Aristotle’s dilemma

In the Nicomachean Ethics, Aristotle appears to use an elegant short argument to attack Plato’s doctrine of the good, which argument equally appears to attack Aristotle’s own doctrine of the good. I consider these two questions: First: Why does Aristotle reverse the judgment of Socrates/Plato on the issue: Which is better – things that are (only) good in themselves, or things that are both good in themselves and good for their consequences? Second: Why does Aristotle attack Plato’s doctrine that the Form of the Good is the chief good, with an argument that appears to threaten his own view that eudaimonia is the chief good? I think the answers to these two questions are related. The elegant short argument in question I call “Aristotle’s Fast Argument.”After apologizing for criticizing views held by friends of his, Aristotle deploys the Fast Argument as a clincher to cap off his refutation of Plato’s view that the Form of the Good is the chief good: “And one might ask the question, what in the world they mean by ‘a thing itself’, if in man himself and in a particular man the account of man is one and the same. For in so far as they are men, they will in no respect differ; and if this is so, neither will there be a difference in so far as they are good. But again it will not be good any the more for being eternal, since that which lasts long is no whiter than that which perishes in a day.” (Aristotle, Nichomachean Ethics, 1096 a34–b4). I explore this sketchily presented Fast Argument. I consider why Aristotle may think it is valid and why he does not seem to realize that, on readings that make it effective against Plato’s view, his Fast Argument also seems to apply to his own view that eudaimonia is the chief good. This is what I will call “Aristotle’s Dilemma.” If the Fast Argument is interpreted too narrowly, its point about the whiteness of a white thing being independent of its duration will not apply to the goodness of the Form of the Good. If it is interpreted broadly enough to undermine the claim of the Form of the Good to be the chief good, it will equally undermine that claim for eudaimonia. Finally, I discuss some of the things Plato and Aristotle say about the chief good, and comparable things Immanuel Kant says about the good will. I draw some speculative conclusions that focus on the importance for Aristotle of the goodness of the chief good not being at risk.     

Logics with the Qualitative Probability Operator

The paper presents several strongly complete axiomatizationsof qualitative probability within the framework of probabilisticlogic. We show that in the proposed semantics qualitative probabilitiesare characterized by probability functions, so they also arecomparative probabilities.     

Non-Classical Negation in the Works of Helena Rasiowa and Their Impact on the Theory of Negation

The paper is devoted to the contributions of Helena Rasiowa to the theory of non-classical negation. The main results of Rasiowa in this area concerns–constructive logic with strong (Nelson) negation,–intuitionistic negation and some of its generalizations: minimal negation of Johansson and semi-negation.We discuss also the impact of Rasiowa works on the theory of non-classical negation.A lecture presented at the International Conference Trends in Logic III : A. Mostowski, H. Rasiowa and C. Rauszer in memoriam, Warsaw, Ruciane-Nida September 23-26, 2005.     

关于克里普克模态性的一个自然主义解释

The Kripkean metaphysical modality (i.e. possibility and necessity) is one of the most important concepts in contemporary analytic philosophy and is the basis of many metaphysical speculations. These metaphysical speculations frequently commit to entities that do not belong to this physical universe, such as merely possible entities, abstract entities, mental entities or qualities not realizable by the physical, which seems to contradict naturalism or physicalism. This paper proposes a naturalistic interpretation of the Kripkean modality, as a naturalist’s response to these metaphysical speculations. It will show that naturalism can accommodate the Kripkean metaphysical modality. In particular, it will show that naturalism can help to resolve the puzzles surrounding Kripke’s a posteriori necessary propositions and a priori contingent propositions. __________ Translated from Zhexue yanjiu 哲学研究 (Philosophical Researches), 2008, (1): 18–26     

Inexact Knowledge with Introspection

Standard Kripke models are inadequate to model situations of inexact knowledge with introspection, since positive and negative introspection force the relation of epistemic indiscernibility to be transitive and euclidean. Correlatively, Williamson’s margin for error semantics for inexact knowledge invalidates axioms 4 and 5. We present a new semantics for modal logic which is shown to be complete for K45, without constraining the accessibility relation to be transitive or euclidean. The semantics corresponds to a system of modular knowledge, in which iterated modalities and simple modalities are not on a par. We show how the semantics helps to solve Williamson’s luminosity paradox, and argue that it corresponds to an integrated model of perceptual and introspective knowledge that is psychologically more plausible than the one defended by Williamson. We formulate a generalized version of the semantics, called token semantics, in which modalities are iteration-sensitive up to degree n and insensitive beyond n. The multi-agent version of the semantics yields a resource-sensitive logic with implications for the representation of common knowledge in situations of bounded rationality.     

Predicate Logical Extensions of some Subintuitionistic Logics

The paper presents predicate logical extensions of some subintuitionistic logics. Subintuitionistic logics result if conditions of the accessibility relation in Kripke models for intuitionistic logic are dropped. The accessibility relation which interprets implication in models for the propositional base subintuitionistic logic considered here is neither persistent on atoms, nor reflexive, nor transitive. Strongly complete predicate logical extensions are modeled with a second accessibility relation, which is a partial order, for the interpretation of the universal quantifier. Presented by Melvin Fitting     

Proof Systems Combining Classical and Paraconsistent Negations

New propositional and first-order paraconsistent logics (called L _ω and FL _ω , respectively) are introduced as Gentzen-type sequent calculi with classical and paraconsistent negations. The embedding theorems of L _ω and FL _ω into propositional (first-order, respectively) classical logic are shown, and the completeness theorems with respect to simple semantics for L _ω and FL _ω are proved. The cut-elimination theorems for L _ω and FL _ω are shown using both syntactical ways via the embedding theorems and semantical ways via the completeness theorems. Presented by Yaroslav Shramko and Heinrich Wansing     

Bounded contraction and Gentzen-style formulation of Łukasiewicz logics

In this paper, we consider multiplicative-additive fragments of affine propositional classical linear logic extended with n-contraction. To be specific, n-contraction (n 2) is a version of the contraction rule where (n+ 1) occurrences of a formula may be contracted to n occurrences. We show that expansions of the linear models for (n + 1)- valued ukasiewicz logic are models for the multiplicative-additive classical linear logic, its affine version and their extensions with n-contraction. We prove the finite axiomatizability for the classes of finite models, as well as for the class of infinite linear models based on the set of rational numbers in the interval [0, 1]. The axiomatizations obtained in a Gentzen-style formulation are equivalent to finite and infinite-valued ukasiewicz logics.Presented by Jan Zygmunt