Finite Fragments Research Articles

The Ontological argument in neoclassical context: Reply to friedman

In his article, 'Necessity and the Ontological Argument',* Professor Fried? man correctly identifies the two major assumptions of Hartshorne's on? tological argument: (PI) It is possible that God exists (perfection is not impossible); (P2) it is necessary that if God exists, God necessarily exists (Anselm's Principle; perfection could not exist contingently). The basic argument of Friedman's paper is that, while Hartsthorne's ontological proof is formally valid in Lewis' S5 system of modal logic, it is not known a priori to be sound. In general, Hartshorne has not been "sufficiently sensitive to the various senses of necessity" (Friedman, p. 307), and hence his argument is based on "acute modal confusion" (p.307). More specifi? cally, for any single notion of de dicto necessity, Friedman contends, either one of the five axioms of S5 or one of the premises of the ontological argument is not known to be true. Thus Friedman concludes that Harts? horne's modal reconstruction of the ontological argument fails, because "there is no single interpretation of necessity which would give us an a priori known sound ontological argument and a priori known sound S5 (or finite fragment thereof)" (p. 324). I am convinced that Friedman's challenge can be met by examining and defending the neoclassical context within which Hartshorne reconstructs Anselm's famous proof. In my opionion, Hartshorne's chief contributions to the contemporary discussion of the ontological argument are two: (1) the substitution of the abstract-concrete (dipolar) understanding of God for the monopolar classical conception of God, and (2) the insistence on a coextensiveness between necessity de re and necessity de dicto in the proof. Both contributions are directly derived from Hartshorne's meta? physics of temporal process. In this reply, I will concentrate on the two sections of Friedman's paper that deal with logical necessity in the Carnapian and in the Kripkean sen? ses. Friedman has shown very well how the axioms of S5 can be known

Production of light nuclear clusters in heavy-ion collisions

Quantum statistics are taken into account in the study of chemical equilibrium in the collision of two heavy ions. The results are compared with those of classical Maxwell-Boltzmann statistics. It is proved that there are more tritons than 3He when the initial system is proton deficient. The problem of Bose condensation of alpha particles and the effect of finite fragment volumes are discussed.

Infrared spectra and resonance interactions of amide-I and II vibration of alpha-helix.

AbstractAmide‐I and II vibrations of α‐helix have been treated on the basis of the perturbation theory in a dipole–dipole approximation. The infinite helix and its finite fragments have been considered as models. The calculated infrared spectra for the infinite helix are in good agreement with the spectra of synthetic polypeptides. In the case of finite fragments of the α‐helix, the characteristic contours of the amide‐I and II bands appear when the nuimber of peptide groups is about 10 and 6, respectively.

Infrared spectra and resonance interaction of amide-I vibration of the antiparallel-chain pleated sheet.

AbstractTheoretical treatment of resonance interaction of amide‐I vibration has been done in a dipole–dipole approximation on the basis of perturbation theory. A single infinite antiparallel‐chain pleated sheet as well as different kinds of its finite fragments have been considered. A good agreement has been obtained between calculated spectral parameters of amide I of the infinite sheet and observed ones in infrared and Raman spectra of synthetic polypeptides and fibrous proteins. A theoretical dependence of the resonance frequency shift of the main component and frequency splitting of two components active in the infrared spectra on the number of polypeptide chains in the finite sheet has been found.

Infrared spectra and resonance interaction of amide-I vibration of the paraellel-chain pleated sheets.

AbstractResonance vibrational interactions of amide I for the parallel‐chain pleated‐sheet structure have been treated on the basis of the perturbation theory in a dipole–dipole approximation. The infinite sheet and finite fragments of different types have been considered. The possibility of experimental observation by infrared spectra of parallel‐chain pleated‐sheet fragments in globular proteins is discussed.