In the history of Greek civilisation the being/not-being problem is associated to the name of Parmenides and is the core of his poem ''about the nature'': ''Peri Phuseos'' Here we find the beginning of the philosophical evolution of those terms, crucial for the whole western civilisation. They are used as substantive and are subjected, for the first time, to a radical enquiry. For Coxon in the Parmenideaneimithere is
...an existential understanding of the verb, or else with an archaic failure to distinguish between its existential and copulative uses. (COXON 1986)
and for Mourelatos (MOURELATOS 1970) is:
... a strange term. It is a hybrid between the 'is' of predication and 'is' of identity. What appears to its right is not an ordinary predicate, but a constitutive predicate. ... the matching values on the right will also have to be of the categorial rank of individuals. And in the case of individuals, negation could not fail to be unrestricted. ...Parmenides did stipulate that there are no predicate-families.(79)
i.e., is a term with a sure existential flavour in itself and a predication/identification ambiguity as a copular link between two words. Leszl (LESZL 1988) underlines the beginning of a technical usage of not-being, in which it shows a strong negative connotation, also without displaying any explicit negation of existence of a well determined ''something''. In the same direction Kahn (KAHN 1973) advocates the new link between truth and being, and thus the development of the veridical usage of 'being' and the nexal usage of the 'negative' which were crucial for the birth of Greek ontology. The Parmenideaneimidoes not show any kind of differentiation among the meanings mentioned in the above section. We have to recall Eudemus's assertion that Plato was the first to discriminate between ''substantial'' and ''attributive'' uses of 'eimi', and that the Aristotelian critics to Parmenides was founded on the single sense he ascribed to being, to be articulated instead, according to Aristotle, between 'substance' and 'accident', between reality and judgement, and in the ''categorical'' framework.
For Parmenides the starting point was the need, common to all the Greek philosophers, but Heraclitus, of something stable in the flux of becoming: without some kind of fixed 'objects' neither knowledge nor language are possible. In the Platonic dialogue Sophist it is clear that this aim, to be reached by Parmenides, needed the critique against the presence in naturalistic philosophy and in Pythagorean cosmology of a dualism introduced to account for the change. The argument runs roughly as follows: if you say, for example, that the principles are 'cold' and 'warm', you have to find something to which to apply such adjectives and say if and what they are. If one of them is the being, the other one either is (and hence coincides with the first) or is not and then does not exist. If you look for a third principle (a 'substance'), the two principles, because they are, must belong to such substance and hence we come back to some sort of monism: the indo-european uniformity in the semantic field ofeimidid not leave out any other hypothesis. It means we have to fix something, something being. And this being must be, most of all, object of thought and language. This way, the only thing we can actually fix is being. So, we have the first structure of the semiotic triangle in Parmenides:
...for the same thing is for conceiving as is for being (Parmenides, in (COXON 1986) DK 3,1)It is necessary to assert and conceive that this is being (Parmenides, in (COXON 1986) DK 6,1)
Guthrie (GUTHRIE 1962) and Snell (SNELL 1978) underlined that the verb 'noein' (to conceive) conveyed an idea of immediate recognition, directly connected with the sense of vision (the verb noew) and hence was not to be applied to something not being. This rejection against the negative is the first appearance of the negative judgemet paradox. Also the words 'legein/logos' defined a large field of meanings connecting speech and reason, name and object (fig.6): in Greek culture, only with Aristotle and somehow with Plato , there is the emergence in the theory of knowledge of a sharp difference between prevalent active (thinking) and passive (senses) functions: this is confirmed by the slow progressive evolution of the 'mental' terminology from a sensorial and somatic one (see Snell (SNELL 1978)), and from the history of the theories of perception in Greek philosophy (see Guthrie (GUTHRIE 1962)). In Respublica, beyond many analogies between vision and knowledge (the myth of the cave, the idea of 'good' as the sun, ignorance as blindness, dialectics as sight) there are explicit identity statements (between existence and knowledge, 477a, between science and sight and hearing, 477c). Aristotle in 'de anima' 427a21, and Metaph. 1009 b12, refers that the ancient philosophers reduced thought to sensation.
In his poem Parmenides describes three roads: the first is the being, the second the not-being, the third the confusion between being and not-being. <Note: Leszl claims instead the existence in Parmenides of only two roads: the first corresponding to the first two before mentioned, and the second to the third. In this approach the human belief is substantially the 'contradictory' road. Untersteiner (UNTERSTEINER 1958) instead faces the third road to the first one, as the domain of temporality versus the atemporal being>. Slightly different translations have been proposed, but the core is that the first is the road of 'aletheia', that is the 'truth'. What aletheia meant, at the beginning of Greek philosophy, has always been the battlefield for philosophers and linguists. Some authors stressed an 'objective' meaning, truth as reality, correspondence between words and reality. This concept was obviously somehow present in Greek, but originally otherwise expressed. More 'subjectively', ''sincerity'' was the interpretation of Kahn (KAHN 1973), ''what happened'', ''unconcealedness'' that of Mourelatos (MOURELATOS 1970), and Unverborgenheit, ''unconcealedness'', that of Heidegger (HEIDEGGER 1959), who advocated a more complex existential approach, by placing the aletheia in the 'noein' more than in the logos; other authors underlined an explicit 'subjective' meaning: Unvergessenheit, ''unforgettability'' for Snell (SNELL 1978), the truth reminded by the Muses and that cannot be forgotten, in which other sense-linked meanings progressively united (for example 'eteon', 'real', opposite to 'false' in prophecies and thus expressing their objective consequences). Another 'subjective' translation is that employed by Leszl (LESZL 1988) by the term ''unveiling''.
However, our main aim is not so much the 'right' translation of aletheia as instead its 'setting' in a field of basic 'knowledge-shaping' terms, centred on being and its formal usage. To this aim, Detienne embeds aletheia in a structured network of concepts, meaning both the quality of Muses' words and the remembrance and unforgetting of the poetry verses. Thus it is almost coincident with mnhmosunh ('remembrance') and its opposite is 'lethe' ('forgetting'), and not 'pseudes' ('false, lie')((DETIENNE 1967)). From this point of view it is noteworthy that in Parmenides the appearance of the non-contradiction principle and the signposts on the road of aletheia were formal conditions of being (ungenerated, imperishable, entire, unique, unmoved, perfect) for the access to the truth. We could say that Parmenides tries to yield a sort of algebra of the formal usage ofeimiand the two negatives. Thus the fragments B2 3-8 and B8 7-9 could be translated, to enhance such algebra, as:
on the one hand, that it is and then is not possible to deny, is the road of Persuasion (to truth in fact it follows); on the other hand, that is not and then is necessary to deny, this I say to you to be an unknown road. And in fact you could not think and say the denied (in fact not possible). I shall not allow you to say and to think about the denied. In fact neither said nor thought is what is not
In these translations 'me einai' becomes ''to deny'', and 'esti' in the first verse becomes ''is possible''. The meaning, by observing the equivalence between ''is not possible'' and ''necessary is not'', amounts to a strict coincidence between reality and necessary assertion, preserving the negatives. And this interpretation seems coherent with the rest of the poem.
The second road is blocked and the third is the 'human' form of knowledge, the road of belief. The existence of two forms of knowledge, a divine and a human one, is homogeneous to the prephilosophical Greek thinking and is a bridge, without any discontinuity, to the modern epistemology, which always must somehow distinguish between ''common sense'' and ''scientific'' knowledge. For the ionian philosophers human and divine knowledge are different and there is no special intermediate role to be played by philosophy and philosophers (LESZL 1988) . For Parmenides the divine road is open to the mortals, so overcoming the 'scepticism' also of its master Xenophanes
Xenophanes had borrowed from Homer the equation of knowing with present perception and concluded that, with regard to Gods and other matters beyond the range of the senses, human beings can have no knowledge but only belief. Parmenides answers that the mind not only may have an immediate awareness of 'absent things' but that its vision of Being is 'steady'.((COXON 1986), 185)
if the mortals obey to a condition: to follow the road of being and ignore the road of not-being. By the way in any case it had not to be completely closed, for a great part of Parmenides' poem is about the teaching of such belief, concerning cosmology and cosmogony. Here, in my opinion, there is the beginning of the establishment of a new 'professional lexicon' to deal with the knowledge problems: something absent in ionian philosophers and in Heraclitus, crucial instead in classic Greek philosophy. This Parmenidean principle has been recognised as the first occurrence of the ''non-contradiction principle'' as a formal one. Perhaps this is not thoroughly convincing, but it is surely a big step in that direction, for it is the beginning of the 'formal' character of philosophy. We could say that the coincidence between the three worlds of the syntactic paradigm, conceiving, asserting and being, is the ''road of truth'', the first formal principle in the history of the paradigm, seed both of the ''non contradiction'' and ''truth as correspondence'' principles. Anyway, in the poem, Parmenides states somehow explicitly the non-contradiction principle and employs implicitly, according to (UNTERSTEINER 1958), the third excluded and identity (everything must be identical to itself) principles.
What is the status of 'coherence' in the mythological thinking? It would be wrong to claim that the pre-Parmenidean philosophy was incoherent. According to Levi-Strauss (LEVI-STRAUSS 1962), coherence can be found also in more 'primitive' thinking. But there, it is a piece of concrete logic, inner to the intimate interweaving between words and world, given by the earliest aspect of oral language performances as social events. Levi-Strauss' analysis in north and south American myths, developed in his Mythologiques, is also supported by the enquiry accomplished by Luria in Uzbekistan in 1930-1931 among illiterate populations facing the mass instruction projects of the soviet state (LURIA 1976). The author underlined the role played by school and written language in overcoming the ancient ''concrete situational'' reasoning for a ''formal'' one. More in detail, the interviews of the illiterate farmers displayed the difficulties in dealing with ''abstract definitions'' instead of ''active and concrete usage'', and in getting rid of the ''open concrete environment'' to accept a ''closed logic world'' in which to accomplish syllogisms or to solve problems. In my opinion, this is the real step forward to turn 'concrete' into 'formal' thinking: to break the unity of the linguistic praxis, and conceive the language as an autonomous 'immaterial' world, the language, to match with another autonomous 'deaf-and-dumb' world, the reality. Thus, we have convergent support to the idea of a crucial distinction, in a general practically coherent behaviour, between an earlier, concrete and situational reasoning in myth-based and oral cultures, and a modern formal reasoning, linked to that new form of cultural reproduction, based on mass school and extended social usage of writing, which appears in western civilisation since classic Greek culture.
In Parmenides the non-contradiction principle begins its career as a ruling principle in the signs world. This principle is set against the naturalistic thinkers, who addressed the becoming of reality, the changes in things and attributes, the continuous mixture of being and not-being, features of a philosophy for which, according to Parmenides, the road to the divine knowledge was precluded. This bridge between human and divine knowledge gives to philosophy an almost divine nature, and then an almost divine nature also to the soul. From Pythagoras to Plato this process was accomplished by the 'embedding' of the 'demon' in the Homeric 'soul', a power partaking of the divine in a pale shadow. (see (ZAIDMAN 1989), 232, (ROHDE 1890)) The road of human belief, the third, remained open: this is the knowledge about the real world, in which there are differences and there are names ''imprinted on the things as signs on the coins'' . < Note: It is worthwhile to remind another 'economic' metaphor in Heraclitus, where the relationship between the fire and the things is analogised to the relationship between the gold and the other goods (DK 90 (DIELS 1964),(MARCOVICH 1978)). We advocate that the shift from Heraclitus to Parmenides marks somehow the passage to a new form of social organisation, as mirrored in the shift from a gold-exchange to a pure coin-exchange (more syntactic) economy>. We have to underline both continuity and rupture in Parmenides with respect to the old mythological culture
In the core of his philosophy are the aletheia and the being, of these representations the first is linked to Muses, the second to the seeing. But both with a new content. ((SNELL 1978), 101)
We must point out this Snell's thesis of a changing correspondence between aletheia and 'on', truth and being. Such a correspondence is well-established in classic Greek philosophy as in our modern culture, and it is the basis both of the non-contradiction principle and of the truth-as-correspondence principle, but it was present also in the mythological thinking, and it would be misleading to believe that this long-lasting correspondence has never changed from the existential-veridical role of indo-european 'being' to Tarski. The link between being and knowledge/truth is deeply embedded in any form of human social life, linked to the very existence and role of an intellectual class, who advocates the truth as its own realm and its power on reality as the 'raison d'etre' of its social role. In the ancient mythological framework the language is most of all just 'spoken' and it is a network of events in the real social life. It plays an intellectual role through memory, in the form of myths, epics and proverbs. Aletheia is a 'narrated' truth, which founds the rules and origins of nature and society, and gives to the things their names as substantial and not as conventional. It is a thought unscathed from its inner changes and contradictions, which gives the rationale to the human reality shown by the senses and dominated by flux and change. In the ''mythological thinking'' there was no problem of 'functionally' confronting reality and language. The 'stable' ground was memorised as myths, special pieces of language and not real 'facts': their connection with reality was only in giving the name and the genetic rationale of natural properties or of peculiar natural objects as mountains, stars or rivers, and in motivating and describing social and ritual institutions. The 'connective' tissue of the myth, as in the dreams, seems to bear the same burden of coherence of a real fact, whereas its crucial and most meaningful features show absurd and illogical aspects. On the other hand, the language in the everyday life usage was a part of the social life, event among events, changing and flowing with a very little commitment to 'matching' reality, but always just as a part of the same reality. In Homer we find many examples of 'double names': the same river or bird has got a divine name and a different human one, and there is no clear relationship in-between. We can try to depict a scheme of the mythological paradigm in fig.6: the dotted lines represent 'fuzzy' relations. Parmenides claims instead a tight matching between reality and the word 'einai', so creating the idea of being as real. It is the beginning of the ''syntactic paradigm''.
In the VIII century the diffusion of the alphabetic writing begins an epochal change, whose depth can be felt in the words of Plato's Phaedrus. The language is no longer a set of events among other real events, but becomes a world in its own. The speech is written, at the beginning often without dividing the words, and then with the single words separated as objects in their own world, which must nevertheless mirror the real world. The writing in the age of the polis loses its initial mythical and ritual role to become the core of the social and political activities, and hence it has to cope with the human and natural world of change, on which the word has to impose an order and a rule. The Platonic dialogue Protagoras shows a typical 'dialectic duel' between the great Sophist master and Socrates: the language looks like a set of battle weapons, with tactics and techniques, and the audience judges and plays a role in the agon. But in the same time it must deal with the description of reality and its knowledge, it is philosophy. The knowledge is no longer founded in the memory of a timeless foundation, but in the development of the correspondence between the reality and the language world. The word aletheia absorbs a richer set of meanings and, most of all, develops the idea of a truth as correspondence between reality and language/thought. It is noteworthy that in Cratylus, 421b, the 'privative' aspect of aletheia is lost, and Plato's etymology is aletheia, that is 'divine wandering' (see also (LUTHER 1966)). As paradigm of the new intellectuality of this age, Detienne((DETIENNE 1967)) and Vernant((VERNANT 1971)) remind the Greek poet Simonides (second half of VI century). He claimed that the word was an image of reality, he was the first to sell his poetries, he improved the Greek alphabet and developed the 'mnemotechnique' as a professional skill.
To grasp the real significance of the Parmenidean philosophy, we need to follow its development, in Athens, during the Sophists and Socratic age. There we can see Gorgias and Protagoras, Socrates and his followers, maybe also the old and awe-inspiring Parmenides with his young student Zeno. Then we encounter Plato, while dealing with the consequences of the negative judgement paradox, at the beginning of the axiomatic-deductive geometry and at the birth of the modern idea of education. Finally, after Plato, we find the architecture of the Aristotelian philosophy and the well-established modern idea of school, with the age of paradoxes left in the past sophistry. Detienne pointed out the role played by the 'school', as bridge between the autonomy of the new written thing and the new writing technology, to found a new organisation of knowledge based on alphabetic writing ((DETIENNE 1988)). The new role of the 'school' is the red thread throughout the whole dialogue 'Republica'. In the 'Timeus' 51 d-e there is the explicit opposition: intelligence, teaching, true reasoning versus true opinion, persuasion, irrationality.
Platonic dialectics, with its never ending, often boring, series of rough ''analogies'' to clear and state precise concepts and definitions, and with its sometimes 'forced' deductions, aimed to take the antagonist toward contradictions, can be read as the crucial step in the slow process, from Parmenides to Aristotle, of extracting a formal logic from a concrete one, as embedded in the normal linguistic usage. Moreover, minor authors, with no differences between Sophists and Socratic scholars, confirm the crisis due to the impossibility of matching the new role of the language with the homogeneity of the semantic field of 'eimi'. Stilpo does not distinguish between ''Athena (the goddess) is by Zeus'' and ''Athena (the statue) is by Phidias'' or between being a general term (man, vegetable) and being an instance of such term. Menedemus from the difference of two things (''conferring benefits'' and ''good'') induces that there is no being connection between them (''to confer benefits is not good''), and rejects negative propositions. Antisthenes sets the first definition of ''statement'' (logos): ''a statement is that which sets forth what a thing was or is'' (in Diogenes Laertius VI,3) and so confirms the isomorphism between reality and language and hence the preclusion toward false-speaking: it is impossible to conceive or to say a statement concerning something which is not. Such an utterance could sound so paradoxical in Sophist's Athens to produce a real KO in the dialectic agon. <Note: Among the verbs meaning 'to say', the most important is credibly 'phemi', which means 'to declare, to report', but whose negative 'ou phemi' means 'to deny'. It is not easy to find a 'modern' verb with the same 'negative' behaviour. No 'utterance' verb is similar, neither 'knowledge' verbs are. Only 'perceptual' verbs and the copula display sometimes a similar behaviour. Another verb meaning 'to say' is 'legein', whose original meaning is 'to pick up, to enumerate', (but Boeder (BOEDER 1958) underlines an earlier 'to lay, to set' meaning) and from which the word logos derives. The earliest expression employed to mean 'not to say' is probably 'meketi legometha', 'speaks no longer' (Hom. Od. II,435), and to say 'to lie', 'ouden legein' can be employed.>
Gorgias was one of the greatest Sophists and we know the core of his learning in the thesis:(a) that nothing exists, (b) that even if it does, it is incomprehensible to man, (c) that, even if it is comprehensible to anyone, it is not communicable to anyone else.(DK 82 B3)
For the aim of our analysis we have just to underline that i) the non-existence is developed on all the three worlds of the semiotic triangle, with increasing strength from reality to thought and language, reflecting the same hierarchy above stressed about the 'size' of the three worlds in the syntactic paradigm. The order is now, however, 'upside-down', entailing an inclusion of the language world in the real world. Thus here we find the opposite to the above-mentioned common sense inclusion based on that any 'fact' can be expressed in 'words'. This relation will be of great importance in the modern paradoxes. ii) the trace of the non-existence proof of not-being reflects Parmenidean steps, but the non-existence is extended also to being and to the mixture of being and not-being. This widening of the eleatic criticism will be common in Sophists' themes and can be found also in Parmenides' figure in the homonymous Platonic dialogue. In addition, we have to observe that now the aim is onthologic, i.e. concerning the existence, instead of substantially only epistemological, i.e. concerning the knowledge, as in Parmenides; iii) there is, in the arguments, evidence of the uniform use of being terms together with an uniform use of mental terms (seeing, hearing, thinking, saying) that in our modern culture play different roles, more 'passive' (seeing, hearing) and more 'active' (thinking, saying). Concerning the semiotic triangle, we have to observe that the presence of the mental register in Gorgias must not to be overevaluated: from Parmenides to Socrates it is always structured as a sensorial function, seeing-like. But its not thorough equivalence with the other two worlds is a first sign of the future Platonic Forms world.
The debate between the Sophists and Socrates/Plato seems to be an evolution of the Parmenidean rupture: the Platonic dialogue Parmenides shows the old philosopher with his scholar Zeno in a quite sceptic mood expressing theses that, such as the classic zenonian paradoxes, seem to enhance the use of eleatic techniques less to defend the monism that to fight the dualism, and somehow to draw the features of a global crisis in the Greek philosophy. Parmenides achieves this way the conclusion of a sort of total mutual connection of the more general philosophical terms (same, other, equal, like, motion, rest), caused by the lack of the splitting in the semantic field of 'eimi', and a following substantial impossibility of any knowledge. This eleatic 'lesson' will be overcome in the Sophist. We can recognise an inner coherence between the evolution of Parmenides'philosophy, through Zeno and the Sophists, and the fictional Parmenides figure outlined in the Platonic dialogue. The compelling rationale of this evolution is that the tight matching between being and truth cannot be extended to cover, coherently, a larger set of non-empirical words (not, one/many, rest/motion, same/other, equal). The consequence, in the Sophists age, is the widening of the fracture centred on the ''negative judgement paradox''.
It is easy to underevaluate this period, but it would be wrong. Most of the modern historians and philosophers have analysed these paradoxes with the techniques of modern formal logic, arguing for the rhetorical or ironic value of these 'exercises'. It was instead an age of so radical and deep change to be opaque also to thinkers belonging to the next generation. Plato in his Theaetetus, 184a, shows Socrates reminding his personal acquaintance, in his youth, with Parmenides. And Socrates says he fears that we do not understand anymore the words and thoughts of the old philosopher. The same 'oblivion' hits the Eleatic Stranger in Sophist 243 b1. (PLATO 1964) Indeed, this critical age was the cradle of the dialectic reasoning. We can observe the elegance of these thinkers, even in a simple minor sophistic didactic text as the ''Dissoi logoi'' (''double speeches''), in which we can recognise one of the earliest examples of self-referential statement about the truth:
...if those who maintain that true and false are the same are asked whether their own argument is true or false, and if they reply 'false' then they admit that true and false are different; if they say 'true', then by their own hypothesis the same argument is also false. A true piece of evidence is also false, a truthful man is a liar. (DK 90.4)
<Note: A similar argument can be found in Chinese philosophy: ''According to Chuang-tzu all statements are shih (right) and all statements are fei (wrong) for the man who finds the correct viewpoint at the axis of the Tao. The Mohist reject both claims as self-contradictory. Canon: To think all statements mistaken is mistaken. Explanation: it is own statement Explanation: 'Mistaken' is inadmissible. If this man's statement is admissible, that is to say not mistaken, it follows that there is an admissible statement. If this man's statement is inadmissible, to suppose that it fits the facts necessarily does not fit the facts.''(GRAHAM 1967) >
We can speak here of an epochal cultural 'crisis' even if it is quite clear that Greek people employed without problems different uses ofeimiand negatives, and it does not surprise that the philosophers were victims of the comedy writers. But the cultural environment was unable to solve the problem: maybe something similar to our quantum mechanics paradoxes or logic limitative theorems, not relevant and quite funny for common sense, but deeply embedded, and somehow embarrassing, in our science. But maybe, as we shall see, something also deeper.