Firstly I characterize Simple Partial Logic (SPL) as the generalization and extension of a certain two-valued logic. Based on the characterization I present two definitions of validity in SPL. Finally I show that given my characterization these two definitions are more appropriate than other definitions that have been prevalent, since both have some desirable semantic properties that the others lack.
Łukasiewicz has often been criticized for his motive for inventing his three-valued logic, namely the avoidance of determinism. First of all, I want to show that almost all of the critcism along this line was wrong. Second I will indicate that he made mistakes, however, in constructing his system, because he had other motives at the same time. Finally I will propose some modification of his system and its interpretation which can attain his original purpose in some sense.
Firstly I define a hole as a dependent matter-less endurant, which is a little modification of Casati and Varzi’s definition. Adopting this definition, holes seem to invite three problems about causation: (1)causal closure, (2)ungrounded disposition and (3)causal overdetermination. I will defend my definition against all these problems by showing that holes are limiting cases of physical endurants rather than their opposition and that they have causal powers in a broad sense.
In this paper I give consideration to some apparent impossibilities for the time travelers to the past. After criticizing the views of D. Lewis and K. Vihvelin, I will show in what sense they are really impossible.
Recently, Bourne constructed a system of three-valued logic that he supposed to replace Łukasiewicz’s three-valued logic in view of the problems of future contingents. In this paper, I will show first that Bourne’s system makes no improvement to Łukasiewicz’s system. However, finding some good motivations and lessons in his attempt, next I will suggest a better way of achieving his original goal in some sense. The crucial part of my way lies in reconsidering the significance of the intermediate truth-value so (...) as to reconstruct Łukasiewicz’s three-valued logic as a kind of extensional modal logic based on partial logic. (shrink)
Casati and Varzi have developed a theory of boundary based on extensional mereotopology and the distinction between fiat and bona fide boundaries. Firstly, I point out some problems in their theory that are related to the contact of bodies. Next, I propose a way of classification of boundaries into four kinds based on substance ontology and an alternative distinction between potential and actual boundaries. Finally, I will show that my way of classification makes it possible to solve the problems above.
M. Johnston proposed an adverbialist solution to the problem of intrinsic change of enduring things. D. Lewis interpreted it as a way of tensing the copula. In his view, it has the defect of replacing having a property simpliciter by standing in a triadic relation to a property and a time, and so is threatened by Bradley’s Regress. I agree with Lewis on requiring having a property to be non-relational, while I disagree with him on restricting it to having simpliciter. (...) I tense the copula non-relationally and yet more seriously than Johnston, by characterizing tense as a copulative de re modality concerning endurance, which I relate to R. Taylor’s ‘pure becoming’. I will show that my way gives a better solution to the problem of intrinsic change than those by other endurantists, because of its close connection to an account of tense, endurance and becoming. (shrink)
There are two types of theories regarding many worlds: one is modal, while the other is temporal. The former regards reality as consisting of many possible worlds, while the latter holds that reality consists of many momentary worlds, which are usually called moments. I compare these two theories, paying close attention to the concept of transworld identity and compare trans-possible world identity with trans-momentary world identity (or transmoment identity). I characterize time from the point of many-worlds view, believing this to (...) be one of the best ways of grasping the reality of time. First, I show that there is reason to adopt the many-worlds view because transworld identity is meaningful for both of them, while it is not for space. Second, I argue that transmoment identity is different from transpossible world identity concerning reality. The former is a realistic relation, while the latter is not. Thus, I find that the reality of time is in the relation of transmoment identity. Such a view, I contend, has merit on the basis that it recognizes the reality of time in a sense that is not true of space. (shrink)
Simple partial logic (=SPL) is, broadly speaking, an extensional logic which allows for the truth-value gap. First I give a system of propositional SPL by partializing classical logic, as well as extending it with several non-classical truth-functional operators. Second I show a way based on SPL to construct a system of tensed ontology, by representing tensed statements as two kinds of necessary statements in a linear model that consists of the present and future worlds. Finally I compare that way with (...) other two ways based on Łukasiewicz’s three-valued logic and branching temporal logic. (shrink)
In my paper 'Validity in Simple Partial Logic'(2002) I made comparison between several definitions of validity in Simple Partial Logic(SPL) and adopted two of them as most appropriate. In this paper, after elaborating more on these two definitions than in my previous paper and considering the characteristics of Partial Semantics, in which these definitions are given, I construct a tableau proof system and prove its soundness and completeness. Then, based on the characterization of Partial Semantics, I will show that we (...) can regard SPL as a logic of extensional alethic modality. (shrink)