The ideas of fixed points (Kripke in Recent essays on truth and the liar paradox. Clarendon Press, London, pp 53–81, 1975; Martin and Woodruff in Recent essays on truth and the liar paradox. Clarendon Press, London, pp 47–51, 1984) and revision sequences (Gupta and Belnap in The revision theory of truth. MIT, London, 1993; Gupta in The Blackwell guide to philosophical logic. Blackwell, London, pp 90–114, 2001) have been exploited to provide solutions to the semantic paradox and have achieved admirable (...) success. This happy situation naturally encourages one to look for other philosophical areas of their further applications where paradoxical results seem to follow from intuitively acceptable principles. In this paper, I propose to extend the use of these ideas to give two new treatments of abstract objects. Sections 1 and 2 below check several abstractionist theories and their main defects. Section 3 shows how the two ideas can be applied to generate consistent theories of abstract objects without any ad hoc restriction on any principle. (shrink)

FoLLI-LNCS is the publication platform for the Association of Logic, Language and Information. The Association was founded in 1991 to advance research and education on the interface between logic, linguistics, computer science, and cognitive science. The FoLLI Publications on Logic, Language and Information aim to disseminate results of cutting-edge research and tutorial materials in these interdisciplinary areas. This LNCS volume is part of FoLLi book serie and contains the papers presented at the 5th International Workshop on Logic, Rationality and Interaction/, (...) held in October 2015 in Taipei, Taiwan. The topics covered in this program well represent the span and depth that hasby now become a trademark of the LORI workshop series, where logic interfaceswith disciplines as diverse as game theory and decision theory, philosophyand epistemology, linguistics, computer science and artificial intelligence. (shrink)

Gideon Rosen proposes a view called "modal fictionalism" which Rosen thinks has all the benefits of modal realism without its ontological costs. Whereas modal realists have a paraphrase r(0) of a modal claim "0", modal fictionalists claim that the correct translation of "0" is rather the result of prefixing "according to the hypothesis of a plurality of worlds" to r(0). Rosen takes the prefix to be primitive and defines other modal notions in terms of it. Bob Hale, however, thinks the (...) fictionalist's project suffers from a "simple" dilemma. The purpose of this paper is to show that Rosen is right in taking the prefix as primitive and Hale is wrong in thinking fictionalism as being threatened by the dilemma. (shrink)

Gideon Rosen proposes a view called "modal fictionalism" which Rosen thinks has all the benefits of modal realism without its ontological costs. Whereas modal realists have a paraphrase r of a modal claim "0", modal fictionalists claim that the correct translation of "0" is rather the result of prefixing "according to the hypothesis of a plurality of worlds" to r. Rosen takes the prefix to be primitive and defines other modal notions in terms of it. Bob Hale, however, thinks the (...) fictionalist's project suffers from a "simple" dilemma. The purpose of this paper is to show that Rosen is right in taking the prefix as primitive and Hale is wrong in thinking fictionalism as being threatened by the dilemma. (shrink)

In order to reply to the contemporary skeptic’s argument for the conclusion that we don’t have any empirical knowledge about the external world, several authors have proposed different fallibilist theories of knowledge that reject the epistemic closure principle. Holliday, 1–62 2015a), however, shows that almost all of them suffer from either the problem of containment or the problem of vacuous knowledge or both. Furthermore, Holliday suggests that the fallibilist should allow a proposition to have multiple sets of relevant alternatives, each (...) of which is sufficient while none is necessary, if all its members are eliminated, for knowing that proposition. Not completely satisfied with Holliday’s multi-path reply to the skeptic, the author suggests a new single-path relevant-possibility theory of knowledge and argues that it can avoid both the problem of containment and the problem of vacuous knowledge of a certain sort while rejecting skepticism about the external world. (shrink)

This essay is a study of Non-actualism, the thesis that there are objects which do not exist. There are several difficulties surrounding this thesis. First, there is the question about how to make sense of this very thesis. Second, there is the problem about what evidences there are for such a thesis. Third, there is a serious doubt about whether such thesis can be held consistently. ;The first question is usually claimed to be answered by Non-actualists by distinguishing two kinds (...) of quantifiers: existential quantifiers and a "broader" sort of quantifiers. My suggestion in this essay is, however, that there is a more ordinary use of the phrase "there is" which makes the Non-actualist thesis perfectly intelligible. After clarifying what I mean by "Non-actualism", especially after clarifying what the phrase "there is" is used to mean, I go on to check what evidences there are for such a doctrine. In the literature, three different sorts of evidences are usually cited by Non-actualists to defend their positions: fictional talk, modal talk, and our experiences about things not existing. I reject the first two but endorse the last one mainly on the ground that non-actual talk is subject to different interpretations and is only remotely related to ontological issues. However, there still is a threat of inconsistency for those Non-actualists who want to defend their positions from the empirical or phenomenological aspect. In this essay, I distinguish three kinds of paradoxes that a Non-actualist has to solve, and show their independence. I call them, separately, the Sosein Paradox, the Sein Paradox and the Cardinality Paradox. Further, I show that most Non-actualist theories which are designed mainly to solve these paradoxes do not really accomplish their task. But, to our surprise, there is a Meinongian thought which solves these paradoxes quite naturally, even though it did not aim at such a solution when it was developed. And I attribute this theory to Butchvarov. (shrink)

I show in this paper how Putnam’s model-theoretical argument can be modified so as to generate a new general tool for Nominalism. I call such a tool “Ockham’s New Razor”. Section I illustrates how the model-theoretical technique that I have in mind can be applied to argue against Meinongian theories. Section II shows how the technique can be generalized to other cases as well. It also contains a brief discussion of the major assumption in the technique. Section III discusses possible (...) objections to my so-called “Ockham’s New Razor”. (shrink)

In several articles, Putnam claims that the direct reference theory (DRT) he endorses has startling consequence for the theory of necessary truth and essentialism, for if DRT is correct, so he claims, it follows that things belonging to natural kinds have their deep structures necessarily. Inspired by Donnellan, Nathan Salmon tries to spell out what Putnam seems to have in mind when making the claim, and Salmon calls the result "the OK mechanism". Salmon shows, in the OK mechanism, it is (...) not DRT, but some other essentialism-entailing premise, that has the claimed startling consequence. In this paper, I argue that Salmon's OK is not the right interpretation of Putnam's intended mechanism. Instead, I present Putnam's intention as the OK* mechanism, and show that, in OK*, DRT does have the startling consequence for the theory of necessary truth and essentialism when supplemented only with other metaphysically innocent, purely empirically verifiable premises. (shrink)

In several articles, Putnam claims that the direct reference theory he endorses has startling consequence for the theory of necessary truth and essentialism, for if DRT is correct, so he claims, it follows that things belonging to natural kinds have their deep structures necessarily. Inspired by Donnellan, Nathan Salmon tries to spell out what Putnam seems to have in mind when making the claim, and Salmon calls the result "the OK mechanism". Salmon shows, in the OK mechanism, it is not (...) DRT, but some other essentialism-entailing premise, that has the claimed startling consequence. In this paper, I argue that Salmon's OK is not the right interpretation of Putnam's intended mechanism. Instead, I present Putnam's intention as the OK* mechanism, and show that, in OK*, DRT does have the startling consequence for the theory of necessary truth and essentialism when supplemented only with other metaphysically innocent, purely empirically verifiable premises. (shrink)

Disagreeing with most authors on vagueness, the author proposes a solution that he calls ‘three-valued semantic pluralism’ to the age-old sorites paradox. In essence, it is a three-valued semantics for a first-order vague language with identity with the additional suggestion that a vague language has more than one correct interpretation. Unlike the traditional three-valued approach to a vague language, three-valued semantic pluralism can accommodate the phenomenon of higher-order vagueness and the phenomenon of penumbral connection when equipped with ‘suitable conditionals’. The (...) author also shows that three-valued semantic pluralism is a natural consequence of a restricted form of the Tolerance principle ) and a few related ideas, and argues that ) is well-motivated by considerations about how we learn, teach, and use vague predicates. (shrink)