Recent evidence in natural and semi-natural settings has revealed a variety of left-right perceptual asymmetries among vertebrates. These include preferential use of the left or right visual hemifield during activities such as searching for food, agonistic responses, or escape from predators in animals as different as fish, amphibians, reptiles, birds, and mammals. There are obvious disadvantages in showing such directional asymmetries because relevant stimuli may be located to the animal's left or right at random; there is no a priori association (...) between the meaning of a stimulus (e.g., its being a predator or a food item) and its being located to the animal's left or right. Moreover, other organisms (e.g., predators) could exploit the predictability of behavior that arises from population-level lateral biases. It might be argued that lateralization of function enhances cognitive capacity and efficiency of the brain, thus counteracting the ecological disadvantages of lateral biases in behavior. However, such an increase in brain efficiency could be obtained by each individual being lateralized without any need to align the direction of the asymmetry in the majority of the individuals of the population. Here we argue that the alignment of the direction of behavioral asymmetries at the population level arises as an “evolutionarily stable strategy” under “social” pressures occurring when individually asymmetrical organisms must coordinate their behavior with the behavior of other asymmetrical organisms of the same or different species. Key Words: asymmetry; brain evolution; brain lateralization; development; hemispheric specialization; laterality; lateralization of behavior; social behavior; theory of games. (shrink)

We present recent results on the model companions of set theory, placing them in the context of a current debate in the philosophy of mathematics. We start by describing the dependence of the notion of model companionship on the signature, and then we analyze this dependence in the specific case of set theory. We argue that the most natural model companions of set theory describe (as the signature in which we axiomatize set theory varies) theories of $H_{\kappa ^+}$, as $\kappa (...) $ ranges among the infinite cardinals. We also single out $2^{\aleph _0}=\aleph _2$ as the unique solution of the continuum problem which can (and does) belong to some model companion of set theory (enriched with large cardinal axioms). While doing so we bring to light that set theory enriched by large cardinal axioms in the range of supercompactness has as its model companion (with respect to its first order axiomatization in certain natural signatures) the theory of $H_{\aleph _2}$ as given by a strong form of Woodin’s axiom $(*)$ (which holds assuming $\mathsf {MM}^{++}$ ). Finally this model-theoretic approach to set-theoretic validities is explained and justified in terms of a form of maximality inspired by Hilbert’s axiom of completeness. (shrink)

We analyse Kit Fine’s proposal of a procedural Postulationism for mathematics. From a linguistic perspective, we argue that Postulationism is better understood in terms of declarative speech acts. Based on this observation, we argue in favor of a form of Declarationism able to account for both the objectivity of mathematics and its creative dimension.

This is an introductory paper to a series of results linking generic absoluteness results for second and third order number theory to the model theoretic notion of model companionship. Specifically we develop here a general framework linking Woodin’s generic absoluteness results for second order number theory and the theory of universally Baire sets to model companionship and show that (with the required care in details) a $$\Pi _2$$ -property formalized in an appropriate language for second order number theory is forcible (...) from some $$T\supseteq \mathsf {ZFC}+$$ large cardinals if and only if it is consistent with the universal fragment of T if and only if it is realized in the model companion of T. In particular we show that the first order theory of $$H_{\omega _1}$$ is the model companion of the first order theory of the universe of sets assuming the existence of class many Woodin cardinals, and working in a signature with predicates for $$\Delta _0$$ -properties and for all universally Baire sets of reals. We will extend these results also to the theory of $$H_{\aleph _2}$$ in a follow up of this paper. (shrink)

The importance of the comparative notion of versimilitude, or truthlikeness, for a realist conception of knowledge follows from two modest ‘realist’ assumptions, namely, that the aim of an enquiry, as an enquiry, is the truth of some matter; and that one false theory may realize this aim better than another. However, there seem to be two ways in which one (false) theory can realize this aim better than another. One (false) theory can be closer to the truth than another either (...) by being preponderantly more accurate in its predictions or by providing more comprehensive information about the system (or class of systems) at issue. This paper presents a model-theoretic approach to the analysis of the comprehensiveness-related component of the comparative notion of versimilitude. The machinery of the ‘semantic’ view of theories is applied to the problem of providing necessary and sufficient conditions for the truth of sentences of the form, ‘B is truth-increasing with respect to A’, where A and B are taken to be sets of structures. (shrink)

In this paper I outline an account of the structure of perceptual justification that develops Wittgenstein’s thought that the possibility of acquiring any degree of justification for our beliefs depends on placing certain propositions outside the route of empirical inquiry, turning them into the ‘hinges’ of our rational evaluations. The proposal is akin to ‘moderate’ accounts of the structure of perceptual justification, but it conjoins Wittgenstein’s insight with explanationist and contrastivist ideas, and so differs in important respects both from such (...) accounts and from other versions of hinge epistemology. I maintain that the basic presuppositions of the epistemic practice of taking experience at face value are not totally refractory to evidential assessment, arguing that they can receive some degree of second-order empirical justification via inference to the best explanation. And I address the worry that the account may face the problem of ‘easy knowledge’ by helping myself to the contrastivist view that empirical knowledge is best understood as a three-place, contrastive relation between an agent, a proposition (or fact) and a contrast. This leads me to replace the usual closure principles for epistemic justification and knowledge with corresponding contrastive principles, filling in the final details of contrastive hinge epistemology. (shrink)

Crispin Wright’s “Unified Strategy” for addressing some familiar sceptical paradoxes exploits a subtle distinction between two different ways in which we can be related to a proposition: (full-blown) belief and (mere) acceptance. The importance of the distinction for his strategy stems from his conviction that we cannot acquire any kind of evidence, either empirical or a priori, for the “cornerstones” of our cognitive projects, i.e., for those basic presuppositions of our inquiries that we must be warranted to endorse if we (...) are to claim warrant for any of the beliefs formed as a result of such inquiries: regarding the idea of a non-evidential warrant to believe a proposition as a kind of “conceptual solecism”, he doesn’t set himself the task of showing that we are evidentially warranted to believe such presuppositions, but only that of showing that we are non-evidentially warranted to accept them. In the present paper, I argue that such choice involves a fatal departure from a basic principle governing doxastic commitment—a principle that requires that we regard cornerstones propositions as propositions we are rationally committed to believe, not just entitled to accept. I press the point by presenting the Acceptance Argument, a sceptical paradox whose consideration leads to the conclusion that the Unified Strategy is caught between the Scylla of incoherently invoking a rather dubious form of epistemic alchemy and the Charybdis of placing an unexpected and apparently ad hoc restriction on the doxastic commitments we undertake by believing the things we believe. My final suggestion is that the Unified Strategy might be spared this dilemma only by undergoing a rather radical revision—a revision that would require setting aside the distinction between belief and acceptance to re-conceptualise its goal unabashedly in terms of (non-evidentially) warranted belief. (shrink)

This article develops a fresh approach to Jørgensen's Dilemma on the basis of Paul Horwich's “minimalist” view that our notion of truth is implicitly defined by the instances of the equivalence schema “The proposition that p is true if and only if p.” The “deflationary” claim that the truth predicate, far from referring to any deep property of propositions, merely plays the logical function of enabling us to take certain attitudes (e.g., acceptance or rejection) towards propositions the content of which (...) we are not completely acquainted with or do not want to state openly is argued to lend powerful support to the claim that normative reasoning is concerned with the “transmission” of truth and falsity in the very sense in which descriptive reasoning is commonly taken to be. This result is all the more valuable since the “minimal” sense in which normative propositions are ascribed the capability of being either true or false involves no questionable ontological commitment to the existence of a “world of norms” as opposed to the familiar world of objects and their properties. (shrink)

In this paper, I discuss the currently most popular argument for alethic pluralism, maintaining that the so-called scope problem provides no compelling reason for abandoning the traditional view that truth is one and the same (substantive) property across the various regions of thought or discourse in which it is ascribed or denied to the things we think or say. I disarm the argument by showing that the scope problem does not arise for a number of non-deflationary, monistic views of truth (...) that meet certain semantic and metaphysical constraints, for one can accept any of these views and provide a plausible account of the fact that mental and linguistic tokenings belonging to different regions of discourse involve radically different ways of engaging with reality? from detecting pre-existing facts to constituting them. (shrink)

Innateness of core knowledge mechanisms (in the form of “cognitive priors”) can be revealed by proper comparisons of altricial and precocial species. Cognitive priors and sensitive periods in their expression may also provide clues for the development of plausible artificial intelligence systems.

It is prima facie uncontroversial that the justification of an assertion amounts to a collection of other (inferentially related) assertions. In this paper, we point at a class of assertions, i.e. mathematical assertions, that appear to systematically flout this principle. To justify a mathematical assertion (e.g. a theorem) is to provide a proof—and proofs are sequences of directives. The claim is backed up by linguistic data on the use of imperatives in proofs, and by a pragmatic analysis of theorems and (...) their proofs. Proofs, we argue, are sequences of instructions whose performance inevitably gets one to truth. It follows that a felicitous theorem, i.e. a theorem that has been correctly proven, is a persuasive theorem. When it comes to mathematical assertions, there is no sharp distinction between illocutionary and perlocutionary success. (shrink)

Jakob Ohlhorst’s Trust Responsibly develops a dual process, virtue-theoretic answer to a crucial challenge to hinge epistemology, the so-called “demarcation problem” of distinguishing epistemically good from epistemically bad hinges. The book is packed with insightful ideas about many epistemological issues, offering carefully crafted arguments for a picture of knowledge that merges in an extremely attractive way hinge epistemology, virtue epistemology, and dual process theory. In this contribution to the book symposium on Trust Responsibly, I focus on Ohlhorst’s characterisation of cornerstone (...) propositions, his take on epistemic alchemy, and the internalist credentials of his answer to the sceptical challenge, raising some worries about these aspects of his account. (shrink)

The hypothesis that nonhuman species, lacking verbal language, do not really integrate information from different modules, but use instead information sequentially, appears difficult to put under empirical scrutiny. Evidence is discussed showing that in nonhuman species storing of geometric information occurs spontaneously even when landmark information suffices for spatial reorientation, suggesting simultaneous encoding, if not use, of information from different modules.

The stratification in depth of chromatically homogeneous overlapping figures depends on a minimization rule which assigns the status of being “in front” to the figure that requires the formation of shorter modal contours. This rule has been proven valid also in birds, whose visual neuroanatomy is radically different from that of other mammals, thus suggesting an example of evolutionary convergence toward a perceptual universal. [Shepard].

: In this article we analyze the key concept of Hilbert's axiomatic method, namely that of axiom. We will find two different concepts: the first one from the period of Hilbert's foundation of geometry and the second one at the time of the development of his proof theory. Both conceptions are linked to two different notions of intuition and show how Hilbert's ideas are far from a purely formalist conception of mathematics. The principal thesis of this article is that one (...) of the main problems that Hilbert encountered in his foundational studies consisted in securing a link between formalization and intuition. We will also analyze a related problem, that we will call "Frege's Problem", form the time of the foundation of geometry and investigate the role of the Axiom of Completeness in its solution. (shrink)