Let L ω ∞ω be the infinitary language obtained from the first-order language of graphs by closure under conjunctions and disjunctions of arbitrary sets of formulas, provided only finitely many distinct variables occur among the formulas. Let p(n) be the edge probability of the random graph on n vertices. It is shown that if p(n) ≪ n -1 satisfies certain simple conditions on its growth rate, then for every σ∈ L ω ∞ω , the probability that σ holds for the (...) random graph on n vertices converges. In fact, if $p(n) = n^{-\alpha}, \alpha > 1$ , then the probability is either smaller than 2 -n d for some $d > 0$ , or it is asymptotic to cn -d for some $c > 0, d \geq 0$ . Results on the difficulty of computing the asymptotic probability are given. (shrink)
For every k ∈ ω, there is an infinite set $A_k \subseteq \omega$ and a d(k) ∈ ω such that for all $Q_0, Q_1 \subseteq A_k$ where |Q 0 | = |Q 1 or $d(k) , the structures $\langle \omega, +, Q_0\rangle$ and $\langle \omega, +, Q_1\rangle$ are indistinguishable by first-order sentences of quantifier depth k whose atomic formulas are of the form u = v, u + v = w, and Q(u), where u, v, and w are variables.
Using a sample of over 700 business people and students, this study tested the premise of promise-keeping as a core ethical value in the work place.The exercise consisted of in-basket planning for layoffs within an organization. Only one of the five employees within the group had been given an express commitment/promise of continued employment for a two year period. The layoffs were being considered six months after the two year promise had been made. All five employees were performing their jobs (...) adequately, and each had either personal or work attributes representing competing values that would have made it difficult to choose among them. (shrink)
Like William James before him, Huw Price has influentially argued that truth has a normative role to play in our thought and talk. I agree. But Price also thinks that we should regard truth-conceived of as property of our beliefs-as something like a metaphysical myth. Here I disagree. In this paper, I argue that reflection on truth's values pushes us in a slightly different direction, one that opens the door to certain metaphysical possibilities that even a Pricean pragmatist can (...) love. (shrink)
William F. Lynch, S. J. An Approach to the Metaphysics of Plato through the Parmenides, Georgetown University Press, 1959, 255 pp. $ 6.00 Robert S. Brumbaugh, Plato on the One. The Hypotheses in the Parmenides, Yale University Press, New Haven 1961, 365 pp. $ 6.50.
Advocates of traditional views on truth such as the correspondence and coherence theories converge on two theses about truth: substantivism and monism. According to the former thesis, truth consists in some substantive property or relation F. According to the latter thesis, there is exactly one property or relation (whether substantive or not) in terms of which truth is to be accounted for across all truth-apt domains of discourse. The correspondence theorist thus has it that a proposition is true just in (...) case it corresponds with reality, i.e. just in case a certain substantive relation holds between language and the world. Furthermore, this is so for any truth-apt discourse: whether we are dealing with propositions about mathematics, medium-sized dry goods, or legal matters truth always and everywhere consists in correspondence with reality.1 Recently, resistance to alethic traditionalism has emerged from two camps. The deflationist takes issue with substantivism: there is nothing more to truth than what is captured by instances of the following well-known schema: (T) 〈p〉 is true iff p. 2 According to the deflationist, substantive properties (or relations) such as correspondence and coherence have no role to play in an account of truth. At most, a deflationist will allow that all true propositions share a “lightweight” property of falling under the concept of truth. Deflationists about truth thus reject the metaphysical project that aims to uncover the deep or substantive nature of truth. Truth, according to the deflationist, is merely a logical device that serves certain functions such as endorsing a proposition and making (potentially infinite) generalizations. For instance, instead of saying that the empty set is a subset of every set and that Bob believes 〈the empty set is a subset of every set〉, the power set of an infinite set is uncountable and Bob believes 〈the power set of an infinite set is uncountable〉, and so on for Bob’s other beliefs about set.... (shrink)
