In the 1951 Gibbs lecture, Gödel asserted his famous dichotomy, where the notion of informal proof is at work. G. Priest developed an argument, grounded on the notion of naïve proof, to the effect that Gödel’s first incompleteness theorem suggests the presence of dialetheias. In this paper, we adopt a plausible ideal notion of naïve proof, in agreement with Gödel’s conception, superseding the criticisms against the usual notion of naïve proof used by real (...) working mathematicians. We explore the connection between Gödel’s theorem and naïve proof so understood, both from a classical and a dialetheic perspective. (shrink)

While non-classical theories of truth that take truth to be transparent have some obvious advantages over any classical theory that evidently must take it as non-transparent, several authors have recently argued that there's also a big disadvantage of non-classical theories as compared to their “external” classical counterparts: proof-theoretic strength. While conceding the relevance of this, the paper argues that there is a natural way to beef up extant internal theories so as to remove their proof-theoretic disadvantage. It is (...) suggested that the resulting internal theories should seem preferable to their external counterparts. (shrink)

There are passages in Kant’s writings according to which empirical intuitions have to be (a) singular, (b) object-dependent, and (c) immediate. It has also been argued that empirical intuitions (d) are not truth-apt, and (e) need to provide the subject with a proof of the possibility of the cognized object. Having relied on one or another of the a-e constraints, the naïve realist readers of Kant have argued that it is not possible for empirical intuitions to be representations. (...) Instead they have argued for a relationalist reading of empirical intuitions in terms of an acquaintance relation between the subject and the intuited object. -/- For the sake of argument, I will grant the naïve realist reader of Kant that empirical intuitions should satisfy all the a-e constraints. Nevertheless, by incorporating these constraints, one by one, into a representationalist theory of empirical intuitions, I will show that not only doesn’t a naïve realist reading of empirical intuitions follow, but also that the naïve realist has hastily overlooked a range of perfectly representationalist readings of intuitions available to Kant and his representationalist allies. On the positive side, I will argue that there is an extra constraint on intuitions—i.e., that givenness does not require presence to consciousness—that directly goes against any naïve realist account of intuitions. (shrink)

This paper presents a range of new triviality proofs pertaining to naïve truth theory formulated in paraconsistent relevant logics. It is shown that excluded middle together with various permutation principles such as A → (B → C)⊩B → (A → C) trivialize naïve truth theory. The paper also provides some new triviality proofs which utilize the axioms ((A → B)∧ (B → C)) → (A → C) and (A → ¬A) → ¬A, the fusion connective and the Ackermann (...) constant. An overview over various ways to formulate Leibniz’s law in non-classical logics and two new triviality proofs for naïve set theory are also provided. (shrink)

We defend hylomorphism against Maegan Fairchild’s purported proof of its inconsistency. We provide a deduction of a contradiction from SH+, which is the combination of “simple hylomorphism” and an innocuous premise. We show that the deduction, reminiscent of Russell’s Paradox, is proof-theoretically valid in classical higher-order logic and invokes an impredicatively defined property. We provide a proof that SH+ is nevertheless consistent in a free higher-order logic. It is shown that the unrestricted comprehension principle of property abstraction (...) on which the purported proof of inconsistency relies is analogous to naïve unrestricted set-theoretic comprehension. We conclude that logic imposes a restriction on property comprehension, a restriction that is satisfied by the ramified theory of types. By extension, our observations constitute defenses of theories that are structurally similar to SH+, such as the theory of singular propositions, against similar purported disproofs. (shrink)

In recent years there has been a revitalised interest in non-classical solutions to the semantic paradoxes. In this paper I show that a number of logics are susceptible to a strengthened version of Curry's paradox. This can be adapted to provide a proof theoretic analysis of the omega-inconsistency in Lukasiewicz's continuum valued logic, allowing us to better evaluate which logics are suitable for a naïve truth theory. On this basis I identify two natural subsystems of Lukasiewicz logic which (...) individually, but not jointly, lack the problematic feature. (shrink)

Substructural logics and their application to logical and semantic paradoxes have been extensively studied, but non-reflexive systems have been somewhat neglected. Here, we aim to fill this lacuna, at least in part, by presenting a non-reflexive logic and theory of naive consequence (and truth). We also investigate the semantics and the proof-theory of the system. Finally, we develop a compositional theory of truth (and consequence) in our non-reflexive framework.

Une preuve est pure si, en gros, elle ne réfère dans son développement qu’à ce qui est « proche » de, ou « intrinsèque » à l’énoncé à prouver. L’infinité des nombres premiers, un théorème classique de l’arithmétique, est un cas d’étude particulièrement riche pour les recherches philosophiques sur la pureté. Deux preuves différentes de ce résultat sont ici considérées, à savoir la preuve euclidienne classique et une preuve « topologique » plus récente proposée par Furstenberg. D’un point de vue (...) naïf, il semblerait que la première soit pure et la seconde impure. Des objections à cette vue naïve sont ici considérées et réfutées. Concernant la preuve euclidienne, la question relève de la logique, notamment de la définissabilité arithmétique de l’addition en termes de successeur et de divisibilité telle que démontrée par Julia Robinson, tandis qu’en ce qui concerne la preuve topologique, la question relève de la sémantique, notamment pour tout ce qui touche au problème de savoir ce qui est « inclus » dans le contenu d’énoncés particuliers.A proof is pure, roughly, if it draws only on what is « close » or « intrinsic » to the statement being proved. The infinitude of prime numbers, a classical theorem of arithmetic, is a rich case study for philosophical investigation of purity. Two different proofs of this result are considered, namely the classical Euclidean proof and a more recent « topological » proof by Furstenberg. Naively the former would seem to be pure and the latter to be impure. Objections to these naive views are considered and met. In the case of the former the issue rests on logical matters, specifically the arithmetic definability of addition in terms of successor and divisibility shown by Julia Robinson, while in the case of the latter the issue rests on semantic matters, specifically with respect to what is « contained » in the content of particular statements. (shrink)

Our visual experience seems to suggest that no continuous curve can cover every point of the unit square, yet in the late nineteenth century Giuseppe Peano proved that such a curve exists. Examples like this, particularly in analysis (in the sense of the infinitesimal calculus) received much attention in the nineteenth century. They helped instigate what Hans Hahn called a “crisis of intuition”, wherein visual reasoning in mathematics came to be thought to be epistemically problematic. Hahn described this “crisis” as (...) follows: Mathematicians had for a long time made use of supposedly geometric evidence as a means of proof in much too naive and much too uncritical a way, till the unclarities and mistakes that arose as a result forced a turnabout. Geometrical intuition was now declared to be inadmissible as a means of proof... (p. 67) Avoiding geometrical evidence, Hahn continued, mathematicians aware of this crisis pursued what he called “logicization”, “when the discipline requires nothing but purely logical fundamental concepts and propositions for its development.” On this view, an epistemically ideal mathematics would minimize, or avoid altogether, appeals to visual representations. This would be a radical reformation of past practice, necessary, according to its advocates, for avoiding “unclarities and mistakes” like the one exposed by Peano. (shrink)

Karl Pfeifer attempts to present a coherent view of panentheism that eschews Pickwickian senses of “in” and aligns itself with, and builds upon, familiar diagrammed portrayals of panentheism. The account is accordingly spatial-locative and moreover accepts the proposal of R.T. Mullins that absolute space and time be regarded as attributes of God. In addition, however, it argues that a substantive parthood relation between the world and God is required. Pfeifer’s preferred version of panpsychism, viz. panintentionalism, is thrown into the mix (...) as an optional add-on. On this account, God is conceived of as a “spiritual field” whose nature can be made more intelligible by regarding “God” as having a mass-noun sense in some contexts. Pfeifer closes with the suggestion that we look to topology and mereology for further development of the position outlined in his paper. (shrink)

Despite extensive discussion of naïve realism in the wider philosophical literature, those influenced by the phenomenological movement who work in the philosophy of perception have hardly weighed in on the matter. It is thus interesting to discover that Edmund Husserl’s close philosophical interlocutor and friend, the early twentieth-century phenomenologist Johannes Daubert, held the naive realist view. This article presents Daubert’s views on the fundamental nature of perceptual experience and shows how they differ radically from those of Husserl’s. The author (...) argues, in conclusion, that Daubert’s views are superior to those of Husserl’s specifically in the way that they deal with the phenomenon of perceptual constancy. (shrink)

It has been claimed that naïve realism predicts phenomenological similarities where there are none and, thereby, mischaracterises the phenomenal character of perceptual experience. If true, this undercuts a key motivation for the view. Here, we defend naïve realism against this charge, proposing that such arguments fail (three times over). In so doing, we highlight a more general problem with critiques of naïve realism that target the purported phenomenological predictions of the view. The problem is: naïve realism, (...) broadly construed, doesn’t make phenomenological predictions of the required sort. So, as a result, opponents must resign themselves to attacking specific incarnations of naïve realism, or approach matters quite differently. (shrink)

Visual experiences seem to exhibit phenomenological particularity: when you look at some object, it – that particular object – looks some way to you. But experiences exhibit generality too: when you look at a distinct but qualitatively identical object, things seem the same to you as they did in seeing the first object. Naïve realist accounts of visual experience have often been thought to have a problem with each of these observations. It has been claimed that naïve realist (...) views cannot account for the generality of visual experiences, and that the naïve realist explanation of particularity has unacceptable implications for self- knowledge: the knowledge we have of the character of our own experiences. We argue in this paper that neither claim is correct: naïve realism can explain the generality of experiences, and the naïve realist explanation of particularity raises no problems for our self-knowledge. (shrink)

Naïve Realists think that the ordinary mind-independent objects that we perceive are constitutive of the character of experience. Some understand this in terms of the idea that experience is diaphanous: that the conscious character of a perceptual experience is entirely constituted by its objects. My main goal here is to argue that Naïve Realists should reject this, but I’ll also highlight some suggestions as to how Naïve Realism might be developed in a non-diaphanous direction.

Early twentieth-century philosophers of perception presented their naïve realist views of perceptual experience in anti-Kantian terms. For they took naïve realism about perceptual experience to be incompatible with Kant’s claims about the way the understanding is necessarily involved in perceptual consciousness. This essay seeks to situate a naïve realist account of visual experience within a recognisably Kantian framework by arguing that a naïve realist account of visual experience is compatible with the claim that the understanding is (...) necessarily involved in the perceptual experience of those rational beings with discursive intellects. The resultant view is middle way between recent conceptualist and non-conceptualist interpretations of Kant, holding that the understanding is necessarily involved in the kind of perceptual consciousness that we, as rational beings, enjoy whilst allowing that the relations of apprehension which constitute perceptual consciousness are independent of acts of the understanding. (shrink)

Unconscious perceptions have recently become a focal point in the debate for and against naive realism. In this paper I defend the naive realist side. More specifically, I use an idea of Martin’s to develop a new version of naive realism—neuro-computational naive realism. I argue that neuro-computational naive realism offers a uniform treatment of both conscious and unconscious perceptions. I also argue that it accommodates the possibility of phenomenally different conscious perceptions of the same items, and that it can answer (...) a further challenge to naive realism raised by Berger and Nanay. (shrink)

Recently, it has been objected that naïve realism is inconsistent with an empirically well-supported claim that mental states of the same fundamental kind as ordinary conscious seeing can occur unconsciously (SFK). The main aim of this paper is to establish the following conditional claim: if SFK turns out to be true, the naïve realist can and should accommodate it into her theory. Regarding the antecedent of this conditional, I suggest that empirical evidence renders SFK plausible but not obvious. (...) For it is possible that what is currently advocated as unconscious perception of the stimulus is in fact momentaneous perceptual awareness (or residual perceptual awareness) of the stimulus making the subject prone to judge in some way rather than another, or to act in some way rather than another. As to the apodosis, I show that neither the core of naïve realism nor any of its main motivations is undermined if SFK is assumed. On the contrary, certain incentives for endorsing naïve realism become more tempting on this assumption. Since the main motivations for naïve realism retain force under SFK, intentionalism is neither compulsory nor the best available explanation of unconscious perception. (shrink)

It seems possible to see a star that no longer exists. Yet it also seems right to say that what no longer exists cannot be seen. We therefore face a puzzle, the traditional answer to which involves abandoning naïve realism in favour of a sense datum view. In this article, however, I offer a novel exploration of the puzzle within a naïve realist framework. As will emerge, the best option for naïve realists is to embrace an eternalist (...) view of time, and claim that in the relevant case, one sees a still existent star‐stage located somewhere in the distant past. (shrink)

It is well-known that naïve realism has difficulty accommodating perceptual error. Recent discussion of the issue has focused on whether the naïve realist can accommodate hallucination by adopting disjunctivism. However, illusions are more difficult for the naïve realist to explain precisely because the disjunctivist solution is not available. I discuss what I take to be the two most plausible accounts of illusion available to the naïve realist. The first claims that illusions are cases in which you (...) are prevented from perceiving properties you would ordinarily perceive and subsequently form a mistaken judgment about the perceived object. The second appeals to an unusual look or appearance that the perceived object instantiates. I argue that neither account is satisfactory and that, consequently, naïve realism ought to be rejected. (shrink)

This paper studies proof systems for the logics of super-strict implication ST2–ST5, which correspond to C.I. Lewis’ systems S2–S5 freed of paradoxes of strict implication. First, Hilbert-style axiomatic systems are introduced and shown to be sound and complete by simulating STn in Sn and backsimulating Sn in STn, respectively(for n=2,...,5). Next, G3-style labelled sequent calculi are investigated. It is shown that these calculi have the good structural properties that are distinctive of G3-style calculi, that they are sound and complete, (...) and it is shown that the proof search for G3. ST2 is terminating and therefore the logic is decidable. (shrink)

This paper elaborates on an argument in my book *Perception*. It has two parts. In the first part, I argue against what I call "basic" naive realism, on the grounds that it fails to accommodate what I call "internal dependence" and it requires an empirically implausible theory of sensible properties. Then I turn Craig French and Ian Phillips’ modified naïve realism as set out in their recent paper "Austerity and Illusion". It accommodates internal dependence. But it may retain the (...) empirically implausible theory of sensible properties. And it faces other empirical problems. Representationalism about experiences avoids those problems and is to be preferred. (shrink)

Perceptual experience has representational content. My argument for this claim is an inference to the best explanation. The explanandum is cognitive penetration. In cognitive penetration, perceptual experiences are either causally influenced, or else are partially constituted, by mental states that are representational, including: mental imagery, beliefs, concepts and memories. If perceptual experiences have representational content, then there is a background condition for cognitive penetration that renders the phenomenon prima facie intelligible. Naïve realist or purely relational accounts of perception leave (...) cognitive penetration less well-explained, even when formulated with so-called ‘standpoints’ or ‘third relata.’. (shrink)

Relationalism maintains that perceptual experience involves, as part of its nature, a distinctive kind of conscious perceptual relation between a subject of experience and an object of experience. Together with the claim that perceptual experience is presentational, relationalism is widely believed to be a core aspect of the naive realist outlook on perception. This is a mistake. I argue that naive realism about perception can be upheld without a commitment to relationalism.

In a recent paper, Berger and Nanay consider, and reject, three ways of addressing the phenomenon of unconscious perception within a naïve realist framework. Since these three approaches seem to exhaust the options open to naïve realists, and since there is said to be excellent evidence that perception of the same fundamental kind can occur, both consciously and unconsciously, this is seen to present a problem for the view. We take this opportunity to show that all three approaches (...) considered remain perfectly plausible ways of addressing unconscious perception within a naïve realist framework. So far from undermining the credibility of naïve realism, Berger and Nanay simply draw our attention to an important question to be considered by naïve realists in future work. Namely, which of the approaches considered is most likely to provide an accurate account of unconscious perception in each of its purported incarnations? (shrink)

Much of the discussion of Naive Realism about veridical experience has focused on a consequence of adopting it—namely, disjunctivism about perceptual experience. However, the motivations for being a Naive Realist in the first place have received relatively little attention in the literature. In this paper, I will elaborate and defend the claim that Naive Realism provides the best account of the phenomenal character of veridical experience.

Different authors offer subtly different characterizations of naïve realism. We disentangle the main ones and argue that illusions provide the best proving ground for naïve realism and its main rival, representationalism. According to naïve realism, illusions never involve per- ceptual error. We assess two leading attempts to explain apparent perceptual error away, from William Fish and Bill Brewer, and conclude that they fail. Another lead- ing attempt is assessed in a companion paper, which also sketches an alternative (...) representational account. (shrink)

Naive realists hold that experience is to be understood in terms of an intimate perceptual relation between a subject and aspects of the world, relative to a certain standpoint. Those aspects of the world themselves shape the contours of consciousness. But blurriness is an aspect of some of our experiences that does not seem to come from the world. I argue that this constitutes a significant challenge to some forms of naive realism. But I also argue that there is a (...) robust form of naive realism which is unfazed by the blurriness of some of our experiences, even when that blurriness is understood as a subjective modification of consciousness. (shrink)

This paper sets out a novel response to the ‘screening off problem’ for naïve realism. The aim is to resist the claim (which many naïve realists accept) that the kind of experience involved in hallucinating also occurs during perception, by arguing that there are causal constraints that must be met if an hallucinatory experience is to occur that are never met in perceptual cases. Notably, given this response, it turns out that, contra current orthodoxy, naïve realists need (...) not adopt any particular view about the psychological nature of hallucinatory experience to handle the screening off problem. Consequently, room opens up for naïve realists to endorse whatever theory of hallucinatory experience seems to best capture the distinctive nature of such episodes. (shrink)

I begin by describing what I call simple naïve realism. Then I describe relevant empirical results. Next, I develop two new empirical arguments against simple naive realism. Then I briefly look at two new, more complex forms of naïve realism: one due to Keith Allen and the other due to Heather Logue and Ori Beck. I argue that they are not satisfactory retreats for naive realists. The right course is to reject naive realism altogether. My stalking horse is (...) contemporary naive realism but there is a larger, positive lesson: new empirical results support a brain-based theory of sensory consciousness. (shrink)

Beall and Murzi :143–165, 2013) introduce an object-linguistic predicate for naïve validity, governed by intuitive principles that are inconsistent with the classical structural rules. As a consequence, they suggest that revisionary approaches to semantic paradox must be substructural. In response to Beall and Murzi, Field :1–19, 2017) has argued that naïve validity principles do not admit of a coherent reading and that, for this reason, a non-classical solution to the semantic paradoxes need not be substructural. The aim of (...) this paper is to respond to Field’s objections and to point to a coherent notion of validity which underwrites a coherent reading of Beall and Murzi’s principles: grounded validity. The notion, first introduced by Nicolai and Rossi, is a generalisation of Kripke’s notion of grounded truth, and yields an irreflexive logic. While we do not advocate the adoption of a substructural logic, we take the notion of naïve validity to be a legitimate semantic notion that points to genuine expressive limitations of fully structural revisionary approaches. (shrink)

It’s generally thought that we naively or pre-theoretically represent the future to be open. While philosophers have modelled future openness in different ways, it’s unclear which, if any, captures our naïve sense that the future is open. In this paper we focus on just one way the future might count as being open: by being nomically open, and empirically investigate whether our naïve representation of the future as open is partly constituted by representing the future as nomically open. (...) We also investigate the connection between our naïve representation of the future as open, and our representation of time. One of the purported advantages of the growing block theory of time is that it captures our naive sense that the future is open, and the past closed. We investigate whether there is an explanatory connection between people representing the future to be nomically open and representing our world to be a growing block and reflect on the implications of our findings for theorising about future openness and temporal ontology. (shrink)

The project of a 'naive physics' has been the subject of attention in recent years above all in the artificial intelligence field, in connection with work on common-sense reasoning, perceptual representation and robotics. The idea of a theory of the common-sense world is however much older than this, having its roots not least in the work of phenomenologists and Gestalt psychologists such as K hler, Husserl, Schapp and Gibson. This paper seeks to show how contemporary naive physicists can profit from (...) a knowledge of these historical roots of their discipline, which are shown to imply above alla critique of the set-theory-based models of reality typically presupposed by contemporary work in common-sense ontology [1]. (shrink)

Naïve realism, often overlooked among philosophical theories of perception, has in recent years attracted a surge of interest. Broadly speaking, the central commitment of naïve realism is that mind-independent objects are essential to the fundamental analysis of perceptual experience. Since the claims of naïve realism concern the essential metaphysical structure of conscious perception, its truth or falsity is of central importance to a wide range of topics, including the explanation of semantic reference and representational content, the nature (...) of phenomenal consciousness, and the basis of perceptual justification and knowledge. One of the greatest difficulties surrounding discussions of naïve realism, however, has been lack of clarity concerning exactly what affirming or denying it entails. In particular, it is sometimes unclear how naïve realism is related to the claim that perceptual experience is in some sense direct or unmediated, and also to what extent the view is compatible with another widely discussed thesis in the philosophy of perception, the claim that perceptual experiences are states with representational content. In this essay, I discuss how recent work on these issues helps to clarify both the central commitments of naïve realism, as well as its relation to representationalist theories of perception. Along the way, I will attempt to shed light on the different ways in which each approach tries to address the various theoretical challenges facing a philosophical theory of perception, and also to assess the prospects for views that attempts to combine features of each approach. (shrink)

This paper defends the idea that phenomenological approaches to self-consciousness can enrich the current analytic philosophy of perception, by showing how phenomenological discussions of minimal self-consciousness can enhance our understanding of the phenomenology of conscious perceptual experiences. As a case study, I investigate the nature of the relationship between naïve realism, a contemporary Anglophone theory of perception, and experiential minimalism (or, the ‘minimal self’ view), a pre-reflective model of self-consciousness originated in the Phenomenological tradition. I argue that naïve (...) realism is not only compatible with, but can be supplemented with experiential minimalism in a novel way. The suggestion is that there are reasons to combine naïve realism and experiential minimalism. My focus here will be on drawing a connection between the notion of minimal self and two core theoretical commitments of naïve realism, relationalism and transparency. (shrink)

Naïve realism (also called ‘relationalism’ or ‘object view’) is becoming increasingly popular, but the specific outline of its commitments remains often underspecified by proponents and misunderstood by critics. Naïve realism is associated with two claims, both concerning genuine, veridical perceptual experience (where this excludes hallucinations). Constitutive Claim (CC): The phenomenal character of perception is (partly) constituted by the mind-independent objects in one’s surrounding and their properties. Relational Claim (RC): Perception is a relation to mind-independent objects in the environment (...) and their properties. Some philosophers use the two claims interchangeably while talking about naïve realism, while others use only one or the other, although they do not explicitly discuss if the other claim is also a core commitment of naïve realism, or if naïve realism can be held without the other claim. This raises the question of how RC and CC relate to one another, together with the most pressing question of what each claim ultimately commits one to. After discussing the shortcomings of alternative interpretations, I argue that naïve realism should be understood as committed to, first and foremost, RC. This should be understood as a claim about the phenomenal character of perception, rather than about its nature, structure or essence (whatever that means). CC, on the other hand, should be understood as a corollary of RC. This doesn’t only offer a better characterisation of how naïve realists understand phenomenal character: it also helps us understand how we can simultaneously claim that the object of perception is a constitutive element of perception, while also allowing for it to play a causal role in determining perception. (shrink)

Neo-Russellians like Salmon and Braun hold that: the semantic contents of sentences are structured propositions whose basic components are objects and properties, names are directly referential terms, and a sentence of the form ‘n believes that S’ is true in a context c iff the referent of the name n in c believes the proposition expressed by S in c. This is sometimes referred to as ‘the Naive Russellian theory’. In this talk, I will discuss the Naive Russellian theory primarily (...) in connection with a problem known as Schiffer’s puzzle. Schiffer first presented the puzzle as an argument against the Naive Russellian theory. Schiffer’s argument proceeds in two steps. In step one, Schiffer argues that the Naive Russellian theory is committed to two principles regarding de re belief; the special-case consequence and Frege’s constraint. Then, in step two, Schiffer argues that the special-case consequence is not consistent with Frege’s constraint. Salmon and Braun reply to Schiffer’s argument that although the Naive Russellian theory is committed to Frege’s constraint, it is not committed to the special-case consequence. However, in this paper, I will argue with a new Schiffer-case that even if the Naive Russellian theory is not committed to the special-case consequence, it is still not consistent with Frege’s constraint. Concluding, I will discuss the possibility to reject Frege’s constraint within the Naive Russellian theory. (shrink)

Rejecting the Cut rule has been proposed as a strategy to avoid both the usual semantic paradoxes and the so-called v-Curry paradox. In this paper we consider if a Cut-free theory is capable of accurately representing its own notion of validity. We claim that the standard rules governing the validity predicate are too weak for this purpose and we show that although it is possible to strengthen these rules, the most obvious way of doing so brings with it a serious (...) problem: an internalized version of Cut can be proved for a Curry-like sentence. We also evaluate a number of possible ways of escaping this difficulty. (shrink)

Should we use the same standard of proof to adjudicate guilt for murder and petty theft? Why not tailor the standard of proof to the crime? These relatively neglected questions cut to the heart of central issues in the philosophy of law. This paper scrutinises whether we ought to use the same standard for all criminal cases, in contrast with a flexible approach that uses different standards for different crimes. I reject consequentialist arguments for a radically flexible standard (...) of proof, instead defending a modestly flexible approach on non-consequentialist grounds. The system I defend is one on which we should impose a higher standard of proof for crimes that attract more severe punishments. This proposal, although apparently revisionary, accords with a plausible theory concerning the epistemology of legal judgments and the role they play in society. (shrink)

This paper argues for the conjunctive thesis of naïve realism and phenomenal intentionalism about perceptual experiences. Naïve realism holds that the phenomenology of veridical perceptual experience is constituted by environmental objects that the subject perceives. Phenomenal intentionalism about perceptual experience states that perceptual experience has intentionality in virtue of its phenomenology. I first argue that naïve realism is not incompatible with phenomenal intentionalism. I then argue that phenomenal intentionalists can handle two objections to it by adopting (...) class='Hi'>naïve realism: the first objection is that phenomenal intentionalism cannot explain how a veridical perceptual experience is directed at a particular object rather than any other object of the same kind. The second objection is that phenomenal intentionalism cannot explain how a perceptual experience is directed at a type of external object rather than other types of objects without appealing to a resemblance relation between a perceptual experience and an external object, which is considered to be problematic. (shrink)

Nontransitive responses to the validity Curry paradox face a dilemma that was recently formulated by Barrio, Rosenblatt and Tajer. It seems that, in the nontransitive logic ST enriched with a validity predicate, either you cannot prove that all derivable metarules preserve validity, or you can prove that instances of Cut that are not admissible in the logic preserve validity. I respond on behalf of the nontransitive approach. The paper argues, first, that we should reject the detachment principle for naive validity. (...) Secondly, I show how to add a validity predicate to ST while avoiding the dilemma. (shrink)

Along with hallucinations and illusions, afterimages have shaped the philosophical debate about the nature of perception. Often referred to as optical or visual illusions, experiences of afterimages have been abundantly exploited by philosophers to argue against naïve realism. This paper offers an alternative account to this traditional view by providing a tentative account of the colors of the afterimages from an objectivist perspective. Contrary to the widespread approach to afterimages, this paper explores the possibility that the colors of afterimages (...) are not ontologically different from “ordinary” colors and that experiences of afterimages fail to provide a motivation for rejecting naïve realism. (shrink)

In this paper I will develop a lambda-term calculus, lambda-2Int, for a bi-intuitionistic logic and discuss its implications for the notions of sense and denotation of derivations in a bilateralist setting. Thus, I will use the Curry-Howard correspondence, which has been well-established between the simply typed lambda-calculus and natural deduction systems for intuitionistic logic, and apply it to a bilateralist proof system displaying two derivability relations, one for proving and one for refuting. The basis will be the natural deduction (...) system of Wansing's bi-intuitionistic logic 2Int, which I will turn into a term-annotated form. Therefore, we need a type theory that extends to a two-sorted typed lambda-calculus. I will present such a term-annotated proof system for 2Int and prove a Dualization Theorem relating proofs and refutations in this system. On the basis of these formal results I will argue that this gives us interesting insights into questions about sense and denotation as well as synonymy and identity of proofs from a bilateralist point of view. (shrink)

This paper develops the idea that valid arguments are equivalent to true conditionals by combining Kripke’s theory of truth with the evidential account of conditionals offered by Crupi and Iacona. As will be shown, in a first-order language that contains a naïve truth predicate and a suitable conditional, one can define a validity predicate in accordance with the thesis that the inference from a conjunction of premises to a conclusion is valid when the corresponding conditional is true. The validity (...) predicate so defined significantly increases our expressive resources and provides a coherent formal treatment of paradoxical arguments. (shrink)

Which rules for aggregating judgments on logically connected propositions are manipulable and which not? In this paper, we introduce a preference-free concept of non-manipulability and contrast it with a preference-theoretic concept of strategy-proofness. We characterize all non-manipulable and all strategy-proof judgment aggregation rules and prove an impossibility theorem similar to the Gibbard--Satterthwaite theorem. We also discuss weaker forms of non-manipulability and strategy-proofness. Comparing two frequently discussed aggregation rules, we show that “conclusion-based voting” is less vulnerable to manipulation than “premise-based (...) voting”, which is strategy-proof only for “reason-oriented” individuals. Surprisingly, for “outcome-oriented” individuals, the two rules are strategically equivalent, generating identical judgments in equilibrium. Our results introduce game-theoretic considerations into judgment aggregation and have implications for debates on deliberative democracy. (shrink)

The traditional view of evidence in mathematics is that evidence is just proof and proof is just derivation. There are good reasons for thinking that this view should be rejected: it misrepresents both historical and current mathematical practice. Nonetheless, evidence, proof, and derivation are closely intertwined. This paper seeks to tease these concepts apart. It emphasizes the role of argumentation as a context shared by evidence, proofs, and derivations. The utility of argumentation theory, in general, and argumentation (...) schemes, in particular, as a methodology for the study of mathematical practice is thereby demonstrated. Argumentation schemes represent an almost untapped resource for mathematics education. Notably, they provide a consistent treatment of rigorous and non-rigorous argumentation, thereby working to exhibit the continuity of reasoning in mathematics with reasoning in other areas. Moreover, since argumentation schemes are a comparatively mature methodology, there is a substantial body of existing work to draw upon, including some increasingly sophisticated software tools. Such tools have significant potential for the analysis and evaluation of mathematical argumentation. The first four sections of the paper address the relationships of evidence to proof, proof to derivation, argument to proof, and argument to evidence, respectively. The final section directly addresses some of the educational implications of an argumentation scheme account of mathematical reasoning. (shrink)

Many arguments against naïve realism are arguments against its corollary: disjunctivism. But there is a simpler argument—due to Mehta —that targets naïve realism directly. In broad strokes, the argument is the following. There are certain experiences that are, allegedly, in no way phenomenally similar. Nevertheless, naïve realism predicts that they are phenomenally similar. Hence, naïve realism is false. Mehta and Ganson successfully defend this argument from an objection raised by French and Gomes :451–460, 2016). However, all (...) parties to this dispute have missed the real problem with Mehta’s argument. As I see it, the real problem is twofold. First, despite his claims to the contrary, the experiences Mehta cites are phenomenally similar. Moreover, finding experiences that are in no way phenomenally similar turns out to be a difficult task. Second, there are motivated versions of naïve realism that are immune to Mehta’s argument. The upshot is that even if Mehta’s argument is sound, the most that it can show is that one version of naïve realism is false. (shrink)

The naive theory of properties states that for every condition there is a property instantiated by exactly the things which satisfy that condition. The naive theory of properties is inconsistent in classical logic, but there are many ways to obtain consistent naive theories of properties in nonclassical logics. The naive theory of classes adds to the naive theory of properties an extensionality rule or axiom, which states roughly that if two classes have exactly the same members, they are identical. In (...) this paper we examine the prospects for obtaining a satisfactory naive theory of classes. We start from a result by Ross Brady, which demonstrates the consistency of something resembling a naive theory of classes. We generalize Brady’s result somewhat and extend it to a recent system developed by Andrew Bacon. All of the theories we prove consistent contain an extensionality rule or axiom. But we argue that given the background logics, the relevant extensionality principles are too weak. For example, in some of these theories, there are universal classes which are not declared coextensive. We elucidate some very modest demands on extensionality, designed to rule out this kind of pathology. But we close by proving that even these modest demands cannot be jointly satisfied. In light of this new impossibility result, the prospects for a naive theory of classes are bleak. (shrink)

W dziełach Arystotelesa, lub z medievals, jak również w pismach późniejszych zdroworozsądkowe filozofów, takich jak Thomas Reid czy GE Moore’a, możemy znaleźć rodzinę różnych prób uporania się ze strukturami rozsądku i wspólnego -sense świat, który jest nam dany w normalnym, doświadczenie pre-teoretycznym. Będziemy argumentować, co wynika, że ​​teoria takich struktur stanowi ważny i dotychczas niedoceniany związek między wczesnym psychologii Gestalt z jednej strony, oraz współczesnych osiągnięć w filozofii i sztucznej inteligencji badań na innych.