In this paper several assumptions concerning omniscience and future contingents on the one side, and omniscience and self-reference on the other, areexamined with respect to a classical and a three-valued semantic setting (the latter pertains especially to Łukasiewicz’s, Kleene’s and Blau’s three-valued logics).Interesting features of both settings are highlighted and their basic assumptions concerning omniscience are explored. To generate a context in which the notion of omniscience does not deviate from some basic intuitions, two special futurity operators are introduced in (...) this article: one for what will definitely take place and another one for what is indeterminate as to whether it will take place. Once these operators are introduced, some puzzles about omniscience in combination with future contingents are removed. An analogous solution to some puzzles concerning omniscience and selfreferentiality is also provided. (shrink)

After a short presentation of Aristotle’s views on morally acceptable pleasures vis-á-vis the hedonist and the Platonic views, the Byzantine commentaries published in CAG 19.2 and 20 on knowledge as pleasure are discussed. It is shown that the Byzantine commentators are eventually keen in discovering problems in the Aristotelian account, in a way reminiscent of their Christian premises and akin to Platonism.

I try to explain the difference between three kinds of negation: external negation, negation of the predicate and privation. Further I use polygons of opposition as heuristic devices to show that a logic which contains all three mentioned kinds of negation must be a fragment of a Łukasiewicz-four-valued predicate logic. I show, further, that, this analysis can be elaborated so as to comprise additional kinds of privation. This would increase the truth-values in question and bring fragments of (more generally speaking) (...) Łukasiewicz-n-valued predicate logics into the scene. (shrink)

An eleventh-century Greek text, in which a fourth-century patristic text is discussed, gives an outline of a solution to the Liar Paradox. The eleventh-century text is probably the first medieval treatment of the Liar. Long passages from both texts are translated in this article. The solution to the Liar Paradox, which they entail, is analysed and compared with the results of modern scholarship on several Latin solutions to this paradox. It is found to be a solution, which bears some analogies (...) to contemporary game semantics. Further, an overview of other Byzantine scholia on the Liar Paradox is provided. The findings and the originality of the discussed solution to the Liar Paradox suggest a change in the way in which Byzantine Logic is traditionally regarded in contemporary scholarship. (shrink)

This article discusses rationality gaps triggered by self-referential/cyclic choice, the latter being understood as choosing according to a norm that refers to the choosing itself. The Crocodile Paradox is reformulated and analyzed as a game—named CP—whose Nash equilibrium is shown to trigger a cyclic choice and to invite a rationality gap. It is shown that choosing the Nash equilibrium of CP conforms to the principles Wolfgang Spohn and Haim Gaifman introduced to, allegedly, guarantee acyclicity but, in fact, does not prevent (...) self-referential/cyclic choice and rationality gaps. It is shown that CP is a counter-example to Gaifman's solution of the rationality gaps problem. (shrink)

In this article, I offer two different formalizations for prescriptions which correspond to two different forms of biblical prohibitions. I discuss the known fact that the prohibitive commandments of the Decalogue according to the Septuagint and the Vulgate, Exodus 20 and Deuteronomy 5, are formulated with normative future tense indicatives. However, the Greek and Latin sources provide in Mark 10:19 variants of five biblical prohibitive commandments which are formulated with prohibitive subjunctives. I argue that there are semantic differences between normative (...) future tense indicatives and prohibitive subjunctives. These semantic differences are of importance for the understanding of the Decalogue. (shrink)

Aristotle produced several arguments to vindicate the futura contingentia and to refute the conception of modalities which do not allow incidental facts. This conception was coined mainly by Diodorus Cronus and implied the view that whatever may happen, is to happen necessarily. Although Aristotle condemned this view and refuted the theology which it implies, Diodorean modalities were employed by the scholastics to support their theology. Abaelard's Diodorean formula reads: God wishes no more and no less than what He is able (...) to do - i. e. God's ability to do something implies necessity. In the Summa theologiae, Thomas Aquinas employed Diodorean modalities along with this result of Abaelard's. Leibniz himself confessed his debt to Diodorean modalities as well as to the work of Abaelard in formulating his own ontological proof. Kurt Gödel was under the influence of Leibniz when he wrote his »Ontological Proof«, which employs Diodorean modalities. — For the Greek-speaking scholars of the Middle Ages, however, Aristotelian influences were stronger than Diodorean as regards theory building on modalities. Philosophers from the East from the 2nd to the 11th century A.D., such as Alexander of Aphrodisias, John Philoponus and Michael Psellos, condemned Diodorean modalities as fallacious. In the same period, Greek Church Fathers such as Cyril of Alexandria, Maximus Confessor and John of Damascus gave an orthodox account of God and the modalities, according to which God is able to do whatever He wishes. The absence of Leibniz-like modal ontological proofs in the Greek tradition seems more plausible under these circumstances. (shrink)

As far as the law of preservation of matter and the existence of ether are concerned, Kant, Lomonossow and Lavoisier had very similar views. Nevertheless, according to historical evidence they worked out their theories never taking each other's results for granted. Whereas it is well known that Lavoisier did not base his experiments on the former ones by Lomonossow, it has been argued that Kant based his philosophy of nature on Lavoisier's experiments. I try to show here, that Kant had (...) his philosophy of nature done, prior to Lavoisier's Elements of Chemistry. Further that the only one to have been able to influence Kant was not Lavoisier but Lomonossow. But Kant never mentioned Lomonossow. There is strong evidence that the similarity of views in Kant, Lomonossow and Lavoisier is not due to any kind of interaction between them. This also holds of the mistakes, which Kant and Lomonossow made. The only substantial difference is that Kant thought, that some laws of nature may be logically inferred without experiments. (shrink)

Aristotle produced several arguments to vindicate the futura contingentia and to refute the conception of modalities which do not allow incidental facts. This conception was coined mainly by Diodorus Cronus and implied the view that whatever may happen, is to happen necessarily. Although Aristotle condemned this view and refuted the theology which it implies, Diodorean modalities were employed by the scholastics to support their theology. Abaelard's Diodorean formula reads: God wishes no more and no less than what He is able (...) to do - i. e. God's ability to do something implies necessity. In the Summa theologiae, Thomas Aquinas employed Diodorean modalities along with this result of Abaelard's. Leibniz himself confessed his debt to Diodorean modalities as well as to the work of Abaelard in formulating his own ontological proof. Kurt Gödel was under the influence of Leibniz when he wrote his »Ontological Proof«, which employs Diodorean modalities. — For the Greek-speaking scholars of the Middle Ages, however, Aristotelian influences were stronger than Diodorean as regards theory building on modalities. Philosophers from the East from the 2nd to the 11th century A.D., such as Alexander of Aphrodisias, John Philoponus and Michael Psellos, condemned Diodorean modalities as fallacious. In the same period, Greek Church Fathers such as Cyril of Alexandria, Maximus Confessor and John of Damascus gave an orthodox account of God and the modalities, according to which God is able to do whatever He wishes. The absence of Leibniz-like modal ontological proofs in the Greek tradition seems more plausible under these circumstances. (shrink)