Elementary particles are considered as local oscillators under the influence of zeropoint fields. Such oscillatory behavior of the particles leads to the deviations in their path of motion. The oscillations of the particle in general may be considered as complex rotations in complex vector space. The local particle harmonic oscillator is analyzed in the complex vector formalism considering the algebra of complex vectors. The particle spin is viewed as zeropoint angular momentum represented by a bivector. It has (...) been shown that the particle spin plays an important role in the kinematical intrinsic or local motion of the particle. From the complex vector formalism of harmonic oscillator, for the first time, a relation between mass $m$ and bivector spin $S$ has been derived in the form $\varvec{\sigma }_3 mc^2{\mathcal {J}}_{\pm } =\lambda \Omega _{\mathbf{s}} \cdot \mathrm{{S}} {\mathcal {J}}_{\pm }$ . Where, $\Omega _{s}$ is the angular velocity bivector of complex rotations, $c$ is the velocity of light. The unit vector $\varvec{\sigma }_3$ acts as an operator on the idempotents ${\mathcal {J}}_{+}$ and ${\mathcal {J}}_{-}$ to give the eigen values $\lambda =\pm 1.$ The constant $\lambda $ represents two fold nature of the equation corresponding to particle and antiparticle states. Further the above relation shows that the mass of the particle may be interpreted as a local spatial complex rotation in the rest frame. This gives an insight into the nature of fundamental particles. When a particle is observed from an arbitrary frame of reference, it has been shown that the spatial complex rotation dictates the relativistic particle motion. The mathematical structure of complex vectors in space and spacetime is developed. (shrink)

In this work, we investigate the representation of counterfactual conditionals using the vector logic, a matrix-vector formalism for logical functions and truth values. Inside this formalism, the counterfactuals can be transformed in complex matrices preprocessing an implication matrix with one of the square roots of NOT, a complex matrix. This mathematical approach puts in evidence the virtual character of the counterfactuals. This happens because this representation produces a valuation of a counterfactual that is the superposition of (...) the two opposite truth values weighted, respectively, by two complex conjugated coefficients. This result shows that this procedure gives an uncertain evaluation projected on the complex domain. After this basic representation, the judgement of the plausibility of a given counterfactual allows us to shift the decision towards an acceptance or a refusal. This shift is the result of applying for a second time one of the two square roots of NOT. (shrink)

Time-symmetric formulation of quantum mechanics—the two-state vector formalism—is presented as a tool for studying past behaviour of quantum systems. A role of weak measurement and weak values in the Cheshire Cat effect and a nested (Vaidman) three-path interferometer are discussed. Interpretation of a particle’s faint trace indicating possibility of discontinuous paths of particles passing the Vaidman interferometer is given. Consistent histories are presented as one of alternative approaches. Multitude of controversial issues is briefly reviewed and discussed.

The idea of ensembles which are both pre- and post-selected was introduced by Aharonov, Bergmann, and Lebowitz and developed by Aharonov and his school. To derive formulae for the probabilities of outcomes of a measurement performed on such an ensemble at a time intermediate between pre-selection and post-selection, the latter group introduces a two-vector formulation of quantum mechanics, one vector propagating in the forward direction in time and one in the backward direction. The formulae which they obtain by (...) this radical generalization are vindicated by a rigorous derivation using Bayes’s theorem together with standard quantum mechanical predictions regarding ensembles that are only pre-selected. Their own two-vector derivation, however, suffers from a serious lacuna. (shrink)

The two-state-vector formalism presents a time-symmetric approach to the standard quantum mechanics, with particular importance in the description of experiments having pre- and post-selected ensembles. In this paper, using the correspondence limit of the quantum harmonic oscillator in the two-state-vector formalism, we produce harmonic oscillators that possess a classical behavior while having a complex-valued position and momentum. This allows us to discover novel effects that cannot be achieved otherwise. The proposed classical behavior does not describe the (...) classical physics in the usual sense since this behavior is subjected to the feature that only after the final measurement is performed, as a boundary condition, the complex-valued classical effects occur between the initial and the final boundary conditions. This classical behavior breaks down if one does not follow the decided boundary conditions during the experiment, since otherwise, one will contradict the impossibility of retrocausality. (shrink)

Despite their important applications in metrology and in spite of numerous experimental demonstrations, weak measurements are still confusing for part of the community. This sometimes leads to unjustified criticism. Recent papers have experimentally clarified the meaning and practical significance of weak measurements, yet in Kastner, Kastner seems to take us many years backwards in the the debate, casting doubt on the very term “weak value” and the meaning of weak measurements. Kastner appears to ignore both the basics and frontiers of (...) weak measurements and misinterprets the weak measurement process and its outcomes. In addition, she accuses the authors of Aharonov et al. in statements completely opposite to the ones they have actually made. There are many points of disagreement between Kastner and us, but in this short reply I will leave aside the ontology and focus mainly on the injustice in her criticism. I shall add some general comments regarding the broader theory of weak measurements and the two-state-vector formalism, as well as supporting experimental results. Finally, I will point out some recent promising results, which can be proven by projective measurements, without the need of employing weak measurements. (shrink)

The analysis, with the use of two state vectors, of a quantum system, during the time interval between two measurements, leads to some amazing results, which seem to contradict our usual “quantum common sense.” We explore the questions of compatibility with the conventional quantum theory, uniqueness of pre- and post-selected ensembles, commutativity, simultaneity and reality of strong and weak values in the intermediate time, and the meaning of the weak value. Common criticisms are shown to be unfounded.

This paper relates both to the metaphysics of probability and to the physics of time asymmetry. Using the formalism of decoherent histories, it investigates whether intuitions about intrinsic time directedness that are often associated with probability can be justified in the context of no-collapse approaches to quantum mechanics. The standard approach to time symmetry in the decoherent histories literature is criticised, and an alternative approach is proposed, based on two decoherence conditions within the one-vector formalism. In turn, (...) considerations of forwards and backwards decoherence and of decoherence and recoherence suggest that a time-directed interpretation of probabilities, if adopted, should be both contingent and perspectival. (shrink)

The most general expression of electromagnetic theory is examined in the light of (1) Faraday's interpretation of the field as a potentiality for the force of charged matter to act upon a test body, and (2) Einstein's view of the field equations as an example of a covariant expression of special relativity. Faraday's original interpretation, in which all physical variables must be expressible as nonsingular fields, implies a particular generalization of the standard forms of the conservation equations and leads to (...) a removal of the problem of the infinite self-energy of point sources. A further generalization of the mathematical expression of electromagnetism occurs when it is asserted that the form of the laws must be compatible with the symmetry requirements of the irreducible representations of the Poincaré group. This yields a factorization of the vector field equations, giving a set of two uncoupled two-component spinor equations. It is shown that the latter lead to twice as many conservation equations for electromagnetism, compared with the vector formalism, thus making extra predictions that are not made in the latter formalism. It is shown that the extra conservation equations reveal themselves only when incorporating the requirements of Faraday's interpretation of the field solutions. (shrink)

A Gedanken experiment is presented where an excited and a ground-state atom are positioned such that, within the former’s half-life time, they exchange a photon with 50% probability. A measurement of their energy state will therefore indicate in 50% of the cases that no photon was exchanged. Yet other measurements would reveal that, by the mere possibility of exchange, the two atoms have become entangled. Consequently, the “no exchange” result, apparently precluding entanglement, is non-locally established between the atoms by this (...) very entanglement. This quantum-mechanical version of the ancient Liar Paradox can be realized with already existing transmission schemes, with the addition of Bell’s theorem applied to the no-exchange cases. Under appropriate probabilities, the initially-excited atom, still excited, can be entangled with additional atoms time and again, or alternatively, exert multipartite nonlocal correlations in an interaction free manner. When densely repeated several times, this result also gives rise to the Quantum Zeno effect, again exerted between distant atoms without photon exchange. We discuss these experiments as variants of interaction-free-measurement, now generalized for both spatial and temporal uncertainties. We next employ weak measurements for elucidating the paradox. Interpretational issues are discussed in the conclusion, and a resolution is offered within the Two-State Vector Formalism and its new Heisenberg framework. (shrink)

Why do forces compose according to the parallelogram of forces? This question has been controversial; it is one episode in a longstanding, fundamental dispute regarding which facts are not to be explained dynamically. If the parallelogram law is explained statically, then the laws of statics are separate from and “transcend” the laws of dynamics. Alternatively, if the parallelogram law is explained dynamically, then statical laws become mere corollaries to the dynamical laws. I shall attempt to trace the history of this (...) controversy in order to identify what it would be for one or the other of these rival views to be correct. I shall argue that various familiar accounts of natural law not only make it difficult to see what the point of this dispute could have been, but also improperly foreclose some serious scientific options. I will sketch an alternative account of laws that helps us to understand what this dispute was all about. (shrink)

This paper presents a new Symmetrical Interpretation (SI) of relativistic quantum mechanics which postulates: quantum mechanics is a theory about complete experiments, not particles; a complete experiment is maximally described by a complex transition amplitude density; and this transition amplitude density never collapses. This SI is compared to the Copenhagen Interpretation (CI) for the analysis of Einstein’s bubble experiment. This SI makes several experimentally testable predictions that differ from the CI, solves one part of the measurement problem, resolves some inconsistencies (...) of the CI, and gives intuitive explanations of some previously mysterious quantum effects. (shrink)

We develop some ideas about gauge symmetry in the context of Maxwell’s theory of electromagnetism in the Hamiltonian formalism. One great benefit of this formalism is that it pairs momentum and configurational degrees of freedom, so that a decomposition of one side into subsets can be translated into a decomposition of the other. In the case of electromagnetism, this enables us to pair degrees of freedom of the electric field with degrees of freedom of the vector potential. (...) Another benefit is that the formalism algorithmically identifies subsets of the equations of motion that represent time-dependent symmetries. For electromagnetism, these two benefits allow us to define gauge-fixing in parallel to special decompositions of the electric field. More specifically, we apply the Helmholtz decomposition theorem to split the electric field into its Coulombic and radiative parts, and show how this gives a special role to the Coulomb gauge (i.e. div \((\mathbf{A}) = 0\) ). We relate this argument to Maudlin’s (Entropy, 2018. https://doi.org/10.3390/e20060465 ) discussion, which advocated the Coulomb gauge. (shrink)

The paper has two related aims. One is to outline a proposal for a spatially motivated model of discourse, called Discourse Space Theory. The other is to use this framework to explore, in a relatively formalised way, the spatial basis of the conceptual complexities arising in the uses of the English progressive verb form. The theory utilises an abstract space in three dimensions. Verb stems are associated with Aktionsart schemas; aspectual forms like the progressive are viewed as operations on these (...) schemas. The proposal is that geometric concepts, specifically coordinate systems and vectors, can provide a motivated formalism for investigating conceptual structures generated by a human discourse processor. (shrink)

The problem of indeterminism in quantum mechanics usually being considered as a generalization determinism of classical mechanics and physics for the case of discrete (quantum) changes is interpreted as an only mathematical problem referring to the relation of a set of independent choices to a well-ordered series therefore regulated by the equivalence of the axiom of choice and the well-ordering “theorem”. The former corresponds to quantum indeterminism, and the latter, to classical determinism. No other premises (besides the above only mathematical (...) equivalence) are necessary to explain how the probabilistic causation of quantum mechanics refers to the unambiguous determinism of classical physics. The same equivalence underlies the mathematical formalism of quantum mechanics. It merged the well-ordered components of the vectors of Heisenberg’s matrix mechanics and the non-ordered members of the wave functions of Schrödinger’s undulatory mechanics. The mathematical condition of that merging is just the equivalence of the axiom of choice and the well-ordering theorem implying in turn Max Born’s probabilistic interpretation of quantum mechanics. Particularly, energy conservation is justified differently than classical physics. It is due to the equivalence at issue rather than to the principle of least action. One may involve two forms of energy conservation corresponding whether to the smooth changes of classical physics or to the discrete changes of quantum mechanics. Further both kinds of changes can be equated to each other under the unified energy conservation as well as the conditions for the violation of energy conservation to be investigated therefore directing to a certain generalization of energy conservation. (shrink)

One of the long-standing problems in particle physics is the covariant description of higher spin states. The standard formalism is based upon totally symmetric Lorentz invariant tensors of rank-K with Dirac spinor components, $\psi _{\mu _1 \cdots \mu _K } $ , which satisfy the Dirac equation for each space time index. In addition, one requires $\partial ^{\mu _1 } \psi _{\mu _1 \cdots \mu _K } = 0{\text{ }}and{\text{ }}\gamma ^{\mu _1 } \psi _{\mu _1 \cdots \mu _K (...) } = 0$ . The solution obtained this way (so called Rarita–Schwinger framework) describes “has–been” spin-(K+ $ - \frac{1}{2}$ ) particles in the rest frame and particles of indefinite (fuzzy) spin elsewhere. Problems occur when $\psi _{\mu _1 \cdots \mu _K } $ constrained this way are placed within an electromagnetic field. In this case, the energy of the spin-(K+ $ - \frac{1}{2}$ ) state becomes imaginary and it propagates acausally (Velo–Zwanziger problem). Here I consider two possible avenues for avoiding the above problems. First I make the case that specifically for baryon excitations there seems to be no urgency so far for a formalism that describes isolated higher-spin states as all the observed nucleon and Δ(1232) excitations (up to Δ(1600)) are exhausted by unconstrained ψ μ , $\psi _\mu ,\psi _{\mu _1 \cdots \mu _3 } {\text{ }}and{\text{ }}\psi _{\mu _1 \cdots \mu _5 } ,$ , structures which originate from rotational and vibrational excitations of an underlying quark–diquark string. Second, I show that the $\gamma ^{\mu _1 } \psi _{\mu _1 \cdots \mu _K } = 0$ constraint is a short-hand of a more general definition of the parity-singlet invariant subspace of the squared Pauli–Lubanski vector, W 2. I consider the simplest case of K=1 and construct the covariant projector onto that very state as $ - \frac{1}{3}(\frac{1}{{m^2 }}W^2 + \frac{3}{4})$ . I suggest to work in the sixteen dimensional vector space, Ψ, of the direct product of the four-vector, A μ , with the Dirac spinor, ψ, i.e., Ψ=A μ ⊗ψ, rather than keeping space-time and spinor indices separated and to consider $( - \frac{1}{3}(\frac{1}{{m^2 }}W^2 + \frac{3}{4}) - 1)\Psi = 0$ as the principal wave equation without invoking any further supplementary conditions. In gauging the equation minimally and, in calculating the determinant, one obtains the energy-momentum dispersion relation. The latter turned out to be well-behaved and free from pathologies, thus avoiding the classical Velo–Zwanziger problem. (shrink)

The claim that distant simultaneity with respect to an inertial observer is conventional arose in the context of a space-and-time rather than a spacetime ontology. Reformulating this problem in terms of a spacetime ontology merely trivializes it. In the context of flat space, flat time, and a linear inertial structure (a purely space-and-time formalism), we prove that the hyperplanes of space for a given inertial observer are determined by a purely spatial criterion that depends for its validity only on (...) the two-way light principle, which is universally regarded as empirically verified. All (empirically determined) “spacetime” entities, such as the conformal structure or light surface equation, are used in a purely mathematical manner that is independent of and hence isneutral with respect to the ontological status that is ascribed to them. In this regard, our criterion is significantly stronger than thespacetime criterion recently advanced by D. Malament, which appeals explicitly to the conformal orthogonality of spacetime vectors and to the invariance of the conformal-orthogonal structure of spacetime under the causal automorphisms of spacetime. Once the hyperplanes of space for a given inertial observer have been determined by our empirical and purely spatial criterion, the following holds: there exists one and only one $\vec \varepsilon $ -synchronization procedure, namely the standard procedure proposed by Einstein, such that the planes of common time are thesame as the nonconventional hyperplanes of space for the inertial observer. It follows that our criterion provides an empirical even if indirect method for determining that the one-way speed of light is the same as the average two-way speed of light. In addition, two inertial observers that are not at rest with respect to each other necessarily havedifferent hyperplanes of space, and consequently their respective spatial views cannot be encompassed in a single three-dimensional space. Hence, our purely spatial criterion provides an empirical motivation for adopting the more comprehensive spacetime ontology. (shrink)

continent. 2.1 (2012): 29–35. Translated by Vincent W.J. van Gerven Oei from Jeroen Mettes. "Politieke Poëzie: Enige aantekeningen, Poëtica bij N30 (versie 2006)." In Weerstandbeleid: Nieuwe kritiek . Amsterdam: De wereldbibliotheek, 2011. Published with permission of Uitgeverij Wereldbibliotheek, Amsterdam. L’égalité veut d’autres lois . —Eugène Pottier The modern poem does not have form but consistency (that is sensed), no content but a problem (that is developed). Consistency + problem = composition. The problem of modern poetry is capitalism. Capitalism—which has no (...) image: the unrepresentable Idea of “everything.” The problem is that a poem cannot be justified. There is no excuse for it. Political poetry— pure poetry—has to be problematic, though not in a mannerist way. Yes, its problem is first its own problem—poetry’s existence in the same world as the newspaper—but therefore also always everybody’s problem (the problem of any world at all). The cult of the sublime points at a suspect desire for transcendence, nostalgia for paradise lost (the womb?). Melancholia of the post-. But a problem neither sorrows nor mourns, it is alive, and the fact that it is alive is the problem—the problem for death (rigidity, the status quo). Our symbols and ideologies do not hide any god: symbolic = state; imaginary = human; real = money. Problem: the possibility of communal speech (poetry) in the absence of a “we.” Or: what is a “we” that is not a collective subject (or in any case is not a volonté générale )? What is a universal history that is not a History? This work was started in the shade of the anti-globalization protests at the end of November 1999. I considered N30 to be the closure of the nineties, of my adolescence, and of the a seemingly total extinction of social desire. From the beginning I was skeptical about the alterglobalization movement as the avant-garde of a new politics, but something was happening . Maybe this event did not show that, as the slogan would have it, “another world” is possible, but for me it indicated that such possibility was at least still possible. That naked possibility is carrying forward. And if the fundamental tone of this work sounds more desperate than utopian, this is not caused by the catastrophic sequence that since 1999 has plunged us ever deeper into the right-wing nightmare—a nightmare that this work also gives an account for—but because my hope as yet remains empty. Composition . Composition is no design, but the production of an autonomous block of affects (i.e. a POEM), rhythmically subtracted from the language of a community. A poem does something. Is something. New Sentence . Choosing the non sequitur as compositional unit has the advantage that an abstract composition is subjected to the stress of concrete, social references. Where there is a sentence, there is always a world. (This does not hold necessarily for words on their own.) And where sentences collide, something akin to a textual civil war takes place. It is not about “undermining” whatever, or de-scribing the raging global civil war, but about writing social (or even: ontological) antagonism -- including all its catastrophic and utopian possibilities. Minor resistance. Why would poetry be the no protest zone par excellence? It is nothing but protest, not simply qua “content,” but in its most fundamental essence: rhythm. Rhythm is resistance against language, time, and space, and the basis of (what we will continue to call) autonomy. Rhythm starts with the anti-rhythmic caesura as Hölderlin remarked about Sophocles, a disruption of the quotidian drone. The destruction of everything that is dead inside of us. The noise of the avant-garde has never been the representation of the noise of (post)modernity (from the television or shopping mall), but the sober noise of the systematic exchange of an unbearable worldview. The poet does not describe, but looks for a way out: There is a Grain of Sand in Lambeth that Satan cannot find Nor can his Watch Fiends find it, tis translucent & has many Angles But he who finds it will find Oothoons palace, for within Opening into Beulah every angle is a lovely heaven William Blake was not mad. And there has always been only one poetry: the poetry of paradise. The principle is that there is something in art (the essentially creative element) that is disgusted by that which, unlike art, does not aim for the supreme. Wonder is not supreme, tranquility is not supreme, beauty is not supreme. Even amusement is not supreme! The supreme is supremely open, “das Einfache,/ Das Schwer zu machen ist” 1 : paradise. That is abstract. Literally. For me it is not about a concrete imagination, an idyll or utopia. There is no doubt a need for that, but it is not so much the supposed lack of imagination or ideals (human rights are ideals), but a fundamental lack of desire (human rights are no desires) that we suffer from, and from which we do not need to remove Nietzsche’s label of “nihilism.” “We.” George Oppen: “ Of Being Numerous asks the question whether or not we can deal with humanity as something which actually exists.” What is less actual than humanity? Nowadays it appears as a lifeless ideology of cynical power politics. Or as what makes one think. It is a shame to be human. The event is the caesura that defines rhythm. Writing toward the event is not the description of the event, but marking an abstract and intense space in which the event may unfold and keep itself. It is a task. “Remember that thou blesseth the day on which I seized thee, because such is thy obligation.” The event is a contraction (or a series of contractions) with its own rhythm and unique qualities. It is more than an explosion or demonstration. But at the same time less. The endless repetition of images and stories in the media points to a fear for the indeterminate and indeterminable void of the event. In the end there is nothing to see. We do not live in disaster’s shade or miracle’s light, but rather in the rhythm, which is contracted time, having little to do with omnipresent representations. For this book I did not intend a rhythm of evental representations (a narrative rhythm), but a rhythm which would be an event itself , because it draws the border between artwork and history. My desire for a direct engagement with the “extra-textual reality” has nothing to do with the representation of “rumor in the streets.” (What has less street cred than representation?) Naturally, a poem is no historical event and does not change anything. But a poem is a part of history that wants to be repeated forever, constructed in such a way that it is worthy of repetition. It is a part of desire (composition) made consistent (durable). The “historical event” flares up and burns down, and has to burn down to be effective. The leftovers are images and stories (representations), History—no event. The artwork—that is the ambition— remains event (though monumental and inefficient/inoperable). (No wonder that a historical singularity, a revolution, reminds us of a work of art; the resurrection yearns for a judgment, an affirmation; everything depends on it.) Hence the title does not summarize the book, let alone contract its “content” into a quasi-transcendental signifier. The title is juxtaposed to the book, like everything else inside the book, and in that relation it precisely forms a part of it. The ideal work is an open whole, lacking nothing but to which everything may be added. I have been interested in this “everything,” the world, or as I said above: capitalism. “Everything” is not the space for “wonder”—a code word, a shibboleth for petty bourgeois imagination (I recognize myself in the strangest things, a speaking dog, a canal, a pond standing straight—oh my god). No. The world is a social world, not YOUR world, poet. Power is number one. I will call “Dutch,” or “shitty,” whatever denies this power. That hurts, but this pain is an expression of the desire in the world to write another world, or as Blanchot says, “the other of all worlds” 2 : the world. Not as what “is there,” but rather as that which urges for an escape from what “is.” This is a testament of how radical reality has become, for me—or rather, a writing body—in a having-been-written. I am not interested in the problem of “meaning” as misunderstood by literary scholarsi: “order” in “chaos,” “symbolization.” Bullshit. What is there, hop, hope, now: the meaning of the taste in my mouth. Bullshit. I am not interested in the frustration of interpretation; I am writing for readers who do not want to interpret. I do not know how many “professional readers” will hear the music of a paragraph like: Sun. Sushi. Volvo. I hope more than I would think. There is a suggestion (or rather, an actual production) of speed and infinitive owing to the absence of plosives, i.e. articulations such as /k/, /t/, or /p/. Can you hear the slick suaveness? Driving car dark, vocal chiaroscuro of the word “sushi.” The unstressed /i/ stands in the middle of dark vowels and thus acquires its own special out of focus , like a momentary flash or brilliance—an obscure light. It is not about recognizing a story, but about avoiding any story whatsoever: the car disappears in the glow, cars and raw fish have nothing in common except their articulation in a language that brings them together, blurring them. A world appears in its disappearance. For a moment, light is a metaphor for language, though it cannot be reduced to tenor. It is not necessary to be a linguist or philosopher to hear this—a “difficult” poem all too often becomes an allegory of its own impenetrable being-language. The only demand: leave your hermeneutical fetish at home. This was no interpretation. Most shit has been stolen etcetera. That is no longer interesting. You cannot shoot the body with information and let your lawyers reclaim the bullets. So every sentence has been stolen. Also the ones “out” “of” “my” “head.” Why would I be allowed to steal from myself and not from others? Man takes what he needs to move forward. Whatever he encounters, finds in front of him, “occurs” to him. The writer as text editor, or singing pirate. Nothing new here. Important difference with for example Sybren Polet’s 4 montage technique: anti-thematicism. Most of the time ferocious citation from whatever I was reading, listening to, ended up in, and so on. I wrote chapter 12 on my laptop while watching CNN. On the air instead of en plein air . I often employed search engines to generate material. Chapter 20 offers the purest example of this. Often I stop recognizing a particular citation after some time. It is not uncommon for a stolen sentence to conform itself to the paragraph in which it finds itself. Sometimes I nearly arbitrarily replace words. Arbitrariness as a guarantee for absolute democracy. It is a poetics of the non sequitur : a conclusion that does not follow from the premises, the strange element in the discourse. A discourse of strangers. No logical, narrative, thematic unity. There is unity in speed/flight. It has to be read linearly, but not necessarily (not preferably) from beginning to end. The shortest distance between two points is a straight line, but this line precedes every point. The middle, the acceleration, comes first. A point occurs where two lines cross. It has been written from up close, at the level of the tension between sentences. Nothing to be seen from a distance: no form except the exchange of form, no geometrical or mythical meaning. You have to get in, “groping toward a continuous present, a using everything a beginning again and again” (Stein). 5 In Dutch, experimental poetry has been mainly dense: a small rectangular form filled with a maximum amount of poetic possibility. But at the moment the poem starts to relax, the anecdotical content seems to increase. This is what is called “epic”: long, narrative. I believe that an epic is more than that, in fact something completely different. An epic is “a poem including history,” 6 a long poem tied up with the life of community, that as a whole does not need to be narrative. The American poets of the twentieth century (Pound, Williams, Zukofsky, Oppen, Olson, Silliman) have put the epic back on the map by interpreting the poem itself as a map, and writing it as navigation. They have invented the experimental epic, a genre that has generated little original following in “our” poetry. N30 is the middle part—“always start in the middle”—of a trilogy, the contours of which remain as of yet unclear, although each episode investigates one of the three “ecstasies of time”—past, present, future—concerning society X. N30 concerns itself with the PRESENT: not with the description of actual facts but of the rhythm and the intense depth in which facts appear to us. Where are we? We are camping in the desert. Sometimes we are looking at the stars. As opposed to maximum density and minimal tension (a characteristic of most (post-)experimental lyricism), I have sought a minimal density and maximum tension in this book, considered as a long non-narrative prose poem. On the one hand, the minimal density is obtained by the inherent formlessness of prose, on the other hand by the conscious refusal of any active (formal, non-rhythmic) synthesis: the poem tells nothing, shows nothing, has no theme. I did not seek maximum tension either by loading the quotidian with epiphanic radioactivity (“wonder,” confirmation from above), or by means of the intensity of the linguistic structure. I want an abstract tension, but social in its abstraction, in other words, not neutralized by and subjected to Form. Instead of form (transcendent): composition (immanent). The concept is series. Ideal: every unit is necessary for the efficacy of the others and the whole, their relation is purely linear, i.e. non-hierarchic, non-syllogistic, non-discursive, non-narrative. Sentence related to sentence like paragraph to paragraph and chapter to chapter; the whole means nothing and represents nothing. Inside the sentence: syntax (Chomsky’s tree, a type of parallel circuit), outside: parataxis (coordination, an asyntactic line through language and world). I consider duration—the energy of duration (rhythm)—to be the fundament of a poem, the temporal inclination to delimit a “space.” Being as consistency, its consistency. A spatial part of time is not merely a metaphor for an inevitable trajectory, an inescapable time, something like “our time.” Not merely—because rhythm comes from language and is not projected onto it; the poem derives from the world like a scent and a color and a life from a flower. A series, a sequence: nothing potential, but truly infinite—the movement of an infinitude. The infinite series = everything minus totality. That means that there is no container—no Form, no Self, no Image, no Structure, not even a Fragment—just “the prose of the world.” No representation, but also no staging of the impossibility of representation (the postmodern sublime). These are no fragments, no image of a fragmented world or personality, no cautious incantations around the Void. It does not exist. It is a movement. Buying bread, a flock of birds, a bomb falling—they do not depict or represent anything, not literally, not metaphorically. There is an Idea, which is however nothing more than a rhythm, in the same way that capitalism is nothing more than a pure function. Parataxis: the white space between two sentences stresses, which is nevertheless always there, also between words, even between letters: the out of focus of idle talk, the gutter, the irreducible Mallarméan mist which renders even the seemingly most transparent text legible. The white space suggests a neutral medium for free signification, a substance of language. A non sequitur is an element from a foreign discourse, which stresses the white space as space, and problematizes freedom for supra-sentential signification. I start by withdrawing material, leaving the initiative to the sentences. In general a word presupposes less often a discourse than a sentence. What discourse is presupposed by “dog”? We could think of several, but why would we? It is more probable that, when faced with the naked word, we think of its naked (dictionary) meaning, of its denotative signified. By means of two simple interventions we may also write the word as sentence: Dog. In no way this suggests the discourse from which this sentence originates, but in any case we’re presupposing one. This is shown by questions like: “Whose dog? Who’s a dog? What kind of dog?” Etc. (Sentences are question marks.) A sentence implies/is a microcosm—a subject, a verb, an object, and so on. Even an incomplete or ungrammatical sentence does so. My main fascination while writing this book is the worldly and social aspect of language, an aspect that often becomes invisible, or rather, transparent in narrativity—the stretching of sentences into stories. Narrativity organizes a new discourse and a new world, and places a sometimes all too dispersing relation of transparence in between. The conventional novel is the brothel of being. I do not intend to prohibit brothels, and I have certainly not intended to write an anti-novel (THIS IS A POEM), but I do consider narrativity (in general, in poetry, in the news, in daily life) to be ontologically secondary with regard to an immediate being in the world through sentences, also if the latter have been withdrawn from a narrative or otherwise externally structured discourse (which in that case would therefore be chronologically primary ). Naturally, two or more sentences are always in danger of telling stories or arguing, just like the world is always in danger of becoming an objective representation, facing us, strangers. That is why need to wage war—against representation and against the interface, against interaction. AGAINST THE “READER.” To the extent that a sentence is worldly, writing is a condensed global war, and in so far as there is ultimately only one world and one open continuum of languages, it is a global civil war. Nice subject for an epic. The elaboration of a singular problem—prose as the outside of poetry, the form of the novel as purely prosodic composition scheme—“expresses” the universal problem: capitalism as Idea of the world vs. poetry as language of an (im)possible community. The paragraphs are blocks of rhythmically contracted social material. By choosing the sentence as the basic compositional component, an abstract whole may contain social sounds, without telling a story or showing an image. Composition is subrepresentative —a rhythmic, passive synthesis, or rather: a synthesis of syntheses. I never write large blocks of prose in one sitting, because there is no obvious organizational vector —plot, theme, conscience—outside the inherent qualities of the material itself. Usually I write down one sentence, sometimes two, but rarely more than three. Those sentences are usually placed in the text which I am editing at the time. In fact, there is no original composition, new chapters split off from chapters which became too long during the editing process. (Revision mainly consists of adding and inserting, displacing and dividing; only during the last phase, when the text has gained enough consistency, there may be subtraction to tighten the composition; each chapter requires a season of daily revision). This constant revision, accompanied by a continuous influx of collective background noise (to speak with Van Bastelaere), 7 makes every chapter a block condensed (“historical” and “personal”) time. The block itself is a-personal and a-historic; it is ontologically autonomous. If there is such a thing as a spirit of the times, I do not try to offer an image of it, but rather to cancel something of it by erecting a monument of its own excrement within its own boundaries. Tuning and dis-tuning , “in de taal der neerslachtigen een eigen geluid doen klinken,” 8 in other words, desiring in an Elysian way. In this sense I have intended to be able to write a political poetry. The ultimate political poem is the epic, “the tale of the tribe.” I consider N30 to be a prolegomenon to a future epic (of which it in the end will form a part a structural moment, as introduction-in-the-middle), an extended pile on top of an epic as narrative, a question of the tribe and question of its history. I was burdened by too much satire, too much bullshit. But: satire willy-nilly = the only justifiable satire. Against the abstract universalism of the market (“globalism”): concrete disgust, a positive way of saying “No.” Moreover, disgust is a specifically total attitude, which ultimately concerns the world as a whole. I hate this or that, but I am disgusted by EVERYTHING (when I am disgusted), and so it appears that satire is in fact related to the epic, in so far as it concerns society, the cosmos, history. Maybe it is no coincidence that the Dutch literary canon knows no great poet of disgust; what could be more fearful to us than society, the cosmos, and history? The T-tendency (T from Tollens 9 ) clearly points into the direction of the small, friendly, ironic, melancholic, acquiescent, wondrous, and so on. The anti-political, anti-cosmic, anti-historical. (Why am I so philosophical? To scare away the Dutchies.) And most of all: the “poetical” (the pseudo-mysticism from the backyard). Yes, the N in N30 also stands for the Netherlands (just like 30 indicates the number of chapters). I was not in Seattle, I do not live in Iraq. But is not the whole world bleeding to death on Dutch paving stones? Let’s hope that we mowed away something with this total satire, also “in myself.” The arrogant stupidity that definitely thinks to know the essence of freedom (the free development of esthetic needs inside the void), that cannot take anything serious, only believes in the disciplined bestiality of the individual (“norms and values”) and the mere functioning of a social factory which finds no justification whatsoever outside its functioning (“get to work”)… Who knows. A certain aimed destruction leaves grooves and craters, mapping out a next adventure. Pound’s periplum : sailing while mapping the coasts. Immanent orientation. The terrain changes with the map, history changes with the poem. Maps never merely organize the chaos, transcendent schemes imposed on a formless Ding-an-sich . They organize from within, surfing. But they are most of all routes back into the chaos or forward to paradise (final identity of chaos and paradise; Schlegel: “ Nur diejenige Verworrenheit ist ein Chaos aus der eine Welt entspringen kann ”10). A poem is not only a piece of history, it is also a flight from history. Maps give chaos to the form of reality , open escape routes, break through representations, make us shivery and dazed. Paradise is immanent to a fleeting desire. History is the history of labor—this is Adam’s curse—and the poet works too: For to articulate sweet sounds together Is to work harder than all these, and yet Be thought an idler by the noisy set Of bankers, school masters, and clergymen The martyrs call the world 11 But: the poet works in paradise. The paradox of the artwork, the work that is no work, the piece of history that cannot be reduced to History—this is explained by The Space of Literature , a virtual space, an autonomous rhythm, not outside, but in the midst of the noise, a piece of paradise in hell, a postcard from the vale of tears addressed to paradise, to X. Political poetry means: a poetry that dares to think about itself, about its language and about its world and about the problematic relation between both, which is this relation as problem. A poetry that thinks at all, articulates its problem. It has nothing to do with journalism or morality or debate, let alone the law or the state. It has nothing to do with “criticism” if this means the replacement of incorrect representations by other, more correct representations. It has something to do with ethics in the sense of learning to live. It has something to do with the community and the language of the community (whichever that may be) and the role of the poet regarding the community. It concerns justice without judgement or measure. In the end the just word is just a word , to paraphrase Godard: it is from a future that is unimaginable. It Is no rational engagement, but an aversion against everything that obstructs life, and love for everything what is worthy of having been loved. The world is engaged with me, not the other way round. First Exodus, then Sinai. A desire does not start with an agenda. To answer the question whether I am really so naive as to want to change the world: “We only want the world.” Justice is the world appealing to us to liberate it from all possible chains, from each organization and inequality, to be it, smooth, equal, under a clear sky—a desert and a people in a desert. That moment between Egypt and the Law. It is not a revolution, but the sky above the revolution. Poetry = the science of escape. There is no art that we already know. The weakness of modernistic epic poetry seems to me to be the unwillingness to completely abandon narrative as a structural principle, in favor of a composition “around” or from an event. The China Cantos and Adams Cantos are the low point, and the Pisan Cantos the high point of Pound’s poetry. Two types of research: archival representation of the past vs. ontology of the present (which virtually presupposes the entire history). Presupposing an event means that it is impossible for the poet to stage his own absence, but in no way makes the work personal. An event is the unknown, the new invading into the business as usual, so also the personal. The question heading this research is not: “Who am I?” but “What is happening?” The book is as little illegible as Mondrian’s work is invisible. Form is of interest only to the extent that it empowers liberation. Ron Silliman So no formalism, but what it means to live in this world and to have a future in it. I want something that holds together that’s not smooth. Bruce Andrews The past above, the future below and the present pouring down: the roar, the roar of the present, a speech— William Carlos Williams If my confreres wanted to write a work with all history in its maw, I wished, from the beginning to start all over again, attempting to know nothing but a will to create, and matter at hand. Ronald Johnson NOTES 1) “The easy thing/ that is difficult to make.” Bertold Brecht, Lob des Kommunismus . (All footnotes are the translator’s) 2) Maurice Blanchot, The Space of Literature , trans. Ann Smock. Lincoln/London: University of Nebraska Press (1989), 75. 3) Mettes uses the word “Neerlandicus,” which refers to scholars of Dutch language and literature. 4) Dutch poet. 5) Gertrude Stein. “Composition as Explanation.” A Stein Reader . Ed. Ulla E. Dydo. Evanston, IL: Northwestern University Press (1993), 495-503. 6) Ezra Pound. 7) Flemish poet. 8) “Resounding an original sound in the language of the despondent.” A. Roland Holst, De afspraak . 9) Dutch poet. 10) “Only such a confusion is a chaos which can give rise to a world.” 11) W.B. Yeats, “Adam’s Curse.&rdquo. (shrink)

A new form of the Hyperbolic Pythagorean Theorem, which has a striking intuitive appeal and offers a strong contrast to its standard form, is presented. It expresses the square of the hyperbolic length of the hypotenuse of a hyperbolic right-angled triangle as the “Einstein sum” of the squares of the hyperbolic lengths of the other two sides, Fig. 1, thus completing the long path from Pythagoras to Einstein. Following the pioneering work of Varičak it is well known that relativistic velocities (...) are governed by hyperbolic geometry in the same way that prerelativistic velocities are governed by Euclidean geometry. Unlike prerelativistic velocity composition, given by the ordinary vector addition, the composition of relativistic velocities, given by the Einstein addition, is neither commutative nor associative due to the presence of Thomas precession. Following the discovery of the mathematical regularity that Thomas precession stores, it is now possible to extend Thomas precession by abstraction, (i) allowing hyperbolic geometry to be studied by means of analogies that it shares with Euclidean geometry; and, similarly (ii) allowing velocities and accelerations in relativistic mechanics to be studied by means of analogies that they share with velocities and accelerations in classical mechanics. The abstract Thomas precession, called the Thomas gyration, gives rise to gyrovector space theory in which the prefix gyro is used extensively in terms like gyrogroups and gyrovector spaces, gyroassociative and gyrocommutative laws, gyroautomorphisms, gyrotranslations, etc. We demonstrate the superiority of our gyrovector space formalism in capturing analogies by deriving the Hyperbolic Pythagorean Theorem in a form fully analogous to its Euclidean counterpart, thus contrasting it with the standard form in which the Hyperbolic Pythagorean Theorem is known in the literature. The hyperbolic metric, which supports the Hyperbolic Pythagorean Theorem, has a dual metric. We show that the dual metric does not support a Pythagorean theorem but, instead, it supports the π-Theorem according to which the sum of the three dual angles of a hyperbolic triangle is π. (shrink)

Due to the inherent chaotic and fractal dynamics in the price series of Bitcoin, this paper proposes a two-stage Bitcoin price prediction model by combining the advantage of variational mode decomposition and technical analysis. VMD eliminates the noise signals and stochastic volatility in the price data by decomposing the data into variational mode functions, while technical analysis uses statistical trends obtained from past trading activity and price changes to construct technical indicators. The support vector regression accepts input from a (...) hybrid of technical indicators and reconstructed variational mode functions. The model is trained, validated, and tested in a period characterized by unprecedented economic turmoil due to the COVID-19 pandemic, allowing the evaluation of the model in the presence of the pandemic. The constructed hybrid model outperforms the single SVR model that uses only TI and rVMF as features. The ability to predict a minute intraday Bitcoin price has a huge propensity to reduce investors’ exposure to risk and provides better assurances of annualized returns. (shrink)

Recent literature in experimental philosophy has postulated the existence of the abstract/concrete paradox : the tendency to activate inconsistent intuitions depending on whether a problem to be analyzed is framed in abstract terms or is described as a concrete case. One recent study supports the thesis that this effect influences judicial decision-making, including decision-making by professional judges, in areas such as interpretation of constitutional principles and application of clear-cut rules. Here, following the existing literature in legal theory, we argue that (...) the susceptibility to such an effect might depend on whether decision-makers operate in a legal system characterized by the formalist or particularist approach to legal interpretation, with formalist systems being less susceptible to the effect. To test this hypothesis, we compare the results of experimental studies on ACP run on samples from two countries differing in legal culture: Poland and Brazil. The lack of significant differences between those results suggests that ACP is a robust effect in the legal context. (shrink)

RESUMOA climatologia está no centro de um dos debates mais polarizados da atualidade, apresentado como confronto entre os defensores da existência de um aquecimento global antropogênico e aqueles que rejeitam sua existência. A instituição chave para esse tema é o Painel Intergovernamental sobre Mudanças Climáticas, um corpo simultaneamente científico e político. O debate surge aí mesclado com a discussão política sobre as respostas adequadas ao aquecimento global. Mas, rechaçados nesse terreno, os negacionistas transpõem o debate para a mídia, onde mobilizam (...) a pseudociência para deslegitimar as conclusões das disciplinas científicas ligadas ao entendimento do clima. Temos, assim, uma produção consciente da ignorância em larga escala sobre o tema do aquecimento global, demandando o uso da agnotologia para desvendar o mecanismo de produção da ignorância. A climatologia revela-se, então, um campo exemplar para o estudo da inserção histórico-social do conhecimento científico e das tensões e trajetórias conflitivas no seu interior, dos dilemas éticos que coloca e das possibilidades universalistas do conhecimento científico na era da tecnociência. ABSTRACTClimatology is at the center of one of the most polarized debates of today. It is presented as a confrontation between supporters of the existence of anthropogenic global warming and those who deny its existence. The key institution for this theme is the Intergovernmental Panel on Climate Change, which is both a scientific and political body. In this context, the debate arises merged with the political discussion on appropriate responses to global warming. However, contested on this ground, the deniers transfer the debate to the media, mobilizing pseudo-science to delegitimize the conclusions of the scientific disciplines related to climate understanding. Therefore, we have a deliberate production of large-scale ignorance on this subject, which requires the use of agnotology to unravel it. Thus, climatology reveals itself an exemplary space to study the historical and social roots of scientific knowledge and the tensions and conflicting trajectories inside it, the ethical dilemmas posed and the universalist possibilities of scientific knowledge in the age of technoscience. (shrink)

A compartmental model is described for the spread of Gambian sleeping sickness in a spatially heterogeneous environment in which vector and human populations migrate between two "patches": the village and the plantations. The number of equilibrium points depends on two "summary parameters": gr the proportion removed among human infectives, and R0, the basic reproduction number. The origin is stable for R0 1. Control strategies are assessed by studying the mix of vector control between the two patches that bring (...) R0 below 1. The results demonstrate the importance of vector control in the plantations. For example if 20 percent of flies are in the village and the blood meal rate in the village is 10 percent, then a 20 percent added vector mortality in the village must be combined with a 9 percent added mortality in the plantations in order to bring R0 below 1. The results are quite insentive to the blood meal rate in the village. Optimal strategies (that minimize the total number of flies trapped in both patches) are briefly discussed. (shrink)

This paper uncovers the basic reason for the mysterious change of sign from plus to minus in the fourth coordinate of nature's Pythagorean law, usually accepted on empirical grounds, although it destroys the rational basis of a Riemannian geometry. Here we assume a genuine, positive-definite Riemannian space and an action principle which is quadratic in the curvature quantities (and thus scale invariant). The constant σ between the two basic invariants is equated to1/2. Then the matter tensor has the trace zero. (...) In consequence of the constancy of the scalar curvature and the divergence identity of the matter tensor, the perturbation metric has to satisfy a scalar and a vector condition, with a negative sign in the fourth coordinate. These conditions lead to the Lorentz condition and the wave equation for the vector potential. Thus the entire Maxwell-Lorentz type of electrodynamics becomes logically derivable, making no concession to any irrationality. (shrink)

Vector models of language are based on the contextual aspects of language, the distributions of words and how they co-occur in text. Truth conditional models focus on the logical aspects of language, compositional properties of words and how they compose to form sentences. In the truth conditional approach, the denotation of a sentence determines its truth conditions, which can be taken to be a truth value, a set of possible worlds, a context change potential, or similar. In the (...) class='Hi'>vector models, the degree of co-occurrence of words in context determines how similar the meanings of words are. In this paper, we put these two models together and develop a vector semantics for language based on the simply typed lambda calculus models of natural language. We provide two types of vector semantics: a static one that uses techniques familiar from the truth conditional tradition and a dynamic one based on a form of dynamic interpretation inspired by Heim’s context change potentials. We show how the dynamic model can be applied to entailment between a corpus and a sentence and provide examples. (shrink)

A two boundary quantum mechanics incorporating a big bang/big crunch universe is carefully considered. After a short motivation of the concept we address the central question how a proposed a-causal quantum universe can be consistent with what is known about macroscopia and how it might find experimental support.

The paper contains a discussion on two kinds of coincidence experiments. First, a standard two-photon coincidence experiment is considered and it is shown that its outcomes are incompatible with any classical radiation theory because of the role of the state vector reduction phenomenon in such an experiment. In the second part of the paper a proposed new kind of photon coincidence experiment is discussed. The classical and quantum predictions for the outcomes of this experiment differ dramatically and therefore the (...) experiment should constitute a new limitation to the classical radiation theories. The proposed experiment should also yield information about the kinematics of the reduction of the state vector process. (shrink)

The objective of this article is to provide a formalism to deal with the special theory of relativity (STR, in short) as riewed by Reichenbach, according to which STR involves an ineradicableconventionality of simultaneity. One of the two postulates of STR asserts that, in empty space, the one-way speed of light relative to inertial frames is constant. Experimental evidence, however, is related to the constancy of the round-trip speed of light and has no bearing on one-way speeds. Following Reichenbach's (...) viewpoint, we relax the second postulate of STR, abandoning the constancy of the one-way speed of light to the more realistic one asserting the constancy of the round-trip speed of light. This, in turn, results in a formalism to deal with Reichenbach's special theory of relativity (RSTR, in short) in which the two one-way speeds of light in empty space, C±, in the two senses of a round-trip are arbitrarily selected in such a way that their harmonic mean is the measurable round-trip speed of light, c. Experimentally, RSTR and STR are indistinguishable and, hence, represent the same physical theory. It is only the formalism that we use to deal with STR which is extended in RSTR to accommodate the immeasurability of one-way velocities. The usefulness of the proposed formalism to study special relativity is demonstrated. (shrink)

In this paper I provide an ontology for the co‐variant vectors, contra‐variant vectors and tensors that are familiar from General Relativity. This ontology is developed in response to a problem that Timothy Maudlin uses to argue against universals in the interpretation of physics. The problem is that if vector quantities are universals then there should be a way of identifying the same vector quantity at two different places, but there is no absolute identification of vector quantities, merely (...) a path‐relative one.My solution to the problem is to use the mathematical characterization of vectors as differential operators on scalar fields. On the proposed hypothesis a scalar field is a conjunctive state of affairs, and vector and tensor fields are relations instantiated by scalar fields. (shrink)

We show that vector space semantics and functional semantics in two-sorted first order logic are equivalent for pregroup grammars. We present an algorithm that translates functional expressions to vector expressions and vice-versa. The semantics is compositional, variable free and invariant under change of order or multiplicity. It includes the semantic vector models of Information Retrieval Systems and has an interior logic admitting a comprehension schema. A sentence is true in the interior logic if and only if the (...) ‘usual’ first order formula translating the sentence holds. The examples include negation, universal quantifiers and relative pronouns. (shrink)

Carnap's position on mathematical truth in The Logical Syntax of Language has been attacked from two sides: Kreisel argues that it is formalistic but should not be, and Friedman argues that it is not formalistic but needs to be. In this paper I argue that the Carnap of Syntax does not eliminate our ordinary notion of mathematical truth in favour of a formal analogue; so Carnap's notion of mathematical truth is not formalistic. I further argue that there is no conflict (...) between Carnap's use of informal notions and his principle of tolerance; so Carnap's definition of mathematical truth need not be formalistic. CiteULike Connotea Del.icio.us What's this? (shrink)

The development and applicability of complex numbers is often cited in defence of the formalist philosophy of mathematics. This view is rejected through an examination of hamilton's development of the notion of complex numbers as ordered pairs of reals, And his later development of the quaternion theory, Which subsequently formed the basis of vector analysis. Formalism, By protecting informal assumptions from critical scrutiny, Constrained rather than encouraged the development of mathematics.

In teaching jurisprudence, I typically distinguish between two different families of theories of adjudication—theories of how judges do or should decide cases. “Formalist” theories claim that the law is “rationally” determinate, that is, the class of legitimate legal reasons available for a judge to offer in support of his or her decision justifies one and only one outcome either in all cases or in some significant and contested range of cases ; and adjudication is thus “autonomous” from other kinds of (...) reasoning, that is, the judge can reach the required decision without recourse to nonlegal normative considerations of morality or political philosophy. I also note that “formalism” is sometimes associated with the idea that judicial decision-making involves nothing more than mechanical deduction on the model of the syllogism—Beccaria, for example, expresses such a view. I call the latter “Vulgar Formalism” to emphasize that it is not a view to which anyone today cares to subscribe. (shrink)

Goodman’s account of the ‘grue’ paradox stands at a crossroads in the history of twentieth century epistemology. Published in 1954, Fact, Fiction, and Forecast is a reaction to the logical empiricist views that held sway in the first half of the last century and anticipates many of the conventionalist and/or relativist moves popular throughout the second half. Through his evaluation of Hume’s problem of induction, as well as his own novel reformulation of it, Goodman comes to reject a number of (...) the fundamental parts of logical empiricism. In particular, Goodman argues that the formal epistemic methods the logical empiricists wanted to rely upon are insufficient. This leads him to turn towards conventionalism, which is the basis of his rejection of the objective view of knowledge. In his conventionalism he is a precursor of writers such as Hanson, Kuhn and Feyerabend, who, seeing the inadequacy of formalism, sought to fill the gaps it left in epistemic methodology with scientific values, tacit knowledge and linguistic practices. Making use of Susan Haack’s distinction between three different kinds of foundationalism, we analyse Goodman’s position and its relation to the views of the logical empiricists. The two are reflections of each other in that, where the logical empiricists are foundationalists in their views on empirical evidence, methods used and objective criteria of justification, Goodman consistently opts for the corresponding coherentist options. As it turns out, this choice of options makes it impossible for Goodman to deal with the very objections he raises against the logical empiricists. In adding the new problem of induction to the old one, Goodman adds a problem which clearly can not be resolved by a purely syntactic solution. The charge Goodman raises is that logical empiricists cannot determine which predictions are sound and which are not. We argue that his method of identifying acceptable predictions based on the use of entrenchment is, in the end, arbitrary and only postpones the underlying problem. (shrink)

An effective formalism is developed to handle decaying two-state systems. Herewith, observables of such systems can be described by a single operator in the Heisenberg picture. This allows for using the usual framework in quantum information theory and, hence, to enlighten the quantum features of such systems compared to non-decaying systems. We apply it to systems in high energy physics, i.e. to oscillating meson–antimeson systems. In particular, we discuss the entropic Heisenberg uncertainty relation for observables measured at different times (...) at accelerator facilities including the effect of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathcal{CP}$\end{document} violation, i.e. the imbalance of matter and antimatter. An operator-form of Bell inequalities for systems in high energy physics is presented, i.e. a Bell-witness operator, which allows for simple analysis of unstable systems. (shrink)

In 1939, Curry proposed a philosophy of mathematics he called formalism. He made this proposal in two works originally written then, although one of them was not published until 1951. These are the two philosophical works for which Curry is known, and they have left a false impression of his views. In this article, I propose to clarify Curry’s views by referring to some of his later writings on the subject. I claim that Curry’s philosophy was not what is (...) now usually called formalism, but is really a form of structuralism. (shrink)

In a narrow sense, the formalistic conception of art cannot range and explain a wide variety of contemporary art phenomena. In a wide sense, formalism – rejecting the reductionist definition of the essence of art, involving the conceptual dimension of the artwork, and expanding the dimension of sensibility – becomes a productive philosophical art theory allowing one to explain and investigate some part of the contemporary art (modern and postmodern) phenomena. In the expanded conception, the basic principles of aesthetic (...) formalism include a wide scale of the principles of the creation and comprehension of the artwork – from an abstract form (perceived by senses) to a conceptual form. The article gives an illustration of these principles discussing abstractionism and surrealism as two different types of the contemporary formalistic visual art. (shrink)

Programming artificial intelligence to make fairness assessments of texts through top-down rules, bottom-up training, or hybrid approaches, has presented the challenge of defining cross-cultural fairness. In this paper a simple method is presented which uses vectors to discover if a verb is unfair or fair. It uses already existing relational social ontologies inherent in Word Embeddings and thus requires no training. The plausibility of the approach rests on two premises. That individuals consider fair acts those that they would be willing (...) to accept if done to themselves. Secondly, that such a construal is ontologically reflected in Word Embeddings, by virtue of their ability to reflect the dimensions of such a perception. These dimensions being: responsibility vs. irresponsibility, gain vs. loss, reward vs. sanction, joy vs. pain, all as a single vector. The paper finds it possible to quantify and qualify a verb as fair or unfair by calculating the cosine similarity of the said verb’s embedding vector against FairVec—which represents the above dimensions. We apply this to Glove and Word2Vec embeddings. Testing on a list of verbs produces an F1 score of 95.7, which is improved to 97.0. Lastly, a demonstration of the method’s applicability to sentence measurement is carried out. (shrink)

An open formalism for arithmetic is presented based on first-order logic supplemented by a very strictly controlled constructive form of the omega-rule. This formalism (which contains Peano Arithmetic) is proved (nonconstructively, of course) to be complete. Besides this main formalism, two other complete open formalisms are presented, in which the only inference rule is modus ponens. Any closure of any theorem of the main formalism is a theorem of each of these other two. This fact is (...) proved constructively for the stronger of them and nonconstructively for the weaker one. There is, though, an interesting counterpart: the consistency of the weaker formalism can be proved finitarily. (shrink)

Let M = 〈M, +, <, 0, {λ}λ∈D〉 be an ordered vector space over an ordered division ring D, and G = 〈G, ⊕, eG〉 an n-dimensional group definable in M. We show that if G is definably compact and definably connected with respect to the t-topology, then it is definably isomorphic to a 'definable quotient group' U/L, for some convex V-definable subgroup U of 〈Mⁿ, +〉 and a lattice L of rank n. As two consequences, we derive Pillay's (...) conjecture for a saturated M as above and we show that the o-minimal fundamental group of G is isomorphic to L. (shrink)

This dissertation is intended to provide a formalism for those generics that trigger nonmonotonic inferences. The formalism is to reflect intentionality and exception-tolerating features of generics, and has an emphasis on the axiomatization of generic reasoning that encodes nonmonotonicity. ;A modal conditional approach is taken to formalize the nonmonotonic reasoning in general at the level of object language. A serial of logic systems---MN, NID, NCUM, N STCUM---are constructed in an increasing strength of the characterized nonmonotonic inference relation. In (...) these systems, two binary modal operators ⩾ and > are introduced in their syntax, and a ⊛ function lifted from the traditional * function is deployed in their semantics. These systems are shown to be sound and complete with respect to certain classes of frames defined in the semantics. They are decidable as well. The nonmonotonic inference is argued to be a ternary relation "[phi], Gamma |∼ alpha", and is defined in the system NSTCUM. Many widely discussed nonmonotonic inference patterns such as Defeasible Modus Ponens, Defeasible Transitivity, the Penguin Principle etc. are justified. The specificity rule is proved to be a theorem of the system N STCUM. The impact of negated defaults on an inference is also investigated and accounted for. ;A canonical form to read off generics is proposed: All generic sentences with subject-predicate structure can be re-written into their canonical form S . If S is a plural noun phrase, it can be further refined to be . Normal objects are selected based on the "meaning" of the subject and predicate terms. The second parameter provides an aspect with respect to which certain objects of a kind are considered normal. Due to such a way to select normal objects, the drowning problem is solved. ;The inference behaviors of generics are axiomatized in the system G, which is a quantificational extension of the system NSTCUM. It is proved to be sound and complete with respect to the class of L⩾,G -frames. Those benchmark examples of generic inferences are examined in the system G. (shrink)

Legal formalism is the foil for many theories of law. Yet formalism remains controversial, meaning that its critics focus on claims that are not central. This paper sets out a view of formalism using a methodology that embraces one of formalism’s most distinct claims, that formalism is a scientific theory of law. This naturalistic view of formalism helps to distinguish two distinct types of formalism, “doctrinal formalism,” the view that judicial behaviour can (...) be represented using rules, and “rule formalism,” the view that judges follow external rules when they are deciding cases. Doctrinal formalism, understood in naturalistic terms, overcomes many of the criticisms that have been levelled at formalism and can also be used to rehabilitate the currently out‐of‐favour “declaratory theory of law.” Doctrinal formalism is also a longstanding view of law, reflecting both what the original formalists thought of law, and what many present‐day doctrinal lawyers seem to believe. The naturalistic methodology is used to show that the main dispute between doctrinal formalism and American legal realism can be explained by a difference of assumptions concerning whether the values of judges are relative to society, or relative to other judges. (shrink)

A modal accessibility relation is just a transition relation, and so can be represented by a {0, 1} valued transition matrix. Starting from this observation, I first show that the machinery of matrices, over Boolean algebras more general than the two-valued one, is appropriate for investigating multi-modal semantics. Then I show that bisimulations have a rather elegant theory, when expressed in terms of transformations on Boolean vector spaces. The resulting theory is a curious hybrid, fitting between conventional modal semantics (...) and conventional linear algebra. I don’t know where the investigations begun here will ultimately wind up, but in the meantime the approach has a kind of curious charm that others may find appealing. (shrink)