This note clarifies an error in the proof of the main theorem of “The Ricean Objection: An Analogue of Rice’s Theorem for First-Order Theories”, Logic Journal of the IGPL, 16(6): 585–590(2008).

I consider the first-order modal logic which counts as valid those sentences which are true on every interpretation of the non-logical constants. Based on the assumptions that it is necessary what individuals there are and that it is necessary which propositions are necessary, Timothy Williamson has tentatively suggested an argument for the claim that this logic is determined by a possible world structure consisting of an infinite set of individuals and an infinite set of worlds. He notes that (...) only the cardinalities of these sets matters, and that not all pairs of infinite sets determine the same logic. I use so-called two-cardinal theorems from model theory to investigate the space of logics and consequence relations determined by pairs of infinite sets, and show how to eliminate the assumption that worlds are individuals from Williamson’s argument. (shrink)

The logics of formal inconsistency (LFIs, for short) are paraconsistent logics (that is, logics containing contradictory but non-trivial theories) having a consistency connective which allows to recover the ex falso quodlibet principle in a controlled way. The aim of this paper is considering a novel semantical approach to first-order LFIs based on Tarskian structures defined over swap structures, a special class of multialgebras. The proposed semantical framework generalizes previous aproaches to quantified LFIs presented in the literature. The (...) case of QmbC, the simpler quantified LFI expanding classical logic, will be analyzed in detail. An axiomatic extension of QmbC called QLFI1o is also studied, which is equivalent to the quantified version of da Costa and D'Ottaviano 3-valued logic J3. The semantical structures for this logic turn out to be Tarkian structures based on twist structures. The expansion of QmbC and QLFI1o with a standard equality predicate is also considered. (shrink)

Panqualityism, recently defended by Sam Coleman, is a variety of Russellian monism on which the categorical properties of fundamental physical entities are qualities, or, in Coleman’s exposition, unconscious qualia. Coleman defends a quotationalist, higher-order thought version of panqualityism. The aim of this paper is, first, to demonstrate that a first-order representationalist panqualityism is also available, and to argue positively in its favor. For it shall become apparent that quotationalist and first-order representationalist panqualityism are, in (...) spite of their close similarities, radically different theories: quotationalist panqualityism locates qualities in the subject of an experience, while first-order panqualityism locates qualities in the world. I argue that this makes quotationalist panqualityism implausible and first-order, representationalist panqualityism a highly natural, elegant, and intuitive theory. (shrink)

In this paper paraconsistent first-order logic LP^{#} with infinite hierarchy levels of contradiction is proposed. Corresponding paraconsistent set theory KSth^{#} is discussed.Axiomatical system HST^{#}as paraconsistent generalization of Hrbacek set theory HST is considered.

We discuss cases where subjects seem to enjoy conscious experience when the relevant first-order perceptual representations are either missing or too weak to account for the experience. Though these cases are originally considered to be theoretical possibilities that may be problematical for the higher-order view of consciousness, careful considerations of actual empirical examples suggest that this strategy may backfire; these cases may cause more trouble for first-order theories instead. Specifically, these cases suggest that (I) (...) recurrent feedback loops to V1 are most likely not the neural correlate of first-order representations for conscious experience, (II) first-order views seem to have a problem accounting for the phenomenology in these cases, and either (III) a version of the ambitious higher-order approach is superior in that it is the simplest theory that can account for all results at face value, or (IV) a view where phenomenology is jointly determined by both first-order and higher-order states. In our view (III) and (IV) are both live options and the decision between them may ultimately be an empirical question that cannot yet be decided. (shrink)

A uniform construction for sequent calculi for finite-valued first-order logics with distribution quantifiers is exhibited. Completeness, cut-elimination and midsequent theorems are established. As an application, an analog of Herbrand’s theorem for the four-valued knowledge-representation logic of Belnap and Ginsberg is presented. It is indicated how this theorem can be used for reasoning about knowledge bases with incomplete and inconsistent information.

This article addresses the recent reception of Franz Brentano's writings on consciousness. I am particularly interested in the connection established between Brentano's theory of consciousness and higher-order theories of consciousness and, more specifically, the theory proposed by David Rosenthal. My working hypothesis is that despite the many similarities that can be established with Rosenthal's philosophy of mind, Brentano's theory of consciousness differs in many respects from higher-order theories of consciousness and avoids most of the criticisms generally (...) directed to them. This article is divided into eight parts. The first two sections expound the basic outline of Rosenthal's theory, and the third summarizes the principal objections that Rosenthal addresses to Brentano, which I, then, examine in sections 4 and 5. In sections 6 and 7, I discuss Brentano's principle of the unity of consciousness, and in section 8, I consider the scope of the changes that Brentano brings to his theory of consciousness in his later writings, which follow the 1874 publication of Psychology. I then draw the conclusion that Brentano's theory rests on a view of intransitive and intrinsic self-consciousness. (shrink)

In his book Modal Logic as Metaphysics, Timothy Williamson defends first-order necessitism using simplicity as a powerful argument. However, simplicity is decomposed into two different, even antagonistic, sides: elegance and parsimony. On the one hand, elegance is the property of theories possessing few and simple principles that allow them to deploy all their theoretical power; on the other hand, parsimony is the property of theories having the fair and necessary number of ontological entities that allow such (...) theories give an account of themselves. Since necessitism endorses Barcan Formulae for the sake of elegance, it is committed to a vast number of contingently non-concrete objects, so one may think that it is not qualitatively parsimonious. I argue that necessitism could be viewed as an additive case in the sense that Alan Baker characterizes the adjective so quantitative parsimony should be considered when it comes to necessitism instead of qualitative parsimony. (shrink)

In 1942 Haskell B. Curry presented what is now called Curry's paradox which can be found in a logic independently of its stand on negation. In recent years there has been a revitalised interest in non-classical solutions to the semantic paradoxes. In this article the non-classical resolution of Curry’s Paradox and Shaw-Kwei' sparadox without rejection any contraction postulate is proposed. In additional relevant paraconsistent logic C ̌_n^#,1≤n<ω, in fact,provide an effective way of circumventing triviality of da Costa’s paraconsistent Set (...) class='Hi'>Theories〖NF〗n^C. (shrink)

According to higher-order theories of consciousness, a mental state is conscious only when represented by another mental state. Higher-order theories must predict there to be some brain areas (or networks of areas) such that, because they produce (the right kind of) higher-order states, the disabling of them brings about deficits in consciousness. It is commonly thought that the prefrontal cortex produces these kinds of higher-order states. In this paper, I first argue that this (...) is likely correct, meaning that, if some higher-order theory is true, prefrontal lesions should produce dramatic deficits in visual consciousness. I then survey prefrontal lesion data, looking for evidence of such deficits. I argue that no such deficits are to be found, and that this presents a compelling case against higher-order theories. (shrink)

It is widely taken that the first-order part of Frege's Begriffsschrift is complete. However, there does not seem to have been a formal verification of this received claim. The general concern is that Frege's system is one axiom short in the first-order predicate calculus comparing to, by now, the standard first-order theory. Yet Frege has one extra inference rule in his system. Then the question is whether Frege's first-order calculus is still deductively (...) sufficient as far as the first-order completeness is concerned. In this short note we confirm that the missing axiom is derivable from his stated axioms and inference rules, and hence the logic system in the Begriffsschrift is indeed first-order complete. (shrink)

Proponents of the higher‐order (HO) theory of consciousness (e.g., Lau and Rosenthal) have recently appealed to brain lesion evidence to support their thesis that mental states are conscious when and only when represented by other mental states. This article argues that this evidence fails to support HO theory, doing this by first determining what kinds of conscious deficit should result when HO state‐producing areas are damaged, then arguing that these kinds of deficit do not occur in the studies (...) to which HO theorists appeal. The article also develops an apparatus that can be used to evaluate whether other lesion evidence confirms or disconfirms HO theory. (shrink)

Interesting as they are by themselves in philosophy and mathematics, paradoxes can be made even more fascinating when turned into proofs and theorems. For example, Russell’s paradox, which overthrew Frege’s logical edifice, is now a classical theorem in set theory, to the effect that no set contains all sets. Paradoxes can be used in proofs of some other theorems—thus Liar’s paradox has been used in the classical proof of Tarski’s theorem on the undefinability of truth in sufficiently rich languages. This (...) paradox (as well as Richard’s paradox) appears implicitly in Gödel’s proof of his celebrated first incompleteness theorem. In this paper, we study Yablo’s paradox from the viewpoint of first- and second-order logics. We prove that a formalization of Yablo’s paradox (which is second order in nature) is non-first-orderizable in the sense of George Boolos (1984). (shrink)

According to what Birch (2022) calls the theory-heavy approach to investigating nonhuman-animal consciousness, we select one of the well-developed theories of consciousness currently debated within contemporary cognitive science and investigate whether animals exhibit the neural structures or cognitive abilities posited by that theory as sufficient for consciousness. Birch argues, however, that this approach is in general problematic because it faces what he dubs the dilemma of demandingness—roughly, that we cannot use theories that are based on the human case (...) to assess consciousness in nonhuman animals and vice versa. We argue here that, though this dilemma may problematize the application of many current accounts of consciousness to nonhuman animals, it does not challenge the use of standard versions of the higher-order thought theory (“HOTT”) of consciousness, according to which a creature is in a conscious mental state just in case it is aware of being in that state via a suitable higher-order thought (“HOT”). We show this in two ways. First, we argue that, unlike many extant theories of consciousness, HOTT is typically motivated by a commonsense, and more importantly, neutral condition on consciousness that applies to humans and animals alike. Second, we offer new empirical and theoretical reasons to think that many nonhuman animals possess the relevant HOTs necessary for consciousness. Considering these issues not only reveals the explanatory power of HOTT and some of its advantages over rival accounts, but also enables us to further extend and clarify the theory. (shrink)

Given a class of linear order types C, we identify and study several different classes of trees, naturally associated with C in terms of how the paths in those trees are related to the order types belonging to C. We investigate and completely determine the set-theoretic relationships between these classes of trees and between their corresponding first-order theories. We then obtain some general results about the axiomatization of the first-order theories of some (...) of these classes of trees in terms of the first-order theory of the generating class C, and indicate the problems obstructing such general results for the other classes. These problems arise from the possible existence of nondefinable paths in trees, that need not satisfy the first-order theory of C, so we have started analysing first order definable and undefinable paths in trees. (shrink)

The English Synopsis is after the text of the book. The book presents an original and generalizing substantive vision of the philosophy of science through the prism of a detailed analysis of the polysystem structure of scientific theories. Theories are considered, firstly, as complex specialized forms of developed scientific thinking about the realities studied by natural science, secondly, as constantly improving tools for producing new knowledge in interaction with experimental research, and thirdly, as carriers of ordered and verified (...) knowledge. Emphasis is placed on their nominal and ontic subsystems. The book develops personal and joint research of the authors (theoretical physicist and philosopher), the experience of teaching philosophy of physics at NaUKMA, philosophy of science at the Higher School of Philosophy at the H. Skovoroda Institute of Philosophy of the National Academy of Sciences of Ukraine and theoretical physics at the National Technical University "Ihor Sikorsky Kyiv Polytechnic Institute". The research is based on a significant source base covering works of modern Western researchers in natural science and philosophy of science. For students, teachers, and scientists who are interested in the problems of modern philosophy of science and have a certain amount of scientific knowledge. It will also be useful for high school students who are eager to become scientists. (shrink)

Provided here is an account, both syntactic and semantic, of first-order and monadic second-order quantification theory for domains that may be non-atomic. Although the rules of inference largely parallel those of classical logic, there are important differences in connection with the identification of argument places and the significance of the identity relation.

The massive debate in philosophy and psychology and neuroscience about higher-order theories of consciousness has not adequately distinguished between the following two claims. (Necessary Awareness): For any conscious mental state M and subject S, if S is in M, then S is aware of M. (The Higher-Order Theory): For any conscious mental state M and subject S, if S is in M, then M is conscious because S is aware of M. -/- While I will assume that (...) the first claim is true, I will argue that we should reject higher-order theories of consciousness. We should turn them on their head to go with the following theory: (The Ascending Road): For any conscious mental state M and subject S, if S is in M, then S is aware of M because M is conscious. (shrink)

We study the first-order theories of some natural and important classes of coloured trees, including the four classes of trees whose paths have the order type respectively of the natural numbers, the integers, the rationals, and the reals. We develop a technique for approximating a tree as a suitably coloured linear order. We then present the first-order theories of certain classes of coloured linear orders and use them, along with the approximating technique, (...) to establish complete axiomatisations of the four classes of trees mentioned above. (shrink)

This chapter provides an introduction to higher-order metaphysics as well as to the contributions to this volume. We discuss five topics, corresponding to the five parts of this volume, and summarize the contributions to each part. First, we motivate the usefulness of higher-order quantification in metaphysics using a number of examples, and discuss the question of how such quantifiers should be interpreted. We provide a brief introduction to the most common forms of higher-order logics used in (...) metaphysics, and indicate a number of questions which can be raised in such systems using logical vocabulary alone. Using a further example, we return to applications of higher-order logics in metaphysics. We also mention key developments in the history of higher-order logic as it pertains to metaphysics. Finally, we mention certain arguments which have been raised against the use of higher-order logic, and some ways of responding to them. (shrink)

Theorists have long debated whether John Rawls’ conception of justice as fairness can be extended to nonideal (i.e. unjust) social and political conditions, and if so, what the proper way of extending it is. This paper argues that in order to properly extend justice as fairness to nonideal conditions, Rawls’ most famous innovation – the original position – must be reconceived in the form of a “nonideal original position.” I begin by providing a new analysis of the ideal/nonideal theory (...) distinction within Rawls’ theoretical framework. I then systematically construct a nonideal original position, showing that although its parties must have Rawls’ principles of ideal justice and priority relations as background aims, the parties should be entirely free to weigh those aims against whatever burdens and benefits they might face under nonideal conditions. Next, I show that the parties ought to aim to secure for themselves a special class of nonideal primary goods: all-purpose goods similar to Rawls’ original primary goods, but which in this case are all-purpose goods individuals might use to (A) promote Rawlsian ideals under nonideal conditions, (B) weigh Rawls’ principles of ideal justice and priority relations against whatever burdens and benefits they might face under nonideal conditions, and (C) effectively pursue their most favored weighting thereof. I then defend a provisional list of nonideal primary goods which include opportunities to participate effectively in equitable and inclusive grassroots reform movements guided by a series of substantive aims. Finally, I briefly speculate on how the parties to the nonideal original position might deliberate to principles of nonideal justice for distributing nonideal primary goods, suggesting that those goods should be distributed in proportion to unjust disadvantage. (shrink)

This paper argues that, given the representational theory of mind, one cannot know a priori that one knows that p as opposed to being incapable of having any knowledge states; but one can know a priori that one knows that p as opposed to some other proposition q.

W. V. Quine famously defended two theses that have fallen rather dramatically out of fashion. The first is that intensions are “creatures of darkness” that ultimately have no place in respectable philosophical circles, owing primarily to their lack of rigorous identity conditions. However, although he was thoroughly familiar with Carnap’s foundational studies in what would become known as possible world semantics, it likely wouldn’t yet have been apparent to Quine that he was fighting a losing battle against intensions, due (...) in large measure to developments stemming from Carnap’s studies and culminating in the work of Kripke, Hintikka, and Bayart. These developments undermined Quine’s crusade against intensions on two fronts. First, in the context of possible world semantics, intensions could after all be given rigorous identity conditions by defining them (in the simplest case) as functions from worlds to appropriate extensions, a fact exploited to powerful and influential effect in logic and linguistics by the likes of Kaplan, Montague, Lewis, and Cresswell. Second, the rise of possible world semantics fueled a strong resurgence of metaphysics in contemporary analytic philosophy that saw properties and propositions widely, fruitfully, and unabashedly adopted as ontological primitives in their own right. This resurgence — happily, in my view — continues into the present day. -/- For a time, at any rate, Quine experienced somewhat better success with his second thesis: that higher-order logic is, at worst, confused and, at best, a quirky notational alternative to standard first-order logic. However, Quine notwithstanding, a great deal of recent work in formal metaphysics transpires in a higher-order logical framework in which properties and propositions fall into an infinite hierarchy of types of (at least) every finite order. Initially, the most philosophically compelling reason for embracing such a framework since Russell first proposed his simple theory of types was simply that it provides a relatively natural explanation of the paradoxes. However, since the seminal work of Prior there has been a growing trend to consider higher-order logic to be the most philosophically natural framework for metaphysical inquiry, many of the contributors to this volume being among the most important and influential advocates of this view. Indeed, this is now quite arguably the dominant view among formal metaphysicians. -/- In this paper, and against the current tide, I will argue in §1 that there are still good reasons to think that Quine’s second battle is not yet lost and that the correct framework for logic is first-order and type-free — properties and propositions, logically speaking, are just individuals among others in a single domain of quantification — and that it arises naturally out of our most basic logical and semantical intuitions. The data I will draw upon are not new and are well-known to contemporary higher-order metaphysicians. However, I will try to defend my thesis in what I believe is a novel way by suggesting that these basic intuitions ground a reasonable distinction between “pure” logic and non-logical theory, and that Russell-style semantic paradoxes of truth and exemplification arise only when we move beyond the purely logical and, hence, do not of themselves provide any strong objection to a type-free conception of properties and propositions. -/- Most of my arguments in §1 are largely independent of any specific account of the nature of properties and propositions beyond their type-freedom. However, I will in addition argue that there are good reasons to take propositions, at least, to be very fine-grained. My arguments are thus bolstered significantly if it can be shown that there are in fact well-defined examples of logics that are not only type-free but which comport with such a conception of propositions. It is the purpose of §2 to lay out a logic of this sort in some detail, drawing especially upon work by George Bealer and related work of my own. With the logic in place, it will be possible to generalize the line of argument noted above regarding Russell-style paradoxes and, in §3, apply it to two propositional paradoxes — the Prior-Kaplan paradox and the Russell-Myhill paradox — that are often taken to threaten the sort of account developed here. (shrink)

Conscious mental states are states we are in some way aware of. I compare higher-order theories of consciousness, which explain consciousness by appeal to such higher-order awareness (HOA), and first-order theories, which do not, and I argue that higher-order theories have substantial explanatory advantages. The higher-order nature of our awareness of our conscious states suggests an analogy with the metacognition that figures in the regulation of psychological processes and behaviour. I argue (...) that, although both consciousness and metacognition involve higher-order psychological states, they have little more in common. One thing they do share is the possibility of misrepresentation; just as metacognitive processing can misrepresent one’s cognitive states and abilities, so the HOA in virtue of which one’s mental states are conscious can, and sometimes does, misdescribe those states. A striking difference between the two, however, has to do with utility for psychological processing. Metacognition has considerable benefit for psychological processing; in contrast, it is unlikely that there is much, if any, utility to mental states’ being conscious over and above the utility those states have when they are not conscious. (shrink)

A first-order theory T has the Independence Property provided deduction of a statement of type (quantifiers) (P -> (P1 or P2 or .. or Pn)) in T implies that (quantifiers) (P -> Pi) can be deduced in T for some i, 1 <= i <= n). Variants of this property have been noticed for some time in logic programming and in linear programming. We show that a first-order theory has the Independence Property for the class of (...) basic formulas provided it can be axiomatized with Horn sentences. The existence of free models is a useful intermediate result. The independence Property is also a tool to decide that a sentence cannot be deduced. We illustrate this with the case of the classical Caratheodory theorem for Pasch-Peano geometries. (shrink)

Subverting a once widely held Quinean paradigm, there is a growing consensus among philosophers of logic that higher-order quantifiers (which bind variables in the syntactic position of predicates and sentences) are a perfectly legitimate and useful instrument in the logico-philosophical toolbox, while neither being reducible to nor fully explicable in terms of first-order quantifiers (which bind variables in singular term position). This article discusses the impact of this quantificational paradigm shift on metaphysics, focussing on theories of (...) properties, propositions, and identity, as well as on the metaphysics of modality. (shrink)

This chapter explores the metaphysical views about higher-order logic held by two individuals responsible for introducing it to philosophy: Gottlob Frege (1848–1925) and Bertrand Russell (1872–1970). Frege understood a function at first as the remainder of the content of a proposition when one component was taken out or seen as replaceable by others, and later as a mapping between objects. His logic employed second-order quantifiers ranging over such functions, and he saw a deep division in nature between (...) objects and functions. Russell understood propositional functions as what is obtained when constituents of propositions are replaced by variables, but eventually denied that they were entities in their own right. Both encountered contradictions when supposing there to exist as many objects as functions, and both adopted views about the meaningfulness of higher-order discourse that were difficult to state from within their own strictures. (shrink)

(1) This is Part 2 of the semantic theory I call TM. In Part 1, I developed TM as a theory in the analytic philosophy of language, in lexical semantics, and in the sociology of relating occasions of statement production and comprehension to formal and informal lexicographic conclusions about statements and lexical items – roughly, as showing how synchronic semantics is a sociological derivative of diachronic, person-relative acts of linguistic behavior. I included descriptions of new cognitive psychology experimental paradigms which (...) would allow us to precisely measure the two constituents of semantics – meaning and reference – both at the level of individual speech acts and at the level of societal convergences, i.e. at both the token and type levels. -/- (2) In the Introduction, I recapitulate the arguments of Part 1. The Introduction also develops some analytic philosophical and lexical semantics themes not discussed in Part 1. -/- (3) After the Introduction, I present neural TM (nTM) as a theory of the neural mechanisms and processes which give rise to these person/occasion-relative acts of linguistic behavior. I develop nTM at three levels, the first two of which describe linguistic/semantic functions independently of their cortical locations. At the first level, I describe individual word-to-word and word-to-object connections. At the second level, I describe the corresponding structuralist networks of which they are the individual components. At this level, I introduce some key linguistic concepts of TM – its graded meaning, reference, and generalization sets, and the types of statements which express various levels of word-to-word and word-to-object relationships among lexical items which, because of the constraints they impose on the use of those lexical items in statements we produce and comprehend, are concepts. This constitutes the second structural level of nTM. -/- (4) At the third level, I associate the non-localized structures of the previous levels with cortically located neural structures and with the fasciculi that connect them. I distinguish neural areas in which primary (phonetic) and secondary (orthographic) lexicons are stored in long-term memory. I also describe the embodied concepts which co-exist in the anterior temporal lobes with the images they lexicalize. These concepts are often said to name physical objects and their features, although what they in fact name are kinds of physical objects and features. I describe how conceptual constraints and referential constraints interact to channel our intentions to say how things are into statements which are semantically well-formed, and which consequently successfully communicate information. -/- (5) Following this presentation of nTM, I examine five prominent neural semantic theories. I point out what is wrong with each of them as far as their explanations of semantics are concerned, and I also indicate how nTM can replace the “semantic cores” of those theories. -/- (6) The two basic mistakes made by neuroscience semantic theories, as I will explain, are (i) that all but one of them regard semantics as a matter of the association of words with perceptual images, and of generalizations from those associations; and (ii) that they all rely on an unspecified set of neural structures which purportedly encode the meaning of concepts in abstraction from their phonological and orthographic forms. nTM maintains, in contrast, that there are no abstract neural representations of semantic content. Neural constraints on our linguistic behavior, especially on our ascriptive and co-ascriptive use of words, express the semantic constraints on those words which make them concepts. That is the semantic content of words. -/- (7) I next consider several results from neuroscience experimental data which have been given one interpretation by one or another of the standard neurosemantic theories, but to which nTM gives a different interpretation. I include several predictions which I have found neither confirmed nor disconfirmed in the experimental neuroscience literature. -/- (8) After a concluding section in which I summarize the major changes to neurosemantic theory introduced by TM, and the analytic philosophy of language and lexical semantics contexts within which TM is situated, there follows an appendix in which I discuss neural net AI, and make some recommendations for implementing nTM in silicon. (shrink)

First-order evidence is evidence which bears on whether a proposition is true. Higher-order evidence is evidence which bears on whether a person is able to assess her evidence for or against a proposition. A widespread view is that higher-order evidence makes a difference to whether it is rational for a person to believe a proposition. In this paper, I consider in what way higher-order evidence might do this. More specifically, I consider whether and how higher- (...) class='Hi'>order evidence plays a role in determining what it is rational to believe distinct from that which first-order evidence plays. To do this, I turn to the theory of reasons, and try to situate higher-order evidence within it. The only place I find for it there, distinct from that which first-order evidence already occupies, is as a practical reason, that is, as a reason for desire or action. One might take this to show either that the theory of reasons is inadequate as it stands or that higher-order evidence makes no distinctive difference to what it is rational to believe. I tentatively endorse the second option. (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)

Recent authors have drawn attention to a new kind of defeating evidence commonly referred to as higher-order evidence. Such evidence works by inducing doubts that one’s doxastic state is the result of a flawed process – for instance, a process brought about by a reason-distorting drug. I argue that accommodating defeat by higher-order evidence requires a two-tiered theory of justification, and that the phenomenon gives rise to a puzzle. The puzzle is that at least in some situations involving (...) higher-order defeaters the correct epistemic rules issue conflicting recommendations. For instance, a subject ought to believe p, but she ought also to suspend judgment in p. I discuss three responses. The first resists the puzzle by arguing that there is only one correct epistemic rule, an Über-rule. The second accepts that there are genuine epistemic dilemmas. The third appeals to a hierarchy or ordering of correct epistemic rules. I spell out problems for all of these responses. I conclude that the right lesson to draw from the puzzle is that a state can be epistemically rational or justified even if one has what looks to be strong evidence to think that it is not. As such, the considerations put forth constitute a non question-begging argument for a kind of externalism. (shrink)

Nonnaturalist realism is the view that normative properties are unique kind of stance-independent properties. It has been argued that such views fail to explain why two actions that are exactly alike otherwise must also have the same normative properties. Mark Schroeder and Knut Olav Skarsaune have recently suggested that nonnaturalist realists can respond to this supervenience challenge by taking the primary bearers of normative properties to be action kinds. This paper develops their response in two ways. First, it provides (...) additional motivation for the previous claim about the bearers of normative properties by drawing from the work of H. A. Prichard. Second, and more importantly, it formulates a plausible metaphysical framework based on the contemporary trope theory to explain why action kinds would have their second-order properties, including their normative properties, necessarily. (shrink)

In order to explain delusional beliefs, one must first consider what factors should be included in a theory of delusion. Unlike a one-factor theory, a two-factor theory of delusion argues that not only anomalous experience (the first factor) but also an impairment of the belief-evaluation system (the second factor) is required. Recently, two-factor theorists have adopted various Bayesian approaches in order to give a more accurate description of delusion formation. By reviewing the progression from a one-factor (...) theory to a two-factor theory, I argue that in light of the second factor’s requirements, different proposed impairments can be unified within a consistent belief-evaluation system. Under this interpretation of the second factor, I further argue that the role of a mechanism responsible for detecting bizarreness is wrongly neglected. I conclude that the second factor is a compound system which consists of differing functional parts, one of which functions to detect bizarreness in different stages of delusion; moreover, I hold that the impairment can be one or several of these functional parts. (shrink)

Critics have often misunderstood the higher-order theory (HOT) of consciousness. Here we clarify its position on several issues, and distinguish it from other views such as the global The higher-order theory (HOT) of consciousness has often been misunderstood by critics. Here we clarify its position on several issues, and distinguish it from other views such as the global workspace theory (GWT) and early sensory models (e.g. first-order local recurrency theories). For example, HOT has been criticized (...) for over-intellectualizing consciousness. We show that while higher-order states are cognitively assembled, the requirements are actually considerably less than often presumed. In this sense HOT may be viewed as an intermediate position between GWT and early sensory views. Also, we clarify that most proponents of HOT do not stipulate consciousness as equivalent to metacognition or confidence. Further, compared to other existing theories, HOT can arguably account better for complex everyday experiences, such as of emotions and episodic memories. This makes HOT particularly useful as a framework for conceptualizing pathological mental states. (shrink)

Many theories of rational belief give a special place to logic. They say that an ideally rational agent would never be uncertain about logical facts. In short: they say that ideal rationality requires "logical omniscience." Here I argue against the view that ideal rationality requires logical omniscience on the grounds that the requirement of logical omniscience can come into conflict with the requirement to proportion one’s beliefs to the evidence. I proceed in two steps. First, I rehearse an (...) influential line of argument from the "higher-order evidence" debate, which purports to show that it would be dogmatic, even for a cognitively infallible agent, to refuse to revise her beliefs about logical matters in response to evidence indicating that those beliefs are irrational. Second, I defend this "anti-dogmatism" argument against two responses put forth by Declan Smithies and David Christensen. Against Smithies’ response, I argue that it leads to irrational self-ascriptions of epistemic luck, and that it obscures the distinction between propositional and doxastic justification. Against Christensen’s response, I argue that it clashes with one of two attractive deontic principles, and that it is extensionally inadequate. Taken together, these criticisms will suggest that the connection between logic and rationality cannot be what it is standardly taken to be—ideal rationality does not require logical omniscience. (shrink)

Higher-order logic augments first-order logic with devices that let us generalize into grammatical positions other than that of a singular term. Some recent metaphysicians have advocated for using these devices to raise and answer questions that bear on many traditional issues in philosophy. In contrast to these 'higher-order metaphysicians', traditional metaphysics has often focused on parallel, but importantly different, questions concerning special sorts of abstract objects: propositions, properties and relations. The answers to the higher-order and (...) the property-theoretic questions may coincide sometimes but will often come apart. I argue that when they do, the higher-order questions are closer to the metaphysical action and so it would be better for these debates to proceed in higher-order terms. (shrink)

This paper seeks to carve out a distinctive category of conspiracy theorist, and to explore the process of becoming a conspiracy theorist of this sort. Those on whom I focus claim their beliefs trace back to simply trusting their senses and experiences in a commonsensical way, citing what they take to be authoritative firsthand evidence or observations. Certain flat Earthers, anti-vaxxers, and UFO conspiracy theorists, for example, describe their beliefs and evidence this way. I first distinguish these conspiracy theorists (...) by contrasting them with another group that has recently received a lot of attention from the media, philosophers, and academics more broadly. I then dig more deeply into the nature of these conspiracy theorists’ epistemic self-understanding, in order to give an account of the process by which one becomes such a conspiracy theorist. I conclude with some takeaways and implications: first, I explore the implications of my account for whether these conspiracy theorists’ beliefs are rational; then, I argue that my account has practical takeaways about counteracting beliefs in misinformation, since strategies appropriate to this kind of conspiracy theorist may not be the same ones that are appropriate for other kinds. (shrink)

According to Rosenthal’s Higher-Order Thought (HOT) theory of consciousness, first-order mental states become conscious only when they are targeted by HOTs that necessarily represent the states as belonging to self. On this view a state represented as belonging to someone distinct from self could not be a conscious state. Rosenthal develops this view in terms of what he calls the ‘thin immunity principle’ (TIP). According to TIP, when I experience a conscious state, I cannot be wrong about (...) whether it is I who I think is in that state. We first suggest that TIP is a direct consequence of the HOT theory. Next we argue that somatoparaphrenia—a pathology in which sensations are sometimes represented as belonging to other people—shows that TIP can be violated. This violation of TIP in turn shows that the HOT theory’s claim that conscious states are necessarily represented as belonging to self is in error. Rosenthal’s attempt to account for pathological cases is found to be inadequate when applied to somatoparaphrenia, and other possible defenses are also shown to be incapable of preserving TIP. We further conclude by suggesting that the HOT theory’s failing in this regard is not a failing that is peculiar to this theory of consciousness. (shrink)

Context: The problems that are most in need of interdisciplinary collaboration are “wicked problems,” such as food crises, climate change mitigation, and sustainable development, with many relevant aspects, disagreement on what the problem is, and contradicting solutions. Such complex problems both require and challenge interdisciplinarity. Problem: The conventional methods of interdisciplinary research fall short in the case of wicked problems because they remain first-order science. Our aim is to present workable methods and research designs for doing second-order (...) science in domains where there are many different scientific knowledges on any complex problem. Method: We synthesize and elaborate a framework for second-order science in interdisciplinary research based on a number of earlier publications, experiences from large interdisciplinary research projects, and a perspectivist theory of science. Results: The second-order polyocular framework for interdisciplinary research is characterized by five principles. Second-order science of interdisciplinary research must: 1. draw on the observations of first-order perspectives, 2. address a shared dynamical object, 3. establish a shared problem, 4. rely on first-order perspectives to see themselves as perspectives, and 5. be based on other rules than first-order research. Implications: The perspectivist insights of second-order science provide a new way of understanding interdisciplinary research that leads to new polyocular methods and research designs. It also points to more reflexive ways of dealing with scientific expertise in democratic processes. The main challenge is that this is a paradigmatic shift, which demands that the involved disciplines, at least to some degree, subscribe to a perspectivist view. Constructivist content: Our perspectivist approach to science is based on the second-order cybernetics and systems theories of von Foerster, Maruyama, Maturana & Varela, and Luhmann, coupled with embodied theories of cognition and semiotics as a general theory of meaning from von Uexküll and Peirce. (shrink)

Most descriptions of higher-order vagueness in terms of traditional modal logic generate so-called higher-order vagueness paradoxes. The one that doesn't is problematic otherwise. Consequently, the present trend is toward more complex, non-standard theories. However, there is no need for this.In this paper I introduce a theory of higher-order vagueness that is paradox-free and can be expressed in the first-order extension of a normal modal system that is complete with respect to single-domain Kripke-frame semantics. This (...) is the system QS4M+BF+FIN. It corresponds to the class of transitive, reflexive and final frames. With borderlineness defined logically as usual, it then follows that something is borderline precisely when it is higher-order borderline, and that a predicate is vague precisely when it is higher-order vague.Like Williamson's, the theory proposed here has no clear borderline cases in Sorites sequences. I argue that objections that there must be clear borderline cases ensue from the confusion of two notions of borderlineness—one associated with genuine higher-order vagueness, the other employed to sort objects into categories—and that the higher-order vagueness paradoxes result from superimposing the second notion onto the first. Lastly, I address some further potential objections. (shrink)

On an optimistic version of realist moral epistemology, a significant range of ordinary moral beliefs, construed in realist terms, constitute knowledge—or at least some weaker positive epistemic status, such as epistemic justification. The “debunking challenge” to this view grants prima facie justification but claims that it is “debunked” (i.e., defeated), yielding the final verdict that moral beliefs are ultima facie unjustified. Notable candidate “debunkers” (i.e., defeaters) include the so-called “evolutionary debunking arguments,” the “Benacerraf-Field Challenge,” and persistent moral disagreement among epistemic (...) peers. Such defeaters are best treated as higher-order evidence—viz., evidence contesting the merits of the first-order evidence on which moral beliefs are based. This chapter first develops a theory of higher-order defeat in general, which it then applies to debunking in particular. The result: the challenge fails entirely on epistemic grounds—regardless of whether or not its empirical and metaphysical presuppositions are correct. An advantage of this purely epistemic defense over alternative strategies is that the former extends even to laypersons who themselves lack the expertise necessary to formulate an adequate response. However, this leaves open the prospects for non-epistemological interpretations of debunking (e.g., moral or ontological). The chapter therefore concludes with brief suggestions in that direction. (shrink)

The higher-order thought (HOT) theory of consciousness is a reductive representational theory of consciousness which says that what makes a mental state conscious is that there is a suitable HOT directed at that mental state. Although it seems that any neural realization of the theory must be somewhat widely distributed in the brain, it remains unclear just how widely distributed it needs to be. In section I, I provide some background and define some key terms. In section II, I (...) argue against the view that HOT theory should treat first-order (i.e. world-directed) conscious states as requiring prefrontal cortical activity though it is reasonable to suppose that conscious states are realized in the brain. In section III, I then explore some of the key background metaphysical issues involved in understanding the nature of consciousness, such as the debate between realism and idealism as well as the prospects for solving the so-called “hard problem” of consciousness. Some of the differences in question often mirror the traditional differences between Western and Eastern perspectives on the nature of consciousness. Overall, I argue that some form of realism and physicalism is more plausible than the opposing views. I also argue that materialists (and especially HOT theorists) can offer plausible replies to the hard problem. (shrink)

It’s widely accepted that higher-order defeaters, i.e., evidence that one’s belief is formed in an epistemically defective way, can defeat doxastic justification. However, it’s yet unclear how exactly such kind of defeat happens. Given that many theories of doxastic justification can be understood as fitting the schema of proper basing on propositional justifiers, we might attempt to explain the defeat either by arguing that a higher-order defeater defeats propositional justification or by arguing that it defeats proper basing. (...) It has been argued that the first attempt is unpromising because a variety of prominent theories of propositional justification don’t imply that we lose propositional justification when gaining higher-order defeaters. This leads some scholars to take the second attempt. In this paper, I criticize this second attempt, and I defend the first attempt by arguing that a theory of propositional justification that requires intellectual responsibility can nicely account for higher-order defeat. My proposal is that we lose doxastic justification when we gain higher-order defeaters because there is no intellectually responsible way for us to maintain our original beliefs due to the defeaters. (shrink)

Aside from the systematic theory of recognition, Honneth’s work in the last decade has also centered around a less commented-upon theme: the critical social theoretic diagnosis of social pathologies. This paper claims first that his diverse diagnoses of specific social pathologies can be productively united through the conceptual structure evinced by second-order disorders, where there are substantial disconnects, of various kinds, between first-order contents and second-order reflexive understandings of those contents. The second major claim of (...) the paper is that once we understand social pathologies as second-order disorders, it becomes apparent that critical social theory must do more than accurately identify and explicate these disorders at the phenomenological and action-theoretic levels. It must further engage in insightful sociological explanations of the social causes of those pathologies in order to further the prognostic and therapeutic tasks implied by the aim of developing a social theory with emancipatory intent. The paper argues that the identificatory and explicative components of diagnostic social theory have been fulfilled by Honneth to a much greater degree than the latter components of explanation, prognosis and therapy. (shrink)

The proof theory of many-valued systems has not been investigated to an extent comparable to the work done on axiomatizatbility of many-valued logics. Proof theory requires appropriate formalisms, such as sequent calculus, natural deduction, and tableaux for classical (and intuitionistic) logic. One particular method for systematically obtaining calculi for all finite-valued logics was invented independently by several researchers, with slight variations in design and presentation. The main aim of this report is to develop the proof theory of finite-valued first (...) order logics in a general way, and to present some of the more important results in this area. In Systems covered are the resolution calculus, sequent calculus, tableaux, and natural deduction. This report is actually a template, from which all results can be specialized to particular logics. (shrink)

First-order normative theories concerning what’s right and wrong, good and bad, etc. and metanormative theories concerning the nature of first-order normative thought and talk are widely regarded as independent theoretical enterprises. This paper argues that several debates in metanormative theory involve views that have first-order normative implications, even as the implications in question may not be immediately recognizable as normative. I first make my claim more precise by outlining a general recipe (...) for generating this result. I then apply this recipe to three debates in metaethics: the modal status of basic normative principles, normative vagueness and indeterminacy, and the determination of reference for normative predicates. In each case I argue that certain views on each issue carry first-order normative commitments, in accordance with my recipe. (shrink)

In this paprer a class of so called mathematically acceptable (shortly MA) languages is introduced First-order formal languages containing natural numbers and numerals belong to that class. MA languages which are contained in a given fully interpreted MA language augmented by a monadic predicate are constructed. A mathematical theory of truth (shortly MTT) is formulated for some of these languages. MTT makes them fully interpreted MA languages which posses their own truth predicates, yielding consequences to philosophy of mathematics. (...) MTT is shown to conform well with the eight norms presented for theories of truth in the paper 'What Theories of Truth Should be Like (but Cannot be)' by Hannes Leitgeb. MTT is also free from infinite regress, providing a proper framework to study the regress problem. (shrink)

This chapter presents a new argument for thinking of traditional ethical theories as methods that can be used in first-order ethics - as a kind of deliberation procedures rather than as criteria of right and wrong. It begins from outlining how ethical theories, such as consequentialism and contractualism, are flexible frameworks in which different versions of these theories can be formulated to correspond to different first-order ethical views. The chapter then argues that, as (...) a result, the traditional ethical theories cannot be evaluated in terms of their truth or correctness. Instead, I will suggest that these theories should be understood as providing different kind of ways of thinking about difficult moral problems. I then recommend a certain form of pragmatic pluralism - it may well be that different moral problems are better approached through different ethical theories. (shrink)