Privation as a specific way of negating is not mentioned in contemporary logic. In contrast, in ancient and medieval logic the theory of privation was quite systematically developed. The reason for this is no doubt the connection between privation theory and certain philosophical theories and problems, such as Aristotle’s theory of matter and form in which privation plays an important role, or the still-influential theory of evil as the privation of the good. The article discusses various forms of privation theory in the history of philosophy and logic, especially in Aristotle and William of Ockham, and then attempts to reconstruct these thoughts in terms of modern logic and semantics, along with the delineation and evaluation of possible challenges for future research. Further, I attempt to find ways of representing these different kinds of privation by means of modern logic and semantics. To this end I work primarily with the conception of John N. Martin, and his use of so-called scalar predicates, but also with the V. Svoboda’s interesting concept of the requisiteness of property. In conclusion I mention some unresolved questions which are connected to the theory of privation.
This paper focuses on a relatively controversial topic of Russellian scholarship, that is, on influences of Neo-Hegelianism in the thought of B.Russell. At first glance, Russell stays explicitly in opposition to Hegelianism, but a closer examination may reveal surprising parallels especially with some ideas of F.H. Bradley, the leader of the English Neo-Hegelianism. The paper is based on Bradley’s book The Principles of Logic, about which Russell himself wrote that he carefully read it. I draw mainly on Bradley’s analysis of judgements, which inspired Russell, especially his thesis that all categorical judgements are hypothetical. With the help of links to wider philosophical bases of Bradley’s attitudes, their comparison with Russell and other theories of judgements I want to point out the often hidden philosophical motivation of logical theories.
The article deals with the reflections on determinism which appeared in the context of ancient and modern logic beginning with Aristotle’s famous Argument of the Sea Battle in the ninth chapter of his On Interpretation. The canonical interpretation of this passage is put forward according to which the unlimited validity of the Principle of Bivalence seems to imply determinism, which in turn constitutes a reason for limiting the validity of that principle while preserving the Principle of Excluded Middle. Several strategies are shown which have been used by various thinkers when coming to terms with this argument, and the argument is ultimately put into the wider context of Aristotle’s philosophy. As a reaction to the aforementioned argument the article then discusses the so-called Master Argument which originates in the Megaric school. Its reconstruction is undertaken, presenting it as an attack on Aristotle’s conception of modality, and certain objections are raised which disqualify the argument in its given form. The Stoics accepted the Argument of the Sea Battle, with its deterministic consequences, and they thus became unequivocal proponents of the unlimited validity of the Principle of Bivalence, something which showed itself in, for example, the Stoic conception of negation. The Principle of Bivalence became, with the Stoics, the foundation for the causal argument for determinism. It seems that the Epicureans, in their polemical exchanges with the Stoics, failed to consider this assumption. In the reflections of Jan Lukasiewicz on the subject of determinism, one can detect a link with the ancient problematic. Lukasiewicz, however, makes the causal argument the premise of a modified Argument of the Sea Battle and, because of a reluctance to accept determinism, infers that the Principle of Bivalence must be limited, which, in the form that he states it, leads to the rise of many-valued logic.
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