minimal disturbance. It is shown that the most natural way of characterizing minimal disturbance leads to contradictory conclusions concerning the final state.

In my presentation I argue for the utility of a philosophical counseling method, called logic-based therapy (LBT), in the treatment of addicted populations. In the context of addiction treatment LBT could be also classified as a philosophical psychotherapy. Philosophical psychotherapy can be understood as an umbrella term for interventions designed to treat mental health disorders, with theoretical foundations that are philosophical. Philosophical psychotherapy would be distinct from philosophical counseling, as the latter does not directly treat mental health disorders. I suggest (...) that LBT has utility beyond philosophical counseling and is a viable intervention in the treatment of certain mental health disorders, like substance use disorders. I provide a brief overview of LBT and then discuss a LBT case study with a client suffering diagnosed with a substance use disorder. In the case study the client was advised to apply the moral philosophy of Friedrich Nietzsche as an uplifting philosophical framework to counteract his unproductive worldview and fallacious thinking. Considering that there is an ostensibly low efficacy rate for the treatment of addiction, articulating the value of philosophical psychotherapies in the context of addiction treatment can assist in the development of novel philosophically-based addiction treatment and recovery-oriented programs––thus expanding the treatment and recovery options available for those seeking recovery from addiction. (shrink)

This is a presentation about the impacts of Logic and Theory of Computation. It starts by some explanations about Theory of Computation and its relations with the other subjects in science. Then we have some explanations about paradoxes and some historical points. In continuation, we present some of the most important paradoxes. Forthcoming, Five subjects around the relations between Logic and Theory of computation is introduced. Finally, we present a new approach to solve P vs NP problem via Paradoxes (Presentation (...) 6/20/2022 In Persian, Online seminar of The Iranian Association for Logic (IAL) . (shrink)

Given a class of linear order types C, we identify and study several different classes of trees, naturally associated with C in terms of how the paths in those trees are related to the order types belonging to C. We investigate and completely determine the set-theoretic relationships between these classes of trees and between their corresponding first-order theories. We then obtain some general results about the axiomatization of the first-order theories of some of these classes of trees in terms of (...) the first-order theory of the generating class C, and indicate the problems obstructing such general results for the other classes. These problems arise from the possible existence of nondefinable paths in trees, that need not satisfy the first-order theory of C, so we have started analysing first order definable and undefinable paths in trees. (shrink)

This short work presents a popular fringe theory as a source of case studies for use in teaching informal logic in an introductory course. It puts forward ancient astronaut theory as the candidate source, together with a characterization of why it fits the bill. The televised material associated with that theory is well suited to being used as case studies given that they are easy to follow, contain a surprising number of arguments and fallacies, and keep students reliably engaged. The (...) paper includes an overview of the forms of argumentation and fallacies that these cases may be used to teach, along with a sketch of how to best implement them in the classroom. (shrink)