An overview of higher-order representational theories of consciousness. Representational theories of consciousness attempt to reduce consciousness to “mental representations” rather than directly to neural or other physical states. This approach has been fairly popular over the past few decades. Examples include first-order representationalism (FOR) which attempts to explain conscious experience primarily in terms of world-directed (or first-order) intentional states (Tye 2005) as well as several versions of higher-order representationalism (HOR) which holds that what makes a mental (...) state M conscious is that it is the object of some kind of higher-order mental state directed at M. The primary focus of this entry is on HOR and especially higher-order thought (HOT) theory. The key question that should be answered by any theory of consciousness is: What makes a mental state a conscious mental state? Section 1 introduces the overall representationalist approach to consciousness and briefly discuss Tye’s FOR. Section 2 presents three major versions of HOR: higher-order thought theory, dispositional higher-order thought theory, and higher-order perception theory. In section 3, a number of common and important objections and replies are presented. Section 4 briefly outlines a close connection between HOT theory and conceptualism, that is, the claim that the representational content of a perceptual experience is entirely determined by the conceptual capacities the perceiver brings to bear in her experience. Section 5 examines several hybrid higher-order and “self-representational” theories of consciousness which all hold that conscious states are self-directed in some way. Section 6 addresses the potentially damaging claim that HOT theory requires neural activity in the prefrontal cortex (PFC) in order for one to have conscious states. (shrink)

Higher‐order theories purport to account for the conscious character of such states in terms of higher‐order representations. This chapter focuses on three classes of higher‐order theory of phenomenal consciousness, including inner‐sense theory, actualist higher‐order thought theory, and dispositionalist higher‐order thought theory. All three of these higher‐order theories purport to offer reductive explanations of phenomenal consciousness. Inner‐sense theory has important positive virtues, but faces problems; whereas actualist higher‐order thought (...) class='Hi'>theory avoids those problems, but at the cost of losing the positive virtues. Actualist higher‐order thought theory has the advantage that no special organs or mechanisms need to be postulated. Dispositionalist higher‐order thought theory claims to split the difference, providing an account that has all of the advantages of inner‐sense theory with none of the flaws. The success of dispositionalist higher‐order thought theory is premised upon the existence of dual analog contents. (shrink)

Ambitious higher-order theories of consciousness aim to account for conscious states when these are understood in terms of what-it-is-like-ness. This paper considers two arguments concerning this aim, and concludes that ambitious theories fail. The misrepresentation argument against HO theories aims to show that the possibility of radical misrepresentation—there being a HO state about a state the subject is not in—leads to a contradiction. In contrast, the awareness argument aims to bolster HO theories by showing that subjects are aware of (...) all their conscious states. Both arguments hinge on how we understand two related notions which are ubiquitous in discussions of consciousness: those of what-it-is-like-ness and there being something it is like for a subject to be in a mental state. This paper examines how HO theorists must understand the two crucial notions if they are to reject the misrepresentation argument but assert the awareness argument. It shows that HO theorists can and do adopt an understanding—the HO reading—which seems to give them what they want. But adopting the HO reading changes the two arguments. On this reading, the awareness argument tells us nothing about those states there is something it is like to be in, and so offers no support to ambitious HO theories. And to respond to the misrepresentation understood according to the HO reading is to simply ignore the argument presented, and so to give no response at all. As things stand, we should deny that HO theories can account for what-it-is-like-ness. (shrink)

Higher-order theories of consciousness come in many varieties, but all adopt the 'transitivity principle' as a central, explanatory premise. The transitivity principle states that a mental state of a subject is conscious if and only if the subject is aware of it. This higher-order awareness is realized in different ways in different forms of higher-order theory. I argue that empirical studies of metacognition have falsified the transitivity principle by showing that there can be awareness of a (...) mental state without that state's becoming conscious. I present two such studies in detail and argue that the measures they employ cannot be interpreted in a way that would make the results compatible with higher-order theory. Since all versions of the theory rely on the transitivity principle, this entails that all forms of higher-order theory are false. (shrink)

We discuss first order theories in which individual concepts are admitted as mathematical objects along with the things that reify them. This allows very straightforward formalizations of knowledge, belief, wanting, and necessity in ordinary first order logic without modal operators. Applications are given in philosophy and in artificial intelligence. We do not treat general concepts, and we do not present any full axiomatizations but rather show how various facts can be expressed.

Emotional states of consciousness, or what are typically called emotional feelings, are traditionally viewed as being innately programed in subcortical areas of the brain, and are often treated as different from cognitive states of consciousness, such as those related to the perception of external stimuli. We argue that conscious experiences, regardless of their content, arise from one system in the brain. On this view, what differs in emotional and non-emotional states is the kind of inputs that are processed by a (...) general cortical network of cognition, a network essential for conscious experiences. Although subcortical circuits are not directly responsible for conscious feelings, they provide non-conscious inputs that coalesce with other kinds of neural signals in the cognitive assembly of conscious emotional experiences. In building the case for this proposal, we defend a modified version of what is known as the higher-order theory of consciousness. (shrink)

In this paper first order theories for nonmonotone inductive definitions are introduced, and a proof-theoretic analysis for such theories based on combined operator forms a la Richter with recursively inaccessible and Mahlo closure ordinals is given.

It is widely held that consciousness is partially constituted by a “pre-reflective” self-consciousness. Further, it’s argued that the presence of pre-reflective self-consciousness poses a problem for “higher-order” theories of consciousness. Higher-order theories invoke reflective representation and so do not appear to have the resources to explain pre-reflective self-consciousness. This criticism is rooted in the Heidelberg School’s deep reflection on the nature of self-consciousness, and accordingly, I will label this challenge the “Heidelberg problem.” In this chapter, I will offer (...) a higher-order answer to the Heidelberg problem. Instead of attacking the problem head-on, I’ll argue that the view can explain why there appears to be a Heidelberg problem, even if consciousness is ultimately realized by higher-order representation. But I’ll also argue that the theory has indexical resources to more directly counter the Heidelberg problem. Either way, I hope to show that the higher-order theory survives its trip to Heidelberg. (shrink)

A maximal chain in a tree is called a path, and a tree is called bounded when all its paths contain leaves. This paper concerns itself with first-order theories of bounded trees. We establish some sufficient conditions for the existence of bounded end-extensions that are also partial elementary extensions of a given tree. As an application of tree boundedness, we obtain a conditional axiomatisation of the first-order theory of the class of trees whose paths are all isomorphic (...) to some ordinal \, given the first-order theories of certain classes of bounded trees. (shrink)

ABSTRACTAmbitious Higher-order theories of consciousness – Higher-order theories that purport to give an account of phenomenal consciousness – face a well-known objection from the possibility of ra...

In lieu of an abstract, here is a brief excerpt of the content:Journal of the History of Ideas 63.3 (2002) 425-446 [Access article in PDF] Giving Orders: Theory and Practice in the Fundamental Constitutions of Carolina Vicki Hsueh Indians. Of Edisto Ashapo and Combohe to the South our friends. Of Wando Ituan Sewee and Sehey to the north came to our assistance and were zealous and resolute in it 1000 bowmen In our want supplied us. Q. Spaniards. What we (...) shall doe to the Spaniards if we invade them we brake the peace, if we sit still we loose our reputation with the Indians our friends. Westoes. Inland man eaters. Country. To the northward more sickly, about Ashley River fertile and of a wonderful growth. Tatchequea. A very fruitfull Country 8. days jorney by the North west the Emperor our friend and enemy to the Westoes and to hard for them. Q. Settlem't. 500 people will secure the settlement 1000 perfect it. desires supplys of necessarys till that time Excerpt from Carolina Memoranda in the handwriting of John Locke, Esq., 15 September 1670 Within the last decade, scholars such as James Tully, Barbara Arneil, and Bhikhu Parekh have performed a crucial intervention on modern constitu-tionalism's behalf. 1 Not only has constitutionalism in the modern age been [End Page 425] plagued by assumptions of cultural uniformity and an on-going inability to adjudicate between competing cultural claims, but it has been unable effectively to diagnose those limitations and dilemmas. The root of the problem, James Tully suggests, is ultimately a matter of historical perspective. "[T]he tendency," he writes, "is not to notice the philosophical and ideological debates over the last three hundred years... only the result of these debates is seen—the victorious modern language of constitutional uniformity—and claims for recognition are viewed through its framework as if it were impartial and universal." 2 In response Tully and others have sought to tackle this predicament at its historical root. Identifying modern constitutionalism's colonial origins as a significant part of the problem, their studies address the development of constitutionalism and colonialism as an entwined phenomenon in the early modern period, focusing particularly on the British-American context. In this sense, Locke's Two Treatises of Government stands as an exemplary illustration of the period's entangled colonial and constitutional temperaments. Well-known for its influential articulation of compact and resistance, the Two Treatises, Barbara Arneil argues "were written as a defence of England's colonial policy in the new world against the sceptics in England and the counter-claims of both the aboriginal nations and other European powers in America." 3 Accordingly, present-day constitutionalism continues to bear the weighty legacy of those colonial rationales. "[T]he language of modern constitutionalism," Tully further explains, "which has come to be authoritative was designed to exclude or assimilate cultural diversity and justify uniformity. The design is difficult to see because this 'modern' language has become the customary way of thinking about, reflecting on and envisioning a just constitutional order." Ultimately, Tully submits, citing Wittgenstein, "A picture held us captive. And we could not get outside it, for it lay in our language and language seemed to repeat it to us inexorably." 4This much-needed thickening of constitutionalism's historical context has enriched our awareness of constitutionalism's vexed origins, as it has proffered potent tools for interrogating current cultural adjudication. Yet, a troubling predicament persists. As if caught within the tenacious grip of the language of modern constitutionalism, Tully, Arneil, and Parekh insistently portray seventeenth-century British-American colonialism solely as a straightforward process of appropriation and assimilation without addressing or incorporating the [End Page 426] complex and contingent elements of that history in its emergence. Lacking the various negotiations and accommodations between settler and indigene in ambition and actualization, their portrayals crucially underplay the dynamic relationship between theories of constitutionalism and practices of colonialism—an approach that ultimately serves to reinscribe the narrative of triumphalist progress within their critiques. 5This problematic is the context for my reading of the Fundamental Constitutions of Carolina,1669... (shrink)

By a classifying topos for a first-order theory , we mean a topos such that, for any topos models of in correspond exactly to open geometric morphisms → . We show that not every first-order theory has a classifying topos in this sense, but we characterize those which do by an appropriate ‘smallness condition’, and we show that every Grothendieck topos arises as the classifying topos of such a theory. We also show that every first- (...) class='Hi'>order theory has a conservative extension to one which possesses a classifying topos, and we obtain a Heyting-valued completeness theorem for infinitary first-order logic. (shrink)

Doerig et al. have set several criteria that theories of consciousness need to fulfill. By these criteria, higher-order theories fare better than most existing theories. But they also argue that higher-order theories may not be able to answer both the ‘small network argument’ and the ‘other systems argument’. In response, we focus on the case of the Perceptual Reality Monitoring theory to explain why higher-order theories do just fine.

Some first-order theories of divisible ℓ-groups are well known, for example the theory of the totally ordered ones and the theories of the projectable ones , Lattice-ordered Groups, Kluwer Academic Press, Dordrecht, 1989, pp. 41–79). In this paper we study some theories of nonprojectable divisible ℓ-groups, the simplest example of which is . We introduce a generalization of the projectability property . We prove that the class of r-projectable special-valued divisible ℓ-groups is an elementary class and give a (...) classification of its completions. (shrink)

We study elementary second order extensions of the theoryID 1 of non-iterated inductive definitions and the theoryPA Ω of Peano arithmetic with ordinals. We determine the exact proof-theoretic strength of those extensions and their natural subsystems, and we relate them to subsystems of analysis with arithmetic comprehension plusΠ 1 1 comprehension and bar induction without set parameters.

Büchi, J. R. The monadic second order theory of [omega symbol]₁.--Büchi, J. R. and Siefkes, D. Axiomatization of the monadic second order theory of [omega symbol]₁.

A touchstone of much modern theorizing about the mind is the idea, still tac- itly accepted by many, that a state's being mental implies that it's conscious. This view is epitomized in the dictum, put forth by theorists as otherwise di-.

We investigate first order sentences valid in completions of a given partial algebraic structure - a partial model. We give semantic and syntactic description of the set of all sentences valid in every completion of the given partial model - first order theory of this model.

In this paper a first order theory for the logics defined through literal paraconsistent-paracomplete matrices is developed. These logics are intended to model situations in which the ground level information may be contradictory or incomplete, but it is treated within a classical framework. This means that literal formulas, i.e. atomic formulas and their iterated negations, may behave poorly specially regarding their negations, but more complex formulas, i.e. formulas that include a binary connective are well behaved. This situation may (...) and does appear for instance in data bases. (shrink)

The standard theory of logic programming is not applicable to Prolog programs even not to pure code. Modifying the theory to take account of reality more is the motivation of this article. For this purpose we introduce the ℓ-completion and the inductive extension of a logic program. Both are first-order theories in a language with operators for success, failure and termination of goals. The ℓ-completion of a logic program is a sound and complete axiomatization of the Prolog (...) depth-first search under certain natural conditions; the inductive extension of the ℓ-completion is a suitable theory for proving termination and equivalence of pure Prolog programs with negation. (shrink)

It is shown by Parsons [2] that the first-order fragment of Frege's logical system in the Grundgesetze der Arithmetic is consistent. In this note we formulate and prove a stronger version of this result for arbitrary first-order theories. We also show that a natural attempt to further strengthen our result runs afoul of Tarski's theorem on the undefinability of truth.

In this paper the modal operator "x is provable in Peano Arithmetic" is incorporated into first-order theories. A provability extension of a theory is defined. Presburger Arithmetic of addition, Skolem Arithmetic of multiplication, and some first order theories of partial consistency statements are shown to remain decidable after natural provability extensions. It is also shown that natural provability extensions of a decidable theory may be undecidable.

We introduce the notion of constructive suprema and of constructively directed sets. The Axiom of Choice turns out to be equivalent to the postulate that every supremum is constructive, but also to the hypothesis that every directed set admits a function assigning to each finite subset an upper bound. The Axiom of Multiple Choice implies a simple set-theoretical induction principle , stating that any system of sets that is closed under unions of well-ordered subsystems and contains all finite subsets of (...) a given set must also contain that set itself. This is not provable without choice principles but equivalent to the statement that the existence of joins for constructively directed subsets of a poset follows from the existence of joins for nonempty well-ordered subsets. Moreover, we establish the equivalence of SIP with several other fundamental statements concerning inductivity, compactness, algebraic closure systems, and the exchange between chains and directed sets. (shrink)

The aim of this paper is to introduce a formal system STW of self-referential truth, which extends the classical first-order theory of pure combinators with a truth predicate and certain approximation axioms. STW naturally embodies the mechanisms of general predicate application/abstraction on a par with function application/abstraction; in addition, it allows non-trivial constructions, inspired by generalized recursion theory. As a consequence, STW provides a smooth inner model for Myhill's systems with levels of implication.

Higher-order theories of consciousness posit that a mental state is conscious by virtue of being represented by another mental state, which is therefore a higher-order representation (HOR). Whether HORs are construed as thoughts or experiences, higher-order theorists have generally contested whether such metarepresentations have any significant cognitive function. In this paper, I argue that they do, focusing on the value of conscious thinking, as distinguished from conscious perceiving, conscious feeling, and other forms of conscious mentality. A thinking (...) process is constituted by propositional-attitude states, and during conscious thinking some or all of these states would be targeted by HORs. Since cases of nonconscious thinking are widely accepted, the question arises as to the use of representing one's thoughts during thinking. Contra the views of Armstrong and Rolls, I argue that HORs do not facilitate first-order thinking. Rather, I propose that such representations enable reasoning about one's act of thinking, and I give various examples of this sort of metacognition in support of the theory. I further argue that the general correlation between complex thinking and its being conscious is merely due to the fact that assessing one's mental act is particularly useful during such thinking, not because consciousness somehow facilitates first-order inference-making, as folk psychology implies. My view is thus consistent with recent empirical evidence that complex thinking sometimes yields better results when nonconscious. (shrink)

We study the groups Gal L and Gal KP, and the associated equivalence relations EL and EKP, attached to a first order theory T. An example is given where EL≠ EKP. It is proved that EKP is the composition of EL and the closure of EL. Other examples are given showing this is best possible.

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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)

Higher Order theories of consciousness have their fair share of sympathisers, but the arguments mustered in their support are—to my mind—unduly persuasive. My aim in this paper is to show that Higher Order theories cannot accommodate the possibility of misrepresentation without either falling into contradiction, or collapsing into a First-Order theory. If this diagnosis is on the right track, then Higher Order theories—at least in the specific versions here considered—fail to give an account of what (...) they set out to explain: what is distinctive of ‘conscious’ phenomena. (shrink)

For every sequence |p n } n of formulas of Peano ArithmeticPA with, every formulaA of the first-order theory diagonalizable algebras, we associate a formula 0 A, called the value ofA inPA with respect to the interpretation. We show that, ifA is true in every diagonalizable algebra, then, for every, 0 A is a theorem ofPA.

Given a theoryTextending that of dense linear orders without endpoints, in a language ℒ ⊇ {<}, we are interested in extensionsT′ ofTin languages extending ℒ by unary relation symbols that are each interpreted in models ofT′ as sets that are both dense and codense in the underlying sets of the models.There is a canonically “wild” example, namelyT= Th andT′ = Th. Recall thatTis o-minimal, and so every open set definable in any model ofThas only finitely many definably connected components. But (...) it is well known that 〈ℝ, <, +, · ℚ 〉 defines every real Borel set, in particular, every open subset of any finite cartesian power of ℝ and every subset of any finite cartesian power of ℚ. To put this another way, the definable open sets in models ofTare essentially as simple as possible, whileT′ has a model where the definable open sets are as complicated as possible, as is the structure induced on the new predicate.In contrast to the preceding example, if ℝalgis the set of real algebraic numbers andT′ Th, then no model ofT′ defines any open set that is not definable in the underlying model ofT. (shrink)

Features are unary operators used to build record-like expressions. The resulting term algebras are encountered in linguistic computation and knowledge representation. We present a general description of feature logic and of a slightly restricted version, called record logic. It is shown that every first-order theory can be faithfully interpreted in a record logic with various additional axioms. This fact is used elsewhere [15] to extend a result of Tarski and Givant [14] on expressing first order theories in (...) relation algebra. (shrink)