. The connection presented in this paper mirror-links two metamathematical structures, the finitary closure operators, and the compact consistency properties, in such a way that a specification of one structure induces a provably equivalent specification of the other.

the standard metalogical set-ups seem to be all based on the idea of consequence (or proof). However, metalogic can also be effectively constructed using some non-standard primmitive ideas. In this paper an outline is given to four metalogical frameworks, alternative to the standard set-ups. They are based, respectively, on the idea of consistency; on an omission (or separation) operator; on an extension operator (called in the paper a Lindenbaum operator); and on the idea of maximality. All these metalogics, including the (...) standard consequence-based one, are one-to-one and proof-preserving translatable, and, in this sense, are seen pairwise equivalent and „externally” consistent. (shrink)

The paper provides a method for a uniform complete Hilbert-style axiomatisation of Post's -conditionals and Post's negation, where m is the number of truth values and u is the number of designated truth values . The main feature of the technique which we employ in this proof generalises the well-known Kalmár Lemma which was used by its author in his completeness argument for the ordinary, two-valued logic.

The method based on the idea of Galois connection is well known. It facilitates investigations into similarities between mathematical structures, including isomorphisms between these structures, the highest degree of similarity. This idea is employed here and adapted so as to get to the core of aspects of the relationship between some metamathematical structures. The focus is put on the relation between traditional methodological orthodoxy based on the idea of proof , on the one hand, and on some alternative methodological set-ups (...) based on other ideas such as consistency or some forms of maximality, on the other hand. (shrink)

By indirect-deduction theorems introduced in the present paper we mean the theorems that allow to formalize indirect reasonings occurring in deductive practice in general and in mathematics in particular. We discuss the relationship between the introduced theorems and some logical calculi being virtually confined to propositional calculi with implication and negation. It is worth to notice that the above theorems are very handy and effective in proving logical theses.

stanislaw lesniewski, Collected Works, Edited by Stanislaw J. Surma, Jan T. Srzednicki and D. I. Barnett, with an annotated bibliography by V. Frederick Rickey. Warsaw:PWN?Polish Scientific Publishers; and Dordrecht, Boston, London: Kluwer. 2 vols., xvi + 794 pp. $274/£163/Dfl. 480.

J. L. Ackrill's work on Plato and Aristotle has had a considerable influence upon ancient philosophical studies in the late twentieth century. In his writings the rigour and clarity of contemporary analytic philosophy are brought to bear upon ancient thought; in many cases he has provided thefirst analytic treatment of a key issue. Gathered now in this volume are the best of Ackrill's essays on the two greatest philosophers of antiquity. With philosophical acuity and philological expertise he examines a wide (...) range of texts and topics--from ethics and logic to epistemology andmetaphysics--which continue to be in the focus of debate. (shrink)

The study of post-Aristotelian philosophy is constantly confused by the perplexing way in which the names of philosophers recur. Zeno, the founder of Stoicism, is sufficiently well known not be confused with either Zeno the Eleatic or the later Stoic, Zeno of Tarsus, a disciple of Chrysippus; but when we come to less distinguished names the opportunity of error is greater. If two philosophers of the same name are prominent members of different schools, there ought to be no obscurity, but (...) in an age of eclecticism one school will sometimes adopt doctrines from another, and so make classification difficult. (shrink)

No tragic poet uses the phrase μxs22EFνος πνxs22EFουσαν, except Aeschylus, who employs it in describing the Erinyes, not a Greek maiden. Similarly Homer of his ‘Mut-schnaubende’ heroes and of the savage steeds of Diomed. Hence, in the Sophoclean passage, some scribe may have mistaken the familiar ΜΕΝΟCΠΝΕΟΤCΑΝ for the more unusual ΜΕΝΕΙCΙCΤΝΟΤCΑΝ. Initial C attached itself to the preceding word, and ΤΝΟΤCΑΝ became ΠΝΟΤCΑΝ, which was promptly changed to πνxs22EFουσαν.

B erkeley wrote of ‘the absolute existence of unthinking things’ as being, ‘words which are without meaning and including a contradiction’. There are few philosophers today who do not regard Berkeley as having been mistaken in this view, in that it is regarded as clearly not meaningless to suppose that there might be many objects about which no one happens to be thinking. Nor is it the aim of this paper entirely to resurrect such a view, though it is my (...) purpose to try to show the subtlety of the logical and ontological issues involved in the problem of independent things. (shrink)

“Multiculturalism”, “pluralism” and “tolerance” have become buzz words in applied ethics. While serious and well thought out work is going on in these areas, a misunderstanding of the importance of tolerance, and the difficulties raised by multicultural moral conflict seems common. In this paper I argue that intolerance of some cultural traditions is morally required, and suggest that the forging of a moral mono-culture is preferable to pluralism.

The statement, that these or those philosophers do not accept the distinction between what is, and what is not, ?given? in perception, has very little content; and should receive only a corresponding degree of emphasis.

Barrett finds lines 1010–15 difficult. He says that ‘hovers between “an heiress as my wife” and “marriage with an heiress”’, that ‘a Greek heiress did not inherit property as her own: it passed not to her but with her, to her husband and ultimately to her children.—In Attic law a widow was never : a man's property went to his legitimate children.

The term Volkskerk in the Church Order of the Nederduitsch Hervormde Kerk van AfrikaThe Nederduitsch Hervormde Kerk states in its Church Order that it is a volkskerk. In this article the term volkskerk and the historical line of how it came to use in the Nederduitsch Hervormde Kerk, is researched. In the light of these statements the term volkskerk and its meaning in the contemporary Order of the Nederduitsch Hervormde Kerk, is dealt with.