Arrangement of the elements

New Scientist

Chemists can’t agree on the best way to arrange the elements, prompting proposals of everything from spiral-shaped alternatives to radically elongated versions


Physics 26 February 2019

new periodic table

This reimagining of the periodic table, proposed by chemist Theodor Benfey in 1964, emphasises the continuity of the elements rather than imposing artificial breaks

By Joshua Howgego

RUN your fingers over the white keys of a piano. The notes get higher and higher as your hand moves to the right. On the eighth key, something beautiful happens: a note hangs in the air that embodies something of the first, only with a different pitch.

We began to twig that something similar was going on with the chemical elements more than 150 years ago. Scientists even called it the law of octaves. And it is this repetition in the properties of the elements that the periodic table captures so beautifully. Similar elements end up stacked in columns or groups. One group comprises noble gases like argon and neon that barely react with anything, another contains reactive metals, some of which, like francium, explode on contact with water.

Read more: The true story of the birth of the periodic table, 150 years ago

But there are doubts over whether the periodic table is in the best possible configuration. Just as notes can be arranged in various ways to produce music, so the essence of the relationships between the elements could be depicted differently. There is no easy way to judge which is better, or more “true”. So arguments over perceived flaws in the current arrangement rumble on, with some chemists arguing that certain elements should be relocated – and others working on more radical ways to recompose the table.

At first, the elements were organised by atomic weight. Now we order them by the number of protons in their nucleus. We also know that their properties are largely determined by the arrangement of the negatively charged electrons that orbit in successive shells around the nucleus.

“One proposed redesign looks like a Christmas tree”

The lightest elements have just one shell, which can hold two of these particles. Heavier elements have more shells that can hold larger numbers of electrons. What really matters for each element’s behaviour, however, is how many electrons it has in its outer shell.

That number tends to fit nicely with the way the table is arranged, namely to place elements with similar properties in the same group. For instance, group 1 elements have one electron in their outer shell and those in group 2 have two. But it doesn’t always fit together quite as neatly as all that.

Where does hydrogen go?

Take the first element. Hydrogen has one electron in its outermost shell so you might assume it belongs exactly where it is, in group 1 above lithium and sodium, which also have one electron in their outermost shell. Yet hydrogen is a gas, not a metal, so its properties don’t fit.

The complication arises because, with an outer shell that can only hold two electrons, hydrogen is one electron away from being full. Given that elements yearn for full outer shells, that makes it very reactive. In this sense, hydrogen resembles the elements in group 17, namely the halogens like chlorine. Their outer shells need only gain one electron to achieve a full shell of eight, which makes them similarly reactive. In terms of its properties, then, hydrogen is closer to chlorine than lithium.

Read more: Elements quiz: How well do you know the periodic table?

Why are mercury and gold so weird?

Lower down the table there are no available spaces for misplaced elements. Even so, a couple of the incumbents look like outliers. Take mercury, also known as quicksilver because it is a liquid at room temperature. In that sense, it is quite different to the other members of group 12, including zinc and cadmium, which are all solid metals. What gives?

The further down the table you go, the more of the positively charged protons an element’s nucleus contains. This creates a stronger pull on the orbiting electrons, meaning they must travel faster and faster. By the time you reach mercury, the electrons are travelling at 58 per cent of the speed of light. According to Einstein’s special theory of relativity, this means their effective mass is significantly higher than an electron’s normal mass, which exacerbates the inward pull they feel.

The upshot is that mercury’s electrons orbit so tightly that they can’t be shared to form bonds with other atoms, as is required to make a solid. The same thing explains why gold is gold, a unique colour among metals: relativistic effects change the way electrons absorb light.

The illusion of order

The F-block conundrum

Group 3 holds two elements that might belong elsewhere. As we move across the upper rows of the table, electrons fill up shells in a sequence of so-called orbitals, waiting until the innermost shell is full before entering the next. By element 57, lanthanum, the electrons begin to enter a new type of orbital, an f-orbital. To account for this, most periodic tables hive off the elements making up this f-block, putting it below the table, leaving a gap in group 3.

Fair enough. But there is debate over which of the elements in the f-block should come first. Some chemists maintain that the decision should come down to electron configuration, which would leave the table as it is, with lanthanum and actinium at the left-hand end of the f-block. Others point out that chemical properties such as atomic radius and melting point make lutetium and lawrencium, currently at the right end, a better bet. In 2016, the International Union of Pure and Applied Chemistry assembled a task group to settle the argument. But no one expects a decision soon.

Starting over

All these niggles have persuaded some chemists that we need to redraw the periodic table – and there is no shortage of ideas. Mark Leach at Manchester Metropolitan University, UK, keeps the internet database of periodic tables, which contains hundreds of versions.

In an attempt to better represent the continuity where one row currently ends, retired Canadian chemist Fernando Dufour developed a 3D periodic system that looks like a Christmas tree, with the elements radiating from a trunk in circles that get larger closer to the bottom. An alternative is the spiral developed by Theodor Benfey, which allows the f-block to bulge outwards (see main image, above).

Going long

Eric Scerri at the University of California, Los Angeles, is among those who has argued for more fundamental changes. He previously proposed that the table could be arranged to maximise the number of “triads”, sets of three elements that share similar properties and are related by their atomic weights. These days, he is backing an even more drastic approach: make the table not 18 but 32 columns by slotting all 30 f-block elements between the current groups 2 and 3 (see “Going long”). This allows the atomic number to run in an uninterrupted sequence.

But Guillermo Restrepo at the Max Planck Institute for Mathematics in the Sciences, Germany, favours an alternative. He has explored whether chemical similarity of elements in the same columns still holds as well as it did 150 years ago, given our increased knowledge of chemical reactivity. His conclusion is that lanthanum belongs in group 3 – that is, out of sequence.

Redesigning the periodic table might seem a quixotic quest, but it could soon take on a new urgency. We are already on the trail of element 119. Where it will go, and how the table will morph to make space for it, remains to be seen.


Habermas and Pragmatism

Notre Dame Philosophical Reviews 2004.03.07,
Aboulafia, Mitchell, Myra Bookman, and Catherine Kemp (eds.), Habermas and Pragmatism, Routledge, 2002, 256pp.
Reviewed by Christopher F. Zurn, University of Kentucky
This volume is a well-conceived and important new addition to the secondary literature on the wide-ranging philosophical work of Jürgen Habermas. …
…The volume is capped by the short three-part “Postscript: Some Concluding Remarks” by Habermas, consisting of, first, a “Response” that acknowledges his debt to the contributors and briefly responds to specific criticisms presented in the volume by Apel and Michelman, second “Reflections on Pragmatism” in the form of responses to six questions posed by Aboulafia to Habermas concerning his relationship to the work of the American pragmatists, and third a short, previously untranslated Die Zeit piece from 1998 “On John Dewey’s Quest for Certainty.”
In this “Postscript,” Aboulafia receives Habermas’s pithiest response to the question “What are the greatest strengths of pragmatism?”: “The combination of fallibilism with anti-skepticism, and a naturalist approach to the human mind and its culture that refuses to yield to any kind of scientism” (p. 228). Of course, we can read this claim not only as a relatively dispassionate assessment of the history of philosophical movements, but also as a self-attribution of what Habermas himself hopes to have achieved in his work by drawing on specific pragmatist insights and philosophical strategies.
Stylizing somewhat, we might even speculate that Habermas aims for a measure of anti-skeptical fallibilism in his methodological and epistemological projects by drawing on C. S. Peirce’s attempt to save the cognitive content of the Kantian ideas of reason without recourse, however, to a metaphysical appeal to the noumenal realm. Perhaps he hopes to have achieved an anti-scientistic—let us say, anti-reductivist—but nevertheless naturalistic theory of human culture and subjectivity by drawing on G. H. Mead’s account of human ontogenesis and phylogenesis in terms of universal structures developed through intersubjective symbolic interaction. The strategy that Habermas shares with Peirce is two-fold: on the one hand, an empirical, hence fallibilistic, appeal to the unavoidable presuppositions built into the everyday use of language, and, on the other hand, an idealizing, hence anti-skeptical, appeal to the meaning of epistemic presuppositions in terms of an asymptotic progress towards truth and objectivity as achieved by an unlimited community of problem-solving interlocutors. The strategy that Habermas shares with Mead is also two-fold: on the one-hand, an appeal to the best contemporary naturalistic accounts of individual and socio-cultural development in terms of the irreducibly intersubjective structures of language use, without, on the other hand, supposing that one could simply ignore the normativity of such developmental structures through a positivistic reduction of the problems of the social sciences and philosophy to the results of the so-called ’hard’ sciences and thereby sidestep the difficult hermeneutic issues raised by the linguistic milieu of the structures.
Of course, realizing such aspirations towards an anti-skeptical fallibilism and an anti-reductivist naturalism involves one in a sort of philosophical high-wire act, finding just the right path between the dead-ends of dogmatism and skepticism, between over-confident rationalism and a dismissal of philosophy as passé. This volume attests to both the interest and the precariousness of that balance through a compelling series of essays which add weight to one or another side in their respective attempts to show the unsustainable character of Habermas’s theoretical equilibrium.
Contemporary English-language philosophers who sail under the banner of pragmatism are, of course, somewhat more skeptical than Habermas about the possibilities for any non-metaphysical, naturalistic, and fully fallibilistic account—no matter how ’detranscendentalized’—of Kantian and post-Kantian ideas of reason such as unconditional truth, objectivity, rational accountability, freedom, normativity, linguistic universals, context-transcendent justification, and so on. …
… By bringing Habermas’s work into explicit conversation with both historical and contemporary forms of philosophical pragmatism, Aboulafia, Bookman and Kemp have put together a book that will be of service to specialists and those new to the field alike. It should also provoke further debates about the tenability of Habermas’s pragmatist-inspired high-wire act, balancing between fallibilism and skepticism, as well as between naturalism and reductivism.

A cross-modal hub for narrative processing

Stories are focused on the protagonist Excerpts from: Journal of Cognitive Neuroscience Volume30 , No. 9

Storytelling Is Intrinsically Mentalistic: A Functional Magnetic Resonance Imaging Study of Narrative Production across Modalities

my notes in: [ ]


 People utilize multiple expressive modalities for communicating narrative ideas about past events. The three major ones are speech, pantomime, and drawing. The current study used functional magnetic resonance imaging to identify common brain areas that mediate narrative communication across these three sensorimotor mechanisms. In the scanner, participants were presented with short narrative prompts akin to newspaper headlines (e.g., “Surgeon finds scissors inside of patient”). The task was to generate a representation of the event, either by describing it verbally through speech, by pantomiming it gesturally, or by drawing it on a tablet.In a control condition designed to remove sensorimotor activations, participants described the spatial properties of individual objects(e.g., “binoculars”). Each of the three modality-specific subtractions produced similar results, with activations in key components of the mentalizing network, including the TPJ,

[temporoparietal junction]

posterior STS [posterior superior temporal sulcus], and posterior cingulate cortex. Conjunction analysis revealed that these areas constitute a cross-modal “narrative hub”that transcends the three modalities of communication. The involvement of these areas in narrative production suggests that people adopt an intrinsically mentalistic and character-oriented perspective when engaging in storytelling, whether using speech,pantomime, or drawing.


Theories of language origin can be divided into“vocal” and “gestural” models (McGinn, 2015;Arbib, 2012;Armstrong & Wilcox, 2007;MacNeilage & Davis, 2005;Corballis, 2002).Gestural models posit that manually produced symbols evolved earlier than those produced vocally and that speech was a replacement for a preestablished symbolic system that was mediated by gesture alone.Importantly, the kind of gesturing that gestural models allude to is“pantomime” or iconic gesturing. Iconic gesturing through pantomime is thought to have predated symbolic gesturing, passing through an intermediate stage that Arbib (2012)refers to as “proto-symbol.”

From a neuroscientific perspective, these theories of language origin establish a fundamental contrast between two different sensorimotor routes for the conveyance of language, namely,the audiovocal route for speech and the visuo-manual route for pantomime. Language is an inherently multimodal phenomenon, not least through the gesturing that accompanies speaking (Beattie, 2016;Kendon, 2015;McNeill, 2005).Humans have yet a third means of conveying semantic ideas, and that is through the generation of images, as occurs through drawing and writing (Elkins, 2001).We have argued elsewhere that the capacity for drawing is an evolutionary offshoot of the system for producing iconic gestures such as pantomimes (Yuan & Brown, 2014).Drawing is essentially a tool-use gesture that “leaves a trail behind” in the form of a resulting image. Overall, speech,pantomime, and image generation comprise a “narrative triad,”representing the three major modalities by which humans have evolved to referentially communicate their ideas to one another.

Perhaps, the most important function of language ist he communication of narrative, conveying the actions of agents, or“who did what do whom.”


Agency is one of the primary elements that is encoded in syntactic structure (Tallerman, 2015).Although word order varies across languages, 96% of languages place the subject (the agent) before the thing that the subject acts upon(Tomlin, 1986).Hence, an “agent first” organization of sentences seems to be an ancestral feature of language grammar (Jackendoff, 1999),and gestural models of language origin highlight this type of sentence organization as well (Armstrong & Wilcox, 2007). Although language is well designed to communicate agency through syntax, it typically does so in a multimodal manner, combining speech and gesture. A basic question for the evolutionary neuroscience of human communication is whether the conveyance of narrative is linked to specific sensorimotor modalities (vocal vs. manual) or whether there are cross-modal narrative areas in the brain that transcend these modalities. This question led us to design an experiment in which we would explore for the first time whether cross-modal brain areas mediate the communication of narrative ideas using speech,pantomime, and drawing as the triad of production modalities.

Most previous neuroimaging studies of cross-modal communication are perceptual, and we are not aware of production studies that have compared any pair of functions among speech,pantomime, and drawing in healthy adults.

Evolutionary Implications

Both vocal and gestural models of language attempt to account for the origins of syntax. As mentioned in the Introduction, language grammar seems to have an intrinsically narrative structure to it,being efficient at describing who did what to whom—in other words,agency. Standard subject–verb–object models of syntactic structure (Tallerman, 2015)essentially encapsulate the kinds of transitive actions that we examined in our headlines. A large majority of languages operate on an agent-first basis, putting the actor before either the action or the target of the action. To the extent that agency is one of the most fundamental things that is conveyed in grammars (and which is lacking in so-called proto-languages; Bickerton, 1995),then our results have application to evolutionary models of language.In particular, the imaging results that were obtained in the most purely linguistic condition (speech) were replicated almost identically in the nonlinguistic conditions of pantomime and drawing.This cross-modal similarity suggests that the capacity of syntax to represent agency can be achieved through nonlinguistic means employing essentially the same brain network.

A number of biological theories of language propose that syntax emerged from basic processes of motor sequencing (Arbib, 2012;Fitch, 2011;Jackendoff, 2011).Although this might account for grammar’s connection with object-directed actions—in other words, the gestural level of representation—it may not do justice to the sense of agency that is well contained in syntactic structure. Hence, we suggest that another important evolutionary ingredient in the emergence of syntax—beyond the “plot” elements contained in motor sequencing—would be the incorporation of circuits that mediate the sense of agency, not least“other” agency. To be clear, we are not arguing that the TPJ and pSTS are syntax areas. We are simply suggesting that, whereas circuits in the IFG [inferior frontal gyrus] more typically associated with syntax (Zaccarella & Friederici, 2017)might mediate the gestural level of language, the TPJ might have a stronger connection with agents in the overall scheme of language,discourse, and narrative. Agency can be conveyed linguistically through speech and sign, but it can also be conveyed nonlinguistically through pantomime (iconic gesturing) and drawing.


In this first three-modality fMRI study of narrative production, we observed results that suggest that people generate stories in an intrinsically mentalistic fashion focused on the protagonist, rather than in a purely gestural manner related to the observable action sequence. The same set of mentalizing and social cognition areas came up with each of the three modalities of production that make up the narrative triad, pointing to a common set of cognitive operations across modalities. These operations are most likely rooted in character processing, as related to a character’s intentions, motivations, beliefs, emotions, and actions. Hence,narratives—whether spoken, pantomimed, or drawn—seem to be rooted in the communication of “other-agency.”


From: Wikipédia

Naissance du personnalisme avant 1930

Le terme personnalisme a été inventé par un pasteur de l’Église réformée, Albin Mazel, dans le cadre d’une étude intitulée « Solidarisme, individualisme et socialisme ». Le terme a été repris ensuite par Charles Renouvier dans une optique kantienne en 19033. Kant pourrait donc passer pour le vrai fondateur du personnalisme. En effet, Kant, en mettant le sujet au centre de l’expérience en général, et de l’expérience morale en particulier, met en pleine lumière la personne capable d’être à elle-même sa propre fin. La philosophie personnaliste doit aussi beaucoup à Nicolas Berdiaev, philosophe orthodoxe russe arrivé à Paris en 1924 avec lequel Mounier collabore dès les premiers numéro d’Esprit. Mounier lui emprunte le concept de personnalisme communautaire et son insistance sur la liberté et la créativité comme fondement de la personne, comme fondement de la spiritualité.

Le Personnalisme au cours des années 1930

À partir des années 1930, le personnalisme est devenu un mouvement intellectuel de réaction à la crise économique profonde de cette décennie, que la jeunesse intellectuelle française percevait comme une crise de civilisation plutôt que comme une crise essentiellement économique. Cette crise, ces jeunes la caractérisent en opposant l’« individu » et la « personne », opposition empruntée d’ailleurs à Charles Péguy, pour manifester leur refus de l’ordre établi exacerbé par la crise économique mondiale qui sévit. Daniel-Rops écrira à ce propos :

  • « Est-il besoin de répéter […] que la personne n’a rien de commun avec l’être schématique mû par des passions élémentaires et sordides, qu’est l’individu. Un personnalisme conscient s’oppose même à l’individualisme dont s’est grisé le XIXe siècle. La personne, c’est l’être tout entier, chair et âme, l’une de l’autre responsable, et tendant au total accomplissement »4.

L’individu, c’est ce qui, en bout de piste, apparaît comme le rejeton des tendances aliénantes du monde moderne. C’est celui qui a sacrifié sa dimension spirituelle et son potentiel d’énergies créatrices et de liberté, au profit d’un idéal petit-bourgeois qui ne vise qu’au bien-être. Pour Emmanuel Mounier : « l’individu, c’est la dissolution de la personne dans la matière. […] Dispersion, avarice, voilà les deux marques de l’individualité. » Aussi, la personne ne peut croître « qu’en se purifiant de l’individu qui est en elle. »5.

Autant la notion d’individu veut exprimer la faillite de la société occidentale que met en relief la crise économique des années 1930, autant celle de personne renferme «comme une absence, un besoin, une tâche et une tension continuellement créatrice»6. Contre le gigantisme des mécanismes sociaux, politiques et économiques qui président aux destinées des hommes ; contre l’idéalisme et le rationalisme abstraits qui ont détaché l’homme de la nature et de ses communautés immédiates, tous les mouvements de la jeunesse française se rejoignent en une même aspiration : celle de renouer avec ce qu’ils appellent l’homme « concret » pour en faire un être responsable, c’est-à-dire capable «de réponse»7.

Cette opposition entre individu et personne, assez répandue au début des années 1930, est donc à la fois un jugement sur la situation et un projet pour la modifier. Ce projet pourrait se formuler de la manière suivante. Le bourgeois, cet être incapable d’élévation spirituelle a, par ses visées égoïstes, inversé l’ordre des valeurs mettant ainsi en péril les possibilités d’épanouissement de la personne et de la civilisation occidentale. Pour mettre un terme à la crise de notre civilisation, la transformation des structures sociales et économiques doit inévitablement s’accompagner d’une révolution spirituelle. Dès 1927, Jacques Maritain soutenait cette Primauté du spirituel. À sa suite, des revues comme la Jeune Droite, l’Ordre Nouveau et Esprit reprendront cette exigence. Ainsi, en mars 1931, l’un des premiers manifestes de l’Ordre Nouveau lançait ce slogan promis à un succès durable: «Spirituel d’abord, économique, ensuite, politique à leur service». Emmanuel Mounier écrira quelque temps plus tard : « Le spirituel commande le politique et l’économique. L’esprit doit garder l’initiative et la maîtrise de ses buts, qui vont à l’homme par-dessus l’homme, et non au bien-être. »8.

Selon ces jeunes intellectuels français, redonner la «primauté à la personne», c’est retrouver la voie de la vraie hiérarchie des valeurs; c’est réunir ce que le monde moderne a eu tendance à séparer. Cette volonté est surtout le souci de la revue Esprit et, dans une moindre mesure, celui de l’Ordre nouveau, revues qui possèdent quelques collaborateurs communs. Toutefois, puisqu’il n’est personne pour croire que cette nouvelle civilisation s’édifiera seulement à coup d’idéal, on a aussi pensé à organiser ce qui relève du matériel sur une base concrète qui puisse permettre d’atteindre la réalisation de cet objectif. Il faut savoir que pour cette génération, Proudhon sera, en ce qui a trait à l’organisation de la dimension matérielle, ce que Charles Péguy représenta pour la dimension spirituelle. Esprit, qui est avant tout Emmanuel Mounier, approfondira surtout la réalité de la personne alors que l’Ordre Nouveau s’attachera plutôt, en s’inspirant plus directement de Proudhon, à définir le cadre organisationnel qui va permettre à l’humanité nouvelle d’émerger.

LHC 07/2018

After running the magnets through the restart cycle, Schaumann and her colleagues tried again, this time with only six bunches. They kept the beam circulating for two hours before intentionally dumping it.

 Physicists are doing these tests to see if the LHC could one day operate as a gamma-ray factory. In this scenario, scientists would shoot the circulating “atoms” with a laser, causing the electron to jump into a higher energy level. As the electron falls back down,it spits out a particle of light. In normal circumstances, this particle of light would not be very energetic, but because the “atom”is already moving at close to the speed of light, the energy of the emitted photon is boosted and its wavelength is squeezed (due to the Doppler effect).

 These gamma rays would have sufficient energy to produce normal“matter” particles, such as quarks, electrons and even muons.Because matter and energy are two sides of the same coin, these high-energy gamma rays would transform into massive particles and could even morph into new kinds of matter, such as dark matter. They could also be the source for new types of particle beams, such as a muon beam.  

LHC collides ions at new record energy

 The accelerator is colliding leads ions at an energy about twice as high as that of any previous collider experiment

25 November, 2015

 After the successful restart of the LargeHadron Collider (LHC) and its first months of data taking with proton collisions at a new energy frontier, the LHC is moving to a new phase, with the first lead-ion collisions of season 2 at an energy about twice as high as that of any previous collider experiment. Following a period of intense activity to re-configure the LHC and its chain of accelerators for heavy-ion beams, CERN’s accelerator specialists put the beams into collision for the first time in the early morning of 17 November2015 and ‘stable beams’ were declared at 10.59am today, marking the start of a one-month run with positively charged lead ions: lead atoms stripped of electrons. The four large LHC experiments will all take data over this campaign, including LHCb,which will record this kind of collision for the first time.Colliding lead ions allows the LHC experiments to study a state of matter that existed shortly after the big bang, reaching a temperature of several trillion degrees.

 Increasing the energy of collisions will increase the volume and the temperature of the quark and gluon plasma, allowing for significant advances in understanding the strongly-interacting medium formed in lead-ion collisions at the LHC. As an example, in season 1 the LHC experiments confirmed the perfect liquid nature of the quark-gluon plasma and the existence of “jet quenching” in ion collisions, a phenomenon in which generated particles lose energy through the quark-gluon plasma.The high abundance of such phenomena will provide the experiments with tools to characterize the behaviour of this quark-gluon plasma. Measurements to higher jet energies will thus allow new and more detailed characterization of this very interesting state of matter.

 “The heavy-ion run will provide a great complement to the proton-proton data we’ve taken this year,” said ATLAS collaboration spokesperson Dave Charlton. “We are looking forward to extending ATLAS’ studies of how energetic objects such as jets and W and Z bosons behave in the quark gluon plasma.”

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By MissMJ – Own work by uploader, PBSNOVA [1], Fermilab, Office of Science, United States Department ofEnergy, Particle Data Group, Public Domain,

Herodotus on corruption

From Book V.

“Milesian stranger, quit Sparta before sunset. This is no good proposal that thou makest to the Lacedaemonians, to conduct them a distance of three months’ journey from the sea.” When he had thus spoken, Cleomenes went to his home.

But Aristagoras took an olive-bough in his hand, and hastened to the king’s house, where he was admitted by reason of his suppliant’s pliant’s guise. Gorgo, the daughter of Cleomenes, and his only child, a girl of about eight or nine years of age, happened to be there, standing by her father’s side. Aristagoras, seeing her, requested Cleomenes to send her out of the room before he began to speak with him; but Cleomenes told him to say on, and not mind the child. So Aristagoras began with a promise of ten talents if the king would grant him his request, and when Cleomenes shook his head, continued to raise his offer till it reached fifty talents; whereupon the child spoke:- “Father,” she said, “get up and go, or the stranger will certainly corrupt thee.” Then Cleomenes, pleased at the warning of his child, withdrew and went into another room.

These same men, if we may believe the Athenians, during their stay at Delphi persuaded the Pythoness by a bribe to tell the Spartans, whenever any of them came to consult the oracle, either on their own private affairs or on the business of the state, that they must free Athens. So the Lacedaemonians, when they found no answer ever returned to them but this, sent at last Anchimolius, the son of Aster- a man of note among their citizens- at the head of an army against Athens, with orders to drive out the Pisistratidae, albeit they were bound to them by the closest ties of friendship. For they esteemed the things of heaven more highly than the things of men.

Pausanias on Greece


“Who the man was who established ten tribes instead of four, and changed their old names to new ones–all this is told by Herodotus.The eponymoi–this is the name given to them–are Hippothoon”…—-[Red:extracted as follows: ] Antiochus, Ajax son of Telamon, Erechtheus, Aegeus, Oeneus,Acamas, Cecrops, Pandion,Erichthonius,Aegeus[Red: one of them, m.b. Erechtheus is uncertain.]

“These are the Athenian eponymoi who belong to the ancients. And of later date than these they have tribes named after the following, Attalus the Mysian and Ptolemythe Egyptian,and within my own time the emperor Hadrian,who was extremely religious in the respect he paid to the deity…”

Polybios’ conception of history

20 years ago I studied classical Greek and Roman historiography and came across Polybios’ conception of history.

                "All historians," according to Polybius,

                     have insisted that the soundest education and
                     training for political activity is the study
                     of history, and that the surest and indeed
                     the only way to learn how to bear bravely the
                     vicissitudes of fortune is to recall the
                     disasters of others.

                Practical experience and fortitude in facing calamity
                are the rewards of studying history and are stressed
                repeatedly throughout the work. History is essentially
                didactic. Pleasure is not to be wholly excluded, but
                the scale comes down sharply on the side of profit. To
                be really profitable, history must deal with political
                and military matters; and this is pragmatiké historia,
                in contrast to other sorts of history (IX,
                1-2)--genealogies and mythical stories, appealing to
                the casual reader, and accounts of colonies,
                foundations of cities, and ties of kindred, which
                attract the man with antiquarian interests. Its nature
                is austere, though it may include contemporary
                developments in art and science. He stands in contrast
                to the sensationalism of many of his predecessors, who
                confuse history with tragedy.

                In Book II, in which he attacks the Greek historian
                Phylarchus for practices that might be called
                unprofessional today, Polybius states:

                     A historian should not try to astonish his
                     readers by sensationalism, nor, like the
                     tragic poets, seek after men's probable
                     utterances and enumerate all the possible
                     consequences of the events under
                     consideration, but simply record what really
                     happened and was said, however commonplace.
                     For the object of history is the very
                     opposite of that of tragedy. The tragic
                     writer seeks by the most plausible language
                     to thrill and charm the audience temporarily;
                     the historian by real facts and real speeches
                     seeks to instruct and convince serious
                     students for all time. There it is the
                     probable that counts, even though it be
                     false, the object being to beguile the
                     spectator; here it is the truth, the object
                     being to benefit the student.

                This attack on Phylarchus is not isolated. Similar
                faults are castigated in other historians judged guilty
                of sensationalism (cf. II, 16, 13-15; III, 48, 8; VII,
                7, 1-2; XV, 34, 1-36). Nor are these their only
                weaknesses. Many historians are prone to
                exaggeration--and that for a special reason. As writers
                of monographs whose subjects are simple and monotonous,
                they are driven "to magnify small matters, to touch up
                and elaborate brief statements and to transform
                incidents of no importance into momentous events and
                actions" (XXIX, 12, 3). In contrast to such practices,
                Polybius stresses the universal character of his own
                theme, which is to narrate "how and thanks to what kind
                of constitution the Romans in under 53 years have
                subjected nearly the whole inhabited world to their
                sole government--a thing unique in history" (I, 1, 5).

                An important place in Polybius' work is occupied by his
                study of the Roman constitution and army and the early
                history of the city in Book VI. His analysis of the
                mixed constitution, which had enabled Rome to avoid the
                cycle of change and deterioration to which simple
                constitutional forms were liable, is full of problems,
                but it has exercised widespread influence, from
                Cicero's De republica down to Machiavelli and

                To cite this page:
                "Polybius" Britannica Online.

                [Accessed 25 February 1998].


From: Encyclopedia Britannica

Metalogic: Semiotic

Originally, the word “semiotic” meant the medical theory of symptoms; however, an empiricist, John Locke, used the term in the 17th century for a science of signs and significations. The current usage was recommended especially by Rudolf Carnap—see his Introduction to Semantics (1942) and his reference there to Charles William Morris, who suggested a threefold distinction. According to this usage, semiotic is the general science of signs and languages, consisting of three parts: (1) pragmatics (in which reference is made to the user of the language), (2) semantics (in which one abstracts from the user and analyzes only the expressions and their meanings), and (3) syntax (in which one abstracts also from the meanings and studies only the relations between expressions).

Considerable effort since the 1970s has gone into the attempt to formalize some of the pragmatics of natural languages. The use of indexical expressions to incorporate reference to the speaker, his or her location, or the time of either the utterance or the events mentioned was of little importance to earlier logicians, who were primarily interested in universal truths or mathematics. With the increased interest in linguistics there has come an increased effort to formalize pragmatics.

At first Carnap exclusively emphasized syntax. But gradually he came to realize the importance of semantics, and the door was thus reopened to many difficult philosophical problems.

Certain aspects of metalogic have been instrumental in the development of the approach to philosophy commonly associated with the label of logical positivism. In his Tractatus Logico-Philosophicus (1922; originally published under another title, 1921), Ludwig Wittgenstein, a seminal thinker in the philosophy of language, presented an exposition of logical truths as sentences that are true in all possible worlds. One may say, for example, “It is raining or it is not raining,” and in every possible world one of the disjuncts is true. On the basis of this observation and certain broader developments in logic, Carnap tried to develop formal treatments of science and philosophy.

It has been thought that the success that metalogic had achieved in the mathematical disciplines could be carried over into physics and even into biology or psychology. In so doing, the logician gives a branch of science a formal language in which there are logically true sentences having universal logical ranges and factually true sentences having universal logical ranges and factually true ones having more restricted ranges. (Roughly speaking, the logical range of a sentence is the set of all possible worlds in which it is true.)

A formal solution of the problem of meaning has also been proposed for these disciplines. Given the formal language of a science, it is possible to define a notion of truth. Such a truth definition determines the truth condition for every sentence—i.e., the necessary and sufficient conditions for its truth. The meaning of a sentence is then identified with its truth condition because, as Carnap wrote:

To understand a sentence, to know what is asserted by it, is the same as to know under what conditions it would be true. . . . To know the truth condition of a sentence is (in most cases) much less than to know its truth-value, but it is the necessary starting point for finding outits truth-value.Influences in other directions

Metalogic has led to a great deal of work of a mathematical nature in axiomatic set theory, model theory, and recursion theory (in which functions that are computable in a finite number of steps are studied).

In a different direction, the devising of Turing computing machines, involving abstract designs for the explication of mechanical logical procedures, has led to the investigation of idealized computers, with ramifications in the theory of finite automata and mathematical linguistics.

Among philosophers of language, there is a widespread tendency to stress the philosophy of logic. The contrast, for example, between intensional concepts and extensional concepts; the role of meaning in natural languages as providing truth conditions; the relation between formal and natural logic (i.e., the logic of natural languages); and the relation of ontology, the study of the kinds of entities that exist, to the use of quantifiers—all these areas are receiving extensive consideration and discussion. There are also efforts to produce formal systems for empirical sciences such as physics, biology, and even psychology. Many scholars have doubted, however, whether these latter efforts have been fruitful.