In 1984, Henson and Rubel [2] proved the following theorem: If p(x₁, ..., x n ) is an exponential polynomial with coefficients in with no zeroes in ℂ, then $p({x_1},...,{x_n}) = {e^{g({x_{1......}}{x_n})}}$ where g(x₁......x n ) is some exponential polynomial over ℂ. In this paper, I will prove the analog of this theorem for Zilber's Pseudoexponential fields directly from the axioms. Furthermore, this proof relies only on the existential closedness axiom without any reference to Schanuel's conjecture.
In this paper, we prove that a pseudo-exponential field has continuum many nonisomorphic countable real closed exponential subfields, each with an order-preserving exponential map which is surjective onto the nonnegative elements. Indeed, this is true of any algebraically closed exponential field satisfying Schanuel’s conjecture.
During the Middle Ages Aristotle's treatises were accessible to intellectuals via translations and commentaries. Among his works on natural philosophy, the zoological books received relatively little scholarly attention, though several medieval commentators carefully studied Aristotle's investigations of the animal kingdom. Averroes completed in 1169 a commentary on an Arabic translation of Aristotle's Parts of Animals and Generation of Animals. In 1323 Gersonides completed his supercommentary on a Hebrew translation of Averroes' commentary. This article examines how these two medieval commentators interpret (...) the first book of Aristotle's Parts of Animals, at the center of which stand methodological questions regarding the study of animals. Aristotle's discussion of classification is presented by Averroes and Gersonides in light of an epistemological debate concerning the requisite method for scientific inquiries and discoveries. Sense perception is contrasted with rational reasoning, and ultimately a combined method is proposed, sense perception maintaining supremacy. These commentators outline a clear link between the systematic arrangement of animal species as offered by Aristotle, and his subsequent logical demonstrations which, according to them, form the core of biological investigations. (shrink)
During the Middle Ages Aristotle’s treatises were accessible to intellectuals via translations and commentaries. Among his works on natural philosophy, the zoological books received relatively little scholarly attention, though several medieval commentators carefully studied Aristotle’s investigations of the animal kingdom. Averroes completed in 1169 a commentary on an Arabic translation of Aristotle’s Parts of Animals and Generation of Animals. In 1323 Gersonides completed his supercommentary on a Hebrew translation of Averroes’ commentary. This article examines how these two medieval commentators interpret (...) the first book of Aristotle’s Parts of Animals, at the center of which stand methodological questions regarding the study of animals. Aristotle’s discussion of classification is presented by Averroes and Gersonides in light of an epistemological debate concerning the requisite method for scientific inquiries and discoveries. Sense perception is contrasted with rational reasoning, and ultimately a combined method is proposed, sense perception maintaining supremacy. These commentators outline a clear link between the systematic arrangement of animal species as offered by Aristotle, and his subsequent logical demonstrations which, according to them, form the core of biological investigations. (shrink)
Christology seems to fall fairly clearly into two divisions. The first is concerned with the truth of the two propositions: ‘Christ is God’ and ‘Christ is a man’. The second is concerned with the mutual compatibility of these propositions. The first part of Christology tends to confine itself to what is sometimes called ‘positive theology’: that is to say, it is largely given over to examining the Jons revelationis —let us not prejudge currently burning issues by asking what this is—to (...) see what evidence can be found for the truth of these propositions. Clearly, the methods used will be above all those of New Testament exegesis. The second part of Christology will necessarily consist entirely of that speculative theology which is contrasted with positive theology. Even if the earliest speculation on this topic is to be found in the New Testament itself and thus becomes fair game for the exegetes, any attempt to relate the primary truths, ‘Christ is God’ and ‘Christ is a man’, to eachother is a work of reflection, and in the terminology I am using speculative. (shrink)
There is a strong tendency in the scholarly and sub-scholarly literature on terrorism to treat it as something like an ideology. There is an equally strong tendency to treat it as always immoral. Both tendencies go hand in hand with a considerable degree of unclarity about the meaning of the term ‘terrorism’. I shall try to dispel this unclarity and I shall argue that the first tendency is the product of confusion and that once this is understood, we can see, (...) in the light of a more definite analysis of terrorism, that the second tendency raises issues of inconsistency, and even hypocrisy. Finally, I shall make some tentative suggestions about what categories of target may be morally legitimate objects of revolutionary violence, and I shall discuss some lines of objection to my overall approach. (shrink)
