When remembering our high school philosophy courses, we have a quite good idea of ionian philosophers, very simple approaches about the origin of the universe, maybe just a naturalistic version of older theogonies, and, after two centuries, we recognise the modernity of Aristotle. In between, we can appreciate Socratic morality and ethics or Plato's rationality, but it is difficult to understand the being problem of Parmenides, Heraclitus looks like a sort of Zen monk and, most of all, it is impossible to accept the idea that the birth of human rationality moves most of all around the debate between Socrates, Plato and the Sophists about the so-called ''paradox of negative judgement'':
''given that an affirmative statement corresponds to a fact in the world, something that is, we have that a negative statement corresponds to something which is not, but a statement about what is not, is about nothing and hence is impossible''.
grounded in Parmenides' philosophy, and defined by Plato in Sophist 238 d2 as ''the greatest and the first quandary''. In fact it is the theme of the central Platonic dialogues about the knowledge, and appears as crucial ingredient in almost all his works. This paradox was substantially unsolved also by Plato, and it is difficult to say that it was 'solved' by Aristotle: we had rather to say that it 'vanished' with Aristotle, as a 'false' problem, overwhelmed with a brand new extended philosophical lexicon. Quite paradoxical, the cradle of human rational thinking was a 'false' problem, vanished as a ghost at the first lights of the dawn. But was it really a false problem?
The core of this report is the ''negation problem'', that is the analysis of the role of negative judgements in human and formal thinking as developed in the V century debate. But now, before proceeding, we have to show that somehow a ''negation problem'' exists also today. A classic book about negation (HORN 1989), and a book about the negative judgement paradox (DENYER 1991) can be used as reference. In the latter, the debate about the paradox is widely analysed, with a strong underevaluation of its depth and a strong overevaluation of the Platonic 'solution'. In the former we can find the history of the debate about the ''symmetry'' between ''positive'' and ''negative'' sentences, and discover a complete spectrum of positions from the radical anti-symmetricalists (Parmenides, Plato, Saint Thomas, Kant, Hegel) through intermediate positions (Aristotle, Russell, Wittgenstein) to the radical symmetricalists (Frege). The arguments for the asymmetry are in a supposed logical, ontological, epistemological, linguistic and psychological priority of the positive: ''negation'' needs a specific connective and peculiar word, presupposes the related affirmative sentence and can be reduced to a speaker denial, whereas the positive describes a fact and can be verified. The symmetry instead can be advocated by the 1-1 correspondence between positive and negative sentences. Symmetricalists try to reduce negation to linguistic and notational conventions: in fact, they say, for many adjectives there are non-negated negations (happy/sad, even/odd, good/bad, etc.), and, as a principle, this could be generalised.
However, I think there are also computational aspects against such symmetry. From a formal-language-theoretic point of view we can point out that there are sets which are semidecidable, i.e. whose complement is undecidable. That is, there are predicates (and adjectives) whose generation and whose related membership problem can be solved by algorithms, whereas the same is not true for their negative counterparts. Natural language description of such sets employs, not casually, structurally positive adjectives without non-negated negations (finite/infinite, halting/unhalting, etc.). And such problems are crucial in predicate calculus (theorems/non-theorems), formal arithmetic (theorems/non-theorems) and theoretical computer science (halting/unhalting programs).
From a ''knowledge representation'' point of view, we can recall the ''negation by failure'' implementation of not in logic programming as a solution destroying the consistency and the semi-decidability of the resolution algorithm, and the problems created by the negatives in the logic of knowledge: if we try to represent the knowledge of a subject 'A' as an ''intelligent data base'', we have that negation-by-failure does not allow to distinguish between ''A knows that not P'' and ''A does not know that P''.(KOWALSKI 1979) For an explicit evidence of the paradox in the culture of our century, we can remind Russell and Quine (On what there is (QUINE 1953)), or a recent Hirst's paper (HIRST 1991) about ''existence'' in knowledge representation. On these topics we will return in a following report.
So, at the beginning of our civilisation there are strange riddles about being and not-being connected to the name of Parmenides. Such riddles are the roots of the ''syntactic paradigm'', but before analysing them it is necessary to say few words also about the general relation between language and thought. Such a connection is one of the most intriguing themes of modern culture and the Greek 'case' has been the nuclear reference of the debate. Some authors advocated a sort of causal link between characters of language and culture, at least in determining its general framework, substantially 'reducing' thought to language. The extreme version of this thesis is the so called Whorf-Sapir hypothesis (WHORF 1956), which substantially advocates the ''linguistic determinism'' (the way of thinking is determined by the language) and the entailed ''linguistic relativism'' (distinctions and concepts expressed in a language need not to appear in another language). Benveniste (BENVENISTE 1966) and in some measure also Snell (SNELL 1982) took an almost radical position, Kahn (KAHN 1973) instead a more prudent one. Obviously, who considers natural language as a simple conventional and faulty approximation of rational thinking or logic, firmly opposes this approach, but as a trivial underlining of the imperfection of the natural languages. The root of this hypothesis maybe can be found in von Humboldt, and, as a rough scheme, its radical supporters advocate the intensional and holistic versions of the syntactic paradigm, versus a greater independence between language and thought in more 'analytic' authors. This does not sound strange, when reminding the features of the paradigm, and we will return to this point at the end of this report.
In Havelock (HAVELOCK 1978), Ong (ONG 1982), Goody (GOODY 1986) we can found a somehow similar thesis advocating as source for the changes in the linguistic habits, and then in the same way of thinking, the alphabetic writing technology, so to claim that ''alphabetic revolution'' eventually ''restructured the mind''. A support for this thesis can also be found today in Mc Luhan's ''The medium is the message'', but its origin is in the 'homeric question', i.e. in the recognition of the oral character of the earliest broadcasting and reproduction of the Iliad. Such discovery has been the starting point of the recognition of the peculiar linguistic and cultural characters of the ''oral'' cultures, that is of those cultures in which the social cultural reproduction is substantially oral: - the language is embedded in the action and any word is never a placeholder of a thought or an abstract symbol; words are always related to the concrete action and their employment is always linked to the real situation, never abstract or formal. Writing transforms instead the words in objects, and, more precisely, in particular, abstract objects, autonomous from their pragmatic context. - learning is based on apprenticeship and memory, and this implies the role of gestures, practice, proverbs, poetry, rythms, etc. Declarative knowledge learning is instead a result of the writing revolution. - the syntax is quite flat and based on simple constructs. Writing allows instead more complex phrase structures. - writing allows the splitting between subject and object of the knowledge. The link between writing and the origin of consciousness has been advocated by Jaynes, as partial cause and effect respectively for the breakdown of the ancient organisation of the human brain bilaterality. It is worthwhile to remind that the role of the writing alphabetic technology is also grouded in its social function at the birth of the Greek polis. How far the alphabetic writing changed the Greek linguistic universe and how crucial was this change in the middle of classic Greek philosophy, can be realised by observing that Aristotle (Categoriae, 5a1) classifies the speech as a discrete quantity, finding no point of contact between two consecutive syllables (and Aristotle definitely speaks about 'oral' speech), whereas still in the Platonic dialogue Cratylus speech is explicitly a continuous and flowing reality.
The existence of these different theories, all claiming a strong influence of linguistic factors on thinking, faces us with the great complexity of the linguistic phenomenon. Thus, even though agreeing with the general statement of a tight connection between Greek language and Greek philosophy, we have to question how far this can be ascribed for example to its indo-european structure or to the alphabetic writing technology. It is then impossible to answer these questions without a deeper understanding of some crucial and comparative aspects of classic languages. To this aim in the following we will refer to ancient Greek and, as sharp counterevidence, archaic Chinese.
To begin, we have to say few words about the verb to be, 'eimi'/'einai' in Greek. Benveniste (BENVENISTE 1966) pointed out that it is a purely ''active'' verb, i.e. it denotes a process beginning in the subject but realised out of the subject, different from the ''medium'' form in which the subject is internal to the process .<Note: Active/medium distinction has not to be confused with the transitive/intransitive pair. We can give some examples to realise the differences between these two fundamental forms: louw (active, 'I wash'), louomai (medium, 'I wash myself'); quei or sanskrit 'yajati' (active, 'He, a priest, sacrifices for others'), quotai or sanskrit 'yajate' (medium, 'He sacrifices for himself') >. In addition, 'eimi' is an intransitive verb which can combine with an adjective: analogous verbs range from 'go', 'flow', 'fall', stand' to 'grow', 'seem', 'appear'. Also Kahn (KAHN 1973) underlined a parallelism with the same verbs and other transitive ones like 'send' or 'give'. It is a verb that in all the Indo-european languages displayed only the imperfective aspect, i.e. expressed repeated events or ongoing processes As to the usage, there are two large classes: copulative and non-copulative. More precisely, a rough list of uses could be:
- copulative predicative ('Socrates is wise'), - identity ('Plato is the master of Aristotle'), - membership ('Socrates is a man'), - locative ('Socrates is here'), - existential ('God is', 'there is a man'), - veridical ('It is the case that the things are so and so'), - belonging ('to me is something' = 'I have something'). A further usage ('water is H2O') will be considered in the following.
Linguistic analysis of the indo-european roots *es, *bhu tends to consider more ancient and fundamental a form of the existential usage (grow, exist), but in many among the oldest texts copulative usage is also common. It is also interesting to observe, not only in the indo-european languages, the large presence of nominal phrases (Socrates wise) in the earliest references. This kind of sentences are reduced to copulative (with an implicit copula), considered as the oldest form, by Kahn (KAHN 1973), who follows a ''transformational grammar'' approach, and are instead considered an earlier form by Havelock (HAVELOCK 1978), who assigned to 'eimi' an original locative meaning and traced a parallel between the development of the copulative usage and the beginning of the rational thinking. A solution of these opposite arguments can be found in Benveniste (BENVENISTE 1966), who claims that nominal and copulative sentences are different: the former lack the temporal, personal, modal features of the verb, are a part of the direct speech and express absolute and proverbial assertions; the latter by the verb inflections allow the above features and actual assertions, as part of a narration. In addition we can remark that, in archaic Chinese ((DOBSON 1959), (DOBSON 1962)), ''nominal'' (or ''determinative'') sentences are considered a well defined kind of sentences, thoroughly distinguished from the sentences containing a verb. Thus the employment of ''be'' as copula could be, at the beginning, only as inflection-holder for time and person features, obviously more suitable for inflected languages like the indo-european ones and less for languages as Chinese which do not employ any kind of inflection. Thus, we can be almost sure that there was a verb in the indo-european languages with both an existential and a rough copulative use (Snell (SNELL 1982)), and we can follow Kahn (KAHN 1973) refusing a pure locative original meaning for a more complex unique linguistic system with a locative focus on which converged predication, existence and truth aspects. By the way the difference between a locative, both spatial and temporal, presence and an existential meaning is not very sensible, most of all when reading the specific usage for example in Homer: in general 'eimi' seems to mark the real or mental appearance, the 'standing out', of something, persons most of all, but also dreams, objects, words, facts. We can also remark that in Chinese, to emphasise the existential, the substantially locative expression 'what is under the sky' was employed. Thus, we can accept the idea of two actually different kinds of sentences: nominal or determinative, and verbal.
To analyse the 'being' usage, we shall employ a linguistic terminology (Svedelins, quoted in the ''speech and brain processes'' item, in (GREGORY 1987)) to distinguish between event sentences, as ''The house is burning'' or ''The boy hits a dog'', which create in our mind 'perceptual' images, and relation sentences, as ''Joe is the father's brother'' or ''Mary is fairer than Cathy'', which express abstract relations. The first kind of sentences is ''syntagmatic'', i.e. their construction and understanding is 'in real time': the construction of the mental image follows linearly the flowing of the sentence, any word building up in the mind the corresponding image, and at the end of the sentence, treated as a pure sequence of words, its 'meaning' is the image of a 'fact'. We shall call in the following this kind of connection the ''flat semantics''. The second kind of sentences is ''paradigmatic'' instead, employing case markers and prepositions. It requires a more complex set of transformations of the input, connected to grammatical rules, to give us a meaning, whose nature is not image-like, but more abstract, relational and taxonomical. We underline that in these relation-sentences the copular usage of ''being'' is quite necessary, oftenAlso in Plato we find traces of this distinction: in Respublica 523 c-d, it is underlined the easiness in dealing with the ''finger'' by its plain perception, and the lack of clarity in dealing with the properties and relations it partakes with respect to something else, for which it can be at the same time (contradictorily) 'greater' and 'smaller'. These 'contradictory' sentences stress the mind to think (523c), for their creating two contradictory 'images' (524d), and, to deal with these contradictions, we have to employ some remedies: computing and measuring (602d), i.e. to enter the realm of signs. We can also remind in this context the question of the 'visual' peculiarity of myths and dreams, stressed by (SNELL 1982). This peculiarity has been pointed out also in a pure methodological context by Weyl (WEYL 1926), who underlines that sensorial data can give only qualities, never relationships.
It is possible to realise how hard it was to embed in a ''flat semantics'' false determinative sentences (''Socrates green''), in which the underlined feature of the image is not in the image, and also simple negations (''Socrates not green'' or ''not Socrates green''), a sort of 'blurring' of an attribute in the image or even a sort of initial 'deletion' of the whole following image. Worse for more complex ''relation sentences'', which required complex transformations to be understood also in their affirmative and true versions. It is clear that, from this point of view, the core of the 'being' usage was in its natural image-producing role: ''to appear, to exist'', also in the 'locative' (comprising the 'social rank' description) or 'belonging' sense. And it is possible to verify, in the first 12 books of Iliad, that, in the indirect speech, where Homer narrates by ''event sentences'', the verb 'being' is quite rare, but for locative or analogous usage in which the verb partakes to the creation of the image of the fact. Vice versa in the direct speech it is possible to find out a greater employment of the verb in 'no image' sentences, often of ''relational'' kind. Often a feature of the necessity of the employment of 'to be' is in the explicit time expression, whereas 'proverbial' sentences are commonly nominal. Analogous usage can be found in Hesiod's Theogony. We could also connect this linguistic dichotomy to the two functions of language enlightened by Detienne ((DETIENNE 1967)) at the dawn of Greek civilisation: the 'true word' of mythology, without time and describing the events and the genesis of the Gods world, and the 'dialogue word', temporal and linked to actions and decisions. The former is the instrument of seers and poets, the latter is the instrument of the council of warriors and furtherly of law and justice in the polis. Among the ionian philosophers we can remind Thales' ''apophtegmata'', referred by Diogenes Laertius (DK 3b11), and all expressed by nominal sentences. A more extended usage of 'to be' in copular sentences can be found in Heraclitus, where it is also used in few sentences to stress the identity between two terms, whereas nominal sentences, in a much larger number, are employed to express simple coincidences or apophtegmata.
Interesting for our analysis are the negative occurrences ofeimitoo. First of all it is important for the following to remind two peculiarities of Greek negative: - the existence of two different forms: the first, 'ou' or 'ouk', is employed in statements, i.e. ''that it is not'', probably originally expressing the simple refusal: no. The second, 'me', is employed for thoughts, i.e. ''that one thinks a thing is not'', supposedly originally confined to prohibition ((MOOREHOUSE 1959), 12). - the negative 'ou' is often repeated without making an affirmative, and is inserted after verbs of denying, disputing and doubting, whereas in our modern language it would be not required and correctly omitted.
Moorehouse ((MOOREHOUSE 1959), 138), analysing the copular usage, underlines that ''In Homer (Il. 1-12) there is no case, out of thirteen sentences of 'ou' followed by 'eimi'''. Negatives precede adjectives or other words, showing the influence of the pure nominal type. More in general, many sentences which in our translations show the use of copular being, in Homer are nominal or accomplished by a unique different verb . Thus, for 'to be' sentences, there is a dominance of the so called ''special'' use of negation ('It is not-white'), versus the ''nexal'' use, in which the negation, put before the verb, affects the whole sentence ('It is-not white'='it is not the case that it is white'). This second use is more common later, for example in Herodotus, together with a larger use of copulative sentences versus nominal ones. Austin (AUSTIN 1986) underlines instead the ''special'' use of negative in Parmenides and this confirms the features of eimi and negatives we are describing throughout this paragraph.
The ''negative judgement paradox'' is connected to the 'complex because ambiguous' semantic structure of 'eimi'. This connection sheds some light on the evolution of the paradox in the V century until the Platonic and Aristotelian philosophy, when we can first find a splitting of this semantic field. The beginning of the rational thinking urged the collapse of the semantic field of eimi in different 'meanings'. Why? Before trying an answer we must realise the dimension of this breakdown. To this aim it is sufficient to remind the different forms of is in our formal logic and mathematic terminology:
- predicate-argument, p(a) (a is p), - set-theoretic membership,a 'belongs to' A (a is an A), - set-theoretic inclusion, A is a subset of B (the A are B), - identity, a=b (a is b), - existential quantification, exists x (there is x), - truth, - P or = P, (it is the case that P, P is true).
Most of recent studies about Greek philosophy, by employing also terminology and techniques from mathematic logic, claimed about a 'confusion' or 'lack of discrimination' among the different uses of eimi from Parmenides to Plato, which were solved between the late Platonic dialogues and Aristotle. And their solution is described as a major breakthrough of the rational thinking toward a more 'logical' language. This is somehow indisputable. However, in classic Chinese there is the opposite situation: there are many different ways of expressing our verb 'to be', and it is doubtful that this abundance fostered the development of a rational thinking, and it is sure that it did not foster the development of a formal thinking in China.
The Chinese structure of the being/not being pair is thoroughly different from the indo-european one (see(GRAHAM 1967) for more details): - the semantic field of 'to be' is, since the earliest historical traces, splitted in many different terms. An exception is the partial lack of distinction between 'identity' and 'membership', which caused paradoxes as the sophisms of Kung-sun Lung (300 BC): ''a white horse is not a horse'', on grounds which prove just that not all horses are white horses. However, Chinese also had a special copula of identity (chi).(GRAHAM 1967), - the 'negation' is analogously splitted; thus the semantic field of 'being/not being' is structured as a set of pairs, and there is no 'general' negative term, as our 'no, not', except for the 'special' negation of verbs/adjectives, where bu is used. Thus, we have the pair you/wu for a sort of 'heideggerian' existential usage
The Chinese concept of you/wu excludes all senses of English 'being' except the existential, but overlaps English 'having'. Thinking in terms of Being, we start from an object which on the one hand is, exists, on the other hand has properties. Thinking in terms of you, we start from an environment which we may or may not determine as the 'world', which has, within which there is, the object; arriving at the object we find that it has, that within it there are form and colour.((GRAHAM 1967),8)
or the nominal sentence (negated by fei) or the pair shih/fei or the pair shih/bu shih, for the copula usage. Other terms characterise identity or locative usage. Graham (GRAHAM 1967) underlines how strong is the connection between the dialectical nature of Chinese logic and philosophy, and its linguistic features, reminding (i) ''the Chinese fondness for forming concepts out of pairs of opposites'' (ta hsiao, 'big small' = 'size', shih fei, 'rightness wrongness'='truth'), (ii) the lack of an unique negative particle, and the connected employment of the negation as a complement and not as an absence of the positive.
It appears that the confusion of many different meanings in an unique verb 'to be' is a peculiarity of indo-european languages, but the existence of ''nominal sentences'' as specific kinds of predication increasingly absorbed in a copular usage is quite general. It is wrong then to charge Parmenides with grammatical mistakes, for what we have said about the earliest use of 'eimi' in Greek shows that, from this point of view, the major Aristotelian breakthrough could be just an equalling 'barbarian' languages! There must be something else in the being/not being problem. Greek philosophy does not simply follow its linguistic structure, but, since its beginning, takes charge of an incredible linguistic revolution, trying to create a brand new province of indo-european linguistic structure. And we face a double process: at the same time an extension of the 'being' employment and the beginning of a splitting and distinguishing in it. Which reasons were there for the extension of the 'being' usage? And which reasons to begin this 'disambiguation' process and distinguish between the different 'meanings' of 'eimi'? And why, with opposite evolution, does the distinction between the different negatives or between the different words for 'true' disappear? These are the themes we are going to analyse in the following sections. Probably at the beginning of the breakdown of the ''mythological paradigm'' there was the need of unifying the unforgettable ''true speech'' of the Muses with the practical 'knowledge' and 'language' of the everyday economic and social life. These two speeches displayed an opposite behaviour with respect to coherence and negation. Myths were genetic and affirmative in their linguistic style, but concretely incoherent in their content, almost as a dream. Everyday language was instead practically coherent in its content, but ruled by change and contradiction in its linguistic form. The logic character of knowledge and sensible character of physis rule out each other. Knowledge requires identity and unchangebleness, a not decomposable unity - nature, as the whole sensible reality, shows us everywhere the opposite of these determinations, only the unlimited vanishing of its presumed being in a simple becoming and the splitting of its presumed consistency in parts, which in turn can be infinitely divided.
An echo of the social troubles connected with this breakdown can be read in Greek tragedy, flourished in the V century, which openly displays ruptures and contradictions in the Greek society between an earlier set of laws and habits and the new polis. The sense of instability of mankind with respect to the other animals is also the core of Sphynx' enigma (VVN1-2) This opposition allowed two solutions: the first, followed by Heraclitus and somehow also by the Chinese civilisation, accepted the language in its natural form as a source of truth, an infinite land to be explored, without any attempt of representing the real, and then substantially incoherent. The second option was the Parmenidean one: to consider the language as a rough matter to be transformed, to find a form by which to represent, and thus to fix, the reality, to overcome its original contradictory character. The first option entailed the ''becoming paradox'':
''if everything is changing and relative, and if knowledge must 'fix' the real by the language, how is it possible to find something to say? ''
the second moved instead toward the above mentioned ''negative judgement paradox''. The history says that the western civilisation chose the second road, through a long process of intellectual building from Parmenides to Aristotle, and, to this aim, it had to deal with this second paradox, linked to being, negative and assertion. And this choice entailed the genesis of the formal thinking.