Levin and Schnorr (independently) introduced the monotone complexity, Km(α), of a binary string α. We use monotone complexity to define the relative complexity (or relative randomness) of reals. We define a partial ordering ≤Km on 2ω by α ≤Km β iff there is a constant c such that Km(α ↾ n) ≤ Km(β ↾ n) + c for all n. The monotone degree of α is the set of all β such that α ≤Km β and β ≤Km α. We (...) show the monotone degrees contain an antichain of size 2N0, a countable dense linear ordering (of degrees of cardinality 2N0), and a minimal pair. Downey, Hirschfeldt, LaForte, Nies and others have studied a similar structure, the K -degrees, where K is the prefix-free Kolmogorov complexity. A minimal pair of K -degrees was constructed by Csima and Montalbán. Of particular interest are the noncomputable trivial reals, first constructed by Solovay. We define a real to be (Km, K)-trivial if for some constant c, Km(α ↾ n) ≤ K(n)+c for all n. It is not known whether there is a Km-minimal real, but we show that any such real must be (Km, K)-trivial. Finally, we consider the monotone degrees of the computably enumerable (c.e.) and strongly computably enumerable (s.c.e.) reals. We show there is no minimal c.e. monotone degree and that Solovay reducibility does not imply monotone reducibility on the c.e. reals. We also show the s.c.e. monotone degrees contain an infinite antichain and a countable dense linear ordering. (shrink)
This volume draws together important selections from the rich history of theories and debates about emotion. Utilizing sources from a variety of subject areas including philosophy, psychology, and biology, the editors provide an illuminating look at the "affective" side of psychology and philosophy from the perspective of the world's great thinkers. Part One features classic readings from Aristotle, Descartes, Spinoza, and Hume. Part Two, entitled "The Meeting of Philosophy and Psychology," samples the theories of thinkers such as Darwin, James, and (...) Freud. The third section presents some of the extensive work on emotion that has been done by European philosophers over the past century, and the final section comprises essays from modern British and American philosophers. (shrink)
We show that the lattice L 20 is not embeddable into the lattice of ideals of computably enumerable Turing degrees (J). We define a structure called a pseudolattice that generalizes the notion of a lattice, and show that there is a Π 2 necessary and sufficient condition for embedding a finite pseudolattice into J.
In their book entitled “Democracy and the American Party System” Austin Ranney and (Willmoore Kendall have brought a charge again the pluralists that they denied the desirability of creating sovereign state and as such, according to them, they were opponents of democracy as well as of the very idea of government. The aim of this paper is to refute their charge and thereby to establish the view that the pluralists are in fact strong supporters of democracy in the real sense (...) of the term and of popular sovereignty. What did most of them was that they made an attempt to bring to light the fact that democracy, as it is being practiced almost everywhere in the world, ultimately leads to denial of popular sovereignty, the basic element of self-government. Self-government can best be realized where the people is the real sovereign neither the state nor the numerical majority. And the government formed by the representatives elected in a traditional party-based election does not therefore, mean self-government. It can at best be called the government of the majority. Majority rule does not anyway mean democracy. It may be called ‘numbersocracy’ after the proper terminology of Ranney and Kendall. Democracy, de facto, is nothing other than majority rule that is best termed by JohnCalhoun, the ex-vice-president of the U.S.A, as the ‘rule by numerical majority’. ‘Numerical’ majority”, says he, “is not the people”. I strongly adhere to the pluralists’ view and therefore, conclude with an insistent assertion that numerical majority rule in disguise of democracy has in fact ruled out popular sovereignty. (shrink)
Common sense realism, by E. G. Bewkes.--Theology and religious experience, by Vergilius Ferm.--A reasoned faith, by G. F. Thomas.--Can religion become empirical? By J. S. Bixler.--Value theory and theology, by H. R. Niebuhr.--The truth in myths, by Reinhold Niebuhr.--Is subjectivism in value theory compatible with realism and meliorism? By Cornelius Krusé.--The semi-detached knower: a note on radical empiricism, by R. L. Calhoun.--The new scientific and metaphysical basis for epistemological theory, by F. S. C. Northrop.--A psychological approach to reality, by (...) Hugh Hartshorne.--A definition of religious liberalism, by D. S. Robinson. (shrink)
Common sense realism, by E. G. Bewkes.--Theology and religious experience, by V. Ferm.--A reasoned faith, by G. F. Thomas.--Can religion become empirical? By J. S. Bixler.--Value theory and theology, by H. R. Niebuhr.--The truth in myths, by R. Niebuhr.--Is subjectivism in value theory compatible with realism and meliorism? By C. Krusé.--The semi-detached knower: a note on radical empiricism, by R. L. Calhoun.--The new scientific and metaphysical basis for epistemological theory, by F. S. C. Northrop.--A psychological approach to reality, by (...) H. Hartshorne.--A definition of religious liberalism, by D. S. Robinson. (shrink)