This is a comprehensive study of the Derveni Papyrus. The papyrus, found in 1962 near Thessaloniki, is not only one of the oldest surviving Greek papyri but is also considered by scholars as a document of primary importance for a better understanding of the religious and philosophical developments in the fifth and fourth centuries BC. Gábor Betegh aims to reconstruct and systematically analyse the different strata of the text and their interrelation by exploring the archaeological context; the interpretation (...) of rituals in the first columns of the text; the Orphic poem commented on by the author of the papyrus; and the cosmological and theological doctrines which emerge from the Derveni author's exegesis of the poem. Betegh discusses the place of the text in the context of late Presocratic philosophy and offers an important preliminary edition of the text of the papyrus with critical apparatus and English translation. (shrink)

A Critical Notice of Thomas KjellerJohansen, Plato’s Natural Philosophy. A Study of the Timaeus-Critias.

The paper first discusses the metaphysical framework that allows the soul's integration into the physical world. A close examination of B36, supported by the comparative evidence of some other early theories of the soul, suggests that the word psuchê could function as both a mass term and a count noun for Heraclitus. There is a stuff in the world, alongside other physical elements, that manifests mental functions. Humans, and possibly other beings, show mental functions in so far as they have (...) a portion of that stuff. Turning to the physical characterization of the soul, the paper argues that B36 is entirely consistent with the ancient testimonies that say that psuchê for Heraclitus is exhalation. But exhalations cover all states of matter from the lowest moist part of atmospheric air to the fire of celestial bodies. If so, psuchê for Heraclitus is both air and fire. The fact that psuchê can manifest the whole range of physical properties along the dry-wet axis guarantees that souls can show different intellectual and ethical properties as well. Moreover, Sextus Empiricus, supported by some other sources, provides us with an answer how portions of soul stuff are individuated into individual souls. The paper closes with a brief discussion of the question whether, and if so with what qualifications, we can apply the term 'physicalism' to Presocratic theories of the soul. (shrink)

Concepts are basic features of rationality. Debates surrounding them have been central to the study of philosophy in the medieval and modern periods, as well as in the analytical and Continental traditions. This book studies ancient Greek approaches to the various notions of concept, exploring the early history of conceptual theory and its associated philosophical debates from the end of the archaic age to the end of antiquity. When and how did the notion of concept emerge and evolve, what questions (...) were raised by ancient philosophers in the Greco-Roman tradition about concepts, and what were the theoretical presuppositions that made the emergence of a notion of concept possible? The volume furthers our own contemporary understanding of the nature of concepts, concept formation, and concept use. This title is part of the Flip it Open Programme and may also be available Open Access. Check our website Cambridge Core for details. (shrink)

Recent works by Fabienne Jourdan, Luc Brisson and Francesc Casadesús emphasize the importance of the similarities between the Derveni papyrus and early Stoicism. The paper examines the se parallelisms – focusing on the method of allegorical interpretation, the cosmological roles of air, fire and pneuma and cosmic teleology – and argues that the similarities, although non-negligible, are not such that would require us to re-interpret the Derveni papyrus against the background of Stoicism. Moreover, the relevant features of the papyrus may (...) be explained from the internal dynamics of the Derveni author’s system, and there is thus no need to modify the date of the papyrus to allow Stoic influence. (shrink)

The short treatise known as Περὶ κόσμου is a learned piece of protreptic addressed to Alexander, ‘the best of princes’, usually identified with Alexander the Great. The treatise is traditionally attributed to Aristotle, and although it does espouse recognizably Aristotelian views, it contains various doctrinal and linguistic elements which have led the large majority of scholars to regard it as inauthentic. The dating of the treatise is a more controversial matter, though most scholars would put it somewhere in the Hellenistic (...) period. (shrink)

This chapter contains sections titled: The Framework of Greek Religion The Conceptualization of the Divine Philosophical Piety Bibliography.

: In this paper we give a detailed reconstruction of the first chapter of De Caelo I.1. Aristotle attempts to prove there that bodies are complete and perfect in virtue of being extended in three dimensions. We offer an analysis of this argument and argue that it gives important insight into the role the notion of body plays in physical science. Contrary to other interpretations, we argue that it is an argument about physical, as opposed to mathematical, bodies and that (...) the perfection and completeness of bodies is due to their nature. Moreover, Aristotle heavily relies in his proof on the premise that the number three implies perfection, a view he ascribes to the Pythagoreans. We review the possible sources of this view, as well as its role in Aristotle’s argumentative strategy. (shrink)

In this first paper dealing with Heraclitus ' doctrine as such, the author examines and discusses two recent controversial articles with the content of which he sympathizes - one by Gábor Betegh on the cosmological status of Heraclitus ' psychê, and the other by Aryeh Finkelberg on Heraclitus ' cosmogony and the reality of a Heraclitean world conflagration. This examination is aimed, first, at fostering "marginal" opinions which the author believes to be fundamentally correct - and the rejection (...) of which since times immemorial he considers to have greatly harmed and hampered our understanding of the Ephesian philosopher ; second, at introducing some personal corrections and additions to these opinions ; and third, at illustrating the advantages of a deliberately un prejudiced approach towards our sources, an approach based on the presumption of innocence, knowledgeability and intelligence for all our informers and on the rejection of any rejection [this is not a dittography!] of any source on ground of mere suspicion.Among the proposed novelties the following particularly deserve to be underscored: the defense of the authenticity of "fr. B 76" DK qua three different fragments and the reconstruction of Heraclitus ' system of four physical exhalations - both of which are connected with the notion of a world soul; and the interpretation of Plat. Soph. 242 C - 243 A [T 132] as confirming Arist. De cael. 279b12 [T 170] and the cosmogonical interpretation of F 31 - both of which presuppose the reality of a Heraclitean ecpyrosis.Yet, since the author's dogmatism does not extend beyond the requirement of having re course to logically sound procedures, he is ready to give up any conclusion of which it can be proven that it is irreconcilably contradicted by a sounder one and supported by none. (shrink)

Contributors in the order of contributions: David Ebrey, Richard Kraut, T. H. Irwin, Leonard Brandwood, Eric Brown, Agnes Callard, Gail Fine, Suzanne Obdrzalek, Gábor Betegh, Elizabeth Asmis, Henry Mendell, Constance C. Meinwald, Michael Frede, Emily Fletcher, Verity Harte, Rachana Kamtekar, and Rachel Singpurwalla. -/- The first edition of the Cambridge Companion to Plato (1992), edited by Richard Kraut, shaped scholarly research and guided new students for thirty years. This new edition introduces students to fresh approaches to Platonic dialogues (...) while advancing the next generation of research. Of its seventeen chapters, nine are entirely new, written by a new generation of scholars. Six others have been thoroughly revised and updated by their original authors. The volume covers the full range of Plato's interests, including ethics, political philosophy, epistemology, metaphysics, aesthetics, religion, mathematics, and psychology. Plato's dialogues are approached as unified works and considered within their intellectual context, and the revised introduction suggests a way of reading the dialogues that attends to the differences between them while also tracing their interrelations. The result is a rich and wide-ranging volume which will be valuable for all students and scholars of Plato. (shrink)

The much-anticipated anthology on Plato’s_Timaeus_—Plato’s singular dialogue on the creation of the universe, the nature of the physical world, and the place of persons in the cosmos—examining all dimensions of one of the most important books in Western Civilization: its philosophy, cosmology, science, and ethics, its literary aspects and reception. Contributions come from leading scholars in their respective fields, including Sir Anthony Leggett, 2003 Nobel Laureate for Physics. Parts of or earlier versions of these papers were first presented at the (...) _Timaeus_ Conference, held at the University of Illinois at Urbana–Champaign in September of 2007._ To this day, Plato’s _Timaeus_ grounds the form of ethical and political thinking called Natural Law—the view that there are norms in nature that provide the patterns for our actions and ground the objectivity of human values. Beyond the intellectual content of the dialogue’s core, its literary frame is also the source of the myth of Atlantis, giving the West the concept of the “lost world.” From Platonic space to Presocratic vortices, from Philosopher-Kings to Craftsman-Gods and from modern physics to the myth of Atlantis, _One Book, The Whole Universe_ presents in one volume the most up-to-date and penetrating scholarship on Plato’s _Timaeus_ by some of the greatest minds alive today. Contributors__ _Ann Bergren Gábor Betegh Sean Carroll Alan Code Zina Giannopoulou Verity Harte Thomas Kjeller Johansen Charles H. Kahn Anthony J. Leggett Anthony A. Long Stephen Menn Richard D. Mohr Kathryn A. Morgan Alexander P.D. Mourelatos Ian Mueller Thomas M. Robinson Barbara M. Sattler Allan Silverman Jon Solomon Anthony Vidler Matthias Vorwerk Donald Zeyl. (shrink)

Let be a countable first order structure and endow the universe of with the discrete topology. Then the automorphism group of becomes a topological group. A tuple of automorphisms is defined to be weakly generic iff its diagonal conjugacy class (in the algebraic sense) is dense (in the topological sense) and the ‐orbit of each is finite. Existence of tuples of weakly generic automorphisms are interesting from the point of view of model theory as well as from the point of (...) view of finite combinatorics.The main results of the present work are as follows. In Theorem 2.6 we characterize the existence of tuples of weakly generic automorphisms with the aid of the profinite topology of free groups. In Corollary 2.12 we will show that if has finite topological rank r (and satisfies a further, mild technical condition) then the existence of a weakly generic tuple in implies the existence of weakly generic tuples in for all natural number. Finally, in Theorem 3.2 we show that if is a countable model of an ℵ0‐categorical, simple theory in which all types over the empty set are stationary and has a pair of weakly generic automorphisms then it has tuples of weakly generic automorphisms of arbitrary finite length.At the technical level we will combine elementary investigations about the profinite topology of free groups with the results of [11] about topological ranks of the automorphism groups of some structures. (shrink)

Here we investigate the classes RCA $^\uparrow_\alpha$ of representable directed cylindric algebras of dimension α introduced by Nemeti[12]. RCA $^\uparrow_\alpha$ can be seen in two different ways: first, as an algebraic counterpart of higher order logics and second, as a cylindric algebraic analogue of Quasi-Projective Relation Algebras. We will give a new, "purely cylindric algebraic" proof for the following theorems of Nemeti: (i) RCA $^\uparrow_\alpha$ is a finitely axiomatizable variety whenever α ≥ 3 is finite and (ii) one can obtain (...) a strong representation theorem for RCA $^\uparrow_\alpha$ if one chooses an appropriate (non-well-founded) set theory as foundation of mathematics. These results provide a purely cylindric algebraic solution for the Finitization Problem (in the sense of [11]) in some non-well-founded set theories. (shrink)

We explain the general significance of integer-based descriptors for natural shapes and show that the evolution of two such descriptors, called mechanical descriptors (the number _N_(_t_) of static balance points and the Morse–Smale graph associated with the scalar distance function measured from the center of mass) appear to capture (unlike classical geophysical shape descriptors) one of our most fundamental intuitions about natural abrasion: shapes get monotonically _simplified_ in this process. Thus mechanical descriptors help to establish a correlation between subjective and (...) objective descriptors of perceived objects. (shrink)

Plato claimed that the regular solids are the building blocks of all matter. His views, commonly referred to as the geometric atomistic model, had enormous impact on human thought despite the fact that four of the five Platonic solids can not fill space without gaps. In this paper we quantify these gaps, showing that the errors in Plato’s estimates were quite small. We also develop a mean field approximation to convex honeycombs using a generalized version of Plato’s idea. This approximation (...) not only admits to view convex mosaics in$$d=3$$d=3dimensions as a continuum but we also find that it is quite accurate, showing that Plato’s geometric intuition may have been remarkable. (shrink)

By a celebrated theorem of Morley, a theory T is ℵ1‐categorical if and only if it is κ‐categorical for all uncountable κ. In this paper we are taking the first steps towards extending Morley's categoricity theorem “to the finite”. In more detail, we are presenting conditions, implying that certain finite subsets of certain ℵ1‐categorical T have at most one n‐element model for each natural number (counting up to isomorphism, of course).

Taking the real Newtonian colour circle – and not the one Palmer depicts as Newton's – we don't have to wait 300 years for Palmer to say no to the Lockean aperçu about the inverted spectrum. One of the aims of this historical detour is to show that one's commitment about the “topology” of the colour space greatly affects Palmer's argument.

If any nature of science perspective is to be incorporated in science-related curricula, it is hard to imagine a satisfactory didactic toolkit that neglects the social studies of science, the academic field of study of the institutional structures and networks of science. Knowledge production takes place in a world populated by actors, instruments, and ideas, and various epistemic cultures are responsible for providing the concepts, abstractions, and techniques that slowly trickle down the information pathways to become stabilized in university curricula (...) or ossified in high-school science, losing much of the tacit knowledge along the way that enabled the production of knowledge in the first place. The discussion of the sociology of science and the sociology of scientific knowledge is followed by a short overview of recent approaches in science studies and the studies of expertise. (shrink)

We show that there is a restriction, or modification of the finite-variable fragments of First Order Logic in which a weak form of Craig's Interpolation Theorem holds but a strong form of this theorem does not hold. Translating these results into Algebraic Logic we obtain a finitely axiomatizable subvariety of finite dimensional Representable Cylindric Algebras that has the Strong Amalgamation Property but does not have the Superamalgamation Property. This settles a conjecture of Pigozzi [12].

We will study the class RSA of -dimensional representable substitution algebras. RSA is a sub-reduct of the class of representable cylindric: algebras, and it was an open problem in Andréka [1] that whether RSA can be finitely axiomatized. We will show, that the answer is positive. More concretely, we will prove, that RSA is a finitely axiomatizable quasi-variety. The generated variety is also described. We note that RSA is the algebraic counterpart of a certain proportional multimodal logic and it is (...) related to a natural fragment of first order logic, as well. (shrink)

This paper attempts to present a general picture of the most important philosophical elements found in the Hungarian writings of Imre Lakatos, later the famous philosopher of science in England, with a focus on his views on science and its social context. In the first section, Lakatos' life in Hungary is summarized, with a special emphasis on those few years when most of the Hungarian works were written. The second section offers a list of his Hungarian publications, each item accompanied (...) by a brief description. Then we examine the lost doctoral dissertation and its possible contents as reconstructed from the reports of the readers and the published texts. Finally we identify the main philosophical sources the young Lakatos could have used, and give a summary of his basic views on science. (shrink)

The essay focuses on controversies where the debated issues are complex, the exchange involves several participants, and extends over long periods. Examples include the Methodenstreit, the Hering-Helmholtz controversy or the debates over Newton’s or Darwin’s views. In these cases controversies lasted for several generations, and polarisation is a recurring trait of the exchanges. The reconstructions and evaluations of the partly polemical exchanges also exhibit heterogeneity and polarisation. Although I pick an early example of the Newtonian controversies, Darwin’s argument in The (...) Origin of Species can also be variously reconstructed. When scientific controversies that involve complex utterances are investigated, a specific problem arises, as in these situations the protagonist presenting a bundle of claims to a non-unified audience cannot fully control meaning-attribution of his utterances, and, given what we know about individual cognition, the more heterogeneous audience he succeeds in persuading, the less clear the meaning becomes. While the acceptance of a position increases potential for action, the growth in consent comes together with a fuzzy content. To problematise the role of polarisation, the significance of this description with respect to knowledge-production is investigated from both an individual and a social epistemological standpoint to answer the question: How is rhetoric epistemic in cases when at least two views on a given issue are seen as persuasively supported by communities? If engaging in a controversy is a means-to-an-end activity aimed at persuasion, directed at achieving attitude-change in recipients, how does the argumentative goal of an individual translate to epistémé in extended scientific controversies? (shrink)

The paper challenges William Alston’s argument against doxastic deontology, the view that we have epistemic duties concerning our beliefs. The core of the argument is that doxastic deontology requires voluntary control over our beliefs, which we do not have. The idea that doxastic deontology requires voluntary control is supposed to follow from the principle that ought implies can. The paper argues that this is wrong: in the OIC principle which regulates our doxastic duties the “can” does not stand for the (...) ability to shape our beliefs voluntarily. As an examination of everyday examples shows, it stands for cognitive competence, the reliable ability to acquire beliefs in compliance with the epistemic norms. The doxastic OIC principle asserts, in brief, that one is only obliged to believe something if one’s cognitive capacities are sufficiently strong. It is also explained why the doxastic duties do not require voluntary control as opposed to moral duties. This understanding of doxastic duties saves our everyday doxastic deontic judgments from Alston’s argument, but does not help the deontological conception of justification, which understands justification as not violating one’s epistemic duties. It actually provides another argument against the deontological conception: if the OIC regulating our doxastic duties is construed as suggested, the deontological conception of justification implies that one’s doxastic duties and, consequently, whether one’s belief is justified depend on one’s cognitive competence. Since cognitive competence varies from person to person, justification will not matter to truth and knowledge in the way epistemic justification is supposed to do. (shrink)

The uniform halting problem (UH) can be stated as follows.Give a decision procedure which for any given Turing machine (TM) will decide whether or not it has an immortal instantaneous description (ID).An ID is called immortal if it has no terminal successor. As it is generally the case in the literature (see e.g. Minsky [3, p. 118]) we assume that in an ID the tape must be blank except for some finite numbers of squares. If we remove this restriction the (...) UH becomes the immortality problem (IP). The UH should not be confused with the initialised uniform halting problem (whether or not a TM has an immortal ID when started in a specified state) which can easily be shown to be undecidable (see e.g. Minsky [3, p. 151]). (shrink)