Saul Kripke has proposed an argument to show that there is a serious problem with many computational accounts of physical systems and with functionalist theories in the philosophy of mind. The problem with computational accounts is roughly that they provide no noncircular way to maintain that any particular function with an infinite domain is realized by any physical system, and functionalism has the similar problem because of the character of the functional systems that are supposed to be realized by organisms. (...) This paper shows that the standard account of what it is for a physical system to compute a function can avoid Kripke's criticisms without being reduced to circularity; a very minor and natural elaboration of the standard account suffices to save both functionalist theories and computational accounts generally. (shrink)

Noam Chomsky and other linguists and psychologists have suggested that human linguistic behavior is somehow governed by a mental representation of a transformational grammar. Challenges to this controversial claim have often been met by invoking an explicitly computational perspective: It makes perfect sense to suppose that a grammar could be represented in the memory of a computational device and that this grammar could govern the device's use of a language. This paper urges, however, that the claim that humans are such (...) a device is unsupported and that it seems unlikely that linguists and psychologists really want to claim any such thing. Evidence for the linguists' original claim is drawn from three main sources: the explanation of language comprehension and other linguistic abilities; evidence for formal properties of the rules of the grammar; and the explanation of language acquisition. It is argued in this paper that none of these sources provides support for the view that the grammar governs language processing in something like the way a program governs the operation of a programmed machine. The computational approach, on the contrary, suggests ways in which linguistic abilities can be explained without the attribution of any explicit representation of rules governing linguistic behavior. (shrink)

Quine's (1969) proposal that the foundationalist programs in epistemology should be abandoned in favor of a scientific study of how we come to hold our theories about the world is still widely misunderstood. It does not eliminate the possibility of rational adjudication of scientific dispute, nor is it essentially tied to behaviorist approaches in psychology. On the contrary, recent work in psychology and philosophy of science can very naturally be seen as embodying the sort of program envisioned by Quine; now (...) freed of behaviorist strictures, it clearly addresses issues that have been of interest in traditional epistemology. This view is defended with particular attention to Quine's concerns with translation and the related concerns with belief individuation which have inspired critics of recent cognitive psychology. (shrink)

By formalizing recent syntactic theories for natural languages Stabler shows how their complexity can be handled without guesswork or oversimplification. By formalizing recent syntactic theories for natural languages in the tradition of Chomsky's Barriers, Stabler shows how their complexity can be handled without guesswork or oversimplification. He introduces logical representations of these theories together with special deductive techniques for exploring their consequences that will provide linguists with a valuable tool for deriving and testing theoretical predictions and for experimenting (...) with alternative formulations of grammatical principles. Stabler's novel approach allows results to be deduced with straightforward calculations and provides a systematic framework for tackling the problem of how speakers can infer the properties of an utterance from principles of the grammar. The special treatment of equality, induction principles, and inclusion of a general method for collecting structures from proofs means that sophisticated linguistic arguments can be carried out in detail, giving a rich perspective to issues in linguistic theory and parsing. (shrink)

Saul Kripke has proposed an argument to show that there is a serious problem with many computational accounts of physical systems and with functionalist theories in the philosophy of mind. The problem with computational accounts is roughly that they provide no noncircular way to maintain that any particular function with an infinite domain is realized by any physical system, and functionalism has the similar problem because of the character of the functional systems that are supposed to be realized by organisms. (...) This paper shows that the standard account of what it is for a physical system to compute a function can avoid Kripke's criticisms without being reduced to circularity; a very minor and natural elaboration of the standard account suffices to save both functionalist theories and computational accounts generally. (shrink)

Linguists rely on intuitive conceptions of structure when comparing expressions and languages. In an algebraic presentation of a language, some natural notions of similarity can be rigorously defined (e.g. among elements of a language, equivalence w.r.t. isomorphisms of the language; and among languages, equivalence w.r.t. isomorphisms of symmetry groups), but it tums out that slightly more complex and nonstandard notions are needed to capture the kinds of comparisons linguists want to make. This paper identihes some of the important notions of (...) structural similarity, with attention to similarity claims that are prominent in the current linguistic tradition of transformational grammar. @ 2002 Elsevier Science B.V. All rights reserved. (shrink)

Four different kinds of grammars that can define crossing dependencies in human language are compared here: (i) context sensitive rewrite grammars with rules that depend on context, (ii) matching grammars with constraints that filter the generative structure of the language, (iii) copying grammars which can copy structures of unbounded size, and (iv) generating grammars in which crossing dependencies are generated from a finite lexical basis. Context sensitive rewrite grammars are syntactically, semantically and computationally unattractive. Generating grammars have a collection of (...) nice properties that ensure they define only “mildly context sensitive” languages, and Joshi has proposed that human languages have those properties too. But for certain distinctive kinds of crossing dependencies in human languages, copying or matching analyses predominate. Some results relevant to the viability of mildly context sensitive analyses and some open questions are reviewed. (shrink)

Minimalist grammars (MGs) and multiple context-free grammars (MCFGs) are weakly equivalent in the sense that they define the same languages, a large mildly context-sensitive class that properly includes context-free languages. But in addition, for each MG, there is an MCFG which is strongly equivalent in the sense that it defines the same language with isomorphic derivations. However, the structure-building rules of MGs but not MCFGs are defined in a way that generalizes across categories. Consequently, MGs can be exponentially more succinct (...) than their MCFG equivalents, and this difference shows in parsing models too. An incremental, top-down beam parser for MGs is defined here, sound and complete for all MGs, and hence also capable of parsing all MCFG languages. But since the parser represents its grammar transparently, the relative succinctness of MGs is again evident. Although the determinants of MG structure are narrowly and discretely defined, probabilistic influences from a much broader domain can influence even the earliest analytic steps, allowing frequency and context effects to come early and from almost anywhere, as expected in incremental models. (shrink)

The performance of a connectionist learning system on a simple problem has been described by Hinton and is briefly reviewed here: a finite set is learned from a finite collection of finite sets, and the system generalizes correctly from partial information by finding simple "features" of the environment. For comparison, a very similar problem is formulated in the Gold paradigm of discrete learning functions. To get generalization similar to the connectionist system, a non-conservative learning strategy is required. We define a (...) simple, non-conservative strategy that generalizes like the connectionist system, finding simple "features" of the environment. By placing an arbitrary finite bound on the number and complexity of the features to be found, learning can be guaranteed relative to a probabilistic criterion of success. However, this approach to induction has essentially the same problems as many others that have failed. (shrink)

We illustrate a novel conception of linguistic invariant which applies to grammars of different natural languages even though they may use different categories and have difl'erent rules. We illustrate formally how semantically defined notions, such as "is an anaphor" may be invariant in all linguistically motivated grammars, and we show that individual morphemes, such as case markers, may be invariant in grammars that have them in exactly the same sense in which properties, such as "is a Verb Phrase" or relations (...) such as "is a constituent of". (shrink)

Plotinus’ famous treatise against the Gnostics (33), together with contemporary and thematically related treatises on Intelligible Beauty (31), on Number (34), and on Free Will and the Will of the One (39), can be seen as providing the essential components of a Plotinian defense of polytheism against conceptual moves that, while associated for him primarily with Gnostic sectarians overlapping with Platonic philosophical circles, will become typical of monotheism in its era of hegemony. When Plotinus’ Gnostics ‘contract’ divinity into a single (...) God, they not only devalue the cosmos for its multiplicity and diversity, but also multiply intelligible principles unreasonably. This is because they have foreclosed the distinction, which is to become increasingly explicit in the later antique Platonists, between the intelligible and that which is given existentially, the domain belonging to Plotinus’ indeterminate multiplicity of ‘intelligible Gods’, as opposed to the dialectically determinate number of intelligible principles. Plotinus is prescient in recognizing that incipient monotheism threatens to erase the distinction between philosophy and theology, and between both of these and psychology, the final outcome of which can only be solipsism or nihilism. The defense of polytheism is seen in this fashion to be essential to the preservation of the space for philosophical discourse. (shrink)

In this reading of the Euthyphro, Socrates and Euthyphro are seen less in a primordial conflict between reason and devotion, than as sincere Hellenic polytheists engaged in an inquiry based upon a common intuition that, in addition to the irreducible agency of the Gods, there is also some irreducible intelligible content to holiness. This reading is supported by the fact that Euthyphro does not claim the authority of revelation for his decision to prosecute his father, but rather submits it to (...) elenchus, and that Euthyphro does not embrace the ‘solution’ of theological voluntarism when Socrates explicitly offers it. Since the goal of this inquiry is neither to eliminate the noetic content of the holy, nor to eliminate the Gods’ agency, the purpose of the elenchus becomes the effort to articulate the results of this productive tension between the Gods and the intelligible on the several planes of Being implied by each conception of the holy which is successively taken up and dialectically overturned to yield the conception appropriate to the next higher plane, a style of interpretation characteristic of the ancient Neoplatonists. (shrink)

The essay explores the systematic relationship in the work of Giordano Bruno (1548-1600) between his monadology, his metaphysics as presented in works such as De la causa, principio et uno, the mythopoeic cosmology of Lo spaccio de la bestia trionfante, and practical works like De vinculis in genere. Bruno subverts the conceptual regime of the Aristotelian substantial forms and its accompanying cosmology with a metaphysics of individuality that privileges individual unity (singularity) over formal unity and particulars over substantial forms without (...) sacrificing a metaphysical perspective on the cosmos. The particular is individuated as a unique site of desire, continually transforming but able to entrain itself and others through phantasmatic ‘bonding’, the new source of regularity in Bruno’s polycentric universe. Bruno thus tries to do justice to the demands of intelligibility as well as transformative eros. The essay concludes with a note on Bruno’s geometry as it relates to his general conception of form. (shrink)

Continuing the systematic henadological interpretation of Proclus' Platonic Theology begun in "The Intelligible Gods in the Platonic Theology of Proclus" (Methexis 21, 2008, pp. 131-143), the present article treats of the basic characteristics of intelligible-intellective (or noetico-noeric) multiplicity and its roots in henadic individuality. Intelligible-intellective multiplicity (the hypostasis of Life) is at once a universal organization of Being in its own right, and also transitional between the polycentric henadic manifold, in which each individual is immediately productive of absolute Being, and (...) the formal intellective organization, which is monocentrically and diacritically disposed. Intelligible-intellective multiplicity is generated from the dyadic relationship of henads to their power(s), the phase of henadic individuality expressed in the second intelligible triad, and is mediated, unlike the polycentric manifold, but not by identity and difference, like the intellective organization. Instead, the hypostasis of Life is constituted by ideal motility and spatiality, figural dispositions, and the intersubjective relations depicted in the divine symposium of Plato's Phaedrus. (shrink)

Completing the systematic henadological interpretation of Proclus' Platonic Theology begun in "The Intelligible Gods in the Platonic Theology of Proclus" (Méthexis 21, 2008, pp. 131-143) and "The Second Intelligible Triad and the Intelligible-Intellective Gods" (Methexis 23, 2010, pp. 137-157), the present article concerns the conditions of the emergence of fully mediated, diacritical multiplicity out of the polycentric henadic manifold. The product of the activity of the intellective Gods (that is, the product of the intellective activity of Gods as such), in (...) resolving the contradiction between existential uniqueness and universalizable potencies in the divine natures, also grounds the human exercise of phi- losophical cognition in the founding self-analysis of divine individuals. (shrink)

The comparison drawn by the Neoplatonist Olympiodorus between the Stoic doctrine of the reciprocal implication of the virtues and the Neoplatonic doctrine of the presence of all the gods in each helps to elucidate the latter. In particular, the idea of primary and secondary “perspectives” in each virtue, when applied to Neoplatonic theology, can clarify certain theoretical statements made by Proclus in his Cratylus commentary concerning specific patterns of inherence of deities in one another. More broadly, the “polycentric” nature of (...) Neoplatonic theology provides a theoretical articulation for henotheistic practices within polytheism without invoking evolutionist notions of “monotheistic tendencies.” The Neoplatonic distinction between the modes of unity exhibited by divine individuals (“henads”) and ontic units (“monads”), which is integral to the polycentric theology, also provides a theoretical basis for the non reductive crosscultural comparison between deities. The polycentric theology thus offers a promising foundation for a polytheistic philosophy of religion. (shrink)

In henadological Platonism, the significance of “the One” is understood to lie, not in an eminent singular entity, but in the modes of unity and the ways of being a unit. The science of units qua units is a systematic ground and counterweight to substance-based ontology, and manifests an organic bond with theology as the science of relation to supra-essential individuals or Gods. Because of the basic nature of unity relative to being, doctrines respecting unity tend to situate themselves as (...) critiques of ontology; they exhibit both an analytical and a soteriological value. For its part, bhakti is not a mere sectarian movement but rather an inquiry at once speculative and practical into the nature of the relationship between the human and the divine. It bridges the diverse genres of ancient Indian thought (including the theophanic/cultic, the epic, along with diverse philosophical perspectives) and displays key commonalities with henadological Platonism. This paper begins the process of identifying these common themes with particular reference to the Bhagavadgītā. Chief among its themes is the distinction between structuring cause and structured mixture, which runs through Platonism from the Phaedo to the doctrine of principles, and which parallels the account of action in the Gītā as freedom independent of result, insofar as the latter pertains to the solidarity of worldly causality heteronomous to the agency of the ātman. (shrink)

The Platonist Proclus (c. 412-485 CE) identifies the procession of the angels, daimons, and heroes as operating three universal temporal potencies through which we experience time in the forms of past, present, and future, respectively. This essay explicates the Proclean doctrine of the three forms of time in its context within his system and its wider implications, with particular reference to the form of temporality associated with the heroes. Proclus’ schematic account of heroic temporality offers a systematic metaphysical framework for (...) key themes in the Hellenic literature and cultus of heroes, in particular the dialectic of untimeliness and seasonality in the hero as discussed by Nagy. The heroes are seen to embody a universal relationship of mortal beings to time. In an excursus, the relationship of heroes to time is compared to that of cinema as image of time. (shrink)

This dissertation seeks to demonstrate that Proclus articulates a metaphysics not merely compatible with his polytheism, but to which in fact polytheism is integral. For Proclus the One Itself, which according to the First Hypothesis of the Parmenides neither is, nor is one, is instead as each henad, that is, as each God. The henads or Gods thus form a multiplicity unlike any other. Ontic multiplicities always exhibit mediation, in accord with a logic subordinating the many to the one. Correlatively, (...) ontic unity is formal unity, structured by a logic of wholes and parts. These are the dominant characteristics of the realm of Being. The huperousios, or "supra-essential" domain of the Gods, by contrast, is that of a multiplicity of absolute individuals with no totalizing principle over them and no reciprocal relations between them, insofar as either of these would diminish that quality which they pre-eminently possess, namely unity. The supreme form of unity in Proclus' universe, therefore, is the individuality possessed by each absolutely unique God. Chapters 1--4 are concerned with elucidating the nature of the Gods as such. ;The last three chapters provide a close reading of the third, fourth and fifth books of Proclus' Platonic Theology, which I read as an account of the emergence of ontic unity out of henadic unity through the Gods' progressive self-diremption by which a space of mediation is constituted through which they come ultimately to be conceivable as a multiplicity like any other. The key stages in this process are the ontic hypostases of Being, Life and Intellect. The first represents the analysis of the "elements" of each God as such; the second represents the positing of the Gods in co-emergent groupings or pantheons; the third the emergence of fully reciprocal relations in the actions of mythic narrative. At the end of this cosmogonic process, the basic intellectual structures have been constituted which allow the formulation of the philosophical system. The relationship between the Gods and Being is thus embodied in that between myth and dialectic, theology and philosophy. (shrink)

This article seeks in the Platonic philosophers of late antiquity insights applicable to a new discipline, the philosophy of Pagan religion. An impor¬tant element of any such discipline would be a method of mythological hermeneutics that could be applied cross-culturally. The article draws par¬ticular elements of this method from Sallust and Olympiodorus. Sallust’s five modes of the interpretation of myth (theological, physical, psychical, material and mixed) are discussed, with one of them, the theological, singled out for its applicability to all (...) myths and because it interprets myth in reference exclusively to the nature of the Gods and their relationship to a model of the cosmos in its totality. The other modes of interpretation, while useful in particular contexts, are not uniformly applicable to all myths, interpret the myths as concerning things other than the Gods themselves, and interpret the myths with reference to particular sectors of the cosmos. Accordingly, it is from Sallust’s theological mode of interpre¬tation that the new method draws its inspiration. From Olympiodorus the method derives strategies for interpreting basic narrative attributes that myths share with all stories. Thus temporal sequence is interpreted as an ascent, from our perspective, from less perfect to more perfect manifestations of the powers of the Gods. Passivity, conflict, and transitive relations in general between the Gods are interpreted as expressing attributes of the cosmos to the constitution of which the Gods dedicate their energies, rather than as placing constraint upon the Gods themselves. The article concludes with a series of broad principles meant to guide the new method. (shrink)