Revisionary theories of logic or truth require revisionary theories of mind. This essay outlines nonclassically based theories of rational belief, desire, and decision making, singling out the supervaluational family for special attention. To see these nonclassical theories of mind in action, this essay examines a debate between David Lewis and Derek Parfit over what matters in survival. Lewis argued that indeterminacy in personal identity allows caring about psychological connectedness and caring about personal identity to amount to the same thing. The (...) essay argues that Lewis's treatment of two of Parfit's puzzle cases—degreed survival and fission—presuppose different nonclassical treatments of belief and desire. (shrink)

While there is a growing philosophical interest in analysing olfactory experiences, the mereological structure of odours considered in respect of how they are perceptually experienced has not yet been extensively investigated. The paper argues that odours are perceptually experienced as having a mereological structure, but this structure is significantly different from the spatial mereological structure of visually experienced objects. Most importantly, in the case of the olfactory part-structure, the classical weak supplementation principle is not satisfied. This thesis is justified by (...) referring to empirical results in olfactory science concerning the human ability to identify components in complex olfactory stimuli. Further, it is shown how differences between olfactory and visual mereologies may arise from the way in which these modalities represent space. (shrink)

This paper introduces a novel strategy for responding to skeptical arguments based on the epistemic possibility of error or lack of certainty. I show that a nonclassical logic motivated by recent work on epistemic modals can be used to render such skeptical arguments invalid. That is, one can grant that knowledge is incompatible with the possibility of error and grant that error is possible, all while avoiding the skeptic’s conclusion that we lack knowledge.

Joyce (1998) gives an argument for probabilism: the doctrine that rational credences should conform to the axioms of probability. In doing so, he provides a distinctive take on how the normative force of probabilism relates to the injunction to believe what is true. But Joyce presupposes that the truth values of the propositions over which credences are defined are classical. I generalize the core of Joyce’s argument to remove this presupposition. On the same assumptions as Joyce uses, the credences of (...) a rational agent should always be weighted averages of truth value assignments. In the special case where the truth values are classical, the weighted averages of truth value assignments are exactly the probability functions. But in the more general case, probabilistic axioms formulated in terms of classical logic are violated—but we will show that generalized versions of the axioms formulated in terms of non-classical logics are satisfied. (shrink)

The naive theory of properties states that for every condition there is a property instantiated by exactly the things which satisfy that condition. The naive theory of properties is inconsistent in classical logic, but there are many ways to obtain consistent naive theories of properties in nonclassical logics. The naive theory of classes adds to the naive theory of properties an extensionality rule or axiom, which states roughly that if two classes have exactly the same members, they are identical. In (...) this paper we examine the prospects for obtaining a satisfactory naive theory of classes. We start from a result by Ross Brady, which demonstrates the consistency of something resembling a naive theory of classes. We generalize Brady’s result somewhat and extend it to a recent system developed by Andrew Bacon. All of the theories we prove consistent contain an extensionality rule or axiom. But we argue that given the background logics, the relevant extensionality principles are too weak. For example, in some of these theories, there are universal classes which are not declared coextensive. We elucidate some very modest demands on extensionality, designed to rule out this kind of pathology. But we close by proving that even these modest demands cannot be jointly satisfied. In light of this new impossibility result, the prospects for a naive theory of classes are bleak. (shrink)

Entailment is an interesting sigmatoid: It should mean one thing, but it means another, just for starters. When used in Mathematics, it is usually with the sense of saying that something is definitely true. That would be the use in Classical Logic then. When used in Logic, it became something else. Now it was about how the logical system, which can be any nonclassical one, could be making a proposition become true or false. The major issue we found in 2000, (...) when learning from the own nonclassicists what they do, was that they talk about Nonclassical Logic, therefore a way of thinking that is not Cartesian, yet they stick to the notion of entailment we use in Mathematics, and therefore to the Classical Logic ways. We here discuss exactly this. (shrink)

This article is devoted to the topical aspects of the transformation of society, science, and man in the context of E. László’s work «Macroshift». The author offers his own attempt to consider the attributes of macroshift and then use these attributes to operationalize further analysis, highlighting three essential elements: the world has come to a situation of technological indistinguishability between the natural and the artificial, to machines that know everything about humans. Antiquity aspired to beauty and saw beauty in realistic (...) art, but technology made indistinguishability possible, bringing the risks of deepfakes and post-truth. Following J. Bernal’s logic, the author distinguishes between different types of the future, comparing them with the Kantian triad of ethical questions: (1) What can we know? (2) What should we do? (3) What can I hope for? Under these conditions, the fact that technology has become a real tool of geopolitics is no longer just a matter for discussion, but a subject of deep philosophical consideration. AI is becoming not only an opportunity, but also a threat, on a scale that has never been seen before in our civilizational history. Therefore, the former, linear development of science gives way to nonlinearity. Society in the macroshift will be radically transformed, and the author identifies five main transformations of the current macroshift. The post-nonclassical approach in the analysis of scenarios for modeling the future, both accidentally possible and preferred, is becoming the most important tool of futurology and prognostics. The author describes the future around five social trends that will determine the economy and society of the coming decades. In addition, opportunities for the future development of science are proposed, subject to significant penetration of AI technologies. These technologies will have a fundamental impact on all aspects of our society, economy, and human existence. (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)

True contradictions are taken increasingly seriously by philosophers and logicians. Yet, the belief that contradictions are always false remains deeply intuitive. This paper confronts this belief head-on by explaining in detail how one specific contradiction is true. The contradiction in question derives from Priest's reworking of Berkeley's argument for idealism. However, technical aspects of the explanation offered here differ considerably from Priest's derivation. The explanation uses novel formal and epistemological tools to guide the reader through a valid argument with, not (...) just true, but eminently acceptable premises, to an admittedly unusual conclusion: a true contradiction. The novel formal and epistemological tools concern points of view and changes in points of view. The result is an understanding of why the contradiction is true. (shrink)

The review gives a short description of the content of the book and discusses the treatment of conditionals in it.

The number of independent messages a physical system can carry is limited by the number of its adjustable properties. In particular, systems that have only one adjustable property cannot carry more than a single message at a time. We demonstrate this is the case for the single photons in the double-slit experiment, and the root of the fundamental limit on measuring the complementary aspect of the photons. Next, we analyze the other ‘quantal’ behavior of the systems with a single adjustable (...) property, such as noncommutativity and no-cloning. Finally, we formulate a mathematical theory to describe the dynamics of such systems and derive the standard Hilbert-space formalism of quantum mechanics. Our derivation demonstrates the physical foundation of the quantum theory. (shrink)

As a response to the semantic and logical paradoxes, theorists often reject some principles of classical logic. However, classical logic is entangled with mathematics, and giving up mathematics is too high a price to pay, even for nonclassical theorists. The so-called recapture theorems come to the rescue. When reasoning with concepts such as truth/class membership/property instantiation, if ones is interested in consequences of the theory that only contain mathematical vocabulary, nothing is lost by reasoning in the nonclassical framework. It is (...) shown that this claim is highly misleading, if not simply false. Under natural assumptions, recapture claims are incorrect. (shrink)

In the study of modal and nonclassical logics, translations have frequently been employed as a way of measuring the inferential capabilities of a logic. It is sometimes claimed that two logics are “notational variants” if they are translationally equivalent. However, we will show that this cannot be quite right, since first-order logic and propositional logic are translationally equivalent. Others have claimed that for two logics to be notational variants, they must at least be compositionally intertranslatable. The definition of compositionality these (...) accounts use, however, is too strong, as the standard translation from modal logic to first-order logic is not compositional in this sense. In light of this, we will explore a weaker version of this notion that we will call schematicity and show that there is no schematic translation either from first-order logic to propositional logic or from intuitionistic logic to classical logic. (shrink)

Why should we be means-end rational? Why care whether someone’s mental states exhibit certain formal patterns, like the ones formalized in causal decision theory? This paper establishes a dominance argument for these constraints in a finite setting. If you violate the norms of causal decision theory, then your desires will be aptness dominated. That is, there will be some alternative set of desires that you could have had, which would be more apt (closer to the actual values fixed by your (...) sensibility/ what you intrinsically care about) no matter which world is actual. If we care about having apt desires, then, we should never let ourselves violate these norms of means-end rationality. This argument shares a form with now-standard accuracy arguments for probabilism, opening up a new terrain for that discussion. I show that the foundational assumptions about the shape of accuracy and of aptness required to run the arguments for means-end rationality and for probabilism run closely parallel. I show the argument is robust under different theories of subjective actual value, including nonclassical treatments of indeterminacy in actual value; I show the argument may (but need not!) be generalized to objective theories of value. The upshot is that aptness-domination arguments for decision theories should be added to the philosophical playbook. (shrink)

What is commonly referred to as the Adoption Problem is a challenge to the idea that the principles of logic can be rationally revised. The argument is based on a reconstruction of unpublished work by Saul Kripke. As the reconstruction has it, Kripke extends the scope of Willard van Orman Quine's regress argument against conventionalism to the possibility of adopting new logical principles. In this paper we want to discuss the scope of this challenge. Are all revisions of logic subject (...) to the Adoption Problem? If not, are there significant cases of logical revision that are subject to the Adoption Problem? We will argue that both questions should be answered negatively. (shrink)

Following the pioneering studies of the receptive field (RF), the concept gained further significance for visual perception by the discovery of input effects from beyond the classical RF. These studies demonstrated that neuronal responses could be modulated by stimuli outside their RFs, consistent with the perception of induced brightness, color, orientation, and motion. Lesion scotomata are similarly modulated perceptually from the surround by RFs that have migrated from the interior to the outer edge of the scotoma and in this way (...) provide filling-in of the void. Large RFs are advantageous to this task. In higher visual areas, such as the middle temporal and inferotemporal lobe, RFs increase in size and lose most of their retinotopic organization while encoding increasingly complex features. Whereas lowerlevel RFs mediate perceptual filling-in, contour integration, and figure–ground segregation, RFs at higher levels serve the perception of grouping by common fate, biological motion, and other biologically relevant stimuli, such as faces. Studies in alert monkeys while freely viewing natural scenes showed that classical and nonclassical RFs cooperate in forming representations of the visual world. Today, our understanding of the mechanisms underlying the RF is undergoing a quantum leap. What had started out as a hierarchical feedforward concept for simple stimuli, such as spots, lines, and bars, now refers to mechanisms involving ascending, descending, and lateral signal flow. By extension of the bottom-up paradigm, RFs are nowadays understood as adaptive processors, enabling the predictive coding of complex scenes. Top-down effects guiding attention and tuned to task-relevant information complement the bottom-up analysis. (shrink)

We here make preliminary investigations into the model theory of DeMorgan logics. We demonstrate that Łoś's Theorem holds with respect to these logics and make some remarks about standard model-theoretic properties in such contexts. More concretely, as a case study we examine the fate of Cantor's Theorem that the classical theory of dense linear orderings without endpoints is $\aleph_{0}$-categorical, and we show that the taking of ultraproducts commutes with respect to previously established methods of constructing nonclassical structures, namely, Priest's Collapsing (...) Lemma and Dunn's Theorem in 3-Valued Logic. (shrink)

The first degree entailment (FDE) family is a group of logics, a many-valued semantics for each system of which is obtained from classical logic by adding to the classical truth-values true and false any subset of {both, neither, indeterminate}, where indeterminate is an infectious value (any formula containing a subformula with the value indeterminate itself has the value indeterminate). In this paper, we see how to extend a version of star semantics for the logics whose many-valued semantics lack indeterminate to (...) star semantics for logics whose many-valued semantics include indeterminate. The equivalence of the many-valued semantics and star semantics is established by way of a soundness and completeness proof. The upshot of the novel semantics in terms of the applied semantics of these logics, and specifically infectiousness, is explored, settling on the idea that infectiousness concerns ineffability. (shrink)

We here propose a solution to the problem we have raised. Basically, the mathematical notion of entailment seems to be connected to the inferential rules from Classical Logic, so that if we have P: x belongs to the reals, and Q: x+2=5 => x=3, P |= Q. Notwithstanding, we would also have that if P: x belongs to the interval (7,10), and Q: x+2=5 => x=3, P |= Q. The second instance of entailment does not seem to be justifiable if (...) our intuition is consulted: Even though we could say that absurdity implies anything in Classical Logic, entailment should be a concept that belongs to the metalogic, not to the logic of the system, so that we should not be inside of the Classical Logic World by the time we assess things in what regards entailment. As another point, our discussions in Entailment led us to choose the sense has as a consequence for entailment, so that it is not really acceptable that we have, as a consequence, using normal language, of x being inside of the real interval (7,10) that if x+2=5, then x=3. If x is in that interval, x+2 should not be 5, unless we are talking about moduli of vectors. However, when we transfer to Classical Logic, in having the antecedent false, and the consequent false as well, we have that the implication, which some call material, is true. We here discuss this sort of matter in detail, and hope to get to the bottom of the issue, and perhaps to a universal solution. (shrink)

The paper discusses this year’s Nobel Prize in physics for experiments of entanglement “establishing the violation of Bell inequalities and pioneering quantum information science” in a much wider, including philosophical context legitimizing by the authority of the Nobel Prize a new scientific area out of “classical” quantum mechanics relevant to Pauli’s “particle” paradigm of energy conservation and thus to the Standard model obeying it. One justifies the eventual future theory of quantum gravitation as belonging to the newly established quantum information (...) science. Entanglement, involving non-Hermitian operators for its rigorous description, non-unitarity as well as nonlocal and superluminal physical signals “spookily” (by Einstein’s flowery epithet) synchronizing and transferring some nonzero action at a distance, can be considered to be quantum gravity so that its local counterpart to be Einstein’s gravitation according to general relativity therefore pioneering an alternative pathway to quantum gravitation different from the “secondary quantization” of the Standard model. So, the experiments of entanglement once they have been awarded by the Nobel Prize launch particularly the relevant theory of quantum gravitation grounded on “quantum information science” thus granted to be nonclassical quantum mechanics in the shared framework of the generalized quantum mechanics obeying rather quantum-information conservation than only energy conservation. The concept of “dark phase” of the universe naturally linked to the very well confirmed “dark matter” and “dark energy” and opposed to its “light phase” inherent to classical quantum mechanics and the Standard model obeys quantum-information conservation, after which reversible causality or the mutual transformation of energy and information are valid. The mythical Big Bang after which energy conservation holds universally is to be replaced by an omnipresent and omnitemporal medium of decoherence of the dark and nonlocal phase into the light and local phase. The former is only an integral image of the latter and borrowed in fact rather from religion than from science. Physical, methodological and proper philosophical conclusions follow from that paradigm shift heralded by this year’s Nobel Prize in physics. For example, the scientific theory of thinking should originate from the dark phase of the universe, as well: probably only approximately modeled by neural networks physically belonging to the light phase thoroughly. A few crucial philosophical sequences follow from the break of Pauli’s paradigm: (1) the establishment of the “dark” phase of the universe as opposed to its “light” phase, only to which the Cartesian dichotomy of “body” and “mind” is valid; (2) quantum information conservation as relevant to the dark phase, furthermore generalizing energy conservation as to its light phase, productively allowing for physical entities to appear “ex nihilo”, i.e., from the dark phase, in which energy and time are yet inseparable from each other; (3) reversible causality as inherent to the dark phase; (4) the interpretation of gravitation only mathematically: as an interpretation of the incompleteness of finiteness to infinity, for example, following the Gödel dichotomy (“either contradiction or incompleteness”) about the relation of arithmetic to set theory; (5) the restriction of the concept of hierarchy only to the light phase; (6) the commensurability of both physical extremes of a quantum and the universe as a whole in the dark phase obeying quantum information conservation and akin to Nicholas of Cusa’s philosophical and theological worldview. (shrink)

In this article, on the basis of analysis of the classical definition of a miracle (from D.Hume to C.S.Lewis and R. Swinburne) and the nonclassical one (J.L. Marion and J.P.Manussakis), the phenomenological and the etymological aspects of a miracle are examined.Taking into consideration the historical development of the concept of a miracle, the author proves the connections between contemplation, miracle and novelty. They are necessary for the constituting of religious experience. Faith itself, in theological sense, is not determinative for religious (...) experience.It has sense only when it is integrated into contemplation. True religious experience is based on the art of contemplation which helps a human being to look with astonishment. The author argues that phenomenological approach to a miracle combined with the etymological analysis is a valuable method for the study of a miracle in the context of the history of philosophy. (shrink)

*These notes were folded into the published paper "Probability and nonclassical logic*. Revising semantics and logic has consequences for the theory of mind. Standard formal treatments of rational belief and desire make classical assumptions. If we are to challenge the presuppositions, we indicate what is kind of theory is going to take their place. Consider probability theory interpreted as an account of ideal partial belief. But if some propositions are neither true nor false, or are half true, or whatever—then it’s (...) far from clear that our degrees of belief in it and its negation should sum to 1, as classical probability theory requires (?, cf.). There are extant proposals in the literature for generalizing (categorical) probability theory to a non-classical setting, and we will use these below. But subjective probabilities themselves stand in functional relations to other mental states, and we need to trace the knock-on consequences of revisionism for this interrelationship (arguably, degrees of belief only count as kinds of belief in virtue of standing in these functional relationships). (shrink)

of “Reason and the structure of Davidson’s ‘Desire-Belief-Model’ ” by Henk bij de Weg In the present discussion in the analytic theory of action, broadly two models for the explanation or justification of actions can be distinguished: the internalist and the externalist model. Against this background, I discuss Davidson’s version of the internalist Desire-Belief Model . First, I show that what Davidson calls “pro attitude” has two distinct meanings. An implication of this is that Davidson’s DBM actually comprises two different (...) models: the “classical” DBM and a model that has an extra premise, the “nonclassical” model. However, from another point of view one can say that the classical DBM is the nonclassical model in which a premise is missing. In order to determine which viewpoint is correct, I introduce Schütz’s distinction between “because-motives” and “in-order-to-motives”. With the help of this distinction, I can show that the classical DBM is an incomplete version of the nonclassical model. Besides of the premise that refers to the agent’s pro attitude, we need this extra premise in order to refer to the occasion as experienced by the agent that makes him or her act. Only then can we fully explain or justify an action. (shrink)

Arguments pro and contra convergent realism – underdetermination of theory by observational evidence and pessimistic meta-induction from past falsity – are considered. It is argued that, to meet the counter-arguments challenge, convergent realism should be considerably changed with a help of modification of the propositions from this meta-programme “hard core” or “protecting belt”. Two well-known convergent realism rivals – “entity realism” of Nancy Cartwright and Ian Hacking and John Worrall’s “structural realism” – are considered. Entity realism’s main drawback is fundamental (...) laws underestimation. As for structural realism, its limitation of theoretical propositions by pure structural ones is ineffective. One always can transform propositions about objects into propositions about structures and vice versa. Both conceptions are kinds of “metaphysical revisionism” that tries to reformulate the good old convergent realism propositions using more decent language and applying ad hoc modifications of the solutions first obtained within the anti-realist epistemological meta-programmes. It is stated that to overcome the troubles of convergent realism one has to turn from classical or “metaphysical” realism to nonclassical or “internal” one and to coherent theory of truth. Internal realism has no troubles in solving the problem of empirically-equivalent theoretical descriptions and historical meta-induction problem, but gets the problem of scientific knowledge objectivity instead. Where does this objectivity come from? One of the answers is proposed by the scientific knowledge growth model elaborated by Rinat Nugayev and by Peter Galison. Each paradigm is a local viewpoint determined by the peculiarities of a culture into which its creator . was submerged. However, the meeting of the different paradigms leads to their interaction; as a result, the crossbred theoretical objects are constructed. Through these systems the infiltration of one paradigm on the other’s domain takes place. After the old paradigms’ grinding the new ones emerge that reconcile to each other much better than the old ones. Scientific theories reconcile results in elimination of many contingent details. In the process of competition more universal components survive. It is demonstrated that the process of objective knowledge genesis takes place in modern superstring theory too. The list of its drawbacks is rather long; it is clear that the theory cannot pretend on the role of the Theory of Everything. Nevertheless the process of argumentation pro and contra convergent realism – underdetermination of theory by observational evidence and pessimistic meta-induction from past falsity – are considered. It is argued that, to meet the counter-arguments challenge, convergent realism should be considerably changed with a help of modification of the propositions from this meta-programme “hard core” or “protecting belt”. It is stated that to overcome the troubles of convergent realism one has to turn from classical or “metaphysic” of quantum field theory and general relativity interpenetration have already begun. (shrink)

The article presents the grounds for defining the fetish of artificial intelligence (AI). The fundamental differences of AI from all previous technological innovations are highlighted, as primarily related to the introduction into the human cognitive sphere and fundamentally new uncontrolled consequences for society. Convincing arguments are presented that the leaders of the globalist project are the main beneficiaries of the AI fetish. This is clearly manifested in the works of philosophers close to big technology corporations and their mega-projects. It is (...) proposed to consider the problem of how to use the capabilities of AI to overcome the growing international conflicts and the global crisis in general. The focus is on the problem of subjectness, the solution of which from the standpoint of an anthropomorphic approach to AI is fraught with serious negative consequences. When endowing AI with subjectness, responsibility is implicitly removed from the person who uses this technology, and the established legislative practice is also destroyed. The presentation of AI as an agent endowed with a set of invariant simplified qualities that natural subjects have is proposed. These qualities include: the ability to purposefulness, a kind of reflexivity, communication and simplified elements of sociality. Such a representation of AI as an agent (pseudo-subject) is consistent with the principle of distributed control in biology and psychology, which was called the principle of a dual subject. In combination with the systems of principles and ontologies specified in the concept of post-nonclassical cybernetics of self-developing environments, this will allow the use of AI as a means of social innovation, while maintaining control over AI technologies. And also to pose and solve the problem of integrating the formations of artificial and natural intelligence while maintaining the basic qualities of carriers of natural intelligence. (shrink)

The purpose of the article is to identified the origin and essence of Western individualism. Methods of research. I used the methodology of post-nonclassical metaphysics of history, as well as the methods of epistemological polytheism and comparative. Results. The first sprouts of individualism can be detected in Greek poleis. It is the crisis of the polis system in Ancient Greece that predetermined the disappointment of the Greeks in the old collectivist ideals. Roman collectivism quite naturally got along with ideas about (...) civil liberties and the dignity of an individual citizen. The idea of citizenship was brought to the theoretical perfection by moving it beyond the boundaries of city walls. The Christian ideal is not a self-sufficient person, but the community of believers. It is the weakening of the church’s position and the strengthening of the influence of Antiquity that led to the formation of the Western style of thinking, which became the basis of the new European civilizational project. John Locke rethought the Hobbesian “Roman” theory of the social contract, thereby laying the foundations of liberalism, and hence of individualism. However, radically changing the hierarchical society, even the shaken revolution and the restoration of the Stuarts, no theoretical work could not. But in the New World, free from class barriers, Locke’s ideas found a much more fertile soil. Conclusions. The Western version of individualism emerges as a civilizational ideal at the junction of two completely different paradigms — the Ancient (Greek and Roman) and the Christian. Being present in the “body” of the West, individualism could not access its code. The latter was guarded by numerous barriers, among which the Catholic collectivism and the class divisions of hierarchical society were the most powerful guards. In American society, security barriers were significantly weaker, which allowed individualism to develop in the United States. Then American individualism returned to Europe and is now perceived as an integral element of Western civilization. (shrink)

We present in this paper the neutrosophic randomized variables, which are a generalization of the classical random variables obtained from the application of the neutrosophic logic (a new nonclassical logic which was founded by the American philosopher and mathematical Florentin Smarandache, which he introduced as a generalization of fuzzy logic especially the intuitionistic fuzzy logic ) on classical random variables. The neutrosophic random variable is changed because of the randomization, the indeterminacy and the values it takes, which represent the possible (...) results and the possible indeterminacy. Then we classify the neutrosophic randomized variables into two types of discrete and continuous neutrosophic random variables and we define the expected value and variance of the neutrosophic random variable then offer some illustrative examples. -/- . (shrink)

For many years now, Harnad has argued that transduction is special among cognitive capacities -- special enough to block Searle's Chinese Room Argument. His arguments (as well as Searle's) have been important and useful, but not correct, it seems to me. Their arguments have provided the modern impetus for getting clear about computationalism and the nature of computing. This task has proven to be quite difficult. Which is simply to say that dealing with Harnad's arguments (as well as Searle's) has (...) been difficult. Turing, it turns out, only got us started. But Harnad's (and Searle's) arguments ultimately fail. Turing, it turns out, was on the right track. (shrink)

Graham Priest's book In Contradiction is a bold defense of the existence of true contradictions. Although Priest's case is impressive, and many of his arguments are correct, his approach is not the only one allowing for true contradictions. As against Priest's, there is at least one contradictorialist approach which establishes a link between true contradictions and degrees of truth. All in all, such an alternative is more conservative, closer to mainstream analytical philosophy. The two approaches differ as regards the floodgate (...) problem. Priest espouses a confinement policy banning contradictions except in a few special domains, particularly those of pure semantics and set-theory , whereas the alternative approach admits two negations -- natural or weak negation and strong negation, the latter being classical; accordingly, the alternative approach prohibits any contradiction involving strong negation, thus providing a syntactic test of what contradictions have to be rejected. (shrink)

Consider the set of inferences that are acceptable to use in all our theory building endeavors. Call this set of inferences the universal theory building toolkit, or just ’the toolkit’ for short. It is clear that the toolkit is tightly connected to logic in a variety of ways. Beall, for example, has argued that logic just is the toolkit. This paper avoids making a stand on that issue and instead investigates reasons for thinking that, logic or not, the toolkit is (...) substructural. It is presented as a dialogue for the simple reason that it summarizes a range of dialogues on this subject that the author has had with various folks over the past few years. The method I use to investigate the toolkit is inspired in both philosophical and technical details by Alasdair Urquhart’s work on semantics for relevance logics from the early 1970s. (shrink)

The operational semantics of Urquhart is a deep and important part of the development of relevant logics. In this paper, I present an overview of work on Urquhart’s operational semantics. I then present the basics of collection frames. Finally, I show how one kind of collection frame, namely, functional set frames, is equivalent to Urquhart’s semilattice semantics.