Can identity itself be vague? Can there be vague objects? Does a positive answer to either question entail a positive answer to the other? In this paper we answer these questions as follows: No, No, and Yes. First, we discuss Evans’s famous 1978 argument and argue that the main lesson that it imparts is that identity itself cannot be vague. We defend the argument from objections and endorse this conclusion. We acknowledge, however, that the argument does not by itself establish (...) either that there cannot be vague objects or that there cannot be identity statements that are indeterminate for ontic reasons. And we further acknowledge that it does not by itself establish that there cannot be identity statements that are indeterminate in virtue of the existence of vague objects. We then go on to argue that, despite this, one who believes in vague objects cannot endorse Evans’s argument. To establish this we offer supplementary arguments that show that if vague objects exist then identity is vague, and that if identity is vague then vague objects exist. Finally we draw attention to an argument parallel to that of Evans’s, but safer, which can be employed against the putative ontic indeterminacy in identity of vague objects which can be differentiated by identity-free properties. (shrink)

John Searle distinguished between weak and strong artificial intelligence (AI). This essay discusses a third alternative, mild AI, according to which a machine may be capable of possessing a species of mentality. Using James Fetzer's conception of minds as semiotic systems, the possibility of what might be called ``mild AI'' receives consideration. Fetzer argues against strong AI by contending that digital machines lack the ground relationship required of semiotic systems. In this essay, the implementational nature of semiotic processes posited by (...) Charles S. Peirce's triadic sign relation is re-examined in terms of the underlying dispositional processes and the ontological levels they would span in an inanimate machine. This suggests that, if non-human mentality can be replicated rather than merely simulated in a digital machine, the direction to pursue appears to be that of mild AI. (shrink)

Metaphysically possible worlds have many uses. Epistemically possible worlds promise to be similarly useful, especially in connection with propositions and propositional attitudes. However, I argue that there is a serious threat to the natural accounts of epistemically possible worlds, from a version of Russell’s paradox. I contrast this threat with David Kaplan’s problem for metaphysical possible world semantics: Kaplan’s problem can be straightforwardly rebutted, the problems I raise cannot. I argue that although there may be coherent accounts of epistemically possible (...) worlds with fruitful applications, any such an account must fundamentally compromise the basic idea behind epistemic possibility. (shrink)

What are the objects of knowledge, belief, probability, apriority or analyticity? For at least some of these properties, it seems plausible that the objects are sentences, or sentence-like entities. However, results from mathematical logic indicate that sentential properties are subject to severe formal limitations. After surveying these results, I argue that they are more problematic than often assumed, that they can be avoided by taking the objects of the relevant property to be coarse-grained (“sets of worlds”) propositions, and that all (...) this has little to do with the choice between operators and predicates. (shrink)

In this paper I reconstruct and compare criteria of theoreticity that have been developed by Carnap, Sneed and proponents of the Munich school of structuralist philosophy of science. For this purpose I develop a unified framework in which one can transform model-theoretic theory representations into linguistic ones, and vice versa. This bridges the gap between statement and non-statement view and allows a precise comparison of linguistic and model-theoretic criteria of theoreticity. In the final part I suggest a system of improved (...) definitions of theoreticity and pre-theoreticity. (shrink)

The prospects and limitations of defining truth in a finite model in the same language whose truth one is considering are thoroughly examined. It is shown that in contradistinction to Tarski's undefinability theorem for arithmetic, it is in a definite sense possible in this case to define truth in the very language whose truth is in question.

Turing and Church formulated two different formal accounts of computability that turned out to be extensionally equivalent. Since the accounts refer to different properties they cannot both be adequate conceptual analyses of the concept of computability. This insight has led to a discussion concerning which account is adequate. Some authors have suggested that this philosophical debate—which shows few signs of converging on one view—can be circumvented by regarding Church’s and Turing’s theses as explications. This move opens up the possibility that (...) both accounts could be adequate, albeit in their own different ways. In this paper, I focus on the question of whether Church’s thesis can be seen as an explication in the precise Carnapian sense. Most importantly, I address an additional constraint that Carnap puts on the explicative power of axiomatic systems—an axiomatisation explicates when it is clear which mathematical entities form the theory’s intended model—and that implicitly applies to axiomatisations of recursion theory used in Church’s account of computability. To overcome this difficulty, I propose two possible clarifications of the pre-systematic concept of “computability” that can both be captured in recursion theory, and I show how both clarifications avoid an objection arising from Carnap’s constraint. (shrink)

There are two dominant approaches to quantification: the Fregean and the Tarskian. While the Tarskian approach is standard and familiar, deep conceptual objections have been pressed against its employment of variables as genuine syntactic and semantic units. Because they do not explicitly rely on variables, Fregean approaches are held to avoid these worries. The apparent result is that the Fregean can deliver something that the Tarskian is unable to, namely a compositional semantic treatment of quantification centered on truth and reference. (...) We argue that the Fregean approach faces the same choice: abandon compositionality or abandon the centrality of truth and reference to semantic theory. Indeed, we argue that developing a fully compositional semantics in the tradition of Frege leads to a typographic variant of the most radical of Tarskian views: variabilism, the view that names should be modeled as Tarskian variables. We conclude with the consequences of this result for Frege's distinction between sense and reference. (shrink)

In this paper I argue that in contrast to natural languages, logical languages typically are not compositional. This does not mean that the meaning of expressions cannot be determined at all using some well-defined set of rules. It only means that the meaning of an expression cannot be determined without looking at its form. If one is serious about the compositionality of a logic, the only possibility I see is to define it via abstraction from a variable free language.

This unique anthology of new, contributed essays offers a range of perspectives on various aspects of ontic vagueness. It seeks to answer core questions pertaining to onticism, the view that vagueness exists in the world itself. The questions to be addressed include whether vague objects must have vague identity, and whether ontic vagueness has a distinctive logic, one that is not shared by semantic or epistemic vagueness. The essays in this volume explain the motivations behind onticism, such as the plausibility (...) of mereological vagueness and indeterminacy in quantum mechanics and they offer various arguments both for and against ontic vagueness; onticism is also compared with other, competing theories of vagueness such as semanticism, the view that vagueness exists only in our linguistic representation of the world. Gareth Evans’s influential paper of 1978, “Can There Be Vague Objects?” gave a simple but cogent argument against the coherence of ontic vagueness. Onticism was subsequently dismissed by many. However, in recent years, researchers have become aware of the logical gaps in Evans’s argument and this has triggered a new wave of interest in onticism. Onticism is now widely regarded as at least a coherent view. Reflecting this growing consensus, the present anthology for the first time puts together essays that are focused on onticism and its various facets and it fills in the lacuna in the literature on vagueness, a much-discussed subject in contemporary philosophy. (shrink)

It is now part and parcel of the official philosophical wisdom that models are essential to the acquisition and organisation of scientific knowledge. It is also generally accepted that most models represent their target systems in one way or another. But what does it mean for a model to represent its target system? I begin by introducing three conundrums that a theory of scientific representation has to come to terms with and then address the question of whether the semantic view (...) of theories, which is the currently most widely accepted account of theories and models, provides us with adequate answers to these questions. After having argued in some detail that it does not, I conclude by pointing out in what direction a tenable account of scientific representation might be sought. (shrink)

Science provides us with representations of atoms, elementary particles, polymers, populations, genetic trees, economies, rational decisions, aeroplanes, earthquakes, forest fires, irrigation systems, and the world’s climate. It's through these representations that we learn about the world. This entry explores various different accounts of scientific representation, with a particular focus on how scientific models represent their target systems. As philosophers of science are increasingly acknowledging the importance, if not the primacy, of scientific models as representational units of science, it's important to (...) stress that how they represent plays a fundamental role in how we are to answer other questions in the philosophy of science. This entry begins by disentangling ‘the’ problem of scientific representation, before critically evaluating the current options available in the literature. (shrink)

We examine the question of whether scientific theories can ever be complete. For two closely related reasons, we will argue that they cannot. The first reason is the inability to determine what are “valid empirical observations”, a result that is based on a self-reference Gödel/Tarski-like proof. The second reason is the existence of “meta-empirical” evidence of the inherent incompleteness of observations. These reasons, along with theoretical incompleteness, are intimately connected to the notion of belief and to theses within the philosophy (...) of science: the Quine-Duhem (and underdetermination) thesis and the observational/theoretical distinction failure. Some puzzling aspects of the philosophical theses will become clearer in light of these connections. Other results that follow are: no absolute measure of the informational content of empirical data, no absolute measure of the entropy of physical systems, and no complete computer simulation of the natural world are possible. The connections with the mathematical theorems of Gödel and Tarski reveal the existence of other connections between scientific and mathematical incompleteness: computational irreducibility, complexity, infinity, arbitrariness and self-reference. Finally, suggestions will be offered of where a more rigorous (or formal) “proof” of scientific incompleteness can be found. (shrink)