The book presents a thoroughly elaborated logical theory of generalized truth-values understood as subsets of some established set of truth values. After elucidating the importance of the very notion of a truth value in logic and philosophy, we examine some possible ways of generalizing this notion. The useful four-valued logic of first-degree entailment by Nuel Belnap and the notion of a bilattice constitute the basis for further generalizations. By doing so we elaborate the idea of a multilattice, and most notably, (...) a trilattice of truth values – a specific algebraic structure with information ordering and two distinct logical orderings, one for truth and another for falsity. Each logical order not only induces its own logical vocabulary, but determines also its own entailment relation. We consider both semantic and syntactic ways of formalizing these relations and construct various logical calculi. (shrink)

Slingshot arguments aim to show that an allegedly non-extensional sentential connective—such as “necessarily ” or “the statement that Φ corresponds to the fact that ”—is, to the contrary, an extensional sentential connective. Stephen Neale : 761-825, 1995, 2001) argues that a reformulation of Gödel’s slingshot puts pressure on us to adopt a particular view of definite descriptions. I formulate a revised version of the slingshot argument—one that relies on Kaplan’s notion of “dthat.” I aim to show that if Neale’s version (...) of the slingshot argument is successful, then there is another slingshot available, parallel in structure to Neale’s, but independent of definite descriptions. So either there is a version of the slingshot that succeeds independent of any particular theory of descriptions or else Neale’s slingshot was never threatening to begin with. (shrink)

The famous “slingshot argument” developed by Church, Gödel, Quine and Davidson is often considered to be a formally strict proof of the Fregean conception that all true sentences, as well as all false ones, have one and the same denotation, namely their corresponding truth value: the true or the false. In this paper we examine the analysis of the slingshot argument by means of a non-Fregean logic undertaken recently by A.Wóitowicz and put to the test her claim that the slingshot (...) argument is in fact circular and presupposes what it intends to prove. We show that this claim is untenable. Nevertheless, the language of non-Fregean logic can serve as a useful tool for representing the slingshot argument, and several versions of the slingshot argument in non-Fregean logics are presented. In particular, a new version of the slingshot argument is presented, which can be circumvented neither by an appeal to a Russellian theory of definite descriptions nor by resorting to an analogous “Russellian” theory of λ–terms. (shrink)

The famous “slingshot argument” developed by Church, Gödel, Quine and Davidson is often considered to be a formally strict proof of the Fregean conception that all true sentences, as well as all false ones, have one and the same denotation, namely their corresponding truth value: the true or the false . In this paper we examine the analysis of the slingshot argument by means of a non-Fregean logic undertaken recently by A.Wóitowicz and put to the test her claim that the (...) slingshot argument is in fact circular and presupposes what it intends to prove. We show that this claim is untenable. Nevertheless, the language of non-Fregean logic can serve as a useful tool for representing the slingshot argument, and several versions of the slingshot argument in non-Fregean logics are presented. In particular, a new version of the slingshot argument is presented, which can be circumvented neither by an appeal to a Russellian theory of definite descriptions nor by resorting to an analogous “Russellian” theory of λ–terms. (shrink)

The paper attempts to clarify some fundamental aspects of an explanationof the concept of truth which is neither “deflationary” nor “substantive”.The main aspect examined in detail concerns the ontological dimension of truth, the mind/language-world connection traditionally associated with the concept of truth. It is claimed that it does not make sense to defend or reject a relatedness of truth to the ontological dimension so long as the kind of presupposed or envisaged ontology is not made explicit and critically examined. In (...) particular, it is shown that generally an “objectual” ontology is – often only implicitly – presupposed, i.e., an ontology admitting “objects” (substances), properties, relations, sometimes also facts, events, and the like. The paper demonstrates that such an ontology derives from the Principle of Semantic Sentential Compositionality and that this principle should be rejected. It introduces instead the Principle of Semantic Sentential Contextuality (or Context Principle) as the semantic basis of a new ontology, an ontology of “primary states of affairs”. After sketching such an ontology, it is shown that the relatedness of truth to the ontological dimension becomes intelligible. (shrink)

In his recent book, Stephen Neale provides an extended defence of the claim that Gödel's slingshot has dramatic consequences for fact theorists (and, in particular, for fact theorists who look with favour on referential treatments of definite descriptions). I argue that the book-length treatment provides no strengthening of the case that Neale has made elsewhere for this implausible claim. Moreover, I also argue that various criticisms of Neale's case that I made on a previous occasion have met with no successful (...) resistance. If Neale is serious about facing facts, then he needs to face the fact that his central contentions are unsupportable. (shrink)

RÉSUMÉ: Utilisant ce qu'on appelle l'argument du lance-pierres, Davidson soutient que la théorie correspondantiste de la vérité est intenable. Cet argument dépend de deux présuppositions, dont l'une est qu'une phrase vraie ne devrait pas, par substitution de termes singuliers coréférentiels, en venir à correspondre à quelque chose de différent. Je propose dans cet article un argument nouveau pour montrer que cette supposition n'est pas plausible, particulièrement lorsqu'elle s'applique à des énoncés d'identité, ceux-là mêmes dont dépend pour sa formulation l'argument du (...) lance-pierres. (shrink)

The main purpose of the paper concerns the question of the existence of hard mathematical facts as truth-makers of mathematical sentences. The paper defends the standpoint according to which hard mathematical facts do not exist in semantic models of mathematical theories. The argumentative line in favour of the defended thesis proceeds as follows: slingshot arguments supply us with some reasons to reject various ontological theories of mathematical facts; there are two ways of blocking these arguments: through the rejection of the (...) principle of extensionality for individual terms or through the rejection of the principle of Wittgenstein; the first way cannot be accepted because it leads to the practice of softening mathematical facts; the second way, called fine-graining facts, cannot be accepted because it also results in the practice of softening facts. Hence, only soft mathematical facts can be introduced into semantic models of mathematical theories. Because they should be rather interpreted as mental representations of mathematical objects, they no longer satisfy the semantic role of truth-makers in relation to mathematical sentences. The argument formulated in the paper is based on the analysis of mathematical extensions of the basic non-Fregean logic. Sixty-two definitions of potential fact-identity connectives are also presented. The paper's conclusion may be interpreted as undermining the situational paradigm of building semantics for mathematical languages. (shrink)

The paper presents a new argument supporting the ontological standpoint according to which there are no mathematical facts in any set theoretic model of arithmetical theories. It may be interpreted as showing that it is impossible to construct fact-arithmetic. The importance of this conclusion arises in the context of cognitive science. In the paper, a new type of slingshot argument is presented, which is called hyper-slingshot. The difference between meta-theoretical hyper-slingshots and conventional slingshots consists in the fact that the former (...) are formulated in the semantic meta-language of mathematical theories without the use of the iota-operator or the lambda-operator as the abstractor, whereas the latter require for their expression at least one of these non-standard term-operators. Hyper-slingshots implement simpler language tools in comparison with those used in conventional slingshots. (shrink)

Causal slingshots are formal arguments advanced by proponents of an event ontology of token-level causation which, in the end, are intended to show two things: (i) The logical form of statements expressing causal dependencies on token level features a binary predicate ‘‘... causes ...’’ and (ii) that predicate takes events as arguments. Even though formalisms are only revealing with respect to the logical form of natural language statements, if the latter are shown to be adequately captured within a corresponding formalism, (...) proponents of slingshots usually take the adequacy of their formalizations for granted without justifying it. The first part of this paper argues that the most discussed version of a causal slingshot, viz. the one e.g. presented by Davidson (Essays on actions and events. Oxford, Clarendon Press, 1980), can indeed be refuted for relying on an inadequate formal apparatus. In contrast, the formal means of Gödel’s (The philosophy of Betrand Russell. New York, Tudor, 1944) often neglected slingshot are shown to stand on solid ground in the second part of the paper. Nonetheless, I contend that Gödel’s slingshot does only half the work friends of event causation would like it to do. It provides good reasons for (i) but not for (ii). (shrink)

Fictionalism about fictional characters is a view according to which all claims ostensibly about fictional characters are in fact claims about the content of a story. Claims that appear to refer to or quantify over fictional objects contain an implicit prefix of the form “according to such-and-such story. In.

This paper presents an account of what it is for a property or relation (or ‘attribute’ for short) to be logically simple. Based on this account, it is shown, among other things, that the logically simple attributes are in at least one important way sparse. This in turn lends support to the view that the concept of a logically simple attribute can be regarded as a promising substitute for Lewis’s concept of a perfectly natural attribute. At least in part, the (...) advantage of using the former concept lies in the fact that it is amenable to analysis, where that analysis—i.e., the account put forward in this paper—requires the adoption neither of an Armstrongian theory of universals nor of a primitive notion of naturalness, fundamentality, or grounding. (shrink)

It is argued that the slingshot argument does not soundly challenge the truth-maker correspondence theory of truth, by which at least some distinct true propositions are expected to have distinct truth- makers. Objections are presented to possible exact interpretations of the essential slingshot assumption, in which no fully acceptable reconstruction is discovered. A streamlined version of the slingshot is evaluated, in which explicit contradiction results, on the assumption that identity and nonidentity contexts are purely extensional relations, effectively establishing the intensionality (...) of identity. (shrink)