In this paper we introduce the concept of conservative translation between logics. We present some necessary and sufficient conditions for a translation to be conservative and study some general properties of logical systems, these properties being characterized by the existence of conservative translations between the systems. We prove that the class constituted by logics and conservative translations between them determines a co-complete subcategory of the bi-complete category constituted by logics and translations.

Following a proposal by Kooi and Tamminga, we introduce a conservative translation manual for every four-valued truth-functional propositional logic into a modal logic. However, the application of this translation does not preserve the intuitive reading of the truth-values for every four-valued logic. In order to solve this problem, we modify the translation manual and prove its conservativity by exploiting the method of generalized truth-values.

We provide sufficient conditions for the existence of a conservative translation from a consequence system to another one. We analyze the problem in many settings, namely when the consequence systems are generated by a deductive calculus or by a logic system including both proof-theoretic and model-theoretic components. We also discuss reflection of several metaproperties with the objective of showing that conservative translations provide an alternative to proving such properties from scratch. We discuss soundness and completeness, disjunction property (...) and metatheorem of deduction among others. We provide several illustrations of conservative translations. (shrink)

We study the notion of conservative translation between logics introduced by (Feitosa & D’Ottaviano2001). We show that classical propositional logic (CPC) is universal in the sense that every finitary consequence relation over a countable set of formulas can be conservatively translated into CPC. The translation is computable if the consequence relation is decidable. More generally, we show that one can take instead of CPC a broad class of logics (extensions of a certain fragment of full Lambek calculus FL) including (...) most nonclassical logics studied in the literature, hence in a sense, (almost) any two reasonable deductive systems can be conservatively translated into each other. We also provide some counterexamples, in particular the paraconsistent logic LP is not universal. (shrink)

Certain translational T-schemes of the form True « f, where f can be almost any translation you like of f, will be a conservative extension of Peano arithmetic. I have an inkling that this means something philosophically, but I don’t understand my own inkling.

Certain translational T-schemes of the form True(“f”) « f(f), where f(f) can be almost any translation you like of f, will be a conservative extension of Peano arithmetic. I have an inkling that this means something philosophically, but I don’t understand my own inkling.

The mechanisms used to establish embryonic polarity are still largely unknown. A recent paper(1) describes the expression pattern of the gene glp‐1, which is required for induction events during development of the nematode Caenorhabditis elegans. Although glp‐1 RNA is found throughout the early embryo, Glp‐1 protein is only expressed in anterior cells. This negative translational regulation in posterior cells is shown to be mediated through sequences in the glp‐1 3′ untranslated region (3′UTR). Thus in nematodes, as in Drosophila, translational repression (...) is one mechanism used to establish the embryonic anterior‐posterior axis. (shrink)

Not uncommon for Russian translations of British philosophical classics is the problem of not conveying the notions of imagination and fancy properly. The purpose of this paper is to serve as a reminder of the fact that concepts of fancy and imagination began to grow apart as early as the first part of 18 th century, and it is necessary to treat them accordingly for the translation to be correct. Very soon, the notion of imagination and the distinction between (...) imagination and fancy began to be involved in the contemplation of political reality. Today it is the notion of political imagination that attracts researchers the most, providing a tool for explaining continuity and discontinuities in political process as well as left utopianism and conservative nostalgia. The awareness of the distinction between imagination and fancy could foster research activity in such fields as the history of ideas and intellectual history as well as studies in ideology and power. The distinction is examined on the basis of texts usually considered to be written by authors of conservative strand. It is an interesting fact, indeed, that it was conservatives who made the main contribution to the development of this distinction in English-language philosophy. Among them are Coleridge, who resolutely draw the line between fancy and imagination, and Burke with his appeal to the moral imagination. The kindred typology of imagination was proposed in 20 th century by such thinkers as Irving Babbitt, T.S. Eliot and Russell Kirk. The importance of Kirk lies partly in that fact that he began the discussion of the conservative attitude to imagination and tried to frame it as a coherent narrative. (shrink)

The main objective o f this descriptive paper is to present the general notion of translation between logical systems as studied by the GTAL research group, as well as its main results, questions, problems and indagations. Logical systems here are defined in the most general sense, as sets endowed with consequence relations; translations between logical systems are characterized as maps which preserve consequence relations (that is, as continuous functions between those sets). In this sense, logics together with translations (...) form a bicomplete category of which topological spaces with topological continuous functions constitute a full subcategory. We also describe other uses of translations in providing new semantics for non-classical logics and in investigating duality between them. An important subclass of translations, the conservative translations, which strongly preserve consequence relations, is introduced and studied. Some specific new examples of translations involving modal logics, many-valued logics, para- consistent logics, intuitionistic and classical logics are also described. (shrink)

This paper presents a simple pair of first-order theories that are not definitionally (nor Morita) equivalent, yet are mutually conservatively translatable and mutually 'surjectively' translatable. We use these results to clarify the overall geography of standards of equivalence and to show that the structural commitments that theories make behave in a more subtle manner than has been recognized.

We systematically study conservation theorems on theories of semi-classical arithmetic, which lie in-between classical arithmetic $\mathsf {PA}$ and intuitionistic arithmetic $\mathsf {HA}$. Using a generalized negative translation, we first provide a structured proof of the fact that $\mathsf {PA}$ is $\Pi _{k+2}$ -conservative over $\mathsf {HA} + {\Sigma _k}\text {-}\mathrm {LEM}$ where ${\Sigma _k}\text {-}\mathrm {LEM}$ is the axiom scheme of the law-of-excluded-middle restricted to formulas in $\Sigma _k$. In addition, we show that this conservation theorem is optimal in (...) the sense that for any semi-classical arithmetic T, if $\mathsf {PA}$ is $\Pi _{k+2}$ -conservative over T, then ${T}$ proves ${\Sigma _k}\text {-}\mathrm {LEM}$. In the same manner, we also characterize conservation theorems for other well-studied classes of formulas by fragments of classical axioms or rules. This reveals the entire structure of conservation theorems with respect to the arithmetical hierarchy of classical principles. (shrink)

Dyadic semantics is a sort of non-truth-functional bivalued semantics introduced in Caleiro et al. Logica Universalis, Birkhäuser, Basel, pp 169–189, 2005). Here we introduce an algorithmic procedure for constructing conservative translations of logics characterised by dyadic semantics into classical propositional logic. The procedure uses fresh propositional variables, which we call hidden variables, to represent the indeterminism of dyadic semantics. An alternative algorithmic procedure for constructing conservative translations of any finite-valued logic into classical logic is also introduced. (...) In this alternative procedure hidden variables are also used, but in this case to represent the degree of true or falsehood of propositions. (shrink)

After a brief promenade on the several notions of translations that appear in the literature, we concentrate on three paradigms of translations between logics: ( conservative ) translations , transfers and contextual translations . Though independent, such approaches are here compared and assessed against questions about the meaning of a translation and about comparative strength and extensibility of a logic with respect to another.

A basic result in intuitionism is Π02-conservativity. Take any proof p in classical arithmetic of some Π02-statement , with P decidable). Then we may effectively turn p in some intuitionistic proof of the same statement. In a previous paper [1], we generalized this result: any classical proof p of an arithmetical statement ∀x.∃y.P, with P of degree k, may be effectively turned into some proof of the same statement, using Excluded Middle only over degree k formulas. When k = 0, (...) we get the original conservativity result as particular case. This result was a by-product of a semantical construction. J. Avigad of Carnegie Mellon University, found a short, direct syntactical derivation of the same result, using H. Friedman's A-translation. His proof is included here with his permission. (shrink)

This work presents some basic results on a theory of translations between logics and a short revision about Łukasiewicz's logics. Then, it is shown, using facts about algebraic semantics, that there is a conservative translation from every finite Łukasiewicz's logic into classical logic. However, this is not a constructive result.

I consider Ralph Waldo Emerson’s creative appropriation of a philosophical doctrine that helps to make sense of an attitude towards life, its gifts and its burdens, that is often expressed in Puritan diaries. The doctrine, now known as the doctrine of continuous creation, holds that in conserving the world, God re-creates it at every moment, making the same creative effort at each ever-advancing now that God made at the very beginning. Continuous creation was explicitly endorsed by at least one Puritan (...) diarist, Jonathan Edwards, and it helps to explain the intense self-inspection and valiant response to life to which other Puritan diarists (including Emerson's aunt, Mary Moody Emerson) testify. Continuous creation was an important ingredient in the idealism of Edwards and, once translated, it became an important ingredient in the idealism of Emerson. My primary aim to describe Emerson’s creative translation of the doctrine as Edwards understood it, but I also discuss Emerson's relation to the Puritan diary, considered as a literary form. I close by suggesting that for us, a version of the doctrine of continuous creation can perhaps be a source of optimism and an incentive to action, as I believe it was for Emerson. I also comment briefly on Emerson's grateful reliance on text-to-text translations. When Emerson studied translations of sacred texts from around the world, what he heard was not difference and dissent, but agreement: agreement on the very points that united him with Edwards, different as they were in other ways. (shrink)

Consumers do not always follow their ideological beliefs about the need to engage in environmentally friendly consumption. We propose that Commitment to Beliefs —the general tendency to follow one’s value-based beliefs—can help identify who is most likely to follow their environmental ideologies. We predicted that CTB would amplify the effect of beliefs prescribing environmental stewardship, or neglect, on corresponding intentions, behavior, and purchasing decisions. In two studies, CTB amplified the positive and negative effects of relevant EF ideologies on EF purchase (...) decisions, and consumption and conservation attitudes, intentions, as well as future behavior. In each study, only people with higher levels of CTB demonstrated the most ideologically consistent consumption and conservation intentions and behavior. These findings clarify who is most likely to align their decisions and lifestyles according to their sustainable consumption ideologies. The amplification effect of CTB, and the CTB variable itself, present new contributions to consumer behavior research and the domains of sustainable or ethical consumption in particular and offer wide-ranging potential for marketing practitioners and researchers. (shrink)

The aim of this paper is to describe from a semantic perspective the problem of conservativity of classical first-order theories over their intuitionistic counterparts. In particular, we describe a class of formulae for which such conservativity results can be proven in case of any intuitionistic theory T which is complete with respect to a class of T-normal Kripke models. We also prove conservativity results for intuitionistic theories which are closed under the Friedman translation and complete with respect to a class (...) of conversely well-founded Kripke models. The results can be applied to a wide class of intuitionistic theories and can be viewed as generalization of the results obtained by syntactic methods. (shrink)

The explicit history of the “hidden variables” problem is well-known and established. The main events of its chronology are traced. An implicit context of that history is suggested. It links the problem with the “conservation of energy conservation” in quantum mechanics. Bohr, Kramers, and Slaters (1924) admitted its violation being due to the “fourth Heisenberg uncertainty”, that of energy in relation to time. Wolfgang Pauli rejected the conjecture and even forecast the existence of a new and unknown then elementary particle, (...) neutrino, on the ground of energy conservation in quantum mechanics, afterwards confirmed experimentally. Bohr recognized his defeat and Pauli’s truth: the paradigm of elementary particles (furthermore underlying the Standard model) dominates nowadays. However, the reason of energy conservation in quantum mechanics is quite different from that in classical mechanics (the Lie group of all translations in time). Even more, if the reason was the latter, Bohr, Cramers, and Slatters’s argument would be valid. The link between the “conservation of energy conservation” and the problem of hidden variables is the following: the former is equivalent to their absence. The same can be verified historically by the unification of Heisenberg’s matrix mechanics and Schrödinger’s wave mechanics in the contemporary quantum mechanics by means of the separable complex Hilbert space. The Heisenberg version relies on the vector interpretation of Hilbert space, and the Schrödinger one, on the wave-function interpretation. However the both are equivalent to each other only under the additional condition that a certain well-ordering is equivalent to the corresponding ordinal number (as in Neumann’s definition of “ordinal number”). The same condition interpreted in the proper terms of quantum mechanics means its “unitarity”, therefore the “conservation of energy conservation”. In other words, the “conservation of energy conservation” is postulated in the foundations of quantum mechanics by means of the concept of the separable complex Hilbert space, which furthermore is equivalent to postulating the absence of hidden variables in quantum mechanics (directly deducible from the properties of that Hilbert space). Further, the lesson of that unification (of Heisenberg’s approach and Schrödinger’s version) can be directly interpreted in terms of the unification of general relativity and quantum mechanics in the cherished “quantum gravity” as well as a “manual” of how one can do this considering them as isomorphic to each other in a new mathematical structure corresponding to quantum information. Even more, the condition of the unification is analogical to that in the historical precedent of the unifying mathematical structure (namely the separable complex Hilbert space of quantum mechanics) and consists in the class of equivalence of any smooth deformations of the pseudo-Riemannian space of general relativity: each element of that class is a wave function and vice versa as well. Thus, quantum mechanics can be considered as a “thermodynamic version” of general relativity, after which the universe is observed as if “outside” (similarly to a phenomenological thermodynamic system observable only “outside” as a whole). The statistical approach to that “phenomenological thermodynamics” of quantum mechanics implies Gibbs classes of equivalence of all states of the universe, furthermore re-presentable in Boltzmann’s manner implying general relativity properly … The meta-lesson is that the historical lesson can serve for future discoveries. (shrink)

ABSTRACT This work presents the concepts of translation and conservative translation between logics. By using algebraic semantics we introduce several conservative translations involving the classical propositional calculus and the many-valued calculi of Post and Lukasiewicz.

In 1999, da Silva, D'Ottaviano and Sette proposed a general definition for the term translation between logics and presented an initial segment of its theory. Logics are characterized, in the most general sense, as sets with consequence relations and translations between logics as consequence-relation preserving maps. In a previous paper the authors introduced the concept of conservative translation between logics and studied some general properties of the co-complete category constituted by logics and conservative translations between them. (...) In this paper we present some conservative translations involving classical logic, Lukasiewicz three-valued system L3, the intuitionistic system I1 and several paraconsistent logics, as for instance Sette's system P1, the D'Ottaviano and da Costa system J3 and da Costa's systems Cn, 1≤ n≤ω. (shrink)

In 1999, da Silva, D'Ottaviano and Sette proposed a general definition for the term translation between logics and presented an initial segment of its theory. Logics are characterized, in the most general sense, as sets with consequence relations and translations between logics as consequence-relation preserving maps. In a previous paper the authors introduced the concept of conservative translation between logics and studied some general properties of the co-complete category constituted by logics and conservative translations between them. (...) In this paper we present some conservative translations involving classical logic, Lukasiewicz three-valued system L₃, the intuitionistic system Iⁱ and several para-consistent logics, as for instance Sette's system Pⁱ, the D'Ottaviano and da Costa system J₃ and da Costa's systems $\text{C}_{n}$ , 1 ≤ n ≤ ω. (shrink)

Relevance logic is ordinarily seen as a subsystem of classical logic under the translation that replaces arrows by horseshoes. If, however, we consider the arrow as an additional connective alongside the horseshoe, then another perspective emerges: the theses of relevance logic, specifically the system R, may also be seen as the output of a conservative extension of the relation of classical consequence. We describe two ways in which this may be done. One is by defining a suitable closure relation (...) out of the set of theses of relevance logic; the other is by adding to the usual natural deduction system for it further rules with ‘projective constraints’, whose application restricts the subsequent application of other rules. The significance of the two constructions is also discussed. (shrink)

This is the first time that the Disputations 20-22 have been translated into English. They deal with the divine action of creation, conservation and concurrence.

Europa presents, to the modern reader, the foreign political thought of four major German conservatives from the crucial period between the Second Reich and the Second World War. The texts chosen reveal the spiritual and cultural motives, of German conservatives at the turn of the century, that inspired expansionist policies and the consistent opposition to the Jewish financial rule. The lack of German translations of these important texts so far has clearly been a disadvantage to the modern historian in (...) his assessment of the philosophical significance of the Conservative, as well as of the National Socialist, foreign political ideology. (shrink)

We give a variant of the Gödel-Gentzen-negative translation, and a syntactic characterization which entails conservativity result for formulas.

Recent work on the history of General Relativity by Renn, Sauer, Janssen et al. shows that Einstein found his field equations partly by a physical strategy including the Newtonian limit, the electromagnetic analogy, and energy conservation. Such themes are similar to those later used by particle physicists. How do Einstein's physical strategy and the particle physics derivations compare? What energy-momentum complex did he use and why? Did Einstein tie conservation to symmetries, and if so, to which? How did his work (...) relate to emerging knowledge of the canonical energy-momentum tensor and its translation-induced conservation? After initially using energy-momentum tensors hand-crafted from the gravitational field equations, Einstein used an identity from his assumed linear coordinate covariance x'=Mx to relate it to the canonical tensor. Usually he avoided using matter Euler-Lagrange equations and so was not well positioned to use or reinvent the Herglotz-Mie-Born understanding that the canonical tensor was conserved due to translation symmetries, a result with roots in Lagrange, Hamilton and Jacobi. Whereas Mie and Born were concerned about the canonical tensor's asymmetry, Einstein did not need to worry because his Entwurf Lagrangian is modeled not so much on Maxwell's theory as on a scalar theory. Einstein's theory thus has a symmetric canonical energy-momentum tensor. But as a result, it also has 3 negative-energy field degrees of freedom. Thus the Entwurf theory fails a 1920s-30s a priori particle physics stability test with antecedents in Lagrange's and Dirichlet's stability work; one might anticipate possible gravitational instability. This critique of the Entwurf theory can be compared with Einstein's 1915 critique of his Entwurf theory for not admitting rotating coordinates and not getting Mercury's perihelion right. One can live with absolute rotation but cannot live with instability. Particle physics also can be useful in the historiography of gravity and space-time, both in assessing the growth of objective knowledge and in suggesting novel lines of inquiry to see whether and how Einstein faced the substantially mathematical issues later encountered in particle physics. This topic can be a useful case study in the history of science on recently reconsidered questions of presentism, whiggism and the like. Future work will show how the history of General Relativity, especially Noether's work, sheds light on particle physics. (shrink)

Like belief revision, conceptual change has rational aspects. The paper discusses this for predicate change. We determine the meaning of predicates by a set of imaginable instances, i.e., conceptually consistent entities that fall under the predicate. Predicate change is then an alteration of which possible entities are instances of a concept. The recent exclusion of Pluto from the category of planets is an example of such a predicate change. In order to discuss predicate change, we define a monadic predicate logic (...) with three different kinds of lawful belief: analytic laws, which hold for all possible instances; doxastic laws, which hold for the most plausible instances; and typicality laws, which hold for typical instances. We introduce predicate changing operations that alter the analytic laws of the language and show that the expressive power is not affected by the predicate change. One can translate the new laws into old laws and vice versa. Moreover, we discuss rational restrictions of predicate change. These limit its possible influence on doxastic and typicality laws. Based on the results, we argue that predicate change can be quite conservative and sometimes even hardly recognisable. (shrink)

In this paper, Charles Mills discusses what he calls “white ignorance”, developing one of the main themes of his 1997 book, The Racial Contract. His discussion is concerned with the idea of a cognitive disadvantage based on membership in a social group, which is not strange to the radical philosophical tradition, and that has been explored with more vigor in the recent Social Epistemology, in debates about epistemic injustices, silencing, willful ignorance, cognitive biases, epistemological standpoints, etc. Mills argues for an (...) “Epistemology of the white ignorance”, a racially and socially situated epistemology, which contraposes itself, in a great extent, to the individualistic tendencies of the traditional epistemological work, while conserving the interests in objectivity and truth of this work. (shrink)

The “Treatise on the Relationship of the Real and the Ideal in Nature, or the Development of the First Principles of the Philosophy of Nature and the Principles of Gravity and Light” is one of the last essays on Naturphilosophie that Schelling wrote. It was a topic that had occupied his attention since 1796, and as such it marks the end of an era. It is distinguished by its unusual approach to the problem of matter, which becomes, in his discussion, (...) the problem of force or energy. Without being able to avail himself of the language of the conservation of energy or mass, it can be argued that Schelling makes a valiant attempt to express that insight, using the terminology of the bond and the entities bound by it. The text reaffirms Schelling’s strong affinities with Spinoza, anticipates Schopenhauer, and continues his quarrel with Fichte. (shrink)

Bacteria use trans‐translation to rescue stalled ribosomes and target incomplete proteins for proteolysis. Despite similarities between tRNAs and transfer‐messenger RNA (tmRNA), the key molecule for trans‐translation, new structural and biochemical data show important differences between translation and trans‐translation at most steps of the pathways. tmRNA and its binding partner, SmpB, bind in the A site of the ribosome but do not trigger the same movements of nucleotides in the rRNA that are required for codon recognition by tRNA. tmRNA‐SmpB moves from (...) the A site to the P site of the ribosome without subunit rotation to generate hybrid states, and moves from the P site to a site outside the ribosome instead of to the E site. During catalysis, transpeptidation to tmRNA appears to require the ribosomal protein bL27, which is dispensable for translation, suggesting that this protein may be conserved in bacteria due to trans‐translation. These differences provide insights into the fundamental nature of trans‐translation, and provide targets for new antibiotics that may have decrease cross‐reactivity with eukaryotic ribosomes. (shrink)

In this paper we define an augmentation mHC of the Heyting propositional calculus HC by a modal operator ?. This modalized Heyting calculus mHC is a weakening of the Proof-Intuitionistic Logic KM of Kuznetsov and Muravitsky. In Section 2 we present a short selection of attractive (algebraic, relational, topological and categorical) features of mHC. In Section 3 we establish some close connections between mHC and certain normal extension K4.Grz of the modal system K4. We define a translation of mHC into (...) K4.Grz and prove that this translation is exact, i. e. theorem-preserving and deducibility-invariant. We have established (however, in this note we do not present a proof of this) that the lattice of all extensions of mHC is isomorphic to the lattice of normal extensions of K4.Grz (a generalization of the Kuznetsov and Muravitsky theorem). (shrink)

The NeoSynthesis Research Centre (NSRC) was organized to promote sustainable agriculture and resource conservation in the island nation of Sri Lanka. Staffed by people with varied life and cultural backgrounds, NSRC has attempted to develop frameworks or ways of understanding agriculture from more than a single perspective. It is assumed that even a partial understanding of agriculture requires many perspectives because no single set of opinions or discourse based upon a narrow range of life experiences can account for the life (...) processes that capture and process energy through many species,H. Sapiens included. NSRC participants are expected to relate their respective disciplinary paradigms toward a synthetic approach of resource management to be demonstrated under specific environmental and social conditions. Using ecological and energetic perspectives as baseline conceptual frameworks, both scientific and non-scientific descriptions have been incorporated to provide greater understanding of the functioning of Sri Lanka's living communities. Sustainability is not promoted through sound empirical description alone. Broad community participation is required if resource and management is to be modified in any significant way. The notion of sustainability is again translated into a more political and policy language and the forums involved include the public media, administrative and legislative branches of the national government, and the civil service. Is Sri Lanka on a collision course with disaster because of heavy population pressure and irresponsible and unwise landscape management? From experiences over the past 11 years at the NSRC, the steps toward sustainability seem best cast in terms of a discovery and learning process rather than something to be invented in the abstract. (shrink)

A large number of previous reports described an effect of the pituitary hormone prolactin (PRL) on steroid hormone production by the adrenal cortex. However, those studies remained anecdotal and were never converted into a conceptual and mechanistic framework, let alone being translated into clinical care. In the light of our recently published landmark study where we described PRL signalling as a pivotal regulator of the sexually dimorphic adrenal phenotype in mouse and of adrenal androgen production in humans, we present here (...) the overarching hypothesis that PRL signalling increases the activity of Steroidogenic Factor‐1 (SF‐1/NR5A1), a transcription factor that has an essential role in adrenal gland development and function, to regulate adrenal cortex growth and hormonal production in physiological and pathological conditions. PRL can then be considered as a bona fide adrenocorticotropic hormone synergizing with ACTH in the endocrine control of adrenal cortex function. (shrink)

Between 1825 and 1895, Victorian Britain witnessed a significant blossoming of interest in foreign theological literature. Much of this interest, together with a concomitant anxiety, focused on the negotiation of German biblical criticism and the new challenges and possibilities this criticism introduced. This article thematizes this transnational literary and theological encounter, paying particular attention both to the major book series that undertook to mediate (especially German) criticism to Britain, and to the burgeoning periodical literature that supplied ’foreign intelligence’ and short (...) translations. Translation served as both a liberalizing force as it introduced critical results that troubled some proponents of orthodoxy, but also offered a channel for resistance as doctrinally conservative strands of German biblical scholarship found a warm reception. The article is followed by a chronologically organized bibliography of translated works published in Britain from 1825 to 1895. (shrink)

In the eleventh of his Antiquarian Letters, Gotthold Ephraim Lessing discusses a phrase from Lucian's description of the painting by Zeuxis called A Family of Centaurs: ‘at the top of the painting a centaur is leaning down as if from an observation point, smiling’. ‘This as if from an observation point, Lessing notes, obviously implies that Lucian himself was uncertain whether this figure was positioned further back, or was at the same time on higher ground. We need to recognize the (...) logic of ancient bas-reliefs where figures further to the back look over those at the front, not because they are actually positioned above them but because they are meant to appear as if standing behind.'1 · 1. The passage is in George Lessing, Briefe, antiquarischen Inhalts, p. 81. Panofsky's discussion does not note that the original text of Lucian makes clear that what is described is a copy of the original painting. This means that some of the issues of misunderstanding situated by Lessing and Panofsky in Lucian's court may in principle be attributable to the copyist. This makes no difference to the conceptual thrust of Panofsky's case.—Trans. (shrink)