There has been much discussion recently about the scope and limits of purely symbolic models of the mind and about the proper role of connectionism in cognitive modeling. This paper describes the symbol grounding problem : How can the semantic interpretation of a formal symbol system be made intrinsic to the system, rather than just parasitic on the meanings in our heads? How can the meanings of the meaningless symbol tokens, manipulated solely on the basis of (...) their shapes, be grounded in anything but other meaningless symbols? The problem is analogous to trying to learn Chinese from a Chinese/Chinese dictionary alone. A candidate solution is sketched: Symbolic representations must be grounded bottom-up in nonsymbolic representations of two kinds: iconic representations, which are analogs of the proximal sensory projections of distal objects and events, and categorical representations, which are learned and innate feature-detectors that pick out the invariant features of object and event categories from their sensory projections. Elementary symbols are the names of these object and event categories, assigned on the basis of their categorical representations. Higher-order symbolic representations, grounded in these elementary symbols, consist of symbol strings describing category membership relations. Connectionism is one natural candidate for the mechanism that learns the invariant features underlying categorical representations, thereby connecting names to the proximal projections of the distal objects they stand for. In this way connectionism can be seen as a complementary component in a hybrid nonsymbolic/symbolic model of the mind, rather than a rival to purely symbolic modeling. Such a hybrid model would not have an autonomous symbolic module, however; the symbolic functions would emerge as an intrinsically dedicated symbol system as a consequence of the bottom-up grounding of categories ' names in their sensory representations. Symbol manipulation would be governed not just by the arbitrary shapes of the symbol tokens, but by the nonarbitrary shapes of the icons and category invariants in which they are grounded. (shrink)

Connectionism and computationalism are currently vying for hegemony in cognitive modeling. At first glance the opposition seems incoherent, because connectionism is itself computational, but the form of computationalism that has been the prime candidate for encoding the "language of thought" has been symbolic computationalism (Dietrich 1990, Fodor 1975, Harnad 1990c; Newell 1980; Pylyshyn 1984), whereas connectionism is nonsymbolic (Fodor & Pylyshyn 1988, or, as some have hopefully dubbed it, "subsymbolic" Smolensky 1988). This paper will examine what is and is not (...) a symbol system. A hybrid nonsymbolic/symbolic system will be sketched in which the meanings of the symbols are grounded bottom-up in the system's capacity to discriminate and identify the objects they refer to. Neural nets are one possible mechanism for learning the invariants in the analog sensory projection on which successful categorization is based. "Categorical perception" (Harnad 1987a), in which similarity space is "warped" in the service of categorization, turns out to be exhibited by both people and nets, and may mediate the constraints exerted by the analog world of objects on the formal world of symbols. (shrink)

The symbol grounding problem is concerned with the question of how the knowledge used in AI programs, expressed as tokens in one form or another or simply symbols, could be grounded to the outside world. By grounding the symbols, it is meant that the system will know the actual objects, events, or states of affairs in the world to which each symbol refers and thus be worldly-wise. Solving this problem, it was hoped, would enable the program to understand (...) its own action and hence be truly intelligent ). The problem becomes more acute after a challenge posed by Searle in his now famous Chinese Room Gedanken experiment. Searle argued that no AI programs can be said to understand or have other cognitive states, if all they do is formal symbol manipulation. (shrink)

Every university student has his or her nemesis. Biology and social science students anticipate with great apprehension their required statistics course, while many philosophy students live in fear of formal logic. Math anxiety is the common thread uniting all of them. This article argues that since formal logic is an algebra requiring similar kinds of symbol-manipulation skills needed to succeed in a basic mathematics course, then if logic students have math anxiety, this can impede their progress. Further, (...) it argues that math anxiety is primarily caused by and exacerbated by poor instruction. Formal logic instructors who employ effective instructional techniques for reducing it can help their students overcome math anxiety to foster learning. Methods of instruction leading to anxiety reduction and evidence supporting their efficacy are discussed, including co-operative learning, the mastery goal approach, and self-paced learning. None of these methods holds back more advanced students. (shrink)

Kant’s theory of taste supports his political theory by providing the judgment of beauty as a symbol of the good and example of teleological experience, allowing us to imagine the otherwise obscure movement of nature and history toward the ideal human community. If interpreters are correct in believing that Kant should make room for pure judgments of ugliness in his theory of taste, we will have to consider the implications of such judgments for Kant’s political theory. It is here (...) proposed that pure, formal ugliness symbolizes regressive, counter-teleological trends in nature and history. Kant’s paradoxical stance on the right to rebellion, both condemning and supporting the French Revolution, is interpreted as failing to take into account negative social forces signified by ugliness, and therefore neglecting the role of moral agency in social change. (shrink)

I present a formal language that imposes a structure on processes in macro-chemistry. Each symbol in the language invites a type of analysis that is carried out either by looking into the semantics if the language or by looking at the context. Every formal language has assumptions underlying it. The assumptions made in developing the formal language are meant to help with conceptual analysis by inviting certain types of question.

I present a formal language that imposes a structure on processes in macro-chemistry. Each symbol in the language invites a type of analysis that is carried out either by looking into the semantics if the language or by looking at the context. Every formal language has assumptions underlying it. The assumptions made in developing the formal language are meant to help with conceptual analysis by inviting certain types of question.

I present a formal language that imposes a structure on processes in macro-chemistry. Each symbol in the language invites a type of analysis that is carried out either by looking into the semantics if the language or by looking at the context. Every formal language has assumptions underlying it. The assumptions made in developing the formal language are meant to help with conceptual analysis by inviting certain types of question.

When certain formal symbol systems (e.g., computer programs) are implemented as dynamic physical symbol systems (e.g., when they are run on a computer) their activity can be interpreted at higher levels (e.g., binary code can be interpreted as LISP, LISP code can be interpreted as English, and English can be interpreted as a meaningful conversation). These higher levels of interpretability are called "virtual" systems. If such a virtual system is interpretable as if it had a mind, is (...) such a "virtual mind" real? This is the question addressed in this "virtual" symposium, originally conducted electronically among four cognitive scientists: Donald Perlis, a computer scientist, argues that according to the computationalist thesis, virtual minds are real and hence Searle's Chinese Room Argument fails, because if Searle memorized and executed a program that could pass the Turing Test in Chinese he would have a second, virtual, Chinese-understanding mind of which he was unaware (as in multiple personality). Stevan Harnad, a psychologist, argues that Searle's Argument is valid, virtual minds are just hermeneutic overinterpretations, and symbols must be grounded in the real world of objects, not just the virtual world of interpretations. Computer scientist Patrick Hayes argues that Searle's Argument fails, but because Searle does not really implement the program: A real implementation must not be homuncular but mindless and mechanical, like a computer. Only then can it give rise to a mind at the virtual level. Philosopher Ned Block suggests that there is no reason a mindful implementation would not be a real one. (shrink)

There is a prevalent notion among cognitive scientists and philosophers of mind that computers are merely formal symbol manipulators, performing the actions they do solely on the basis of the syntactic properties of the symbols they manipulate. This view of computers has allowed some philosophers to divorce semantics from computational explanations. Semantic content, then, becomes something one adds to computational explanations to get psychological explanations. Other philosophers, such as Stephen Stich, have taken a stronger view, advocating doing away (...) with semantics entirely. This paper argues that a correct account of computation requires us to attribute content to computational processes in order to explain which functions are being computed. This entails that computational psychology must countenance mental representations. Since anti-semantic positions are incompatible with computational psychology thus construed, they ought to be rejected. Lastly, I argue that in an important sense, computers are not formal symbol manipulators. (shrink)

There is a prevalent notion among cognitive scientists and philosophers of mind that computers are merely formal symbol manipulators, performing the actions they do solely on the basis of the syntactic properties of the symbols they manipulate. This view of computers has allowed some philosophers to divorce semantics from computational explanations. Semantic content, then, becomes something one adds to computational explanations to get psychological explanations. Other philosophers, such as Stephen Stich, have taken a stronger view, advocating doing away (...) with semantics entirely. This paper argues that a correct account of computation requires us to attribute content to computational processes in order to explain which functions are being computed. This entails that computational psychology must countenance mental representations. Since anti-semantic positions are incompatible with computational psychology thus construed, they ought to be rejected. Lastly, I argue that in an important sense, computers are not formal symbol manipulators. (shrink)

According to "computationalism" (Newell, 1980; Pylyshyn 1984; Dietrich 1990), mental states are computational states, so if one wishes to build a mind, one is actually looking for the right program to run on a digital computer. A computer program is a semantically interpretable formal symbol system consisting of rules for manipulating symbols on the basis of their shapes, which are arbitrary in relation to what they can be systematically interpreted as meaning. According to computationalism, every physical implementation of (...) the right symbol system will have mental states. (shrink)

In relation to semantics, “grounding” has two relevant meanings. “Symbol grounding” is the process of connecting symbols to perception and the world. “Communicative grounding” is the process of interactively adding to common ground in dialog. Strategies for grounding in human communication include, crucially, strategies for resolving troubles caused by various kinds of miscommunication. As it happens, these two processes of grounding are closely related. As a side-effect of grounding an utterance, dialog participants may adjust the meanings they assign to (...) linguistic expressions, in a process of semantic coordination. Meanings of at least some expressions include perceptual aspects which enable DPs to classify entities as falling under the expression or not based on their perception of those entities. We show how perceptual grounding of symbols can be achieved in a process of interactively adding to common ground. This requires that perceptual aspects of meaning can be updated as a result of participating in linguistic interaction, thereby enabling fine-grained semantic coordination of perceptually grounded linguistic meanings. A formal semantics for low-level perceptual aspects of meaning is presented, tying these together with the logical-inferential aspects of meaning traditionally studied in formal semantics. The key idea is to model perceptual meanings as classifiers of perceptual input. This requires a framework where intensions are represented independently of extensions, and structured objects which can be modified as a result of learning. We use Type Theory with Records, a formal semantics framework which starts from the idea that information and meaning are founded on our ability to perceive and classify the world, that is, to perceive objects and situations as being of types. As an example of our approach, we show how a simple classifier of spatial information based on the Perceptron can be cast in TTR. (shrink)

Viewed in the light of the remarkable performance of ‘Watson’ - IBMs proprietary artificial intelligence computer system capable of answering questions posed in natural language - on the US general knowledge quiz show ‘Jeopardy’, we review two experiments on formal systems - one in the domain of quantum physics, the other involving a pictographic languaging game - whereby behaviour seemingly characteristic of domain understanding is generated by the mere mechanical application of simple rules. By re-examining both experiments in the (...) context of Searle’s Chinese Room Argument, we suggest their results merely endorse Searle’s core intuition: that ‘syntactical manipulation of symbols is not sufficient for semantics’. Although, pace Watson, some artificial intelligence practitioners have suggested that more complex, higher-level operations on formal symbols are required to instantiate understanding in computational systems, we show that even high-level calls to Google translate would not enable a computer qua ‘formal symbol processor’ to understand the language it processes. We thus conclude that even the most recent developments in ‘quantum linguistics’ will not enable computational systems to genuinely understand natural language. (shrink)

It is unlikely that the systematic, compositional properties of formal symbol systems -- i.e., of computation -- play no role at all in cognition. However, it is equally unlikely that cognition is just computation, because of the symbol grounding problem (Harnad 1990): The symbols in a symbol system are systematically interpretable, by external interpreters, as meaning something, and that is a remarkable and powerful property of symbol systems. Cognition (i.e., thinking), has this property too: Our (...) thoughts are systematically interpretable by external interpreters as meaning something. However, unlike symbols in symbol systems, thoughts mean what they mean autonomously: Their meaning does not consist of or depend on anyone making or being able to make any external interpretations of them at all. When I think "the cat is on the mat," the meaning of that thought is autonomous; it does not depend on YOUR being able to interpret it as meaning that (even though you could interpret it that way, and you would be right). (shrink)

The fundamental assumptions in Dijkstra''s influential article on computing science teaching are challenged. Dijkstra''s paper presents the radical novelties of computing, and the consequent problems that we must tackle through a formal, logic-based approach to program derivation. Dijkstra''s main premise is that the algorithmic programming paradigm is the only one, in fact, the only possible one. It is argued that there is at least one other, the network-programming paradigm, which itself is a radical novelty with respect to the implementation (...) of problems on computers. And, as one might expect of a radical alternative, it shows much of the conventional wisdom concerning computing science, which Dijkstra variously attacks and dispenses, to be special pleading; not universals of computing at all. Finally, we explore what is known of this new paradigm in order to see what light it sheds on the fundamental problems that computing really does present to us. Not surprisingly, some become less problematic, some disappear altogether and others take their place, but, in general, it must be of benefit to modern computer technology to gain a wider perspective on the possibilities instead of seeing everything through the traditional tunnel of programming as formula derivation, and computers as the requisite, special type of symbol manipulation device. (shrink)

A uniform theory of conditionals is one which compositionally captures the behavior of both indicative and subjunctive conditionals without positing ambiguities. This paper raises new problems for the closest thing to a uniform analysis in the literature (Stalnaker, Philosophia, 5, 269–286 (1975)) and develops a new theory which solves them. I also show that this new analysis provides an improved treatment of three phenomena (the import-export equivalence, reverse Sobel-sequences and disjunctive antecedents). While these results concern central issues in the study (...) of conditionals, broader themes in the philosophy of language and formal semantics are also engaged here. This new analysis exploits a dynamic conception of meaning where the meaning of a symbol is its potential to change an agent’s mental state (or the state of a conversation) rather than being the symbol’s content (e.g. the proposition it expresses). The analysis of conditionals is also built on the idea that the contrast between subjunctive and indicative conditionals parallels a contrast between revising and consistently extending some body of information. (shrink)

Given any simply consistent formal theory F of the state complexity L(S) of finite binary sequences S as computed by 3-tape-symbol Turing machines, there exists a natural number L(F ) such that L(S) > n is provable in F only if n < L(F ). On the other hand, almost all finite binary sequences S satisfy L(S) > L(F ). The proof resembles Berry’s..

“Articulate models” subservient to formal intelligence are imagined to be heterarchies of automata capable of performing the “symbolic (quasi-spatial) syntheses” of Luria (1973), where “quasi-spatial” points to the abstract core of spatiality: the symbol productions, combinations, and substitutions of algebraic reckoning. The alleged cognitive role of internal “topographic images” and of “efference copies” is confronted with this background and denied.

This paper presents a view of nature as a network of infocomputational agents organized in a dynamical hierarchy of levels. It provides a framework for unification of currently disparate understandings of natural, formal, technical, behavioral and social phenomena based on information as a structure, differences in one system that cause the differences in another system, and computation as its dynamics, i.e. physical process of morphological change in the informational structure. We address some of the frequent misunderstandings regarding the natural/morphological (...) computational models and their relationships to physical systems, especially cognitive systems such as living beings. Natural morphological infocomputation as a conceptual framework necessitates generalization of models of computation beyond the traditional Turing machine model presenting symbol manipulation, and requires agent-based concurrent resource-sensitive models of computation in order to be able to cover the whole range of phenomena from physics to cognition. The central role of agency, particularly material vs. cognitive agency is highlighted. (shrink)

Description Logics (DLs) are a family of well-known terminological knowledge representation formalisms in modern semantics-based systems. This research focuses on analysing how our developed Occurrence Logic (OccL) can conceptually and logically support the development of a description logic. OccL is integrated into the alternative theory of natural language syntax in `Deviational Syntactic Structures' under the label `EFA(X)3' (or the third version of Epi-Formal Analysis in Syntax, EFA(X), which is a radical linguistic theory). From the logical point of view, OccL (...) is a formal logic that mainly deals with the occurrences of symbols as well as with their priorities within linguistic descriptions, i.e. natural language syntax, semantics and phonology. In this article---based on our OccL-based definitions of the concepts of `strong implication' and `occurrence value' as well as of the logical concept `identical occurrence constructor (IDOC)' that is the most fundamental logical concept in our formalism---we will model Occurrence Description Logic ($\mathcal{ODL}$). Accordingly, we will formally-logically analyse `occurrence(s) of symbol(s)' within descriptions of the world in $\mathcal{ODL}$. In addition, we will analyse and assess the logical concepts of `occurrence' and `occurrence priority' in $\mathcal{ODL}$. This research can make a strong logical background for our future research in the development of a Modal Occurrence Description Logic. (shrink)

In this paper we investigate first order common knowledge logics; i.e., modal epistemic logics based on first order logic with common knowledge operators. It is shown that even rather weak fragments of first order common knowledge logics are not recursively axiomatizable. This applies, for example, to fragments which allow to reason about names only; that is to say, fragments the first order part of which is based on constant symbols and the equality symbol only. Then formal properties of (...) "quantifying into" epistemic contexts are investigated. The results are illustrated by means of epistemic representations of Nash Equilibria for finite games with mixed strategies. (shrink)

One construal of convergent realism is that for each clear question, scientific inquiry eventually answers it. In this paper we adapt the techniques of formal learning theory to determine in a precise manner the circumstances under which this ideal is achievable. In particular, we define two criteria of convergence to the truth on the basis of evidence. The first, which we call EA convergence, demands that the theorist converge to the complete truth "all at once". The second, which we (...) call AE convergence, demands only that for every sentence in the theorist's language, there is a time at which the theorist settles the status of the sentence. The relative difficulties of these criteria are compared for effective and ineffective agents. We then examine in detail how the enrichment of an agent's hypothesis language makes the task of converging to the truth more difficult. In particular, we parametrize first-order languages by predicate and function symbol arity, presence or absence of identity, and quantifier prefix complexity. For nearly each choice of values of these parameters, we determine the senses in which effective and ineffective agents can converge to the complete truth on an arbitrary structure for the language. Finally, we sketch directions in which our learning theoretic setting can be generalized or made more realistic. (shrink)

The Evans-Salmon position on vague identity has deservedly elicited a large response in the literature. I think it is in fact among the most provocative metaphysical ideas to appear in recent years. I will try to show in this paper, however, that the position is vulnerable to a fundamental criticism that seems to have been virtually ignored in the many discussions of it. I take the Evans-Salmon position to consist of the following two theses: Thesis I. There cannot be objects (...) x and y such that it is indeterminate whether x is (identical with) y. Thesis II. The only way for an identity sentence to be indeterminate in truth-value is if one of the expressions flanking the identity symbol is referentially ambiguous.] The argument for Thesis I is essentially as follows. We are assuming that the sense of identity under discussion satisfies the standard formal logic of identity including Leibniz's Law. Suppose, now, that it is indeterminate whether x is y. Since it is determinate that x is x, x differs from y with respect to the property of being determinately x, from which it follows by Leibniz's Law that x is not y. Since the supposition that it is indeterminate whether x is y leads to the conclusion that x is not y, this supposition is incoherent. (shrink)

Let T(Ω) be the ordinal notation system from Buchholz-Schütte (1988). [The order type of the countable segmentT(Ω)0 is — by Rathjen (1988) — the proof-theoretic ordinal the proof-theoretic ordinal ofACA 0 + (Π 1 l −TR).] In particular let ↦Ω a denote the enumeration function of the infinite cardinals and leta ↦ ψ0 a denote the partial collapsing operation on T(Ω) which maps ordinals of T(Ω) into the countable segment TΩ 0 of T(Ω). Assume that the (fast growing) extended Grzegorczyk (...) hierarchy $(F_a )_{a \in T(\Omega )_0 }$ and the slow growing hierarchy $(G_a )_{a \in T(\Omega )_0 }$ are defined with respect to the natural system of distinguished fundamental sequences of Buchholz and Schütte (1988) in the following way: $$\begin{array}{*{20}c} {G_0 (n): = 0,} & {F_0 (n): = (n + 1)^2 ,} \\ {\begin{array}{*{20}c} {G_{a + 1} (n): = G_a (n) + 1,} \\ {G_l (n): = G_{l[n]} (n),} \\ \end{array} } & {\begin{array}{*{20}c} {F_{a + 1} (n): = \underbrace {F_a (...F_a }_{n + 1 - times}(n)...),} \\ {F_l (n): = F_{l[n]} (n),} \\ \end{array} } \\ \end{array}$$ wherel is a countable limit ordinal (term) and (l[n]) n ∈N is the distinguished fundamental sequence assigned tol. For each ordinal (term)a in T(Ω) and each natural numbern letC n (a) be the formal term which results from the ordinal terma by successively replacing every occurence ofψ a by $\psi _{ - 1 + C_n (a)}$ whereψ −1 is considered as a defined function symbol, namely $\psi _{ - 1} b: = F_{\psi _0 b + 1} (n + 1)$ . (Note thatψ a 0=Ω a ) In this article it is shown that for each ordinal termψ 0 a in T(Ω) there exists a natural numbern 0 such thatψ 0 C n (a) ∈ T(Ω) and $G_{\psi _0 a} (n) \leqslant F_{\psi _0 C_n (a) + 1} (n + 1)$ holds for alln≥n 0. This hierarchy comparison theorem yields a plethora of new results on nontrivial lower bounds for the slow growing ordinals — i.e. ordinals for which the slow growing hierarchy yields a classification of the provably total functions of the theory in question — of various theories of iterated inductive definitions (and subsystems ofKPi) and on the number and size of the subrecursively inaccessible ordinals — i.e. ordinals at which the extended Grzegorczyk hierarchy and the slow growing hierarchy catch up — below the proof-theoretic ordinal ofACA 0+(Π 1 l −TR). In particular these subrecursively inaccessibles ordinals are necessarily of the form $\psi _0 \Omega ..._{\Omega _\omega }$. (shrink)

‘It is supposed’, declared the poet Wordsworth in 1802, ‘that by the act of writing in verse an author makes a formal engagement that he will gratify certain known habits of association; that he not only thus apprizes the reader that certain classes of ideas and expressions will be found in his book, but that others will be carefully excluded. This exponent or symbol held forth by metrical language must in different eras of literature have excited very different (...) expectations.’ For his own era of literature Wordsworth proposed a language derived from the ‘simple and unelaborated expressions’ of the ‘language really spoken by men’, at the expense of ‘devices to elevate the style’ and ‘what is usually called poetic diction’. (shrink)

The purpose of this article is to show why consciousness and thought are not manifested in digital computers. Analyzing the rationale for claiming that the formal manipulation of physical symbols in Turing machines would emulate human thought, the article attempts to show why this proved false. This is because the reinterpretation of designation and meaning to accommodate physical symbol manipulation eliminated their crucial functions in human discourse. Words have denotations and intensional meanings because the brain transforms the physical (...) stimuli received from the microworld into a qualitative, macroscopic representation for consciousness. Lacking this capacity as programmed machines, computers have no representations for their symbols to designate and mean. Unlike human beings in which consciousness and thought, with their inherent content, have emerged because of their organic natures, serial processing computers or parallel distributed processing systems, as programmed electrical machines, lack these causal capacities. (shrink)

Both Artificial Life and Artificial Mind are branches of what Dennett has called "reverse engineering": Ordinary engineering attempts to build systems to meet certain functional specifications, reverse bioengineering attempts to understand how systems that have already been built by the Blind Watchmaker work. Computational modelling (virtual life) can capture the formal principles of life, perhaps predict and explain it completely, but it can no more be alive than a virtual forest fire can be hot. In itself, a computational model (...) is just an ungrounded symbol system; no matter how closely it matches the properties of what is being modelled, it matches them only formally, with the mediation of an interpretation. Synthetic life is not open to this objection, but it is still an open question how close a functional equivalence is needed in order to capture life. Close enough to fool the Blind Watchmaker is probably close enough, but would that require molecular indistinguishability, and if so, do we really need to go that far? (shrink)

It is sometimes suggested that the history of computation in cognitive science is one in which the formal apparatus of Turing-equivalent computation, or effective computability, was exported from mathematical logic to ever wider areas of cognitive science and its environs. This paper, however, indicates some respects in which this suggestion is inaccurate. Computability theory has not been focused exclusively on Turing-equivalent computation. Many essential features of Turing-equivalent computation are not captured in definitions of computation as symbol manipulation. Turing-equivalent (...) computation did not play the role in McCulloch and Pitts’s early cybernetic work that is sometimes attributed to it. Finally, various segments of the neuroscientific community invoke a notion of computation that differs from the Turing-equivalent notion.Keywords: Circular causality; Computation; Cortical maps; Neural networks; Symbol manipulation; Turing-equivalent computation. (shrink)

This paper examines the role of formal, aesthetic elements in motivating moral action. It proposes that Blumenberg’s analysis of the existential settings of myth and metaphor provide a useful framework to consider the conception and function of the aesthetic symbol in Kantian moral philosophy. In particular, it explores the hypothesis that Blumenberg’s analysis of ‘pregnance’ and ‘rhetoric’ are useful for identifying and evaluating the processes involved in self-persuasion to the moral perspective.

Dans un texte désormais célèbre, Ferdinand de Saussure insiste sur l’arbitraire du signe dont il vante les qualités. Toutefois il s’avère que le symbole, signe non arbitraire, dans la mesure où il existe un rapport entre ce qui représente et ce qui est représenté, joue un rôle fondamental dans la plupart des activités humaines, qu’elles soient scientifiques, artistiques ou religieuses. C’est cette dimension symbolique, sa portée, son fonctionnement et sa signification dans des domaines aussi variés que la chimie, la théologie, (...) les mathématiques, le code de la route et bien d’autres qui est l’objet du livre La Pointure du symbole. -/- Jean-Yves Béziau, franco-suisse, est docteur en logique mathématique et docteur en philosophie. Il a poursuivi des recherches en France, au Brésil, en Suisse, aux États-Unis (UCLA et Stanford), en Pologne et développé la logique universelle. Éditeur-en-chef de la revue Logica Universalis et de la collection Studies in Universal Logic (Springer), il est actuellement professeur à l’Université Fédérale de Rio de Janeiro et membre de l’Académie brésilienne de Philosophie. SOMMAIRE -/- PRÉFACE L’arbitraire du signe face à la puissance du symbole Jean-Yves BÉZIAU La logique et la théorie de la notation (sémiotique) de Peirce (Traduit de l’anglais par Jean-Marie Chevalier) Irving H. ANELLIS Langage symbolique de Genèse 2-3 Lytta BASSET -/- Mécanique quantique : quelle réalité derrière les symboles ? Hans BECK -/- Quels langages et images pour représenter le corps humain ? Sarah CARVALLO Des jeux symboliques aux rituels collectifs. Quelques apports de la psychologie du développement à l’étude du symbolisme Fabrice CLÉMENT Les panneaux de signalisation (Traduit de l’anglais par Fabien Shang) Robert DEWAR Remarques sur l’émergence des activités symboliques Jean LASSÈGUE Les illustrations du "Songe de Poliphile" (1499). Notule sur les hiéroglyphes de Francesca Colonna Pierre-Alain MARIAUX Signes de vie Jeremy NARBY Visualising relations in society and economics. Otto Neuraths Isotype-method against the background of his economic thought Elisabeth NEMETH Algèbre et logique symboliques : arbitraire du signe et langage formel Marie-José DURAND – Amirouche MOKTEFI Les symboles mathématiques, signes du Ciel Jean-Claude PONT La mathématique : un langage mathématique ? Alain M. ROBERT. (shrink)

For over a decade John Searle's ingenious argument against the possibility of artificial intelligence has held a prominent place in contemporary philosophy. This is not just because of its striking central example and the apparent simplicity of its argument. As its appearance in Scientific American testifies, it is also due to its importance to the wider scientific community. If Searle is right, artificial intelligence in the strict sense, the sense that would claim that mind can be instantiated through a (...) class='Hi'>formal program of symbol manipulation, is basically wrong. No set of formal conditions can provide us with the characteristic feature of mind which is the intentionally of its mental contents. Formally regarded, such intentionally is an irreducible primitive. It cannot be analyzed into non-intentional (purely syntactic, symbolic) components. This paper will argue that this objection is based on a misunderstanding. Intentionality is not simply something given which is incapable of further analysis. It only appears so when we mistakenly abstract it from time. When we regard its temporal structure, it shows itself as a rule-governed, synthetic process, one capable of being instantiated both by machines and men. (shrink)

John Searle has argued that one can imagine embodying a machine running any computer program without understanding the symbols, and hence that purely computational processes do not yield understanding. The disagreement this argument has generated stems, I hold, from ambiguity in talk of 'understanding'. The concept is analysed as a relation between subjects and symbols having two components: a formal and an intentional. The central question, then becomes whether a machine could possess the intentional component with or without the (...) formal component. I argue that the intentional state of a symbol's being meaningful to a subject is a functionally definable relation between the symbol and certain past and present states of the subject, and that a machine could bear this relation to a symbol. I sketch a machine which could be said to possess, in primitive form, the intentional component of understanding. Even if the machine, in lacking consciousness, lacks full understanding, it contributes to a theory of understanding and constitutes a counterexample to the Chinese Room argument. (shrink)

Based on formal-theoretical principles about the sign processes involved, we have built synthetic experiments to investigate the emergence of communication based on symbols and indexes in a distributed system of sign users, following theoretical constraints from C.S.Peirce theory of signs, following a Synthetic Semiotics approach. In this paper, we summarize these computational experiments and results regarding associative learning processes of symbolic sign modality and cognitive conditions in an evolutionary process for the emergence of either symbol-based or index-based communication.

‘It is supposed’, declared the poet Wordsworth in 1802, ‘that by the act of writing in verse an author makes a formal engagement that he will gratify certain known habits of association; that he not only thus apprizes the reader that certain classes of ideas and expressions will be found in his book, but that others will be carefully excluded. This exponent or symbol held forth by metrical language must in different eras of literature have excited very different (...) expectations.’ For his own era of literature Wordsworth proposed a language derived from the ‘simple and unelaborated expressions’ of the ‘language really spoken by men’, at the expense of ‘devices to elevate the style’ and ‘what is usually called poetic diction’. (shrink)

Nominal terms extend first-order terms with binding. They lack some properties of first- and higher-order terms: Terms must be reasoned about in a context of ‘freshness assumptions’; it is not always possible to ‘choose a fresh variable symbol’ for a nominal term; it is not always possible to ‘α-convert a bound variable symbol’ or to ‘quotient by α-equivalence’; the notion of unifier is not based just on substitution. Permissive nominal terms closely resemble nominal terms but they recover these (...) properties, and in particular the ‘always fresh’ and ‘always rename’ properties. In the permissive world, freshness contexts are elided, equality is fixed, and the notion of unifier is based on substitution alone rather than on nominal terms’ notion of unification based on substitution plus extra freshness conditions. We prove that expressivity is not lost moving to the permissive case and provide an injection of nominal terms unification problems and their solutions into permissive nominal terms problems and their solutions. We investigate the relation between permissive nominal unification and higher-order pattern unification. We show how to translate permissive nominal unification problems and solutions in a sound, complete, and optimal manner, in suitable senses which we make formal. (shrink)

The Oxford English Dictionary says that a rite is ‘a formal procedure or act in a religious or other solemn observance’. The word comes into English through the French rite from the Latin ritus . Its original meaning escapes etymologists; and this is a mixed blessing, for we neither can nor must attempt a retrieval of its hidden roots. We are told by respectable etymologists that the word is associated from earliest times with Latin religious usage, but that even (...) in the early Latin it was already extended to ‘custom, usage, manner or way’ of a non-religious sort. [Lewis and Short, A Latin Dictionary .] So, too, in modern languages the terms ‘rite’ and ‘ritual’ have specifically religious meaning, but they are also used in social and cultural settings that we would not call religious. What first strikes us about the terms ’ and ‘ritual’ is an emphasis upon a certain formality, upon a regular and stable way in which an action or set of actions is to be performed. A ritual is more than a formalism, however, since there are formalisms that are not rites, such as the logical rules for making a valid argument. Moreover, the term is frequently associated with the terms ‘myth’, ‘symbol’ and ‘faith’. These, too, are primarily religious, but are also extended to non-religious contexts. Indeed, there seems to be a network of such terms whose usage touches upon some extraordinary quality in things. Like them, the term ‘ritual’ shares both a wide variety of meanings and a certain hint of impropriety. The variety of ritual forms is notorious, ranging from the most sacred religious liturgies to the absurdities of a fraternity initiation; and the impropriety of the term breaks out whenever we brand a certain action ‘ritualistic’, just as we sometimes refer slightingly to an assertion, saying it is ‘mythical’, ‘merely symbolic’ or ‘credulous’. (shrink)

John Searle has argued that one can imagine embodying a machine running any computer program without understanding the symbols, and hence that purely computational processes do not yield understanding. The disagreement this argument has generated stems, I hold, from ambiguity in talk of 'understanding'. The concept is analysed as a relation between subjects and symbols having two components: a formal and an intentional. The central question, then becomes whether a machine could possess the intentional component with or without the (...) formal component. I argue that the intentional state of a symbol's being meaningful to a subject is a functionally definable relation between the symbol and certain past and present states of the subject, and that a machine could bear this relation to a symbol. I sketch a machine which could be said to possess, in primitive form, the intentional component of understanding. Even if the machine, in lacking consciousness, lacks full understanding, it contributes to a theory of understanding and constitutes a counterexample to the Chinese Room argument. (shrink)

Nominal terms extend first-order terms with binding. They lack some properties of first- and higher-order terms: Terms must be reasoned about in a context of ‘freshness assumptions’; it is not always possible to ‘choose a fresh variable symbol’ for a nominal term; it is not always possible to ‘α-convert a bound variable symbol’ or to ‘quotient by α-equivalence’; the notion of unifier is not based just on substitution. Permissive nominal terms closely resemble nominal terms but they recover these (...) properties, and in particular the ‘always fresh’ and ‘always rename’ properties. In the permissive world, freshness contexts are elided, equality is fixed, and the notion of unifier is based on substitution alone rather than on nominal terms’ notion of unification based on substitution plus extra freshness conditions. We prove that expressivity is not lost moving to the permissive case and provide an injection of nominal terms unification problems and their solutions into permissive nominal terms problems and their solutions. We investigate the relation between permissive nominal unification and higher-order pattern unification. We show how to translate permissive nominal unification problems and solutions in a sound, complete, and optimal manner, in suitable senses which we make formal. (shrink)

In his Languages of Art, Nelson Goodman proposes a theory of artistic notation that includes foundational requirements for any system of symbols we might use to specify and communicate the features of an artwork, in architecture or any other art form. Goodmans' theory usefully explains how notation can reveal linguistic-like phenomena of various art forms. But not all art forms can enjoy benefits of a full-blown notational system, in Goodman's view, and he suggests that architecture's symbol systems fall short (...) in this regard. It is a shortcoming of architecture, he believes, that its notation cannot communicate the sum of a given work's essential features. Against this view it may be argued that artworks are generally and inimically historical in character, such that an inability to capture this dimension may result in a failure to pick out the identity of a work. As a consequence, the suggestion of that inability looks like a shortcoming of the general notational theory rather than of the art form or its notation per se. I defend Goodman's background formalism against the criticism that an ahistoricist notation cannot possibly be adequate. But I reject his view that no actual architectural notation can satisfy the formal criteria of his theory. In particular, I propose that the foundational theory for Computer Aided Design (CAD) described by the architect William Mitchell satisfies Goodman's criteria and so yields a notation that enables communication of an architectural work's essential features. If, as I suggest, such a notation is feasible, then we have an additional result that Goodman foresees: a means of abstracting future architectural works from their historical contexts. This in turn yields a consequence at which Goodman only hints-that such architectural works can be intellectually grasped and physically constructed along purely formalist lines. One practical result here is that we introduce economical solutions to architectural design. On a theoretical level, we also expose the inessential character of historical properties to creating or understanding architecture, at least with respect to future possible works. (shrink)

OpenMath is a standard for the representation and communication of mathematical objects, which are built up from symbols and variables using applications, binding expressions, and key-value attributions. OpenMath2 introduced a set of symbol roles that can be specified in content dictionaries to restrict the occurrences of the respective symbols. This yields a simple, high-level notion of well-formed objects. While this system is appealing in its simplicity, the definition of wellformedness is purely extensional without an intuitive or formal condition (...) that distinguishes well-formed objects from ill-formed ones. Moreover, some well-formed objects should arguably rather be ill-formed. We try to remedy that with a refined role system while preserving the simplicity of the existing one. In particular, by distinguishing syntactic and semantic roles, we can capture the intuitive notion of well-formedness better. (shrink)

This article consists of five poems and an introductory essay. The poems are intended on the one hand to make a case for the currently underrated virtues of poetic formalism, i.e., for the revival of rhyme and meter as aspects of poetic practice. On the other they argue for a distinctly philosophical mode of poetry that embraces the values of conceptual or rational discourse as against a romantic-modernist conception premised on the intrinsic superiority of lyric, metaphor, symbol, analogy, and (...) suchlike touchstone values. These issues are laid out programmatically in the opening essay and developed in a more performative as well as formal way in the five poems. (shrink)

This paper discusses the problems of an ontological value of the variable in Russell’s philosophy. The variable is essential in Russell’s theory of denotation, which among other things, purports to prove Meinongian being outside of subsistence and existence to be logically unnecessary. I argue that neither Russell’s epistemology nor his ontology can account for the ontological value of the variable without running into qualities of Meinongian being that Russell disputed. The problem is that the variable cannot be logically grounded by (...) Russell’s theory of denotation. As such, in so far as being is concerned, Meinong and Russell’s theories are much closer than is typically thought. The arguments are supported with concerns raised by Russell, Frege, and Moore regarding the ontological value of the variable. The problem can be summarised as follows: the variable is the fundamental denoting-position of a formal theory that is meant to explain the structure of the ontological. If such a formal theory is meant to ground the ontological, then the formal must also represent the actual structure of the ontological. Yet the variable, the fundamental symbol of denotation in a theory that defines objects, is ontologically indefinable. (shrink)

This paper examines the role of formal, aesthetic elements in motivating moral action. It proposes that Blumenberg’s analysis of the existential settings of myth and metaphor provide a useful framework to consider the conception and function of the aesthetic symbol in Kantian moral philosophy. In particular, it explores the hypothesis that Blumenberg’s analysis of ‘pregnance’ and ‘rhetoric’ are useful for identifying and evaluating the processes involved in self-persuasion to the moral perspective.

Troeltsch and Simmel both feared that the loss of religion on a cultural scale would deprive the modern European world of a potentially effective resource for ethical and spiritual unity. To conserve this resource, Simmel argued for a purely formal spirituality that depended upon no doctrines and no institutions. Troeltsch concluded that on a cultural scale, Simmel's program was a recipe for spiritual and ethical suicide; he recommended instead the possibility of a liberal Christianity. In developing this possibility, Troeltsch (...) used Simmel's analysis of symbols of exchange to present a fruitful new sociological conception of the symbol of Christ as a model for shaping the interaction of Christianity and society. (shrink)

This paper deals with Frege’s early critique of formalism in the philosophy of mathematics. Frege opposes meaningful arithmetic, according to which arithmetical formulas express a sense and arithmetical rules are grounded in the reference of the signs, to formal arithmetic, exemplified in particular by J. Thomae, whose “formal standpoint”, according to Frege, is that arithmetic should be understood as a manipulation of meaningless figures. However, Frege’s discussion of Thomae’s analogy between arithmetic and chess shows that Frege does not (...) understand his main point, which is that we must distinguish conceptually between statements about chess figures, and the chess pieces they represent. Indeed, Thomae’s fruitful use of this comparison undermines the ontological conception of arithmetic represented by Frege. The chess pieces do not go proxy for anything, but playing chess is not for that reason just manipulation of physical chess figures. This is also Wittgenstein’s point when he criticizes Frege for not seeing the “justified side of formalism”. Thomae’s formalism can be clarified by using the distinction between sign and symbol. Symbols are never meaningless or empty forms or signs, since they have a role or function in a symbolism, which one may call their meaning. The discussion of the chess analogy shows that Frege fails to see this operative aspect of the symbolism. We can conclude that the “formal standpoint” that Frege criticizes is his fabrication, rather than anything we can attribute to Thomae. (shrink)