Parity Argument Research Articles

Packings and 2-packings of A-paths

Abstract We investigate the relation between packings and 2-packings of A-paths. We show a similarity to the relation between matchings and 2-matchings in graphs. The former needs parity arguments, while the latter admits a Kőnig-type characterization. The algorithmic method of proof also yields – as a by-product – a generalization of the odd ear-decomposition of a factor-critical graph. For packing non-returning A-paths there are two different natural notions of criticality, we show a decomposition for both. An odd ear-decomposition can be given for (strongly) criticals. For weakly criticals a so-called dragon-decomposition can be given – a decomposition in a specific way into a forest and some strongly criticals.

Power Transition Extended

Regions of War and Peace. By Douglas Lemke. Cambridge: Cambridge University Press, 2002. 252 pp., $65.00 cloth (ISBN: 0-521-80985-1), $23.00 paper (ISBN: 0-521-00772-0). Before the current popularity of strategic models, the study of world politics in the United States after World War II was dominated by structural approaches. Structural arguments took the centrality of the major powers as determinants of the international system as a given. Indeed, relative capabilities among the major powers supposedly held the key to international stability (Waltz 1979; Thompson 1988). The dominant parity school of thought held that the international system was stable when major power capabilities were in rough equivalence, with stability being the absence of system-changing major power war (Morgenthau 1948; Waltz 1959, 1979). Even though parity scholars held much sway in academic circles, they did not go unchallenged. At the end of the 1950s, A. F. K. Organski developed his power transition theory, which held, contrary to the parity argument, that a preponderance of capabilities in the hands of one dominant power is coincident with system stability, and that movements toward rough equivalence lead to war (Organski 1958; Organski and Kugler 1980; Kugler and Organski 1989). The power transition theory, however, is not just another structural approach to international stability. It also speaks to issues of political and economic development, and even state strategy. Indeed, whereas parity scholars talk about system change resulting from the fluidity of alliance patterns, Organski and his followers look domestically at the major states themselves as the source of system change. Although the economic potential for growth exists in most societies, the political organization to harness that potential varies across both time and space. The states that become better organized politically can better harness, direct, and guide economic production, which creates growth. Growth in turn creates power or enhanced …

Testimonial justification: the parity argument

On an individualist view of testimonial justification, a subject’s belief based on testimony is justified ultimately on the basis of nontestimonial beliefs alone. The prevailing version of individualism has been inductive individualism, according to which the nontestimonial basis for a testimonial belief is an inductively based belief in the reliability of the testifier. Here I consider an alternative to inductive individualism, which I call the parity account. This is the view, endorsed in various forms by Allan Gibbard, Richard Foley and Keith Lehrer, that my testimonial beliefs have epistemic standing because there is a cognitive parity between me and others. I may trust the beliefs of others because I may trust my own beliefs. I focus on an argument central to Lehrer’s account: I am worthy of my trust in what I believe; others are as worthy of my trust in what they believe as I am in what I believe; so others are worthy of my trust in what they believe. I examine whether this argument can justify my testimonial beliefs. If the parity account is to succeed, the premises of the argument need support. I criticize diverse ways of supporting the premises suggested by Lehrer and by remarks of Foley. I conclude that the parity argument cannot account for the justification of all my testimonial beliefs. It is at best an adjunct argument that depends for its force on prior justified testimonial beliefs.

More remarks on the electromagnetic properties of a domain wall interacting with charged fermions

The response to a magnetic flux is considered of the vacuum state of charged Dirac fermions interacting with a domain wall made of a neutral spinless field in (3+1) dimensions with the fermion mass having a phase variation across the wall. It is pointed out that due to simple C parity arguments the spontaneous magnetization for this system is necessarily zero, thus invalidating some claims to the contrary in the literature. The cancellation of the spontaneous magnetization is explicitly demonstrated in a particular class of models. The same calculation produces a general formula for the electric charge density induced by the magnetic flux -- an effect previously discussed in the literature for axionic domain walls. The distribution of the induced charge is calculated in specific models.

"Are you my mommy?" On the genetic basis of parenthood.

What exactly is it that makes someone a parent? Many people hold that parenthood is grounded, in the first instance, in the natural derivation of one person's genetic constitution from the genetic constitution of others. We refer to this view as "Geneticism". In Part I we distinguish three forms of geneticism on the basis of whether they hold that direct genetic derivation is sufficient, necessary, or both sufficient and necessary, for parenthood. (Call these 'Sufficiency', 'Necessity', and 'Strong' Geneticism, respectively.) Part I also explores the relationship between geneticism and the debate over surrogacy. Parts two through four examine three arguments for geneticism: the Property argument, the Causal argument, and the Parity argument. We conclude that none of these arguments succeeds. The failure of positive arguments for a view cannot demonstrate that the view is false; however, in light of our arguments we provisionally conclude that 'Strong' and 'Necessity' Geneticism are unacceptable. Our arguments do not undermine 'Sufficiency' Geneticism, so this thesis is considerably more promising than the others. But sufficiency geneticism is also compatible with a much more pluralistic account of the nature of parenthood.

Moral Realism, Social Construction, and Realism, Social Construction, and Communal Ontology

The paper examines two forms of naturalistic moral realism, “Microstructure realism” (MSR) and “Reason realism” (RR). The latter, as we defend it, locates the objectivity of moral facts in socially constructed reality, but the former, as exemplified by David Brink’s model of naturalistic moral realism, secures the objectivity of moral facts in their micro-structure and a nomic supervenience relationship. We find MSR’s parity argument for this account of moral facts implausible; it yields a relationship between moral facts and their natural-scientific constitution that has a queer, slapped-together quality. We argue that the relationship needs to be spelled out by a process of social construction, involving collective intentionality and constitutive rules. We explain how our constructivist model of RR differs from a form of it defended by Michael Smith (1994), which analyzes moral facts by reference not to construction but rather to a hypothetical situation of full rationality. We agree with Smith, as against Bernard Williams, that a rational agent may have reasons for acting that go beyond the agent’s “subjective motivational set,” but we locate such reasons by reference to the agent’s membership in an actual community, and we explore the prospects for moral objectivity given this constraint on moral reasons.

Analysis of the two-photon radiation of metastable atomic hydrogen

The Stirling two-photon coincidence experiment based upon the decay radiation of metastable atomic hydrogen has been applied to the measurements of angular and polarization correlations, an experimental confirmation of the Breit-Teuer hypothesis, Einstein-Podolsky-Rosen (EPR) experiments, and measurements of the two-photon coherence length and time. Based upon angular conservation and parity arguments, a two-photon state vector can be defined and used for polarization correlations of the two-photon radiation. The results of the Einstein-Podolsky-Rosen experiments with two-photon radiation from metastable atomic hydrogen clearly favour quantum mechanics over local realistic theories in common with all other published studies. However, by inserting an additional linear polarizer in one of the two detection arms (a three-polarizer method) it was possible experimentally to confirm the difference of almost 40% between the quantum-mechanical prediction and Bell’s limit for local realistic theories, thereby demonstrating the largest such difference in EPR experiments so far. The coherence time and length of the two-photon emission of metastable atomic hydrogen was measured by inserting retardation (“multiwave”) quartz plates orientated with their fast axis at 45° with respect to the linear polarization, which in turn is determined by the polarization direction of the linear polarizer in the other detection arm. A Stokes parameter analysis of the coincident two photons proves the coherent nature of the two-photon radiation emitted from metastable atomic hydrogen. The coherence length (lcoh = 350 nm) found in this way is extremely short, only about 1.5 times the medium wavelength of 243 nm of the two-photon radiation. The corresponding coherence time (lcoh = lcoh/c) is approximately 10−15s, which confirms that it is not determined by the long lifetime of the metastable 2S-state (≅ 1/8s). Reference will be made to a new and recent theoretical prediction of the preceding coherence parameters.

An interactive solution to the n x n mutilated checkerboard problem

We present a method of modelling parameterized classes of finite state machines in the Boyer-Moore logic so that invariant properties can be verified interactively using the Boyer-Moore theorem prover. We illustrate our approach using an interactive proof of the impossibility of covering an n × n ‘mutilated’ checkerboard completely with dominoes. We model the problem by defining a simulator and formalize the well-known parity argument as a proof by mathematical induction on the length of action sequences executed starting with an empty board. The suitability of our approach for verifying properties depends strongly on the actual Lisp data structures and programs used in the simulation model. We explain some of the choices we made in simplifying the checkerboard problem representation and describe in detail the heuristic guidance given to the theorem prover.

Intersubband resonances in InAs/AlSb quantum wells: Selection rules, matrix elements, and the depolarization field.

We present both theoretical and experimental results on the intersubband resonance in InAs/AlSb quantum wells. From a Kane (k\ensuremath{\cdot}p) description of the band structure we investigate the effect of the large nonparabolicity and of the high Fermi wave vector on the selection rules and matrix elements. The 1-2 transition in parallel excitation (x) is shown to be very weak from simple parity arguments; in perpendicular excitation (z) the matrix element 〈z〉 is shown to be largely unaffected by nonparabolicity. The 1-3 transition turns out to be very weak in both geometries. Two band-gap engineering approaches to enhancing the parallel excitation of 1-2 are considered but the effect remains small as compared to the conventional z excitation. In z excitation the depolarization field condenses all the oscillator strength into essentially one sharp line despite the broadening expected from the nonparabolicity in the band dispersions. Inclusion of the depolarization field in the theory gives us good agreement with both the experimentally determined line shape and 〈z〉 matrix element. \textcopyright{} 1996 The American Physical Society.

Gray Codes for A-Free Strings

For any $q \geq 2$, let $\Sigma_{q}=\{0,\ldots,q\!-\!1\}$, and fix a string $A$ over $\Sigma_{q}$. The $A$-free strings of length $n$ are the strings in $\Sigma_{q}^n$ which do not contain $A$ as a contiguous substring. In this paper, we investigate the possibility of listing the $A$-free strings of length $n$ so that successive strings differ in only one position, and by $\pm 1$ in that position. Such a listing is a Gray code for the $A$-free strings of length $n$. We identify those $q$ and $A$ such that, for infinitely many $n \geq 0$, a Gray code for the $A$-free strings of length $n$ is prohibited by a parity problem. Our parity argument uses techniques similar to those of Guibas and Odlyzko (Journal of Combinatorial Theory A 30 (1981) pp. 183–208) who enumerated the $A$-free strings of length $n$. When $q$ is even, we also give the complementary positive result: for those $A$ for which an infinite number of parity problems do not exist, we construct a Gray code for the $A$-free strings of length $n$ for all $n \geq 0$.

On the complexity of the parity argument and other inefficient proofs of existence

We define several new complexity classes of search problems, “between” the classes FP and FNP. These new classes are contained, along with factoring, and the class PLS, in the class TFNP of search problems in FNP that always have a witness. A problem in each of these new classes is defined in terms of an implicitly given, exponentially large graph. The existence of the solution sought is established via a simple graph-theoretic argument with an inefficiently constructive proof; for example, PLS can be thought of as corresponding to the lemma “every dag has a sink.” The new classes, are based on lemmata such as “every graph has an even number of odd-degree nodes.” They contain several important problems for which no polynomial time algorithm is presently known, including the computational versions of Sperner's lemma, Brouwer's fixpoint theorem, Chévalley's theorem, and the Borsuk-Ulam theorem, the linear complementarity problem for P-matrices, finding a mixed equilibrium in a non-zero sum game, finding a second Hamilton circuit in a Hamiltonian cubic graph, a second Hamiltonian decomposition in a quartic graph, and others. Some of these problems are shown to be complete.

Epistemic Parity and Religious Argument

The notion of epistemic parity appears attractive from the outset. Every ethics should include fairness, and epistemic parity seems to do no more than introduce considerations of fairness into the ethics of belief. Initially the idea seems simple enough. One should demand no more, and no less, by way of justification for beliefs in one area of inquiry than one does in another. Equally stringent standards of rationality should apply in all cognitive domains. For example, belief in God should not have to satisfy higher standards in order to be rational or justified than does belief in the external world or other minds. What could be fairer than that? The trouble is that initial simplicity is likely to turn into unmanageable complexity once a few realistic examples have been subjected to analysis. Consider this scenario. Smith is driving his new camper to his favorite fishing hole and comes to an old bridge. Though he has crossed this bridge often before in a car, he now wonders whether it is safe for a heavier vehicle such as his camper. Glancing about, he notices a sign that looks freshly painted and bears the seal of the state highway department; it says: SAFE FOR LOADS UP TO TEN TONS. Smith concludes that crossing will be safe, and he is justified in so doing. As he crosses in his camper, the bridge makes horrible groaning and creaking sounds. They frighten a nearby resident, who

The Prudence of Religious Commitment

AbstractThis essay adopts Penelhum's analysis of parity arguments to show that Christian theistic faith and atheistic secular humanism are on an epistemic par with each other. It argues that Swinburne's attempt to show that theism is more probable than atheism fails because his ultimate canon of rationality is essentially contested and cannot render theism more probable than atheism. It proposes a way out of the epistemic stalemate by evaluating the prudence of religious commitment. It adapts some of Mavrodes' recent arguments and Swinburne's levels of rationality to analyze the dimensions of prudence. It finally extends this “prudential calculus” to indicate how a theologian could show a religious commitment prudent, and argues that if religious authorities silence theologians, the authorities may also show that commitment to and in their tradition cannot be comprehensively prudent.

On fideism and Alvin Plantinga

Recently Terence Penelhum has suggested, in God and Skepticism, that Alvin Plantinga's critique of classical foundationalism is a version of fideism. It is a fideism that exemplifies itself in what Penelhum refers to as a "permissive parity argument." Plantinga, however, rejects any label of fideism, whether it be of an extreme or moderate variety.1 He maintains that his approach to religious epistemology demonstrates that theistic belief is properly basic and among the "deliverances of reason." Plantinga writes,

Tensorial covariants for the 32 crystal point groups

The recently published tables of Clebsch-Gordan products are applied to derive the tensorial covariants (bases of irreducible or physically irreducible representations) for the 32 crystal point groups. Tensors of the following intrinsic symmetries in Jahn notation are considered: ε (pseudoscalar), V (polar vector), [V2], V[V2], [[V2]2], [V2]2, ε[V2], and εV[V2]. With this choice the most important tensors of optical and other properties are covered. Explicit lists of covariants in components of these tensors are given for the non- centrosymmetric groups; with the use of parity arguments the lists also apply to centrosymmetric groups. Applications, especially for phase transitions with reduction of the point symmetry, are briefly discussed.

A simplified calculation and tabulation of tensorial covariants for magnetic point groups belonging to the same Laue class

Four types of static tensors can be distinguished according to their parity with respect to space inversion and to time reversal. However, all magnetic point groups belonging to the same (oriented) Laue class consist, apart from inversions, of the same proper rotations. Tensors differing only by parities transform identically under the same proper rotations; their transformation properties under different groups of the same Laue class may therefore differ only by an additional change of sign, which depends on the tensor parity and on the way in which inversions are combined with proper rotations in a given group. It is shown that, for a certain natural choice of typical representations of magnetic point groups of the same Laue class, it is sufficient to calculate tensorial covariants (symmetry-adapted tensorial bases) of even parity with respect to both space inversion and time reversal for the group of proper rotations. Tensorial covariants of other parities and for other magnetic point groups of the same Laue class can then be obtained by the use of a simple conversion table and of parity arguments. The scheme is illustrated by an example from the Laue class D4.

THE ELECTRIC AND MAGNETIC DIPOLE MOMENTS OF THE NEUTRON*

In 1950 Purcell and Ramsey1 pointed out that the parity arguments then used to prove that particles and nuclei could not have electric dipole moments, must be based on an experimental rather than a theoretical basis. As a test of this assumption, Smith, Purcell and Ramsey2 used a neutron beam magnetic resonance apparatus to search for a neutron electric dipole moment and concluded that such a moment divided by the proton charge (µe/e) was experimentally less than 5 x 10−20 cm. Later, from the work of Lee and Yang3 and Wu, et al,4 it became apparent that the parity assumption was indeed invalid, but Landau5 and others pointed out that the parity argument against an electric dipole moment could be replaced by one based on time reversal invariance. However, Ramsey6 emphasized that time reversal invariance like parity at an earlier time, was merely assumed and must rest on an experimental basis. In 1964 Christenson, Cronin, Fitch, and Turlay7 discovered the CP violating mode in the decay of the KO L meson into two charged pions, which strongly suggested a violation of time reversal symmetry.