This paper argues that the traditional characterization of the notion of paradox — an apparently valid argument with apparently true premises and an apparently false conclusion — is too narrow; there are paradoxes that do not satisfy it. After discussing, and discarding, some alternatives, an outline of a new characterization of the notion of paradox is presented. A paradox is found to be an apparently valid argument such that, apparently, it does not present the kind of commitment to the conclusion (...) that should be implied by an acceptance of the truth of the premises and the validity of the argument. (shrink)

This article bears on four topics: observational predicates and phenomenal properties, vagueness, strict finitism as a philosophy of mathematics, and the analysis of feasible computability. It is argued that reactions to strict finitism point towards a semantics for vague predicates in the form of nonstandard models of weak arithmetical theories of the sort originally introduced to characterize the notion of feasibility as understood in computational complexity theory. The approach described eschews the use of nonclassical logic and related devices like degrees (...) of truth or supervaluation. Like epistemic approaches to vagueness, it may thus be smoothly integrated with the use of classical model theory as widely employed in natural language semantics. But unlike epistemicism, the described approach fails to imply either the existence of sharp boundaries or the failure of tolerance for soritical predicates. Applications ofmeasurement theory(in the sense of Krantz, Luce, Suppes, & Tversky (1971)) to vagueness in the nonstandard setting are also explored. (shrink)

There is a trade-off between specificity and accuracy in existing models of belief. Descriptions of agents in the tripartite model, which recognizes only three doxastic attitudes—belief, disbelief, and suspension of judgment—are typically accurate, but not sufficiently specific. The orthodox Bayesian model, which requires real-valued credences, is perfectly specific, but often inaccurate: we often lack precise credences. I argue, first, that a popular attempt to fix the Bayesian model by using sets of functions is also inaccurate, since it requires us to (...) have interval-valued credences with perfectly precise endpoints. We can see this problem as analogous to the problem of higher order vagueness. Ultimately, I argue, the only way to avoid these problems is to endorse Insurmountable Unclassifiability. This principle has some surprising and radical consequences. For example, it entails that the trade-off between accuracy and specificity is in-principle unavoidable: sometimes it is simply impossible to characterize an agent’s doxastic state in a way that is both fully accurate and maximally specific. What we can do, however, is improve on both the tripartite and existing Bayesian models. I construct a new model of belief—the minimal model—that allows us to characterize agents with much greater specificity than the tripartite model, and yet which remains, unlike existing Bayesian models, perfectly accurate. (shrink)

The dissertation has two parts, each dealing with a problem, namely: 1) What is the most adequate account of fuzziness -the so-called phenomenon of vagueness?, and 2) what is the most plausible solution to the sorites, or heap paradox? I will try to show that fuzzy properties are those which are gradual, amenable to be possessed in a greater or smaller extent. Acknowledgement of degrees in the instantiation of a property allows for a gradual transition from one opposite to the (...) other, each intermediate stage constituting an overlap in certain proportion of both contraries. Hence, degrees in the possession of a property give rise to simple contradictions. The reason why I have chosen those two questions is that they provide the main philosophical motivation for a particular brand of an infinite valued and paraconsistent logic. I will claim that Classical logic (CL) is not adequate to handle fuzzy situations, and, being deficient, is in need of being expanded to make room for degrees of truth and weak contradictions. One can hardly deny the importance of the debate, since what is ultimately at stake is what the limits of truth, rationality, intelligibility and possibility are. The main disciplines within which the research moves are the philosophy of language, philosophy of logic, and ontology. (shrink)

A solution to the sorites paradox is obtained by distinguishing three formats of the sorites argument and appraising them in the light of four fundamental considerations: (i) the appropriate notion of truth for the application of vague predicates to their borderline cases, (ii) a certain construal of borderline cases, (iii) a certain freedom of use of vague terms not enjoyed by non-Vague terms and (iv) the revocation of that freedom by deductive contexts.

This book proposes a new solution to the problem of vagueness. There are several different ways of addressing this problem and no clear agreement on which one is correct. The author proposes that it should be understood as the problem of explaining vague predicates in a way that systematizes six intuitions about the phenomenon and satisfies three criteria of adequacy for an ideal theory of vagueness. The third criterion, which is called the “criterion of precisification”, is the most controversial one. (...) It is based on the intuition that a predicate is vague only if it is imprecise. The author considers some different definitions of linguistic imprecision, proposing that a predicate is imprecise if and only if there is no sharp boundary between objects to which its application yields some particular truth-value and objects to which its application does not yield that truth-value. The volume critically reviews the current theories of vagueness and proposes a new one, the Theory of Vagueness as Arbitrariness, which defines a vague predicate as an arbitrary predicate that must be precisified in order to contribute to a sentence that has truth-conditions. The main advantages of this theory over the current alternatives are that it satisfies all three criteria and systematizes the relevant intuitions. (shrink)

Colin Howson argues that (1) my sociologistic reliabilism sheds no light on the objectivity of epistemic content, and that (2) sorites does not threaten the reliability of modus ponens . I reply that argument (1) misrepresents my position, and that argument (2) is beside the point.

The Stoics’ theory of kataleptic impressions looks different once we attend to their analysis of the Sorites paradox. In defending this view, I reject the long-standing assumption that the Stoics develop their theory by focusing on sensory impressions. The Stoic approach to vagueness shows, for example, that non-sensory impressions can be seemingly indistinguishable by belonging to a series. It also draws attention to an understudied dimension of Stoic theory: in aiming to assent only to kataleptic impressions, one aims to avoid (...) not only assent to false impressions but also assent to those that are neither true nor false. (shrink)

The noctes Atticae of Aulus Gellius contain almost all the ancient paradoxes. Nevertheless, in comparison with his philosophical sources, the author shows a shift in the perspective of his approach. He analyses the `master argument' of Diodorus Chronus only from an ethical point of view and, among the seven paradoxes attributed to Eubulides of Milet, he quotes the `heap' as an absurdity (absurdum), the `horned one' and the `not-someone' as a trap (captio), the `liar' as a sophism (sophisma). Following the (...) advice of Cynics, Gellius mistrusts deceptive manoeuvres, which highlight gaps in binary logic. At the same time, however, he is interested in argumentative structures, which lead one of two opponents on to victory. The extensive report of the quarrel between Protagoras and Evathlus, and many observations of Gellius on convertible forms of reasoning in literary texts fall within this rhetorical field. (shrink)

The author argues that ancient Skepticism may be most suited to deal with two crises in the Age of COVID-19: both the physical or epidemiological aspects of the pandemic, and the epistemological and ethical crisis of increasing disbelief in the sciences. Following Michel Bitbol, I suggest one way to mitigate this crisis of faith may be for science to become more epistemically modest, renouncing some of its claims to describe reality as it objectively is, and adopting an “intransitive” rather than (...) a “transitive” approach to Nature. This was the attitude adopted by the Greco-Roman medical school of the Empirics, which may also be of assistance in combatting the urgent problem of Fake News. The epistemology of Skepticism and the scientific methodology of the closely related Medical Empiricism shows that an epistemically modest, non-interventionist approach to science is quite compatible with a robust and sophisticated proto-experimental scientific methodology. (shrink)

Q: What did the elephant say to the naked man?A: It looks O.K., but can you breathe through it?Let me begin by justifying that joke for those of you didn’t find it funny. The relationship between the morphology of the physical organs and their activities has long been a vexed issue in the philosophy of biology: the question of whether structure determines function is of course of contemporary importance in evolutionary theory. That there was a relationship between structure and function (...) was not in general a matter of doubt to the Greek theoretical biologists: but both the extent, and crucially the direction, of the dependence was. And the question need not be restricted to a consideration of the function of a particular part in isolation: when Aristotle takes issue with Anaxagoras for asserting that humans are the most intelligent species because they have hands, claiming rather that they have hands because they are intelligent, he is making a claim not just about the direction of explanation involved, but he is also implicitly at least indicating the scope of such explanations. For Aristotle, intelligence is one of the human functions: and that function necessitates the existence and development of certain organic structures. (shrink)

On the epistemic view of vagueness, a vague expression has sharp boundaries whose location speakers of the language cannot recognize. The paper argues that one of the deepest sources of resistance to the epistemic view is the idea that all truths are cognitively accessible from truths in a language for natural science, conceived as precise, in a sense explained. The implications of the epistemic view for issues about the relations between vague predicates and scientific predicates are investigated.

In this paper I develop a semantic theory of vagueness that is immune to worries regarding the use of precise mathematical tools. I call this view semantic quietism. This view has the advantage of being clearly compatible with the phenomenon of vagueness. The cost is that it cannot capture every robust semantic fact.

Q: What did the elephant say to the naked man?A: It looks O.K., but can you breathe through it?Let me begin by justifying that joke for those of you didn’t find it funny. The relationship between the morphology of the physical organs and their activities has long been a vexed issue in the philosophy of biology: the question of whether structure determines function is of course of contemporary importance in evolutionary theory. That there was a relationship between structure and function (...) was not in general a matter of doubt to the Greek theoretical biologists: but both the extent, and crucially the direction, of the dependence was. And the question need not be restricted to a consideration of the function of a particular part in isolation: when Aristotle takes issue with Anaxagoras for asserting that humans are the most intelligent species because they have hands, claiming rather that they have hands because they are intelligent, he is making a claim not just about the direction of explanation involved, but he is also implicitly at least indicating the scope of such explanations. For Aristotle, intelligence is one of the human functions: and that function necessitates the existence and development of certain organic structures. (shrink)

This volume analyzes and studies how vagueness occurs and matters as a specific problem in the context of theories that are primarily about something else.