The CMI Millennium “P vs NP Problem” can be resolved e.g. if one shows at least one counterexample to the "P = NP" conjecture. A certain class of problems being such counterexamples will be formulated. This implies the rejection of the hypothesis that "P = NP" for any conditions satisfying the formulation of the problem. Thus, the solution "P is different from NP" of the problem in general is proved. The class of counterexamples can be interpreted as any quantum superposition (...) of any finite set of quantum states. The Kochen-Specker theorem is involved. Any fundamentally random choice among a finite set of alternatives belong to "NP" but not to "P". The conjecture that the set complement of "P" to "NP" can be described by that kind of choice exhaustively is formulated. (shrink)

Out of a folklore–like fact about the counterexample function to P=NP, a function which grows about as fast as the Busy Beaver function, we review the consequences of our exotic formalization for P=NP and then speculate about possible ways to extend our work.

The GOOGLE and XPRIZE $5,000,000 for the practical and socially useful utilization of the quantum computer is the starting point for ontomathematical reflections for what it can really serve. Its “output by measurement” is opposed to the conjecture for a coherent ray able alternatively to deliver the ultimate result of any quantum calculation immediately as a Dirac -function therefore accomplishing the transition of the sequence of increasingly narrow probability density distributions to their limit. The GOOGLE and XPRIZE problem’s solution needs (...) the initial understanding that the result of any quantum calculation is a wave function, or respectively, a probability (density or not) distribution unlike the Turing machine one, and only a “calculating ray” is able to transform the former into the later without any “curving” disturbances. Thus, the unique capability of the quantum computer due to its inherent quantum parallelism can be conserved for all Gödel unresolvable problems, only on the fast “NP” track of which the quantum computer “Achilles” is able practically to overrun the Turing machine “Tortoise” since the latter can “sprint” only by any “P” calculating speed even on it and unlike “Achilles” himself able for “NP” velocities as well. The way for any material body to “calculate” the certain trajectory of least action also resolves the “traveling salesman problem” in fact, therefore illustrating furthermore what the “NP” output of a quantum computer by a “calculating ray” should mean. Another example is the problem of the number of all prime numbers less than “N”, which is suggested to visualize once again the quantum computer capability to resolve problems by a “NP” speed and thus qualitatively to overrun any competing Turing machine. The technically implemented idea of laser is now reinterpreted to “radiate a wave function” in order to explain the “calculating ray” option for a quantum computer “NP” output. The generalization of an entanglement “trigger ray” described by any non-Hermitian operator (unlike a laser) is suggested as well as those “sci-fi” horizons which it reveals. One of them is meant for elucidating the practical meaning of the “Yang-Mills existence and mass gap problem”, one more of the CMI “Millennium Problems” after that of “P vs NP”. -/- . (shrink)

Based on the computation mode introduced in [13], we deal with the time complexity of computations over arbitrary first-order structures.The main emphasis is on parameter-free computations. Some transfer results for solutions of P versus NP problems as well as relationships to quantifier elimination are discussed. By computation tree analysis using first-order formulas, it follows that P versus NP solutions and other results of structural complexity theory are invariant under elementary equivalence of structures.

The current study investigated the adaptations which occur in visual search behaviour as a function of expertise in rugby union players when completing attacking scenarios. Ten experienced players and ten novice players completed 2 vs. 1 attacking game scenarios. Starting with the ball in hand and wearing a mobile eye tracker throughout, participants were required to score a try against a defender. The scenarios allowed for a pass to their supporting player or trying to run past the defender. No between (...) group differences were found in fixating on the supporting attacking player. However, EP increased the length and frequency looking at the area immediately ahead of the supporting player, particularly when executing a spin pass. NP fixated longer and more frequently at the defender, whilst EP fixated more frequently in the space the supporting player would run into in Switch and Dummy Switch scenarios. More successful passes were completed and tries scored by EP compared to NP. Differences in visual search behaviour between experienced and NP suggest that the experts extract information from areas directly related to guiding the motor action; the space immediately ahead of the support player to pass the ball in. Contrastingly, novices use a more allocentric perspective where the actions from the defender are used to guide their motor actions. (shrink)

We analyze N. C. A. da Costa and F. A. Doria’s “exotic formalization” of the conjecture P = NP [3–7]. For any standard axiomatic PA extension T and any number-theoretic sentence ${\varphi }$ , we let ${\varphi ^{\star} := \varphi \vee \lnot \mathsf{Con}\left( \mathsf{T}\right)}$ and prove the following “exotic” inferences 1–3. 1. ${\mathsf{T}+\varphi ^{\star}}$ is consistent, if so is T, 2. ${\mathsf{T}+\varphi}$ is consistent, provided that ${\mathsf{T}+\varphi ^{\star}}$ is ω-consistent, 3. ${\mathsf{T}+\varphi}$ is consistent, provided that T is consistent and has (...) the same provably total recursive functions as ${\mathsf{T}+\left( \varphi \leftrightarrow \varphi ^{\star }\right) }$ . Furthermore we show that 1–3 continue to hold for ${\varphi ^{\star} := \varphi _{S} :=\varphi \vee \lnot S}$ , where ${S=\forall x\exists yR\left( x,y\right)}$ is any ${\Pi _{2}^{0}}$ sentence satisfying: 4. ${\left( \forall n\in \omega \right) \left( \mathsf{T}\vdash S_{x}\left[ \underline{n}\right] \right) }$ , 5. ${\mathsf{Con}\left( \mathsf{T}\right) \Rightarrow \mathsf{T}\nvdash S}$ . We observe that if ${\varphi :=\left[ \mathsf{P}=\mathsf{NP}\right] }$ and ${S:= \left[\digamma total\right] }$ , where ${\digamma=\digamma _{\mathsf{T}}}$ is da Costa-Doria “exotic” function with respect to T, then 4, 5 are satisfied for most familiar (presumably) consistent T in question, while ${\varphi _{S}}$ becomes equivalent to da Costa-Doria “exotic formalization” ${\left[ \mathsf{P}=\mathsf{NP}\right]^{\digamma}}$ . Moreover, the corresponding “exotic” inferences 1–3 generalize analogous da Costa-Doria results. Hence these “exotic” inferences are universal for all number-theoretic sentences and not characteristic to the conjecture P = NP. Nor do they infer relative consistency of P = NP (see Conclusion 15 in the text). (shrink)

Here, we try to show that the method used in -/- Theory of Fuzzy Time Computation(TC * vs TC, TQC). 2023. ￿hal-04330281￿ -/- is a general method that sheds light on various types of problems. The author choose the navier stocks problem, to check the possibility of solving this problem by this method. This text is a guideline of possible proof of this problem.

The paper introduces and utilizes a few new concepts: “nonstandard Peano arithmetic”, “complementary Peano arithmetic”, “Hilbert arithmetic”. They identify the foundations of both mathematics and physics demonstrating the equivalence of the newly introduced Hilbert arithmetic and the separable complex Hilbert space of quantum mechanics in turn underlying physics and all the world. That new both mathematical and physical ground can be recognized as information complemented and generalized by quantum information. A few fundamental mathematical problems of the present such as Fermat’s (...) last theorem, four-color theorem as well as its new-formulated generalization as “four-letter theorem”, Poincaré’s conjecture, “P vs NP” are considered over again, from and within the new-founding conceptual reference frame of information, as illustrations. Simple or crucially simplifying solutions and proofs are demonstrated. The link between the consistent completeness of the system mathematics-physics on the ground of information and all the great mathematical problems of the present (rather than the enumerated ones) is suggested. (shrink)

Throughout this paper, in a nutshell we try to show a way to check Fuzzy time in general and Fuzzy time-Particle interpretation of Quantum Mechanics, experimentally. . -/- .

In our research about Fuzzy Time and modeling time, "Unexpected Hanging Paradox" plays a major role. Here, we compare this paradox to the Zeno Paradox and the relations of them with our standard models of continuum and Fuzzy numbers. To do this, we review the project "Fuzzy Time and Possible Impacts of It on Science" and introduce a new way in order to approach the solutions for these paradoxes. Additionally, we have a more general discussion about paradoxes, as Philosophical back (...) ground of the subject and in this way, we introduce the concepts of General View, the first picture, BBF-General View. (shrink)

コンピュータの歴史、アルゴリズムの理論の解説を経て、未解決であるミレニアム問題のひとつ、「P≠NP問題」に迫ります!

We show that there is a structure of countably infinite signature with $P = N_{2}P$ and a structure of finite signature with $P = N_{1}P$ and $N_{1}P \neq N_{2}P$ . We give a further example of a structure of finite signature with $P \neq N_{1}P$ and $N_{1}P \neq N_{2}P$ . Together with a result from [10] this implies that for each possibility of P versus NP over structures there is an example of countably infinite signature. Then we show that for (...) some finite ℒ the class of ℒ-structures with $P = N_{1}P$ is not closed under ultraproducts and obtain as corollaries that this class is not $\delta$ -elementary and that the class of ᵍ-structures with $P \neq N_{1}P$ is not elementary. Finally we prove that for all f dominating all polynomials there is a structure of finite signature with the following properties: $P \neq N_{1}P$ . $N_{1}P \neq N_{2}P$ , the levels $N_{2}TIME(n^{i})$ of $N_{2}P$ and the levels $N_{1}TIME(n^{i})$ of $N_{1}P$ are different for different i, indeed $DTIME(n^{i'}) \nsubseteq N_{2}TIME(n^{i})$ if $i' \textgreater i$ ; $DTIME(f) \nsubseteq N_{2}P$ , and $N_{2}P \nsubseteq DEC$ . DEC is the class of recognizable sets with recognizable complements. So this is an example where the internal structure of $N_{2}P$ is analyzed in a more detailed way. In our proofs we use methods in the style of classical computability theory to construct structures except for one use of ultraproducts. (shrink)

We discuss the question of Ralf-Dieter Schindler whether for infinite time Turing machines Pf = NPf can be true for any function f from the reals into ω1. We show that “almost everywhere” the answer is negative.

Background: Heart rate variability (HRV) has been considered as a measure of heart-brain interaction and autonomic modulation, and it is modified by cognitive and attentional tasks. In cognitive tasks, HRV was reduced in participants who achieved worse results. This could indicate the possibility of HRV predicting cognitive performance, but this association is still unclear in a high cognitive load sport such as chess Objective: To analyse modifications on HRV and subjective perception of stress, difficulty and complexity in different chess problem (...) tasks. Design: HRV was assessed at baseline. During the chess problems, HRV was also monitored, and immediately after chess problems the subjective stress, difficulty and complexity were also registered. Method: A total of 16 male chess players, age: 35.19 (13.44) and ELO: 1927.69 (167.78) were analysed while six chess problem solving tasks with different level of difficulty were conducted (two low level, two medium level and two high level chess problems). Participants were classified according to their results into two groups: high performance or low performance. Results: Friedman test showed a significant effect of tasks in HRV indexes and perceived difficulty, stress and complexity in both high and low performance groups. A decrease in HRV was observed in both groups when chess problems difficulty increased. In addition, HRV was significantly higher in the high performance group than in the low performance group during chess problems. Conclusions: An increase in autonomic modulation was observed to meet the cognitive demands of the problems, being higher while the difficulty of the tasks increased. Non-linear HRV indexes seem to be more reactive to tasks difficulty, being an interesting and useful tool in chess training. (shrink)

I criticize the view that top-down causation is a proper model for depicting and justifying belief in mental causation. When properly interpreted, I believe that there are no clear examples of top-down causation, and there is a persuasive case against it. In order to defend these claims, I, first, clarify three preliminary considerations; second, undermine alleged examples of top-down causation; third, present a case for why there is no top-down mental causation; fourth, explain an important option for moving forward in (...) preserving what we all know to be the case—that mental causation is real. (shrink)

There is solid consensus among physicists and philosophers that, in gauge field theory, for a quantity to be physically meaningful or real, it must be gauge-invariant. Yet, every “elementary” field in the Standard Model of particle physics is actually gauge-variant. This has led a number of researchers to insist that new manifestly gauge-invariant approaches must be established. Indeed, in the foundational literature, dissatisfaction with standard methods for reducing gauge symmetries has been expressed: Spontaneous symmetry breaking is deemed conceptually dubious, while (...) gauge fixing suffers the same limitations and is subject to the same criticisms as coordinate choices in General Relativity. An alternative gauge-invariant proposal was recently introduced in the literature, the so-called “dressing field method” (DFM). It is a mathematically subtle tool, and unfortunately prone to be confused with simple gauge transformations, hence with standard gauge fixings. As a matter of fact, in the physics literature the two are often conflated, and in the philosophy community some doubts have been raised about whether there is any substantial difference between them. Clarifying this issue is of special significance for anyone interested in both the foundational issues of gauge theories and their invariant formulation. It is thus our objective to establish as precisely as possible the technical and conceptual distinctions between the DFM and gauge fixing. (shrink)

From the perspectives of Jewish tradition, particularly that of the Halakhah (Jewish law), this paper considers the policy problem of the balance in health care allocations between preventive and curative or crisis medicine. Since the value of human lives has a high degree of supremacy, and the duties to rescue imperiled life and to treat the sick are recognized, it might be argued that a basically curative policy should be favored. On the other hand, the duty of personal health maintenance (...) and safety would appear to argue in favor of a preventive policy. In balancing these considerations, it is suggested that the halakhic tradition can accommodate a preventive policy of health care because the duty to rescue is lessened or negatived by risk to the as-it-were rescuers. It is further suggested that Halakhah permits a non-divertable allocation of tax-generated funds to preventive health care. Keywords: Preventive medicine, curative medicine, value of human lives, duty to rescue, risk taking, Jewish law ( Halakhah ), charity tax CiteULike Connotea Del.icio.us What's this? (shrink)

In the newly discovered letter Hume answers Reid's charge that he held a theory of ideas derived from his predecessors and criticizes Reid's own theory of innate ideas. He defends his own theory that ideas are derived from impressions. I discuss Reid's own puzzlement that in the first _Enquiry_ Hume ascribes a natural belief in necessary connections to the vulgar without an idea--and its influence on subsequent readings of Hume as a 'regularity theorist.' I argue that it was the 'Common (...) Sense' school of philosophers following Reid, rather than Hume, who insisted that beliefs must be based on legitimate ideas. (shrink)

This paper is a supplement to, and provides a proof of principle of, Kuhn vs. Popper on Criticism and Dogmatism in Science: A Resolution at the Group Level. It illustrates how calculations may be performed in order to determine how the balance between different functions in science—such as imaginative, critical, and dogmatic—should be struck, with respect to confirmation (or corroboration) functions and rules of scientific method.

In lieu of an abstract, here is a brief excerpt of the content:The Myrmidon vs. the AbbessHow Contrasting Mechanisms to Resolve Mimetic Contagion in Shakespeare's Troilus and Cressida and Comedy of Errors Stand as a Warning Against the Rejection of Christianity in Favor of Resurgent Homeric EthosBrian P. Quaranta (bio)This investigation started with a question: Why does Shakespeare hate the Iliad?The question arose after first reading Troilus and Cressida (T&C), Shakespeare's play set during the Trojan War. In his retelling, all (...) claims to glory for Homer's heroes are undermined; a world that is presented by Homer as brutal but honorable is replaced, by Shakespeare, with one that is rife with social and physical disease. As I continued to consider why Shakespeare displayed such hostility toward the Iliad, I found myself recognizing multiple, much more subtle, allusions to the Trojan War in another of his plays set in ancient Greece, The Comedy of Errors (COE). In time, it became apparent that the connection of these two plays with each other, and with the Iliad, was deliberate; through this comparison, Shakespeare rejects the Homeric ethos in favor of a Christian one. A consideration of René Girard's work on Shakespeare helps to bring home the connection between the plays and the concern that they illuminate.In his Theatre of Envy, Girard famously claimed that Shakespeare was consciously familiar with the concepts of mimetic desire and its relationship [End Page 183] to collective violence.1 He drew upon T&C and COE for examples: T&C for its explication of the importance of degree, its employment of collective murder, and the association of mimetic contagion with disease,2 and COE primarily for its emphasis on the special role of twins in mimetic theory as exemplars of identical rivals.3 Girard, I believe, is correct that Shakespeare understood the mechanisms and implications of mimetic theory, and he demonstrates how in these plays its consequences play out in a purely pagan world, and then in another in which there is a saving Christian intervention.The intellectual current of Shakespeare's time has been characterized by two primary themes: Reformation and Renaissance. The use of the word reformation, when taken on its own terms, suggests a benign and necessary process. But for an Englishman in the late 16th century, reformation also would have meant violence, displacement, fracture, war, and the disintegration of a once-unified Christendom. This crumbling of the ancient universal catholic church was accompanied by the Renaissance, a term used to refer to the rebirth of interest in, and progressive obsession with, the culture and literature of the ancient Greeks and Romans.4 My argument is that the two plays discussed here can be read as Shakespeare's response to these developments, demonstrating an anxiety over the threat of resurgent pagan values to a troubled Christianity, with T&C's ending standing as a warning of the danger of a return to the scapegoat mechanism, and COE reminding the reader of the power of the Christian alternative.The essay begins with a brief reminder of the depth of the enthusiasm for the classical era that emerged in Europe in the century leading up to, and including, the life of Shakespeare. I then detail the surprising ways in which Shakespeare thoroughly upends expectations in his retelling of the Trojan War story, discrediting the original tale. Next, the similarities of the Comedy of Errors to Troilus and Cressida, and to the Iliad, are documented. Because this area has received little previous scholarly attention, and because it is crucial to the argument, the inversions of the Trojan War in COE are meticulously detailed. Once it has been established that the two plays both respond to the Iliad, Girard's mimetic theory is brought to bear to explain the very different endings of the plays and to reveal Shakespeare's underlying concern about the Homeric ethos.THE RENAISSANCE AND SHAKESPEARE'S RESPONSE TO THE CLASSICSThe emerging triumph of the Greco-Roman pagan world over the renaissance mind, and its intrusion into the Christian realm, are evident in the development [End Page 184] of visual art in the decades preceding Shakespeare's work. Works by Michelangelo, Raphael, and Giulio Romano, depicting... (shrink)

Title: Capitalismo y Religión: La Religión Politica Neoconservadora Publisher: Editorial Sal Terrae ISBN: 8429308970 Author: José Mardones Title: The Challenge of Populism: The Rise of Right-Wing Democratism in Postwar America Publisher: Praeger Publishers ISBN: 0275939065 Author: Michael P. Federici.

In this paper the questions remaining open about NP-completeness of multiplicative and Horn fragments of the Linear Logic and the Linear Logic with the weakening rule are answered.

The key difference between classical mechanics and quantum mechanics, at least in the "orthodox" view of Niels Bohr, is tied to the difference within these two theories of the relationship between the observer and the observed. In classical mechanics the observed system is characterized exactly by what an idealized disembodied observer could know about the system without actually interacting with it, or disturbing it. Thus in classical mechanics the physical system is specified by what could be known by an observer (...) that is conceived to stand apart from the observed system. But according to Bohr science is based on what we can learn from experiment: "The argument is simply that by the word `experiment' we refer to a situation where we can tell others what we have done and what we have learned... This crucial point, which was to become a main theme of the discussions... implies the IMPOSSIBILITY OF ANY SHARP SEPARATION.. (shrink)

The world’s third largest producer of scientific research, Germany, is the origin of the research university and the independent, extra-university research institute. Its dual-pillar research policy differentiates these organizational forms functionally: universities specialize in advanced research-based teaching; institutes specialize intensely on research. Over the past decades this policy affected each sector differently: while universities suffered a lingering “legitimation crisis,” institutes enjoyed deepening “favored sponsorship”—financial and reputational advantages. Universities led the nation’s reestablishment of scientific prominence among the highly competitive European and (...) global science systems after WWII. But sectoral analysis of contributions to science, technology, engineering, mathematics, and medical and health journal publications finds that Germany’s small to medium-sized independent research institutes have made significant, growing contributions, particularly in publishing in higher impact journals proportionally more than their size. Simultaneously—despite dual-pillar policy implications—the university sector continues to be absolutely and relatively successful; not eclipsed by the institutes. Universities have consistently produced two-thirds of the nation’s publications in the highest quality journals since at least 1980 and have increased publications at a logarithmic rate; higher than the international mean. Indeed, they led Germany into the global mega-science style of production. Contrary to assumed benefits of functional differentiation, our results indicate that relative to their size, each sector has produced approximately similar publication records. While institutes have succeeded, the larger university sector, despite much less funding growth, has remained fundamental to German science production. Considering these findings, we discuss the future utility of the dual-pillar policy. (shrink)

Analysts such as Steven Horwitz, with strong prior beliefs, are seldom impressed by mere fact and tend to explain away empirical deviations from their theories. The belief that markets are moved only by fundamentals and not by occasional faddism and overshooting rests on the assumption that market participants form their opinions independently, when in fact they are from time to time driven by emulation. The belief that markets are rational and well?informed but government officials and central bankers incompetent is implausible (...) on its face. The period since 1970 has seen bubble after bubble, some of which seemed likely to lead to financial crisis had it not been for the Federal Reserve. (shrink)

The aim of this research was to establish linear relations (association and prediction) and inferential relations between three constructs at different levels of psychological research –executive dysfunction(microanalysis),self-regulation(molecular level), andself-vs.external regulation(molar level), in the prediction of emotion regulation difficulties. We hypothesized that personal and contextual regulatory factors would be negatively related to levels of executive dysfunction and emotion regulation difficulties; by way of complement, non-regulatory and dysregulatory personal, and contextual factors would be positively related to these same difficulties. To establish relationships, (...) we used a retrospective,ex postfacto design, where 298 university students voluntarily participated by completing standardized self-reports. Linear and structural correlational, predictive analyses were performed, as well as inferential analyses. Results were consistent and validated the proposed hypotheses, for both association and prediction. The most important result refers to the discriminant value of the five-level combination heuristic for predicting Executive Function and External (contextual) Dys-Regulation. In conclusion: (1) both personal and contextual regulation factors must be analyzed in order to better understand the variation in executive functions and emotion regulation difficulties; (2) it is important to continue connecting the different levels of the constructs referring to self-regulation, given their complementary role in the behavioral analysis of regulation difficulties. (shrink)

Non-suicidal self-injury has consistently been associated with self-reported difficulties in emotion reactivity and the regulation of negative emotions; however, less is known about the accuracy of these self-reports or the reactivity and regulation of positive emotions. The present study sought to investigate differences between women with and without a history of NSSI on: self-reported general tendencies of negative and positive emotion reactivity, self-reported general tendencies of negative and positive emotion regulation, and emotion regulation reported in response to a positive and (...) negative mood induction. The sample consisted of 36 women with a recent history of NSSI within the last 2 years and a comparison group with no history of NSSI. Participants completed self-report measures of negative and positive emotion reactivity and regulation. In a separate session, participants underwent both a negative and positive mood induction using a counterbalanced design and reported their experienced emotions. Results from two-way MANOVAs and ANOVAs revealed those with a history of NSSI reported significantly greater difficulties in negative emotion reactivity and regulation than the no-NSSI comparison group; however, no group differences emerged in self-reported reactivity or regulation of positive emotions. In contrast, repeated measures ANOVAs on data from the mood induction task found no group differences in reactivity or regulation for either negative or positive emotions. These findings highlight the possibility that although individuals with a history of NSSI evaluate their ability to manage negative emotions as significantly worse than individuals with no history of self-injury, this may not reflect their actual emotion regulatory processes. (shrink)

1. Belief and mental statesDavidson holds that intentional verbs occurring in the form ‘A Vs that p’ signify propositional attitudes. These are, he claims, mental states, and dispositions. Davidson does not conceive of himself as introducing a special technical sense of the common intentional verbs. He insists that ‘the mental states in question are beliefs, desires, intentions, and so on, as ordinarily conceived'. Consequently he contends that believing that p is a mental state, disposition or dispositional state. These ontological claims (...) about the nature of belief inform his account of the logical form of belief sentences. I shall address the question of whether believing that p can justly be deemed a mental state, a disposition or dispositional state. Subsequently I shall examine Davidson's account of the logical form of belief sentences.Our concept of a mental state, like so many of the concepts which philosophers treat as categorial, is none too sharply defined. It has a respectable use, which can be described. But, like other such general psychological terms, e.g. ‘mental process’, ‘mental activity’, far from being the ‘hardest of the hard’ - a sharply circumscribed categorial term akin to a variable in a well-constructed formal system — it has blurred boundaries and is elastic. Like all our ordinary psychological concepts, it evolved in order to meet everyday needs. As Wittgenstein observed, ‘The concepts of psychology are just everyday concepts. They are not concepts newly fashioned by science for its own purposes, as are the concepts of physics and chemistry.’Although our ordinary concepts can be replaced by technical ones for specialized purposes, they cannot be abused without generating conceptual confusion and incoherence. If the expression ‘mental state’ is being employed in its ordinary sense, then it is wrong to hold that believing that p is to be in any mental state. If it is being employed in a special technical sense, then those who employ it thus owe us an account of what it means and how it is to be used. This Davidson and the many other philosophers who subscribe to the view that believing is a mental state have not done. Until such an account is forthcoming, one may presume that they think of themselves as deploying our ordinary concept of a mental state. And if so, I shall argue, they are misusing it. (shrink)

Davidson’s explanation of first‐person authority in utterance of sentences of the form ‘I V that p’ derives first‐person authority from the requirements of interpretation of speech. His account is committed to the view that utterance sentences are truth‐bearers, that believing that p is a matter of holding true an utterance sentence, and that a speaker’s knowledge of what he means gives him knowledge of what belief he expresses by his utterance. These claims are here faulted. His explanation of first‐person authority (...) by reference to the requirements of interpretability is committed to the view that all understanding involves interpretation. This is argued to be a misconception of understanding and of speaker’s meaning. Davidson’s account involves acceptance of the cognitive assumption that normally when a person Vs that p, he knows that he does. This assumption is challenged. Throughout, Davidson’s conception is compared and contrasted with Wittgenstein’s. (shrink)

The dynamical equations of relativistic quantum mechanics prescribe the motion of wave packets for sets of events which trace out the world lines of the interacting particles. Electromagnetic theory suggests thatparticle world line densities be constructed from concatenation of event wave packets. These sequences are realized in terms of conserved probability currents. We show that these conserved currents provide a consistent particle and antiparticle interpretation for the asymptotic states in scattering processes. The relation between current conservation and unitarity is used (...) to establish relations between pair production and annihilation amplitudes and scattering. The discrete symmetriesC, T, P are studied and it is shown that no Dirac sea (for fermions where such a construction is possible, or bosons where it is not) is required for consistency of the theory. These currents, furthermore, represent the discrete symmetries in a way consistent with their interpretation as particle currents. (shrink)