A complete axiomatic system CTL$_{rp}$ is introduced for a temporal logic for finitely branching $\omega^+$-trees in a temporal language extended with so called reference pointers. Syntactic and semantic interpretations are constructed for the branching time computation tree logic CTL$^{*}$ into CTL$_{rp}$. In particular, that yields a completeaxiomatization for the translations of all valid CTL$^{*}$-formulae. Thus, the temporal logic with reference pointers is brought forward as a simpler (with no path quantifiers), but in a way more expressive (...) medium for reasoning about branching time. (shrink)
Hyperboolean algebras are Boolean algebras with operators, constructed as algebras of complexes (or, power structures) of Boolean algebras. They provide an algebraic semantics for a modal logic (called here a {\em hyperboolean modal logic}) with a Kripke semantics accordingly based on frames in which the worlds are elements of Boolean algebras and the relations correspond to the Boolean operations. We introduce the hyperboolean modal logic, give a completeaxiomatization of it, and show that it lacks the finite model (...) property. The method of axiomatization hinges upon the fact that a "difference" operator is definable in hyperboolean algebras, and makes use of additional non-Hilbert-style rules. Finally, we discuss a number of open questions and directions for further research. (shrink)
We study the modal logic M L r of the countable random frame, which is contained in and `approximates' the modal logic of almost sure frame validity, i.e. the logic of those modal principles which are valid with asymptotic probability 1 in a randomly chosen finite frame. We give a sound and completeaxiomatization of M L r and show that it is not finitely axiomatizable. Then we describe the finite frames of that logic and show that it (...) has the finite frame property and its satisfiability problem is in EXPTIME. All these results easily extend to temporal and other multi-modal logics. Finally, we show that there are modal formulas which are almost surely valid in the finite, yet fail in the countable random frame, and hence do not follow from the extension axioms. Therefore the analog of Fagin's transfer theorem for almost sure validity in first-order logic fails for modal logic. (shrink)
A complete axiomatic system CTL$_{rp}$ is introduced for a temporal logic for finitely branching $\omega^+$-trees in a temporal language extended with so called reference pointers. Syntactic and semantic interpretations are constructed for the branching time computation tree logic CTL* into CTL$_{rp}$. In particular, that yields a completeaxiomatization for the translations of all valid CTL*-formulae. Thus, the temporal logic with reference pointers is brought forward as a simpler (with no path quantifiers), but in a way more expressive (...) medium for reasoning about branching time. (shrink)
We give a completeaxiomatization of the identities of the basic game algebra valid with respect to the abstract game board semantics. We also show that the additional conditions of termination and determinacy of game boards do not introduce new valid identities. En route we introduce a simple translation of game terms into plain modal logic and thus translate, while preserving validity both ways game identities into modal formulae. The completeness proof is based on reduction of game terms (...) to a certain 'minimal canonical form', by using only the axiomatic identities, and on showing that the equivalence of two minimal canonical terms can be established from these identities. (shrink)
How does vagueness interact with metaphysical modality and with restrictions of it, such as nomological modality? In particular, how do definiteness, necessity (understood as restricted in some way or not), and actuality interact? This paper proposes a model-theoretic framework for investigating the logic and semantics of that interaction. The framework is put forward in an ecumenical spirit: it is intended to be applicable to all theories of vagueness that express vagueness using a definiteness (or: determinacy) operator. We will show how (...) epistemicists, supervaluationists, and theorists of metaphysical vagueness like Barnes and Williams (2010) can interpret the framework. We will also present a completeaxiomatization of the logic we recommend to both epistemicists and local supervaluationists. . (shrink)
Logics of joint strategic ability have recently received attention, with arguably the most influential being those in a family that includes Coalition Logic (CL) and Alternating-time Temporal Logic (ATL). Notably, both CL and ATL bypass the epistemic issues that underpin Schelling-type coordination problems, by apparently relying on the meta-level assumption of (perfectly reliable) communication between cooperating rational agents. Yet such epistemic issues arise naturally in settings relevant to ATL and CL: these logics are standardly interpreted on structures where agents move (...) simultaneously, opening the possibility that an agent cannot foresee the concurrent choices of other agents. In this paper we introduce a variant of CL we call Two-Player Strategic Coordination Logic (SCL2). The key novelty of this framework is an operator for capturing coalitional ability when the cooperating agents cannot share strategic information. We identify significant differences in the expressive power and validities of SCL2 and CL2, and present a sound and completeaxiomatization for SCL2. We briefly address conceptual challenges when shifting attention to games with more than two players and stronger notions of rationality. (shrink)
So far, T×W frames have been employed to provide a semantics for a language of tense logic that includes a modal operator that expresses historical necessity. The operator is defined in terms of quantification over possible courses of events that satisfy a certain constraint, namely, that of being alike up to a given point. However, a modal operator can as well be defined without placing that constraint. This paper outlines a T×W logic where an operator of the latter kind is (...) used to express the epistemic property of definiteness. Section 1 provides the theoretical background. Sections 2 and 3 set out the semantics. Sections 4 and 5 show, drawing on established results, that there is a sound and completeaxiomatization of the logic outlined. (shrink)
We study the general problem of axiomatizing structures in the framework of modal logic and present a uniform method for completeaxiomatization of the modal logics determined by a large family of classes of structures of any signature.
It is shown that a completeaxiomatization of classical non-tautologies can be obtained by taking F (falsehood) as the sole axiom along with the two inference rules: (i) if A is a substitution instance of B, then A |– B; and (ii) if A is obtained from B by replacement of equivalent sentences, then A |– B (counting as equivalent the pairs {T, ~F}, {F, F&F}, {F, F&T}, {F, T&F}, {T, T&T}). Since the set of tautologies is also (...) specifiable by purely syntactic means, the resulting picture gives an improved syntactic account of classical sentential logic. The picture can then be completed by considering related systems that prove adequate to specify the set of contradictions, the set of non-contradictions, and the set of contingencies respectively. (shrink)
In previous work, I introduced a completeaxiomatization of classical non-tautologies based essentially on Łukasiewicz’s rejection method. The present paper provides a new, Hilbert-type axiomatization (along with related systems to axiomatize classical contradictions, non-contradictions, contingencies and non-contingencies respectively). This new system is mathematically less elegant, but the format of the inferential rules and the structure of the completeness proof possess some intrinsic interest and suggests instructive comparisons with the logic of tautologies.
Philosophers have spilled a lot of ink over the past few years exploring the nature and significance of grounding. Kit Fine has made several seminal contributions to this discussion, including an exact treatment of the formal features of grounding [Fine, 2012a]. He has specified a language in which grounding claims may be expressed, proposed a system of axioms which capture the relevant formal features, and offered a semantics which interprets the language. Unfortunately, the semantics Fine offers faces a number of (...) problems. In this paper, I review the problems and offer an alternative that avoids them. I offer a semantics for the pure logic of ground that is motivated by ideas already present in the grounding literature, and for which a natural axiomatization capturing central formal features of grounding is sound and complete. I also show how the semantics I offer avoids the problems faced by Fine’s semantics. (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)
A general class of labeled sequent calculi is investigated, and necessary and sufficient conditions are given for when such a calculus is sound and complete for a finite -valued logic if the labels are interpreted as sets of truth values. Furthermore, it is shown that any finite -valued logic can be given an axiomatization by such a labeled calculus using arbitrary "systems of signs," i.e., of sets of truth values, as labels. The number of labels needed is logarithmic (...) in the number of truth values, and it is shown that this bound is tight. (shrink)
Methods available for the axiomatization of arbitrary finite-valued logics can be applied to obtain sound and complete intelim rules for all truth-functional connectives of classical logic including the Sheffer stroke and Peirce’s arrow. The restriction to a single conclusion in standard systems of natural deduction requires the introduction of additional rules to make the resulting systems complete; these rules are nevertheless still simple and correspond straightforwardly to the classical absurdity rule. Omitting these rules results in systems for (...) intuitionistic versions of the connectives in question. (shrink)
Epicurus argued that the good life is the pleasurable life. He also argued that ‘death is nothing to us’. These claims appear in tension. For if pleasure is good, then it seems that death is bad when it deprives us of deeply enjoyable time alive. Here, I offer an Epicurean view of pleasure and the complete life which dissolves this tension. This view is, I contend, more appealing than critics of Epicureanism have allowed, in part because it assigns higher (...) value to pleasures that we produce by exercising our rational capacities and by establishing control over our lives. (shrink)
In their recent book Every Thing Must Go, Ladyman and Ross claim: (i) Physics is analytically complete since it is the only science that cannot be left incomplete. (ii) There might not be an ontologically fundamental level. (iii) We should not admit anything into our ontology unless it has explanatory and predictive utility. In this discussion note I aim to show that the ontological commitment in implies that the completeness of no science can be achieved where no fundamental level (...) exists. Therefore, if claim requires a science to actually be complete in order to be considered as physics,, and if Ladyman and Ross's “tentative metaphysical hypothesis ... that there is no fundamental level” is true,, then there simply is no physics. Ladyman and Ross can, however, avoid this unwanted result if they merely require physics to ever strive for completeness rather than to already be complete. (shrink)
In Nicomachean Ethics 1.8, Aristotle seems to argue that certain external goods are needed for happiness because, in the first place, they are needed for virtuous activity. This has puzzled scholars. After all, it seems possible for a virtuous agent to exercise her virtuous character even under conditions of extreme hardship or deprivation. Indeed, it is natural to think these are precisely the conditions under which one's virtue shines through most clearly. Why then does Aristotle think that a wide range (...) of external goods is required for virtuous activity, and therefore, for happiness? -/- I argue that there is good sense to be made of Aristotle's stance on external goods. Specifically, I explain how, on this view, a range of external goods is required for the full exercise of virtue, and I show that it is only this full exercise that is constitutive of eudaimonia. Drawing on passages in Politics 7.13 and Nicomachean Ethics 3.1, I develop and defend a distinction between the "mere" exercise of virtue, and the full or complete exercise of virtue. I argue that, for Aristotle, the distinguishing feature of this distinction is the value of the virtuous action's ends. An action that fully expresses virtue aims at an end that is unqualifiedly good, while an action that merely exercises virtue does not. I argue that the external goods Aristotle mentions in NE 1.8 are necessary for performing actions with unqualifiedly good ends, and so necessary for the complete exercise of virtue. In addition to providing a more satisfactory account than existing proposals of the role of external goods in Aristotelian happiness, my interpretation has two additional upshots. First, it brings to light an under-appreciated and independently compelling feature of Aristotle's ethical thought: the value of virtuous actions depends in part on the value of the ends they aim to realize. Second, it finds in Aristotle a distinct and powerful way of thinking about the badness of certain kinds of misfortune and deprivation: they are bad in part because they prevent us from fully realizing our capacity for moral agency, from fully engaging with value in the world. (shrink)
We investigate an enrichment of the propositional modal language L with a "universal" modality ■ having semantics x ⊧ ■φ iff ∀y(y ⊧ φ), and a countable set of "names" - a special kind of propositional variables ranging over singleton sets of worlds. The obtained language ℒ $_{c}$ proves to have a great expressive power. It is equivalent with respect to modal definability to another enrichment ℒ(⍯) of ℒ, where ⍯ is an additional modality with the semantics x ⊧ ⍯φ (...) iff Vy(y ≠ x → y ⊧ φ). Model-theoretic characterizations of modal definability in these languages are obtained. Further we consider deductive systems in ℒ $_{c}$ . Strong completeness of the normal ℒ $_{c}$ logics is proved with respect to models in which all worlds are named. Every ℒ $_{c}$ -logic axiomatized by formulae containing only names (but not propositional variables) is proved to be strongly frame-complete. Problems concerning transfer of properties ([in]completeness, filtration, finite model property etc.) from ℒ to ℒ $_{c}$ are discussed. Finally, further perspectives for names in multimodal environment are briefly sketched. (shrink)
In the Transcendental Ideal Kant discusses the principle of complete determination: for every object and every predicate A, the object is either determinately A or not-A. He claims this principle is synthetic, but it appears to follow from the principle of excluded middle, which is analytic. He also makes a puzzling claim in support of its syntheticity: that it represents individual objects as deriving their possibility from the whole of possibility. This raises a puzzle about why Kant regarded it (...) as synthetic, and what his explanatory claim means. I argue that the principle of complete determination does not follow from the principle of excluded middle because the externally negated or ?negative? judgement ?Not (S is P)? does not entail the internally negated or ?infinite? judgement ?S is not-P.? Kant's puzzling explanatory claim means that empirical objects are determined by the content of the totality of experience. This entails that empirical objects are completely determinate if and only if the totality of experience has a completely determinate content. I argue that it is not a priori whether experience has such a completely determinate content and thus not analytic that objects obey the principle of complete determination. (shrink)
A theoretically rigorous approach to the key problems of Molinism leads to a clear distinction between semantic and metaphysical problems. Answers to semantic problems do not provide answers to metaphysical problems that arise from the theory of middle knowledge. The so-called ‘grounding objection’ to Molinism raises a metaphysical problem. The most promising solution to it is a revised form of the traditional ‘essence solution’. Inspired by Leibniz’s idea of a ‘notio completa’ (complete concept), we propose a mathematical model of (...) ‘possibilistic’ (Molinist) complete concepts. They ground middle knowledge within the very being of the agents themselves. Molinist Complete Concepts can thus serve to reject consequence-style arguments against Molinism. They also allow the Molinist to safeguard a robustly libertarian notion of the ability to do otherwise. (shrink)
It is widely taken that the first-order part of Frege's Begriffsschrift is complete. However, there does not seem to have been a formal verification of this received claim. The general concern is that Frege's system is one axiom short in the first-order predicate calculus comparing to, by now, the standard first-order theory. Yet Frege has one extra inference rule in his system. Then the question is whether Frege's first-order calculus is still deductively sufficient as far as the first-order completeness (...) is concerned. In this short note we confirm that the missing axiom is derivable from his stated axioms and inference rules, and hence the logic system in the Begriffsschrift is indeed first-order complete. (shrink)
Consider the following. The first is a one-premise argument; the second has two premises. The question sign marks the conclusions as such. -/- Matthew, Mark, Luke, and John wrote Greek. ? Every evangelist wrote Greek. -/- Matthew, Mark, Luke, and John wrote Greek. Every evangelist is Matthew, Mark, Luke, or John. ? Every evangelist wrote Greek. -/- The above pair of premise-conclusion arguments is of a sort familiar to logicians and philosophers of science. In each case the first premise is (...) logically equivalent to the set of four atomic propositions: “Matthew wrote Greek”, “Mark wrote Greek”, “Luke wrote Greek”, and “John wrote Greek”. The universe of discourse is the set of evangelists. We presuppose standard first-order logic. -/- As many logic texts teach, the first of these two premise-conclusion arguments—sometimes called a complete enumerative induction— is invalid in the sense that its conclusion does not follow from its premises. To get a counterargument, replace ‘Matthew’, ‘Mark’, ‘Luke’, and ‘John’ by ‘two’,’four’, ‘six’ and ‘eight’; replace ‘wrote Greek’ by ‘are even’; and replace ‘evangelist’ by ‘number’. This replacement converts the first argument into one having true premises and false conclusion. -/- But the same replacement performed on the second argument does no such thing: it converts the second premise into the falsehood “Every number is two, four, six, or eight”. As many logic texts teach, there is no replacement that converts the second argument into one with all true premises and false conclusion. The second is valid; its conclusion is deducible from its two premises using an instructive natural deduction. -/- This paper “does the math” behind the above examples. The theorem could be stated informally: the above examples are typical. (shrink)
Kant claims that Aristotles logic as complete, explain the historical and philosophical considerations that commit him to proving the completeness claim and sketch the proof based on materials from his logic corpus. The proof will turn out to be an integral part of Kant’s larger reform of formal logic in response to a foundational crisis facing it.
This article develops an axiom system to justify an additive representation for a preference relation ${\succsim}$ on the product ${\prod_{i=1}^{n}A_{i}}$ of extensive structures. The axiom system is basically similar to the n-component (n ≥ 3) additive conjoint structure, but the independence axiom is weakened in the system. That is, the axiom exclusively requires the independence of the order for each of single factors from fixed levels of the other factors. The introduction of a concatenation operation on each factor A i (...) makes it possible to yield a special type of restricted solvability, i.e., additive solvability and the usual cancellation on ${\prod_{i=1}^{n}A_{i}}$ . In addition, the assumption of continuity and completeness for A i implies a stronger type of solvability on A i . The additive solvability, cancellation, and stronger solvability axioms allow the weakened independence to be effective enough in constructing the additive representation. (shrink)
The Bare Theory was offered by David Albert as a way of standing by the completeness of quantum mechanics in the face of the measurement problem. This paper surveys objections to the Bare Theory that recur in the literature: what will here be called the oddity objection, the coherence objection, and the context-of-the-universe objection. Critics usually take the Bare Theory to have unacceptably bizarre consequences, but to be free from internal contradiction. Bizarre consequences need not be decisive against the Bare (...) Theory, but a further objection—dubbed here the calibration objection—has been underestimated. This paper argues that the Bare Theory is not only odd but also inconsistent. We can imagine a successor to the Bare Theory—the Stripped Theory—which avoids the objections and fulfills the original promise of the Bare Theory, but at the cost of amplifying the bizarre consequences. The Stripped Theory is either a stunning development in our understanding of the world or a reductio disproving the completeness of quantum mechanics. The Bare Theory The usual objections The calibration objection Beyond the Bare Theory. (shrink)
When we think about postmodernism we have to consider its implication in every aspect of society and none would doubt that homosexuality is one of these major implication especially for the contemporary church. The influence of relativism and the paradigm shift in humanity made homosexuality not just acceptable, but in many cases a norm. For a long time the church barricaded herself not only behind her Jewish-christian worldview and theological values, but also behind the absolutes of science that just has (...) to agree that in the beginning there were only male and female. For long time homosexuality has been viewed as a behavior option, but what about if science has come up with a new discovery so called Gay Gene? That is exactly what we want to discuss in this essay. (shrink)
Michael Ryan's Literary Theory: A Practical Introduction, Second Edition introduces students to the full range of contemporary approaches to the study of literature and culture, from Formalism, Structuralism, and Historicism to Ethnic Studies, Gender Studies, and Global English. Introduces readings from a variety of theoretical perspectives, on classic literary texts. Demonstrates how the varying perspectives on texts can lead to different interpretations of the same work. Contains an accessible account of different theoretical approaches An ideal resource for use in introductory (...) courses on literary theory and criticism. Designed to function both as a stand-alone text and a companion to Rivkin and Ryan’s Literary Theory: An Anthology, Second Edition. (shrink)
The deep crisis in modern fundamental science development is ever more evident and openly recognised now even by mainstream, official science professionals and leaders. By no coincidence, it occurs in parallel to the world civilisation crisis and related global change processes, where the true power of unreduced scientific knowledge is just badly missing as the indispensable and unique tool for the emerging greater problem solution and further progress at a superior level of complex world dynamics. Here we reveal the mathematically (...) exact reason for the crisis in conventional science, containing also the natural and unified problem solution in the form of well-specified extension of usual, artificially restricted paradigm. We show how that extended, now causally complete science content provides various "unsolvable" problem solutions and opens new development possibilities for both science and society, where the former plays the role of the main, direct driver for the latter. We outline the related qualitative changes in science organisation, practice and purposes, giving rise to the sustainability transition in the entire civilisation dynamics towards the well-specified superior level of its unreduced, now well understood and universally defined complexity. (shrink)
Preface thoroughly outlines the development and status of dark matter theory at the time of publishing this book. First chapter is like a combat between mathematical counterintuitive physics and human commonsense and explains that human commonsense equipped with proper philosophical approach is capable to deal with the problem of dark matter. Thus the first chapter makes a case for human commonsense and philosophical method.
This review shows how Auden was a philosopher of religion and therefore, this review calls for reassessing the poet Auden as a philosopher concerned with prayer and the necessity of the transcendent in life.
Although many aspects of Inference to the Best Explanation have been extensively discussed, very little has so far been said about what it takes for a hypothesis to count as a rival explanatory hypothesis in the context of IBE. The primary aim of this article is to rectify this situation by arguing for a specific account of explanatory rivalry. On this account, explanatory rivals are complete explanations of a given explanandum. When explanatory rivals are conceived of in this way, (...) I argue that IBE is a more plausible and defensible rule of inference than it would otherwise be. The secondary aim of the article is to demonstrate the importance of accounts of explanatory rivalry by examining a prominent philosophical argument in which IBE is employed, viz. the so-called Ultimate Argument for scientific realism. In short, I argue that a well-known objection to the Ultimate Argument due to Arthur Fine fails in virtue of tacitly assuming an account of explanatory rivalry that we have independent reasons to reject. (shrink)
In this short response to Kerstein and Bognar, we clarify three aspects of the complete lives system, which we propose as a system of allocating scarce medical interventions. We argue that the complete lives system provides meaningful guidance even though it does not provide an algorithm. We also defend the investment modification to the complete lives system, which prioritizes adolescents and older children over younger children; argue that sickest-first allocation remains flawed when scarcity is absolute and ongoing; (...) and argue that Kerstein and Bognar are mistaken to base their allocation principles on differences in personhood. (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)
The article first outlines Edmund Husserl’s idea of “complete transformation” (völlige Umwendung) and the philosophy of “the turn” (Kehre) of Martin Heidegger. In the following chapter it is shown that you can understand both Husserl as well as Heidegger in the light of “the essential turn” in the German mysticism of the fourteenth century. In this way it becomes clear that Husserl’s idea of a “complete transformation” seems to be a forgotten “mystical” impetus of phenomenology, which was much (...) more realized by Martin Heidegger than by Husserl. In this way Heidegger’s philosophy of “the turn” appears as an important modern approach of the mystical philosophy of transformation. (shrink)
Classical interpretations of Goedels formal reasoning, and of his conclusions, implicitly imply that mathematical languages are essentially incomplete, in the sense that the truth of some arithmetical propositions of any formal mathematical language, under any interpretation, is, both, non-algorithmic, and essentially unverifiable. However, a language of general, scientific, discourse, which intends to mathematically express, and unambiguously communicate, intuitive concepts that correspond to scientific investigations, cannot allow its mathematical propositions to be interpreted ambiguously. Such a language must, therefore, define mathematical truth (...) verifiably. We consider a constructive interpretation of classical, Tarskian, truth, and of Goedel's reasoning, under which any formal system of Peano Arithmetic---classically accepted as the foundation of all our mathematical Languages---is verifiably complete in the above sense. We show how some paradoxical concepts of Quantum mechanics can, then, be expressed, and interpreted, naturally under a constructive definition of mathematical truth. (shrink)
This paper concerns “human symbolic output,” or strings of characters produced by humans in our various symbolic systems; e.g., sentences in a natural language, mathematical propositions, and so on. One can form a set that consists of all of the strings of characters that have been produced by at least one human up to any given moment in human history. We argue that at any particular moment in human history, even at moments in the distant future, this set is finite. (...) But then, given fundamental results in recursion theory, the set will also be recursive, recursively enumerable, axiomatizable, and could be the output of a Turing machine. We then argue that it is impossible to produce a string of symbols that humans could possibly produce but no Turing machine could. Moreover, we show that any given string of symbols that we could produce could also be the output of a Turing machine. Our arguments have implications for Hilbert’s sixth problem and the possibility of axiomatizing particular sciences, they undermine at least two distinct arguments against the possibility of Artificial Intelligence, and they entail that expert systems that are the equals of human experts are possible, and so at least one of the goals of Artificial Intelligence can be realized, at least in principle. (shrink)
Stochastic independence (SI) has a complex status in probability theory. It is not part of the definition of a probability measure, but it is nonetheless an essential property for the mathematical development of this theory, hence a property that any theory on the foundations of probability should be able to account for. Bayesian decision theory, which is one such theory, appears to be wanting in this respect. In Savage's classic treatment, postulates on preferences under uncertainty are shown to entail a (...) subjective expected utility (SEU) representation, and this permits asserting only the existence and uniqueness of a subjective probability, regardless of its properties. What is missing is a preference postulate that would specifically connect with the SI property. The paper develops a version of Bayesian decision theory that fills this gap. In a framework of multiple sources of uncertainty, we introduce preference conditions that jointly entail the SEU representation and the property that the subjective probability in this representation treats the sources of uncertainty as being stochastically independent. We give two representation theorems of graded complexity to demonstrate the power of our preference conditions. Two sections of comments follow, one connecting the theorems with earlier results in Bayesian decision theory, and the other connecting them with the foundational discussion on SI in probability theory and the philosophy of probability. Appendices offer more technical material. (shrink)
The writings of Joseph Henry Woodger (1894–1981) are often taken to exemplify everything that was wrongheaded, misguided, and just plain wrong with early twentieth-century philosophy of biology. Over the years, commentators have said of Woodger: (a) that he was a fervent logical empiricist who tried to impose the explanatory gold standards of physics onto biology, (b) that his philosophical work was completely disconnected from biological science, (c) that he possessed no scientific or philosophical credentials, and (d) that his work was (...) disparaged – if not altogether ignored – by the biologists and philosophers of his era. In this paper, we provide the first systematic examination of Woodger’s oeuvre, and use it to demonstrate that the four preceding claims are false. We argue that Woodger’s ideas have exerted an important influence on biology and philosophy, and submit that the current consensus on his legacy stems from a highly selective reading of his works. By rehabilitating Woodger, we hope to show that there is no good reason to continue to disregard the numerous contributions to the philosophy of biology produced in the decades prior to the professionalization of the discipline. (shrink)
Different anesthetics are known to modulate different types of membrane-bound receptors. Their common mechanism of action is expected to alter the mechanism for consciousness. Consciousness is hypothesized as the integral of all the units of internal sensations induced by reactivation of inter-postsynaptic membrane functional LINKs during mechanisms that lead to oscillating potentials. The thermodynamics of the spontaneous lateral curvature of lipid membranes induced by lipophilic anesthetics can lead to the formation of non-specific inter-postsynaptic membrane functional LINKs by different mechanisms. These (...) include direct membrane contact by excluding the inter-membrane hydrophilic region and readily reversible partial membrane hemifusion. The constant reorganization of the lipid membranes at the lateral edges of the postsynaptic terminals (dendritic spines) resulting from AMPA receptor-subunit vesicle exocytosis and endocytosis can favor the effect of anesthetic molecules on lipid membranes at this location. Induction of a large number of non-specific LINKs can alter the conformation of the integral of the units of internal sensations that maintain consciousness. Anesthetic requirement is reduced in the presence of dopamine that causes enlargement of dendritic spines. Externally applied pressure can transduce from the middle ear through the perilymph, cerebrospinal fluid, and the recently discovered glymphatic pathway to the extracellular matrix space, and finally to the paravenular space. The pressure gradient reduce solubility and displace anesthetic molecules from the membranes into the paravenular space, explaining the pressure reversal of anesthesia. Changes in membrane composition and the conversion of membrane hemifusion to fusion due to defects in the checkpoint mechanisms can lead to cytoplasmic content mixing between neurons and cause neurodegenerative changes. The common mechanism of anesthetics presented here can operate along with the known specific actions of different anesthetics. (shrink)
We introduce and study hierarchies of extensions of the propositional modal and temporal languages with pairs of new syntactic devices: point of reference-reference pointer which enable semantic references to be made within a formula. We propose three different but equivalent semantics for the extended languages, discuss and compare their expressiveness. The languages with reference pointers are shown to have great expressive power (especially when their frugal syntax is taken into account), perspicuous semantics, and simple deductive systems. For instance, Kamp's and (...) Stavi's temporal operators, as well as nominals (names, clock variables), are definable in them. Universal validity in these languages is proved undecidable. The basic modal and temporal logics with reference pointers are uniformly axiomatized and a strong completeness theorem is proved for them and extended to some classes of their extensions. (shrink)
A first-order theory T has the Independence Property provided deduction of a statement of type (quantifiers) (P -> (P1 or P2 or .. or Pn)) in T implies that (quantifiers) (P -> Pi) can be deduced in T for some i, 1 <= i <= n). Variants of this property have been noticed for some time in logic programming and in linear programming. We show that a first-order theory has the Independence Property for the class of basic formulas provided it (...) can be axiomatized with Horn sentences. The existence of free models is a useful intermediate result. The independence Property is also a tool to decide that a sentence cannot be deduced. We illustrate this with the case of the classical Caratheodory theorem for Pasch-Peano geometries. (shrink)
Special relativity has changed the fundamental view on space and time since Einstein introduced it in 1905. It substitutes four dimensional spacetime for the absolute space and time of Newtonian mechanics. It is believed that the validities of Lorentz invariants are fully confirmed empirically for the last one hundred years and therefore its status are canonical underlying all physical principles. However, spacetime metric is a geometric approach on nature when we interpret the natural phenomenon. A geometric flaw on this will (...) be exhibited and the alternative is suggested. The reasonable geometric model of space and time is a three dimensional space which is translating along the time direction. This model legitimately represents the true characteristic of nature. (shrink)
Aristotle in Analytica Posteriora presented a notion of proof as a special case of syllogism. In the present paper the remarks of Aristotle on the subject are used as an inspiration for developing formal systems of demonstrative syllogistic, which are supposed to formalize syllogisms that are proofs. We build our systems in the style of J. Łukasiewicz as theories based on classical propositional logic. The difference between our systems and systems of syllogistic known from the literature lays in the interpretation (...) of general positive sentences in which the same name occurs twice (of the form SaS). As a basic assumption of demonstrative syllogistic we accept a negation of such a sentence. We present three systems which differ in the interpretation of specific positive sentences in which the same name occurs twice (of the form SiS). The theories are defined as axiomatic systems. For all of them rejected axiomatizations are also supplied. For two of them a set theoretical model is also defined. (shrink)
In "La science et l’hypothèse" Henri Poincaré scrive: «Compito dello scienziato è ordinare; si fa la scienza con i fatti, come si fa una casa con le pietre; ma un cumulo di fatti non è una scienza, proprio come un mucchio di pietre non è una casa» . Oltre a richiamare qualcosa che a molti potrebbe persino apparire ovvio – cioè che la scienza non possa in alcun modo ridursi ad un mero agglomerato di fatti che il ricercatore registra in (...) ambito osservativo, ma richieda piuttosto un attento processo di elaborazione razionale sia in fase preventiva rispetto al contesto dell’esperienza, sia in fase di valutazione dei dati sperimentali raccolti – questa affermazione ha il merito di ricordarci qualcosa che spesso viene passato sotto silenzio, vale a dire il fatto che durante il nostro tentativo di comprendere il mondo si dia alla conoscenza una materia, un complesso di "oggetti", tale da risultare determinante nella costruzione e nella formulazione delle nostre teorie. Se questo è vero, si può quindi parlare di una materia, e di una forma da essa distinta, della conoscenza scientifica, sebbene con alcune precisazioni. Nel contributo si preciserà questa distinzione facendo riferimento alle assiomatizzazioni di alcune discipline scientifiche condotte nella prima metà del secolo scorso. (shrink)
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