**3.1 From interrogative/indefinite items to definite references**

Basically, an answer looks like an assertion (affirmative or negative) or a consent / refusal, perhaps accompanied by the requested action or even converted into it, without words. It depends on the trigger, whether a question or a request11.

According to Paul Grice, in order for our wording to be effective, our interaction with one another has to follow the "cooperative principle": "make your contribution such as it is required, at the stage at which it occurs, by the accepted purpose or direction of the talk exchange in which you are engaged."

To complement a question or a request means, therefore, to replace indefiniteness with definiteness, thanks to the force appointed to an item to be fulfilled or to the confirmation/disconfirmation of the suspended orientation included.

Too often these alternative possibilities have been replaced in the metalinguistic representation by an oversimplification, i.e. by the reduction of answers to judgements, because of the importance of truth values.

Our choice here, however, is whatever the reply is, to consider its core, or rather the condition of the possibility not only of answers but of queries too; that is to say predication and the structure it involves.

Generally speaking, predicates are conceived as terms of a relation, the output of the act of saying something about something else, of attributing (or applying) something to something

<sup>11</sup> Nevertheless, we have to consider this distinction not as a clear-cut one: indeed with the notion of indirect speech act Searle recalls that "for example, a speaker may utter the sentence *Can you reach the salt?* and mean it not merely as a question but as a request to pass the salt […], cases in which one illocutionary act is performed indirectly by way of performing another." (Searle, 1975)

56 Semantics – Advances in Theories and Mathematical Models

We are all familiar with the expression "to break the ice". To ask proper questions at the right moment may be a good way to break the ice. But sometimes it is so difficult to detect the extension and the boundaries of what we ignore that no questions arise, whereas at some other times correct, precise, punctual questions addressed to the right addressee at the right moment can pave the way to quite important self-disclosures, intelligent and farseeing insights, real turning points. The quality of interviews and interrogatories depends

There are crucial structures which are capable of building answers, as well as questions and requests. These structures are the strategic means to order words syntactically and semantically, in a way which is suitable for "filling" the gaps (of knowledge/action) identified by questions/requests; strategic insofar as they themselves are non-saturated tools, unaccomplished structures, and yet still able to activate accomplishments, and form a

Predication is such a structure, propositional functions are its developments on the way

Basically, an answer looks like an assertion (affirmative or negative) or a consent / refusal, perhaps accompanied by the requested action or even converted into it, without words. It

According to Paul Grice, in order for our wording to be effective, our interaction with one another has to follow the "cooperative principle": "make your contribution such as it is required, at the stage at which it occurs, by the accepted purpose or direction of the talk

To complement a question or a request means, therefore, to replace indefiniteness with definiteness, thanks to the force appointed to an item to be fulfilled or to the

Too often these alternative possibilities have been replaced in the metalinguistic representation by an oversimplification, i.e. by the reduction of answers to judgements,

Our choice here, however, is whatever the reply is, to consider its core, or rather the condition of the possibility not only of answers but of queries too; that is to say predication

Generally speaking, predicates are conceived as terms of a relation, the output of the act of saying something about something else, of attributing (or applying) something to something

11 Nevertheless, we have to consider this distinction not as a clear-cut one: indeed with the notion of indirect speech act Searle recalls that "for example, a speaker may utter the sentence *Can you reach the salt?* and mean it not merely as a question but as a request to pass the salt […], cases in which one

illocutionary act is performed indirectly by way of performing another." (Searle, 1975)

on the skills of their authors and on the cooperation they are able to gain.

**3.1 From interrogative/indefinite items to definite references** 

confirmation/disconfirmation of the suspended orientation included.

depends on the trigger, whether a question or a request11.

bridge to the expected items.

towards complete propositions.

**3. The structure of an answer** 

exchange in which you are engaged."

because of the importance of truth values.

and the structure it involves.

else, as expressions of properties or relations belonging to one or more objects, or the result of making concepts fall into one another.

Actually, in logical-grammatical training, we meet predicates first. Predication as such remains in the background. On the contrary, it is consistent with a pragmatic framework to put the act first and its result afterwards.

Our claim is that without predication we cannot ensure neither the right assessment of the interrogative items in questions (where *wh*-placeholders need to be substituted and their empty place filled), nor the nuclear structure upon which the illocutionary force of the answers can be exerted.

Moreover, we think that while underlining predication as a main device, at the same time we show answers as works in progress, towards the identification of definite references or events, or towards the definition of a yes- or no-answer. In fact, if we consider that, according to a certain semantic paradigm (the Fregean and the Neo-fregean one), truth values are the referents of assertions, we can say that predication allows answers to gain reference both locally and globally (at the level of single constituents and at the level of whole sentences, if assertive, as such).

Once the primacy of the act of predication upon predicates and consequently upon predication as a result is stated (words like predic-*ation* always work both as a *nomen actionis* and as a *nomen rei actae*), we can proceed as follows:


 eventually we will consider the whole structure it builds, from the point of view of the two main paradigms according to which such a structure has been conceived, the Aristotelian and the Fregean one.

#### **3.2 The basic syntagmatic act is predication**

Let us consider the etymology of 'predicate', in English a noun with exactly the same form as the verb (but in the infinitive, not participle mood). Why is this so? According to the reconstruction offered by the Oxford English Dictionary 'predicate' comes from "Middle French *predicat* (French *prédicat* ) that which is said of a subject (1370), quality (1466) and its etymon post-classical Latin *praedicatum*12 that which is said of a subject (6th cent. in Boethius; earlier in senses doctrine, precept (4th cent.), prediction (late 2nd or early 3rd cent. in Tertullian), use as noun of neuter past participle of classical Latin *praedicāre*. ''.

Therefore, if somebody predicates something of something else or of somebody else, then we obtain predicates. We can sum up the whole scene as a predication. Why do I underline such an obvious remark? Because sometimes this "ontogenetic", dynamic reconstruction has been forgotten, leaving as a result the static relation between predicates and their correlates as ready-made.

<sup>12</sup> Gr. *kategoroúmenon*, from *kategoréo*, a typical expression recalling the *agorà* in the *polis*, and its role of attracting citizens called to select (*katà*, in front of everybody, publicly) candidates submitted to public evaluation for the future governance of the *polis* itself.

Queries and Predicate – Argument Relationship 59

"A full analysis of the basic grammatical function – e.g. the function of the subject and predic*ation*, […] the real nature of sentence form*ation* – can be achieved only with the help of the static [not genetically comparative] method by which linguistic phenomena are not unduly separated from the *action of speaking*. […] In the field of *syntax* the general shift of interest from the external aspect of *language* to its *inner life* is exemplified by the emphasizing of the stylistic principle and by the substitution of the functional conception for the traditional formal point of view. Finer methods of linguistic analysis have brought *to light the importance of what I should call the* double-faced character of linguistic phenomena. It consists [of] a *continuous fluctuation between the general and the individual*. […] Linguistic research can either concentrate on what has already become a common possession of all members of the linguistic community or it can study the individual efforts of linguistic creation. The traditional school of linguistics has so exclusively limited itself to the study of commonly accepted means of expression that the individual speaker has disappeared from its ken. As a reaction against this too objective conception of language, a school of an extreme linguistic subjectivism chiefly represented by Professor K. Vossler has appeared, which following the ideas of Wilhelm von Humboldt and Benedetto Croce regards the act of linguistic expression as something [as] individual as artistic creation. […] The proposition maintained by Professor Spitzer '*Nihil est in syntaxi quod non fuerit in stylo*' very clearly shows how the greatest stress is laid by him and his friends on the individual share in linguistic expression. Linguistics as a whole can derive from stylistic syntax and stylistic semasiology a double benefit. [But, Mathesius replies,] It is good that the rule, often neglected, has been emphasized again […] In the study of language, of course, individual utterances are analysed as specimens of the linguistic possibilities of the whole community… . The time has really come for general linguistic problems to be systematically studied. […] The basic functions of linguistic expression should be analysed and the means of linguistic expression catalogued. This means *showing how in all kinds of languages the subject and the predicate are expressed*, which are *the possible forms of* the active, passive, perceptive, qualificative, possessive, etc. *predication*, how the attributive qualification is expressed, *which aspects* of activity or of status *can be expressed in the predication*, etc. It is selfevident that such problems cannot be solved but by the functional and static [i.e. synchronic,

as opposed to diachronic] method of research." (Mathesius, 1926; italics mine).

is this difference that should be the leading principle for a classification of the predicative connexions […] or for short 'predication'. […] Thus 'connexion' is meant to denote one of the two principal categories of combination of morphemes that occur in language ['connexion', term employed by Noreen, on the whole corresponding to Wundt's '*geschlossene Wortgruppe*', as implies that a principal and an accessory element are being combined, in this case equivalent to a subject and a predicate, in contradistinction to 'adjunctive (adjundct) connexion' (Wundt's '*offene Wortverbindung*', that implies a combination already made between a principal and an accessory member, in this case a determinatum and a determinandum: *the laughing child* vs. *the child is laughing*], the other [combination] being called 'adhexion', in which the members combined are independent of each other, e.g. 'You *and* I'; 'he is

A distinction of the different kinds of predicative connexion as met with in Indo-European languages, has not yet been instituted by current grammar. This neglect renders it difficult, may impossible to deal properly with the predicational changes of verbs […] It is indispensable to make this classification if we want to view the verbal changes of meaning we are going to deal with [the phenomenon of transitive verbs used in English as predicate-verbs in the active form with a passive sense: close (of a flower),

conjoin (of roots), divide (of a shell)], in the light of their predicational functions."

reading, *but* she is writing'.

Beyond this, what was the result of an operation of junction and construction has been considered to be something already given, to be analysed, resolved into its parts. This is why traditionally we became acquainted with the practise of grammatical *analysis* centred upon the parts of speech (the whole, i.e. the speech, remaining almost completely out of systematic consideration), and with the practice of logical *analysis*  centred upon logical terms (literally, ends of the proposition: see predicate calculus), rather than upon the unity of proposition itself and of propositions with each other (propositional calculus).

Moreover, the two analyses tended towards reciprocal emancipation: instead of a systematic correlation among forms and functions, a frequent matter was that of the "liberation" or "emancipation" of grammar from the yoke of logic and of logic from the yoke of grammar13.

This caused some confusions and worry throughout long history of Western logic and philosophy.

It would be useful, to begin with, to recall that some technical terms on the matter could work, as *predication*, both as *nomina actionis* and as *nomina rei actae*, such as *articulation, proposition* and *function*. Similarly, not only *predicate*, but also *subject* come from Latin *praedicatum* and *subjectum*, in their turn translations of the past *and* passive Greek participles *kategoroumenon* and *hypokeimenon*: the first one a real passive form, the latter an interesting deponent.

But what could be seen "on the run" was, and still is, rather considered as an achieved goal.

Two independent developments in the 20th century helped to change this point of view, in linguistics as well as in philosophy, the first, functionalism in classical structuralism and the second, pragmatics in analytical philosophy.

"*The basic syntagmatic act*, and at the same time the intrinsic sentence-forming act, is *the predication*", states the second of the 1929 theses of the Prague Linguistic Circle (Vachek 1983). Behind the collective authorship of that text, there was one particular author, Vilém Mathesius, the founder of the Circle, with his syntactical investigations14. In 1926 he wrote:

<sup>13</sup> See (Sériot, Samain, 2008), with a precious extension of the *status quaestionis* to Eastern European and Russian studies.

<sup>14</sup> Although being a detail in the huge panorama here sketchily outlined, it is worth mentioning the particular approach developed by Mathesius himself and by a Swedish Anglicist he quotes as well, K.F. Sundén, in the previous decades (Sundén 1904, 1916) : they both ended up researching "sentencehood" through predic*ation*, and elliptical predication especially, i.e. through effective, though reduced structures, deviating from the canonical bi-member sentences, yet recognisable and understandable as true sentences only via a cooperative inference of the addressee, who had to capture specific semantic intentions orienting each act of predication. Sundén (1916) begins his essay *The Predicational Categories in English* thus: "It is a matter of general observation that the connexion between subject and predicate may from a semological point of view be of different kinds. We are not then alluding to the particular and accidental relation brought about by the different tenses, moods or tense-aspects of the predicate, but to the general qualification of the subject conditioned by the material import of the predicate itself. In other words, we are referring to the different manners in which the predicate qualifies the subject. It

58 Semantics – Advances in Theories and Mathematical Models

Beyond this, what was the result of an operation of junction and construction has been considered to be something already given, to be analysed, resolved into its parts. This is why traditionally we became acquainted with the practise of grammatical *analysis* centred upon the parts of speech (the whole, i.e. the speech, remaining almost completely out of systematic consideration), and with the practice of logical *analysis*  centred upon logical terms (literally, ends of the proposition: see predicate calculus), rather than upon the unity of proposition itself and of propositions with each other

Moreover, the two analyses tended towards reciprocal emancipation: instead of a systematic correlation among forms and functions, a frequent matter was that of the "liberation" or "emancipation" of grammar from the yoke of logic and of logic from the yoke of

This caused some confusions and worry throughout long history of Western logic and

It would be useful, to begin with, to recall that some technical terms on the matter could work, as *predication*, both as *nomina actionis* and as *nomina rei actae*, such as *articulation, proposition* and *function*. Similarly, not only *predicate*, but also *subject* come from Latin *praedicatum* and *subjectum*, in their turn translations of the past *and* passive Greek participles *kategoroumenon* and *hypokeimenon*: the first one a real passive form, the latter an interesting

But what could be seen "on the run" was, and still is, rather considered as an achieved

Two independent developments in the 20th century helped to change this point of view, in linguistics as well as in philosophy, the first, functionalism in classical structuralism and the

"*The basic syntagmatic act*, and at the same time the intrinsic sentence-forming act, is *the predication*", states the second of the 1929 theses of the Prague Linguistic Circle (Vachek 1983). Behind the collective authorship of that text, there was one particular author, Vilém Mathesius, the founder of the Circle, with his syntactical investigations14. In 1926 he wrote:

13 See (Sériot, Samain, 2008), with a precious extension of the *status quaestionis* to Eastern European and

14 Although being a detail in the huge panorama here sketchily outlined, it is worth mentioning the particular approach developed by Mathesius himself and by a Swedish Anglicist he quotes as well, K.F. Sundén, in the previous decades (Sundén 1904, 1916) : they both ended up researching "sentencehood" through predic*ation*, and elliptical predication especially, i.e. through effective, though reduced structures, deviating from the canonical bi-member sentences, yet recognisable and understandable as true sentences only via a cooperative inference of the addressee, who had to capture specific semantic intentions orienting each act of predication. Sundén (1916) begins his essay *The Predicational Categories in English* thus: "It is a matter of general observation that the connexion between subject and predicate may from a semological point of view be of different kinds. We are not then alluding to the particular and accidental relation brought about by the different tenses, moods or tense-aspects of the predicate, but to the general qualification of the subject conditioned by the material import of the predicate itself. In other words, we are referring to the different manners in which the predicate qualifies the subject. It

(propositional calculus).

grammar13.

philosophy.

deponent.

second, pragmatics in analytical philosophy.

goal.

Russian studies.

"A full analysis of the basic grammatical function – e.g. the function of the subject and predic*ation*, […] the real nature of sentence form*ation* – can be achieved only with the help of the static [not genetically comparative] method by which linguistic phenomena are not unduly separated from the *action of speaking*. […] In the field of *syntax* the general shift of interest from the external aspect of *language* to its *inner life* is exemplified by the emphasizing of the stylistic principle and by the substitution of the functional conception for the traditional formal point of view. Finer methods of linguistic analysis have brought *to light the importance of what I should call the* double-faced character of linguistic phenomena. It consists [of] a *continuous fluctuation between the general and the individual*. […] Linguistic research can either concentrate on what has already become a common possession of all members of the linguistic community or it can study the individual efforts of linguistic creation. The traditional school of linguistics has so exclusively limited itself to the study of commonly accepted means of expression that the individual speaker has disappeared from its ken. As a reaction against this too objective conception of language, a school of an extreme linguistic subjectivism chiefly represented by Professor K. Vossler has appeared, which following the ideas of Wilhelm von Humboldt and Benedetto Croce regards the act of linguistic expression as something [as] individual as artistic creation. […] The proposition maintained by Professor Spitzer '*Nihil est in syntaxi quod non fuerit in stylo*' very clearly shows how the greatest stress is laid by him and his friends on the individual share in linguistic expression. Linguistics as a whole can derive from stylistic syntax and stylistic semasiology a double benefit. [But, Mathesius replies,] It is good that the rule, often neglected, has been emphasized again […] In the study of language, of course, individual utterances are analysed as specimens of the linguistic possibilities of the whole community… . The time has really come for general linguistic problems to be systematically studied. […] The basic functions of linguistic expression should be analysed and the means of linguistic expression catalogued. This means *showing how in all kinds of languages the subject and the predicate are expressed*, which are *the possible forms of* the active, passive, perceptive, qualificative, possessive, etc. *predication*, how the attributive qualification is expressed, *which aspects* of activity or of status *can be expressed in the predication*, etc. It is selfevident that such problems cannot be solved but by the functional and static [i.e. synchronic, as opposed to diachronic] method of research." (Mathesius, 1926; italics mine).

is this difference that should be the leading principle for a classification of the predicative connexions […] or for short 'predication'. […] Thus 'connexion' is meant to denote one of the two principal categories of combination of morphemes that occur in language ['connexion', term employed by Noreen, on the whole corresponding to Wundt's '*geschlossene Wortgruppe*', as implies that a principal and an accessory element are being combined, in this case equivalent to a subject and a predicate, in contradistinction to 'adjunctive (adjundct) connexion' (Wundt's '*offene Wortverbindung*', that implies a combination already made between a principal and an accessory member, in this case a determinatum and a determinandum: *the laughing child* vs. *the child is laughing*], the other [combination] being called 'adhexion', in which the members combined are independent of each other, e.g. 'You *and* I'; 'he is reading, *but* she is writing'.

A distinction of the different kinds of predicative connexion as met with in Indo-European languages, has not yet been instituted by current grammar. This neglect renders it difficult, may impossible to deal properly with the predicational changes of verbs […] It is indispensable to make this classification if we want to view the verbal changes of meaning we are going to deal with [the phenomenon of transitive verbs used in English as predicate-verbs in the active form with a passive sense: close (of a flower), conjoin (of roots), divide (of a shell)], in the light of their predicational functions."

Queries and Predicate – Argument Relationship 61

Nearly everybody would label this second term of relation 'subject', due to a more than bimillenarian tradition: a really successful transmission of high culture (Aristotelian logic) to basic education, passed down from the school-teaching of ancient languages to that of

This so well-known schema has induced and still induces another apparently obvious expectancy: that predication involves a two-element structure, be it a question or an answer,

Rather than a relation, this should grant a correlation: if P, then C (= Correlate to P). Immediately after, or even simultaneously, a further if-then (→) prevision: if P, then S (=

But even the briefest glance at real conversations, texts, or messages of any sort would contradict such a prevision, a prevision to be contradicted in many ways, upwards and downwards. Sometimes only one element is enough, sometimes even five or six constituents take place. What has to be corrected? The idea of a correlation to be expected? Its structure as a regular two-element structure? Its epistemological status as a regulative ideal instead of

The expectancy of a correlation is a legitimate one; on one condition however, that of recognising it as a regulative ideal only. This means that we cannot take for granted that in each sentence we will find such an evident correlation. We have elliptical sentences, condensed utterances, such as '*Why?*', '*What?*', '*Fire!*', '*Come!*' '*Yes.*', '*No*'. Sometimes the predicate is absent /cut off because it is the same as in the previous sentence, sometimes it is present but includes the person it refers to, sometimes just an adverb of affirmation or negation is sufficient to substitute the whole predicative correlation. In any case the

But is the predicative relation always a relation to one element (typically the subject), i.e. a

The short (though not careless) answer should be: what is necessary is the unity of the

If we look for a classical image suggesting the idea of one thing being able to look like (and also function as) two, we should recall the image of an elbow or of a knee: being part of an arm or leg does not prevent them articulating the movement of their own limbs. As demonstrated, this basic biological image supports the concept of *articulation,* an ancient and

Such a deep feeling of the original and fundamental unit of any sentence (in this case, specifically, and especially, queries and answers), and, at the same time, of the dynamic role of predication in the sentence, is well attested to by nearly all of the major authors , those who represent real milestones along the path of metalinguistic thought, such as Aristotle,

Humboldt, Frege, Peirce, Bühler and Tesnière, to mention some of the most eminent.

modern ones, without so much as a blink.

or whatever.

Subject).

Firstly:

a statistical regularity?

monadic relation?

Let us proceed step by step.

correlation seems, though not always , to be active.

evergreen metalinguistic tool (Laspia, 1997).

sentence (query or answer), whether the unity be simple or complex.

In a nutshell, syntagmatic acts precede syntax as composition precedes its metalinguistic analysis15.

With a strong similarity, in his *Speech Acts* John Searle identifies predication and reference within the level of expressions, before inquiring into their meaning and their being speech acts. He states: "… in the utterance […] a speaker is characteristically performing at least three distinct kinds of acts: (*a*) the uttering of words (morphemes, sentences); (*b*) referring and predicating; *c*) stating, questioning, commanding, promising etc.

Let us assign names to these under the general heading of speech acts:


[…] The distinction between reference and predication holds, and the correct description is to say that the predicate expression is used to ascribe a property. I do not claim that this description has any *explanatory* power at all. Nobody who does not already have a prior understanding of what it is to use a predicate expression can understand this remark […] At this stage I only claim that it is literally true […] (Searle 1969).

Essentially, summing up cause and effect, act and result has to be done not only for the sake of completeness, but also on the assumption that linguistic structures and their semantics largely underdetermine their meanings and the meaning of their relations, which are often defined by the context in which they occur16. In other words: predicates are not prefab, they are just semi-processed products. They need to be determined within the sentences they belong to, and further assigned to the utterances they are constituents of.

Now that this primacy of predication upon predicates (so to speak) has been grasped, let us move on to the two main models about predicates, that of Aristotle and that of Frege17.

Before sketching an essential outline of their doctrines, it is worth noting the wide influence of models, especially the Aristotelian one, with which not only philosophers became (and still become) acquainted, but also ordinary people, usually young pupils during their first years of school.

#### **3.3 Predicates and their correlates, or the sentence as a unit**

Predication is the act of predicating (saying) something about something else. So we have, *in nuce*, the legitimate expectancy of a second term of relation, of the predicative relation: what is predicated about.

<sup>15</sup> On this very point, of the border between generality and individuality, ten years later Mathesius stated: "The sentence is not entirely the product of a transitory moment, is not entirely determined by the individual situation, and, consequently, does not entirely belong to the sphere of speech, but depends in its general form on the grammatical system of the language in which it is uttered. […] In language we have the word in its conceptual meaning and the sentence as abstract pattern, whereas in speech we have the word as referring to concrete reality and the sentence as concrete utterance." (Mathesius 1936). See (Raynaud, 2008).

<sup>16</sup> See (Frigerio, 2010 a), (Frigerio, 2010 b).

<sup>17</sup> The eminency of Aristotle's and Frege's contributions throughout the whole history of logic are widely recognised: see (Dummett, 1973).

Nearly everybody would label this second term of relation 'subject', due to a more than bimillenarian tradition: a really successful transmission of high culture (Aristotelian logic) to basic education, passed down from the school-teaching of ancient languages to that of modern ones, without so much as a blink.

This so well-known schema has induced and still induces another apparently obvious expectancy: that predication involves a two-element structure, be it a question or an answer, or whatever.

Rather than a relation, this should grant a correlation: if P, then C (= Correlate to P). Immediately after, or even simultaneously, a further if-then (→) prevision: if P, then S (= Subject).

But even the briefest glance at real conversations, texts, or messages of any sort would contradict such a prevision, a prevision to be contradicted in many ways, upwards and downwards. Sometimes only one element is enough, sometimes even five or six constituents take place. What has to be corrected? The idea of a correlation to be expected? Its structure as a regular two-element structure? Its epistemological status as a regulative ideal instead of a statistical regularity?

Let us proceed step by step.

Firstly:

60 Semantics – Advances in Theories and Mathematical Models

In a nutshell, syntagmatic acts precede syntax as composition precedes its metalinguistic

With a strong similarity, in his *Speech Acts* John Searle identifies predication and reference within the level of expressions, before inquiring into their meaning and their being speech acts. He states: "… in the utterance […] a speaker is characteristically performing at least three distinct kinds of acts: (*a*) the uttering of words (morphemes, sentences); (*b*) referring

*c.* stating, questioning, commanding, promising etc. = performing *illocutionary acts.* 

[…] The distinction between reference and predication holds, and the correct description is to say that the predicate expression is used to ascribe a property. I do not claim that this description has any *explanatory* power at all. Nobody who does not already have a prior understanding of what it is to use a predicate expression can understand this remark […] At

Essentially, summing up cause and effect, act and result has to be done not only for the sake of completeness, but also on the assumption that linguistic structures and their semantics largely underdetermine their meanings and the meaning of their relations, which are often defined by the context in which they occur16. In other words: predicates are not prefab, they are just semi-processed products. They need to be determined within the sentences they

Now that this primacy of predication upon predicates (so to speak) has been grasped, let us move on to the two main models about predicates, that of Aristotle and that of Frege17.

Before sketching an essential outline of their doctrines, it is worth noting the wide influence of models, especially the Aristotelian one, with which not only philosophers became (and still become) acquainted, but also ordinary people, usually young pupils during their first

Predication is the act of predicating (saying) something about something else. So we have, *in nuce*, the legitimate expectancy of a second term of relation, of the predicative relation: what

15 On this very point, of the border between generality and individuality, ten years later Mathesius stated: "The sentence is not entirely the product of a transitory moment, is not entirely determined by the individual situation, and, consequently, does not entirely belong to the sphere of speech, but depends in its general form on the grammatical system of the language in which it is uttered. […] In language we have the word in its conceptual meaning and the sentence as abstract pattern, whereas in speech we have the word as referring to concrete reality and the sentence as concrete utterance."

17 The eminency of Aristotle's and Frege's contributions throughout the whole history of logic are

and predicating; *c*) stating, questioning, commanding, promising etc. Let us assign names to these under the general heading of speech acts: *a.* uttering words (morphemes, sentences) = performing *utterance acts.* 

*b.* referring and predicating = performing *propositional acts.* 

this stage I only claim that it is literally true […] (Searle 1969).

belong to, and further assigned to the utterances they are constituents of.

**3.3 Predicates and their correlates, or the sentence as a unit** 

analysis15.

years of school.

is predicated about.

(Mathesius 1936). See (Raynaud, 2008). 16 See (Frigerio, 2010 a), (Frigerio, 2010 b).

widely recognised: see (Dummett, 1973).

The expectancy of a correlation is a legitimate one; on one condition however, that of recognising it as a regulative ideal only. This means that we cannot take for granted that in each sentence we will find such an evident correlation. We have elliptical sentences, condensed utterances, such as '*Why?*', '*What?*', '*Fire!*', '*Come!*' '*Yes.*', '*No*'. Sometimes the predicate is absent /cut off because it is the same as in the previous sentence, sometimes it is present but includes the person it refers to, sometimes just an adverb of affirmation or negation is sufficient to substitute the whole predicative correlation. In any case the correlation seems, though not always , to be active.

But is the predicative relation always a relation to one element (typically the subject), i.e. a monadic relation?

The short (though not careless) answer should be: what is necessary is the unity of the sentence (query or answer), whether the unity be simple or complex.

If we look for a classical image suggesting the idea of one thing being able to look like (and also function as) two, we should recall the image of an elbow or of a knee: being part of an arm or leg does not prevent them articulating the movement of their own limbs. As demonstrated, this basic biological image supports the concept of *articulation,* an ancient and evergreen metalinguistic tool (Laspia, 1997).

Such a deep feeling of the original and fundamental unit of any sentence (in this case, specifically, and especially, queries and answers), and, at the same time, of the dynamic role of predication in the sentence, is well attested to by nearly all of the major authors , those who represent real milestones along the path of metalinguistic thought, such as Aristotle, Humboldt, Frege, Peirce, Bühler and Tesnière, to mention some of the most eminent.

Queries and Predicate – Argument Relationship 63

We have already mentioned the objection of descriptive fallacy (§ 2.2) which can be recalled

Less attracted by the referential and defining purport of speech and more focused on its

Perhaps it would be worth mentioning the subjectivist turn (not yet about sentences, but rather concerning nouns and verbs) taken in the modern era and testified to by Arnauld and Lancelot's *Grammaire générale et raisonnée*,: "The subject of our thoughts, are either things, such as the earth, the sun, water, wood, what we normally call substance. Or the way things are; like being round, being red, being hard, being wise etc. what we call accidents. […] Because those [the words] which refer to substance, are called "substantive nouns or names"; and those which refer to attributes, signalling the subject to which these attributes

And that is the origin of substantive and adjectival nouns. But we didn't stop there: and it so happens that we didn't so much stop at meaning [*signification*], but rather at the manner of meaning [*manière de signifier*]. Because the substance is what exists in its own right, we have given the name substantive nouns to all those which exist by themselves in the discourse, without needing any other name, even if they signify accidents. […] The verb itself should have no other use than to signify the link that we make in our minds between the two terms of the proposition. But there is only the verb "to be" which we call substantive which has this simplicity, we can even say that it only has this simplicity in the third person of the present tense, "is" and in certain contexts."(Arnauld-Lancelot, 1660; italics, beyond

The reflexion on language takes its leave of an insurmountable correspondence between linguistic and world structures. The shape of speech –as is now accepted - depends largely on the activity of speakers. Wilhelm von Humboldt, after a life-long and world-wide

"*Framing the sentence.* The grammatically formed *word* […] in the composition of its elements, and in its unity as a whole, is destined to enter, again as an element, into the *sentence*. So language must here form, higher unity – higher, not merely because it is of greater extent, but also because it depends more exclusively on the ordering inner form of the sense of language, in that sound can only operate on it an auxiliary fashion. […] If *we start from the sentence, as is originally more correct, since every utterance, however incomplete, does really constitute a closed thought in the speaker's mind*, then languages which employ this method [as the Mexican] by no means shatter the unity of the sentence, but try, rather, to knit its construction even more tightly together. But they manifestly derange the boundaries of verbal unity by carrying them over into the domain of sentential unity. […] The Mexican method of incorporation testifies in this to a correct sense of sentence-formation, that it attaches the designation of its relations precisely to the verb, and thus to the point at which

18 While attending corpus linguistics studies, I was prompted to reconsider the role of predication in the

vast field of illocutionary forces and in relation to a variety of objects. It was a rather shocking experience, similar to that of going out in the open air rather than contemplating a panorama from a

empirical research on languages, sums up his theoretical views with great efficacy:

as important due to the reductionism of the proposed formalisation: S is P18 .

building dynamics is Humboldt's view.

examples and technical terms, are mine).

the sentence ties itself together into unity. […]

single window.

pertain, adjectival nouns.

Nevertheless, the tone with which this eminent choir has sung throughout the centuries deserves our careful attention.

Let us begin with Aristotle's insistence upon the "equivalence" between a noun and a definition (Laspia, 2005), expressed through a judgement of identity:

"Since definition [*horismòs* ] means 'an account [*lógos* ] of what a thing is', obviously one kind of definition will be an explanation [*lógos* ] of the meaning of the name, or of an equivalent denomination [*e logos héteros onomatódes* ]" (*Analytica posteriora* B 10, 93 b 29-31).

"The starting-point is from definition; and definition results from the necessity of […] meaning something; because the formula, which […] term implies, will be a definition." (*Metaphysica* Γ 7, 1012 a 23-4).

A reading of the whole dialogue "The Sophist" would be helpful in revealing the reasons why nouns and verbs came on to the philosophical scene: they actually fulfill the requirements of those who seek to discern truth from falsity, or rather of those who contrast the thesis of the indiscernibility of truth and falsity. From this point of view Plato and Aristotle are much closer to each other than usually thought. "Discourse is never composed of nouns alone spoken in succession, nor of verbs spoken without nouns. […] For instance, 'walks', 'runs', 'sleeps' and the other verbs which denote actions, even if you utter all there are of them in succession, do not make discourse for all that. No, - replies Theaethetus to the Stranger – of course not. And again, when 'lion', 'stag', 'horse', and all other names of those who perform these actions are uttered, such a succession of words does not yet make discourse; for in neither case do the words uttered indicate action or inaction or existence of anything that exists or does not exist, until the verbs are mingled with the nouns; then the words fit, and their first combination [*symploké*] is a sentence, about the first and shortest form of discourse.[…] When one says 'a man learns' […] he does not merely gives names, but he reaches a conclusion by combining (*symplékon*) verbs with nouns. […] So, then, just as of things some fit each other and some do not, so too some vocal signs do not fit, but some of them do fit and form discourse (*lógos*)." (Plato *Sophista* 261 d - 262 e)

"Verbs by themselves, then, are nouns, and they stand for or signify something, for the speaker stops his process of thinking and the mind of the hearer acquiesces. However, they do not as yet express positive or negative judgements. […] A sentence is significant speech, of which this or that part may have meaning – as something, that is, that is uttered but not as expressing a judgement of a positive or negative character. […] But while every sentence has meaning, […] not all can be called propositions." (*De interpretatione* 3, 16 b 22-5; 4, 16 b 27-29; 4, 17 a 1-4).

Although not all sentences prove to be units as in the case of a definition, Aristotle nevertheless explains what, in each case, keeps the noun and the verb together, the subject and the predicate: it is the verb 'to be', which paraphrases the relating function of the verb: "The two propositions, 'man walks', 'man is walking' mean just the same thing. "(*De interpretatione* 12, 21 b 9-10)

The term 'copula', although first introduced only in the XIIth century, by Abelard, and therefore not originally Aristotelian, with its huge diffusion, testifies to the "popularity" of the Aristotelian model.

62 Semantics – Advances in Theories and Mathematical Models

Nevertheless, the tone with which this eminent choir has sung throughout the centuries

Let us begin with Aristotle's insistence upon the "equivalence" between a noun and a

"Since definition [*horismòs* ] means 'an account [*lógos* ] of what a thing is', obviously one kind of definition will be an explanation [*lógos* ] of the meaning of the name, or of an equivalent denomination [*e logos héteros onomatódes* ]" (*Analytica posteriora* B 10, 93 b 29-31). "The starting-point is from definition; and definition results from the necessity of […] meaning something; because the formula, which […] term implies, will be a definition."

A reading of the whole dialogue "The Sophist" would be helpful in revealing the reasons why nouns and verbs came on to the philosophical scene: they actually fulfill the requirements of those who seek to discern truth from falsity, or rather of those who contrast the thesis of the indiscernibility of truth and falsity. From this point of view Plato and Aristotle are much closer to each other than usually thought. "Discourse is never composed of nouns alone spoken in succession, nor of verbs spoken without nouns. […] For instance, 'walks', 'runs', 'sleeps' and the other verbs which denote actions, even if you utter all there are of them in succession, do not make discourse for all that. No, - replies Theaethetus to the Stranger – of course not. And again, when 'lion', 'stag', 'horse', and all other names of those who perform these actions are uttered, such a succession of words does not yet make discourse; for in neither case do the words uttered indicate action or inaction or existence of anything that exists or does not exist, until the verbs are mingled with the nouns; then the words fit, and their first combination [*symploké*] is a sentence, about the first and shortest form of discourse.[…] When one says 'a man learns' […] he does not merely gives names, but he reaches a conclusion by combining (*symplékon*) verbs with nouns. […] So, then, just as of things some fit each other and some do not, so too some vocal signs do not fit, but some

"Verbs by themselves, then, are nouns, and they stand for or signify something, for the speaker stops his process of thinking and the mind of the hearer acquiesces. However, they do not as yet express positive or negative judgements. […] A sentence is significant speech, of which this or that part may have meaning – as something, that is, that is uttered but not as expressing a judgement of a positive or negative character. […] But while every sentence has meaning, […] not all can be called propositions." (*De interpretatione* 3, 16 b 22-5; 4, 16 b

Although not all sentences prove to be units as in the case of a definition, Aristotle nevertheless explains what, in each case, keeps the noun and the verb together, the subject and the predicate: it is the verb 'to be', which paraphrases the relating function of the verb: "The two propositions, 'man walks', 'man is walking' mean just the same thing. "(*De* 

The term 'copula', although first introduced only in the XIIth century, by Abelard, and therefore not originally Aristotelian, with its huge diffusion, testifies to the "popularity" of

definition (Laspia, 2005), expressed through a judgement of identity:

of them do fit and form discourse (*lógos*)." (Plato *Sophista* 261 d - 262 e)

deserves our careful attention.

(*Metaphysica* Γ 7, 1012 a 23-4).

27-29; 4, 17 a 1-4).

*interpretatione* 12, 21 b 9-10)

the Aristotelian model.

We have already mentioned the objection of descriptive fallacy (§ 2.2) which can be recalled as important due to the reductionism of the proposed formalisation: S is P18 .

Less attracted by the referential and defining purport of speech and more focused on its building dynamics is Humboldt's view.

Perhaps it would be worth mentioning the subjectivist turn (not yet about sentences, but rather concerning nouns and verbs) taken in the modern era and testified to by Arnauld and Lancelot's *Grammaire générale et raisonnée*,: "The subject of our thoughts, are either things, such as the earth, the sun, water, wood, what we normally call substance. Or the way things are; like being round, being red, being hard, being wise etc. what we call accidents. […] Because those [the words] which refer to substance, are called "substantive nouns or names"; and those which refer to attributes, signalling the subject to which these attributes pertain, adjectival nouns.

And that is the origin of substantive and adjectival nouns. But we didn't stop there: and it so happens that we didn't so much stop at meaning [*signification*], but rather at the manner of meaning [*manière de signifier*]. Because the substance is what exists in its own right, we have given the name substantive nouns to all those which exist by themselves in the discourse, without needing any other name, even if they signify accidents. […] The verb itself should have no other use than to signify the link that we make in our minds between the two terms of the proposition. But there is only the verb "to be" which we call substantive which has this simplicity, we can even say that it only has this simplicity in the third person of the present tense, "is" and in certain contexts."(Arnauld-Lancelot, 1660; italics, beyond examples and technical terms, are mine).

The reflexion on language takes its leave of an insurmountable correspondence between linguistic and world structures. The shape of speech –as is now accepted - depends largely on the activity of speakers. Wilhelm von Humboldt, after a life-long and world-wide empirical research on languages, sums up his theoretical views with great efficacy:

"*Framing the sentence.* The grammatically formed *word* […] in the composition of its elements, and in its unity as a whole, is destined to enter, again as an element, into the *sentence*. So language must here form, higher unity – higher, not merely because it is of greater extent, but also because it depends more exclusively on the ordering inner form of the sense of language, in that sound can only operate on it an auxiliary fashion. […] If *we start from the sentence, as is originally more correct, since every utterance, however incomplete, does really constitute a closed thought in the speaker's mind*, then languages which employ this method [as the Mexican] by no means shatter the unity of the sentence, but try, rather, to knit its construction even more tightly together. But they manifestly derange the boundaries of verbal unity by carrying them over into the domain of sentential unity. […] The Mexican method of incorporation testifies in this to a correct sense of sentence-formation, that it attaches the designation of its relations precisely to the verb, and thus to the point at which the sentence ties itself together into unity. […]

<sup>18</sup> While attending corpus linguistics studies, I was prompted to reconsider the role of predication in the vast field of illocutionary forces and in relation to a variety of objects. It was a rather shocking experience, similar to that of going out in the open air rather than contemplating a panorama from a single window.

Queries and Predicate – Argument Relationship 65

*centre, containing and disseminating life.* Through one and the same synthetic act, it conjoins, by *being*, the *predicate* with the *subject*, yet in such a way that the being which passes, with an energetic predicate, into an action, becomes attributed to the subject itself, so that what is *thought* as merely capable of conjunction becomes, in *reality*, a state or process. […] *The thought, if one may put it so concretely, departs through the verb, from its inner abode, and steps* 

We note with surprise both the profound consonance and the logical and semantic refinement which are apparent between these last lines and the following, written some

"[…] In every judgement, [a judgement, for me, is not the mere comprehension of a thought, but the admission of its truth] no matter how trivial, the step from the level of thoughts to

One might be tempted to regard the relation of the thought to the True not as that of sense to reference, but rather as that of subject to predicate. […] The truth claim arises […] from the form of the declarative sentence […] It follows that the relation of the thought to the True may not be compared with that of subject to predicate. Subject and predicate (understood in the logical sense) are indeed elements of thought; they stand on the same level for knowledge. By combining subject and predicate, one reaches only a thought, never passes from sense to reference, never from a thought to its truth value. One moves at the same level but never advances from one level to the next. A truth value cannot be a part of a thought, any more than, say, the Sun can, for it is not a sense but an object. (Frege, 1952) […] Judgements can be regarded as advances from a thought to a truth value. Naturally this cannot be a definition. Judgement is something quite peculiar and incomparable. One might also say that judgements are distinctions of parts within truth values. Such distinction

One year earlier (1891) Frege had stated a parallelism between equations and statements.

"I am concerned to show that the argument does not belong with the function, but goes together with the *function to make up a complete whole*; for the function by itself must be called incomplete, in need of supplementation or 'unsaturated'. And in this respect functions differ fundamentally from numbers. Since such is the essence of the function, we can explain why, on the one hand, we recognize the same function in '2·1³ + 1' and '2·2³ + 2', even though these expressions stand for different numbers, whereas, on the other hand, we do not find one and the same function in '2·1³ + 1' and '4 – 1' in spite of their equal numerical values. Moreover, we now see how people easily led to regard the form of the expression as what is essential to the function. We recognize the *function* in the expression by imagining the latter

The two parts into which the mathematical expression is thus split up, the sign of the argument and the expression of the function, are *dissimilar*; for the argument is a number, a whole complete in itself, as the function is not. (We may compare this with the division of a line by a point. One is inclined in that case to count the dividing-point along with both

*across into reality*." (Humboldt, 1999; italics added).

occurs by a return to the thought." (Frege, 1952)

20 Cf. (Raynaud, 2002).

"The linguistic form of equations is a statement…. " (Frege, 1952)20

*as split up*, and *the possibility of thus splitting it up is suggested by its structure.*

decades later (1835-1892), always in Germany, by Gottlob Frege:

the level of reference (the objective), has already been taken.

*Sound forms and grammatical requirements. Grammatical formation* arises from the *laws of thinking* in language, and rests on the *congruence of sound-forms* with the latter. […] But deficiency on the one point always reacts back at once upon the other. The perfecting of language demands that every word be stamped as a specific *part of speech*, and carry within it those properties that a philosophical analysis perceives therein. It thus itself presupposes inflection. So the question now is as to how the simplest part of completed language formation, the minting of a word by *inflection* into a part of speech, can be supposed to proceed within the mind of a people? Reflective *consciousness* of the language cannot be presumed in connection with its origin, and would also harbour no creative power for the forming of sounds. Every advantage that a language possesses in this truly vital portion of its organism proceeds originally from the living *sensory world-outlook.* […] An intuition proceeding from the liveliest and most harmonious exertion of powers exhausts everything presented in the intuited, and does not confound the particular, but separates it out in clarity. Now from recognition of this dual relation of objects, from the feeling of their right relationship and the vividness of the impression evoked by each one of them, inflection19 arises, as if automatically, as the verbal expression of what is intuited and felt.

At the same time, however, it is remarkable to see in what various ways the mental outlook arrives here at *sentence-formation.* It does not set out from a prototype, does not laboriously put the sentence together, but achieves this without any forethought, in that it merely confers shape in sound upon the sharp and fully-registered impression of the object. In that this happens correctly each time, and according to the same feeling, the thought becomes coordinated out of the words so formed. […]

*Spontaneous positing in languages.* There are points in the grammatical structure of languages at which this synthesis, and the power that produces it, come nakedly and directly in view, as it were, and with which all the rest of the language-structure is then also necessarily most intimately connected. Since *the synthesis* we are speaking of *is not a state [Beschaffenheit], nor even properly a deed [Handlung], but itself a real action*, always passing with the moment, there can be no special *sign* for it in the words, and the endeavour to find such a sign would already in itself bear witness to a lack of true strength in the act, in that its nature was misunderstood. The real presence of the synthesis must reveal itself *immaterially*, as it were, in the language. […] We may call this act in general – as I have done here in this particular case [if, in a language, a root is marked out by a suffix as a substantive] – the act of *spontaneous positing* by bringing-together (synthesis). It recurs everywhere in language. […]

The *verb* (to speak first of this by itself) *differs in a sharply determinate way from the noun*, and from the other parts of speech that might possibly occur in a simple sentence, in that to it alone is assigned the act of *synthetic positing* as a grammatical function. Like the declined noun, it arose through such an act, in the fusion of its elements, with the stem, but it has also received this form in order to have the office and capacity of itself again performing this act with regard to the sentence. Between it and the other words of the simple sentence, there is therefore a difference which forbids us to count it along with them in the same category. *All the other words of the sentence are like dead matter lying there for combination; the verb alone is the* 

<sup>19</sup> Regarding Leibniz's idea of reducing relations to properties, and therefore the possibility of conceiving, for instance, a declinable root of a verb, with the entities around it as a basis of property with its modifications, see (Orilia, 2000).

64 Semantics – Advances in Theories and Mathematical Models

*Sound forms and grammatical requirements. Grammatical formation* arises from the *laws of thinking* in language, and rests on the *congruence of sound-forms* with the latter. […] But deficiency on the one point always reacts back at once upon the other. The perfecting of language demands that every word be stamped as a specific *part of speech*, and carry within it those properties that a philosophical analysis perceives therein. It thus itself presupposes inflection. So the question now is as to how the simplest part of completed language formation, the minting of a word by *inflection* into a part of speech, can be supposed to proceed within the mind of a people? Reflective *consciousness* of the language cannot be presumed in connection with its origin, and would also harbour no creative power for the forming of sounds. Every advantage that a language possesses in this truly vital portion of its organism proceeds originally from the living *sensory world-outlook.* […] An intuition proceeding from the liveliest and most harmonious exertion of powers exhausts everything presented in the intuited, and does not confound the particular, but separates it out in clarity. Now from recognition of this dual relation of objects, from the feeling of their right relationship and the vividness of the impression evoked by each one of them, inflection19

arises, as if automatically, as the verbal expression of what is intuited and felt.

coordinated out of the words so formed. […]

with its modifications, see (Orilia, 2000).

At the same time, however, it is remarkable to see in what various ways the mental outlook arrives here at *sentence-formation.* It does not set out from a prototype, does not laboriously put the sentence together, but achieves this without any forethought, in that it merely confers shape in sound upon the sharp and fully-registered impression of the object. In that this happens correctly each time, and according to the same feeling, the thought becomes

*Spontaneous positing in languages.* There are points in the grammatical structure of languages at which this synthesis, and the power that produces it, come nakedly and directly in view, as it were, and with which all the rest of the language-structure is then also necessarily most intimately connected. Since *the synthesis* we are speaking of *is not a state [Beschaffenheit], nor even properly a deed [Handlung], but itself a real action*, always passing with the moment, there can be no special *sign* for it in the words, and the endeavour to find such a sign would already in itself bear witness to a lack of true strength in the act, in that its nature was misunderstood. The real presence of the synthesis must reveal itself *immaterially*, as it were, in the language. […] We may call this act in general – as I have done here in this particular case [if, in a language, a root is marked out by a suffix as a substantive] – the act of *spontaneous positing* by bringing-together (synthesis). It recurs everywhere in language. […] The *verb* (to speak first of this by itself) *differs in a sharply determinate way from the noun*, and from the other parts of speech that might possibly occur in a simple sentence, in that to it alone is assigned the act of *synthetic positing* as a grammatical function. Like the declined noun, it arose through such an act, in the fusion of its elements, with the stem, but it has also received this form in order to have the office and capacity of itself again performing this act with regard to the sentence. Between it and the other words of the simple sentence, there is therefore a difference which forbids us to count it along with them in the same category. *All the other words of the sentence are like dead matter lying there for combination; the verb alone is the* 

19 Regarding Leibniz's idea of reducing relations to properties, and therefore the possibility of conceiving, for instance, a declinable root of a verb, with the entities around it as a basis of property *centre, containing and disseminating life.* Through one and the same synthetic act, it conjoins, by *being*, the *predicate* with the *subject*, yet in such a way that the being which passes, with an energetic predicate, into an action, becomes attributed to the subject itself, so that what is *thought* as merely capable of conjunction becomes, in *reality*, a state or process. […] *The thought, if one may put it so concretely, departs through the verb, from its inner abode, and steps across into reality*." (Humboldt, 1999; italics added).

We note with surprise both the profound consonance and the logical and semantic refinement which are apparent between these last lines and the following, written some decades later (1835-1892), always in Germany, by Gottlob Frege:

"[…] In every judgement, [a judgement, for me, is not the mere comprehension of a thought, but the admission of its truth] no matter how trivial, the step from the level of thoughts to the level of reference (the objective), has already been taken.

One might be tempted to regard the relation of the thought to the True not as that of sense to reference, but rather as that of subject to predicate. […] The truth claim arises […] from the form of the declarative sentence […] It follows that the relation of the thought to the True may not be compared with that of subject to predicate. Subject and predicate (understood in the logical sense) are indeed elements of thought; they stand on the same level for knowledge. By combining subject and predicate, one reaches only a thought, never passes from sense to reference, never from a thought to its truth value. One moves at the same level but never advances from one level to the next. A truth value cannot be a part of a thought, any more than, say, the Sun can, for it is not a sense but an object. (Frege, 1952) […]

Judgements can be regarded as advances from a thought to a truth value. Naturally this cannot be a definition. Judgement is something quite peculiar and incomparable. One might also say that judgements are distinctions of parts within truth values. Such distinction occurs by a return to the thought." (Frege, 1952)

One year earlier (1891) Frege had stated a parallelism between equations and statements. "The linguistic form of equations is a statement…. " (Frege, 1952)20

"I am concerned to show that the argument does not belong with the function, but goes together with the *function to make up a complete whole*; for the function by itself must be called incomplete, in need of supplementation or 'unsaturated'. And in this respect functions differ fundamentally from numbers. Since such is the essence of the function, we can explain why, on the one hand, we recognize the same function in '2·1³ + 1' and '2·2³ + 2', even though these expressions stand for different numbers, whereas, on the other hand, we do not find one and the same function in '2·1³ + 1' and '4 – 1' in spite of their equal numerical values. Moreover, we now see how people easily led to regard the form of the expression as what is essential to the function. We recognize the *function* in the expression by imagining the latter *as split up*, and *the possibility of thus splitting it up is suggested by its structure.*

The two parts into which the mathematical expression is thus split up, the sign of the argument and the expression of the function, are *dissimilar*; for the argument is a number, a whole complete in itself, as the function is not. (We may compare this with the division of a line by a point. One is inclined in that case to count the dividing-point along with both

<sup>20</sup> Cf. (Raynaud, 2002).

Queries and Predicate – Argument Relationship 67

In order to arrive at conclusions which oppose mere cumulativity, Bühler writes some memorable pages, at the opening of the fourth part of his *Theory of Language*, on "The Makeup of Human Speech: Elements and Compositions", contrasting the *incipit* of Leibniz's *Monadology* about composites as accumulation or *aggregatum* of simples with the Aristotelian concept of *synthesis*, later encountered in Kant, Hegel, Cassirer, Wundt. He then states: "the old disjunctive question has found a new home in our contemporaries' minds, but with various new names; psychologists who profess the 'idea of *Gestalt*' or some 'holistic view' normally draw boundaries and erect barriers in its name against the '*amas ou aggregatum*' because hardly anyone wants to be counted among the 'atomists' or elementarians. […] On the one hand anyone can mention the so-called summative wholes as an example of an aggregate in the strict sense; and on the other hand the sentence is a handy illustration as a last resort to make even the blind see that Leibniz's analysis cannot be generally applied: it is said that the sentence is obviously more than and different from an aggregate of words. […] We rather will remain on the ground of sematology and try to find out whether *both* claims can be understood and maintained in one breath with respect to significative structures, namely the claim that they are aggregates in one respect and synthemata in another. That is precisely what they are; we shall only be able to gain a correct view of the relationship of the words to the sentence unit by changing the aspect under which we regard the issue, by shifting the approach; we must make this shift of attitude […]. The nature of this shift can be stated without a trace of mystery or of mysticism or paradox. If there are two different sort of thing in the sentence, namely symbols and a field, then two separate counts can without contradiction reach the result **n** in the former case and the result **1** in the latter case. Leibniz, the productive mathematician, will be quite right if he determines the result n as a sum of units; but the one field unit will not be a

We could continue quoting *ad infinitum*, but the purpose here is merely to underline the fact that two different directions need be followed in a complementary way while respectively producing (encoding) and understanding (decoding) a message (a text), at least a sentence to begin with: top-down in the first case – from the whole communicative intention to its segmentation in predication -, bottom-up in the second – from lexemes and morphemes to phrases and their structure. Compositionality (the value of totality is a function of the value of its parts) is then plausible; this, though, is secondary to the primacy of the thesis that the totality is more than the sum of its parts, a thesis according to which we are able to explain

Ultimately we would like to reflect a convergent approach shared by the fathers of the two main contemporary grammatical models: dependency grammar and constituency grammar. Lucien Tesnière, to whom the so-called dependency grammars are ascribed, opens his

"*CONNECTION.* In the sentence *Alfred sings*, how many elements are there?

**Only one**, would be the guess of those who feel the unity of the sentence.

merely symbolic sum." (Bühler, 2011).

sentences as units at their sources.

1. = Alfred 2. = sings

*Esquisse d'une syntaxe structural* (1953) as follows:

**Two**, we would normally answer: *Alfred* and *sings*.

**Three**, we say, taking into account the two previous answers:

segments; but if we want to make a clean division, i.e. so as not to count anything twice over or leave anything out, then we may only count the dividing-point along with one segment. This segment thus becomes fully complete in itself, and may be compared to the argument; whereas the other is lacking in something – vid. the dividing-point, which one may call its endpoint, does not belong to it. Only by completing it with this endpoint, or with a line that has two endpoints, do we get from it something entire." (Frege, 1952 [24-25]).

The "entirety" of the whole starts to become the *Leitmotiv* of so many and so various contributions. Frege emphasises the idea by using two different images: incompleteness means in need of supplementation, while unsaturatedness (chemical suggestion21) is a segment without an endpoint.

Another author, a great logician and semiotician well-endowed with chemical competences22, Charles Sanders Peirce, more or less in the same period (1892-1906), was developing a model which would be accepted and spread from the 20th century onwards.

"A Predicate", Peirce wrote in 1906, "is either non-relative, or a *monad*, that is, is explicitly indefinite in one extensive respect, as is 'black'; or it is a dyadic relative, or dyad, such as 'kills', or it is a polyadic relative, such as 'gives'. These things must be diagrammatized in our system." (Peirce 4.543)

In 1892, the same year in which Frege published his *On Sense and Reference*, Peirce stated: "A rhema is somewhat closely analogous to a chemical atom or radical with unsaturated bonds. A non-relative rhema is like a univalent radicle; it has but one unsaturated bond. A relative rhema is like a multivalent radical. The blanks of a rhema can only be filled by terms, or, what is the same thing, by 'something which' (or the like) followed by a rhema; or, two can be filled together by means of 'itself' or the like. So, in chemistry, unsaturated bonds can only be saturated by joining two of them, which will usually, though not necessarily, belong to different radicles. If two univalent radicles are united, the result is a saturated compound. So, two non-relative rhemas being joined give a complete proposition. […] And we may say that all rhemata are either singular, dual, or plural," (Peirce, 3.421).

But even more important than this multiplication of terms around the predicate is Peirce's thesis of the difference between verbs and proper nouns (or pronouns).

"The proposition, or sentence, signifies that an eternal fitness, or truth, attaches certain hecceities to certain parts of an idea" (Peirce 3.461). "It is - in fact - the connection of an indicative word [of an index] to a symbolic word which makes an assertion (Peirce 4.56)23.

Such a 'dissimilarity' (Frege), or 'asymmetry' (Mathesius), is the condition of that 'fitness' Peirce writes about. Without it, instead of an 'attachment' (Peirce) or of the unity of a line where segments meet (Frege), of an intertwining (Plato), or of a 'synthesis' or a '*syntheke*'24 (Aristotle), a couple (Abelard), we would have just a co-presence25, a juxtaposition, a mere addition.

<sup>21</sup> See Picardi, 1994.

<sup>22</sup> Peirce completed an M.A in chemistry in 1862, and a Bachelor of Science in 1863 at Harvard University.

<sup>23</sup> Cf. (Fumagalli, 1995). The last two quoted passages are dated 1896 and 1893 respectively. 24 See Lo Piparo, 2003.

<sup>25</sup> Against the "two-term theory,"see (Geach, 1972). About a medieval semantics of verb not "reabsorbed" by the semantics of noun see (Marmo, 2004).

66 Semantics – Advances in Theories and Mathematical Models

segments; but if we want to make a clean division, i.e. so as not to count anything twice over or leave anything out, then we may only count the dividing-point along with one segment. This segment thus becomes fully complete in itself, and may be compared to the argument; whereas the other is lacking in something – vid. the dividing-point, which one may call its endpoint, does not belong to it. Only by completing it with this endpoint, or with a line that

The "entirety" of the whole starts to become the *Leitmotiv* of so many and so various contributions. Frege emphasises the idea by using two different images: incompleteness means in need of supplementation, while unsaturatedness (chemical suggestion21) is a

Another author, a great logician and semiotician well-endowed with chemical competences22, Charles Sanders Peirce, more or less in the same period (1892-1906), was developing a model which would be accepted and spread from the 20th century onwards. "A Predicate", Peirce wrote in 1906, "is either non-relative, or a *monad*, that is, is explicitly indefinite in one extensive respect, as is 'black'; or it is a dyadic relative, or dyad, such as 'kills', or it is a polyadic relative, such as 'gives'. These things must be diagrammatized in

In 1892, the same year in which Frege published his *On Sense and Reference*, Peirce stated: "A rhema is somewhat closely analogous to a chemical atom or radical with unsaturated bonds. A non-relative rhema is like a univalent radicle; it has but one unsaturated bond. A relative rhema is like a multivalent radical. The blanks of a rhema can only be filled by terms, or, what is the same thing, by 'something which' (or the like) followed by a rhema; or, two can be filled together by means of 'itself' or the like. So, in chemistry, unsaturated bonds can only be saturated by joining two of them, which will usually, though not necessarily, belong to different radicles. If two univalent radicles are united, the result is a saturated compound. So, two non-relative rhemas being joined give a complete proposition. […] And we may say

But even more important than this multiplication of terms around the predicate is Peirce's

"The proposition, or sentence, signifies that an eternal fitness, or truth, attaches certain hecceities to certain parts of an idea" (Peirce 3.461). "It is - in fact - the connection of an indicative word [of an index] to a symbolic word which makes an assertion (Peirce 4.56)23. Such a 'dissimilarity' (Frege), or 'asymmetry' (Mathesius), is the condition of that 'fitness' Peirce writes about. Without it, instead of an 'attachment' (Peirce) or of the unity of a line where segments meet (Frege), of an intertwining (Plato), or of a 'synthesis' or a '*syntheke*'24 (Aristotle), a

couple (Abelard), we would have just a co-presence25, a juxtaposition, a mere addition.

22 Peirce completed an M.A in chemistry in 1862, and a Bachelor of Science in 1863 at Harvard

23 Cf. (Fumagalli, 1995). The last two quoted passages are dated 1896 and 1893 respectively.

25 Against the "two-term theory,"see (Geach, 1972). About a medieval semantics of verb not

"reabsorbed" by the semantics of noun see (Marmo, 2004).

that all rhemata are either singular, dual, or plural," (Peirce, 3.421).

thesis of the difference between verbs and proper nouns (or pronouns).

has two endpoints, do we get from it something entire." (Frege, 1952 [24-25]).

segment without an endpoint.

our system." (Peirce 4.543)

21 See Picardi, 1994.

24 See Lo Piparo, 2003.

University.

In order to arrive at conclusions which oppose mere cumulativity, Bühler writes some memorable pages, at the opening of the fourth part of his *Theory of Language*, on "The Makeup of Human Speech: Elements and Compositions", contrasting the *incipit* of Leibniz's *Monadology* about composites as accumulation or *aggregatum* of simples with the Aristotelian concept of *synthesis*, later encountered in Kant, Hegel, Cassirer, Wundt. He then states: "the old disjunctive question has found a new home in our contemporaries' minds, but with various new names; psychologists who profess the 'idea of *Gestalt*' or some 'holistic view' normally draw boundaries and erect barriers in its name against the '*amas ou aggregatum*' because hardly anyone wants to be counted among the 'atomists' or elementarians. […] On the one hand anyone can mention the so-called summative wholes as an example of an aggregate in the strict sense; and on the other hand the sentence is a handy illustration as a last resort to make even the blind see that Leibniz's analysis cannot be generally applied: it is said that the sentence is obviously more than and different from an aggregate of words. […] We rather will remain on the ground of sematology and try to find out whether *both* claims can be understood and maintained in one breath with respect to significative structures, namely the claim that they are aggregates in one respect and synthemata in another. That is precisely what they are; we shall only be able to gain a correct view of the relationship of the words to the sentence unit by changing the aspect under which we regard the issue, by shifting the approach; we must make this shift of attitude […]. The nature of this shift can be stated without a trace of mystery or of mysticism or paradox. If there are two different sort of thing in the sentence, namely symbols and a field, then two separate counts can without contradiction reach the result **n** in the former case and the result **1** in the latter case. Leibniz, the productive mathematician, will be quite right if he determines the result n as a sum of units; but the one field unit will not be a merely symbolic sum." (Bühler, 2011).

We could continue quoting *ad infinitum*, but the purpose here is merely to underline the fact that two different directions need be followed in a complementary way while respectively producing (encoding) and understanding (decoding) a message (a text), at least a sentence to begin with: top-down in the first case – from the whole communicative intention to its segmentation in predication -, bottom-up in the second – from lexemes and morphemes to phrases and their structure. Compositionality (the value of totality is a function of the value of its parts) is then plausible; this, though, is secondary to the primacy of the thesis that the totality is more than the sum of its parts, a thesis according to which we are able to explain sentences as units at their sources.

Ultimately we would like to reflect a convergent approach shared by the fathers of the two main contemporary grammatical models: dependency grammar and constituency grammar.

Lucien Tesnière, to whom the so-called dependency grammars are ascribed, opens his *Esquisse d'une syntaxe structural* (1953) as follows:

"*CONNECTION.* In the sentence *Alfred sings*, how many elements are there?

**Two**, we would normally answer: *Alfred* and *sings*.

**Only one**, would be the guess of those who feel the unity of the sentence.

**Three**, we say, taking into account the two previous answers:

1. = Alfred

2. = sings

Queries and Predicate – Argument Relationship 69

*NUCLEAR INTERROGATION*. In the sentence: *Who sings?* the question concerns the subordinate **nucleus**, which is emptied of the meaning *Alfred*, and where only the

When the nuclear interrogation is made with an empty nucleus, the corresponding response is made with a full nucleus: *Who sings? Alfred sings.* It is even enough to fill the nucleus

The sentence: W*hat does Alfred do?* is also a nuclear interrogation. W*hat does Alfred do? Alfred sings* or simply: *He sings.* The only difference is that this time the question is on the

To summarise, the sentence: *Alfred sings*, having two nuclei, can give rise to two nuclear interrogations. We can see from this that a phrase can give rise to **as many nuclear** 

For example: *Which book is Alfred looking at? Alfred is looking at the red book* or simply: *The red* 

*CONNECTIONAL INTERROGATION*. In the sentence: *Does Alfred sing?* the two nuclei *Alfred* and *sings* are full. The question is therefore not nuclear. Effectively, *Alfred* and the action of *singing* are given. What we don't know is whether the two notions should be joined together, that is, if there is a **connection** between them. The questions is thus about the

If the connectional interrogation is made with a full nucleus, the corresponding response is

To summarise, the phrase *Alfred sings* can give rise to three questions, two nuclear and one

As far as Chomsky is concerned, here we shall only recall that in generative, or more precisely in phrase-structure grammar, the start variable (or start symbol) S represents the

Nuclear interrogations are made via **question words**, of which the main ones are:

connection. We would say there is a **connectional interrogation.** […]

made with an empty one. This is why a single word is enough: *yes* or *no*:

interrogative word *Who? exists.* We would say that there is a **nuclear interrogation**.

without repeating the rest of the sentence: W*ho sings? Alfred.* 

*sings sings* │ │  *who? Alfred* 


controlling nucleus.

**interrogations as it has nuclei**.

For circonstants: *where? – when? – how?- why?* 

For agents: *who? – what?* 

Does Alfred sing? – Yes.

whole sentence.

*Yes* means : *There is a connection. No* means *: There is not a connection.* 

connectional." (Tesnière, 1953).

For epithet: *which?* 

*one.*

3. = finally and **above all**, the link which unites unit *Alfred* and *sings*, and without which we would only have two independent **ideas**, with no relationship between them, and no organised thought.

We will give to this link, without which there is no possible sentence, the name **connection.** 

The connection is the soul of the sentence, its vital and organising principle. It ensures **structural function**. […]

*STEMMA.* The structure of the sentence depends upon the architecture of its connections. **Structural syntax** is the science which studies this architecture.

The **stemma** is the graphical representation of the architecture of the connections. […] The stemma may be **linear** or **forked**. The forked stemma may have a **bifurcation**, a **trifurcation** or an even more complex ramification:


[…]

*STEMMATIC ANALYSIS*. The structural syntax method consists essentially of reconstituting the stemma of a given utterance, that is to recognise the internal architecture. The establishment of the stemma constitutes **stemmatic analysis**, which includes both grammatical analysis and logical analysis and which it replaces in a positive and advantageous manner. […]

*VERB*. The verb is the **node of nodes.** It is the verb which, directly or indirectly, controls the whole sentence. As such, it appears at the top of the stemma. This is why, when we establish a stemma, a good way is to start with the verb. […]

The immediate subordinates of the verb are the **agents** and the **circonstants.** 

*AGENTS*. We give the name agents to the subordinates of the verb which participate in any way in the action. […]

*CIRCONSTANTS*. We give the name circonstants to the subordinates of the verb which indicate the circumstances of the action: time, place, manner, etc. The number of the circonstants is unlimited. " (Tesnière, 1953).

In order to remind ourselves that predication is the basic structure of both queries and answers, we refer to Tesnière's proposal about '*interrogation*':

"In the sentence : *Alfred sings*, three questions may arise (which confirms that there are three elements) :



68 Semantics – Advances in Theories and Mathematical Models

3. = finally and **above all**, the link which unites unit *Alfred* and *sings*, and without which we would only have two independent **ideas**, with no relationship between them, and

We will give to this link, without which there is no possible sentence, the name **connection.**  The connection is the soul of the sentence, its vital and organising principle. It ensures

*STEMMA.* The structure of the sentence depends upon the architecture of its connections.

The **stemma** is the graphical representation of the architecture of the connections. […] The stemma may be **linear** or **forked**. The forked stemma may have a **bifurcation**, a **trifurcation**

*Alfred sings Alfred hits Bernard Alfred gives the book to Charles* 

*STEMMATIC ANALYSIS*. The structural syntax method consists essentially of reconstituting the stemma of a given utterance, that is to recognise the internal architecture. The establishment of the stemma constitutes **stemmatic analysis**, which includes both grammatical analysis and logical analysis and which it replaces in a positive and

*VERB*. The verb is the **node of nodes.** It is the verb which, directly or indirectly, controls the whole sentence. As such, it appears at the top of the stemma. This is why, when we establish

*AGENTS*. We give the name agents to the subordinates of the verb which participate in any

*CIRCONSTANTS*. We give the name circonstants to the subordinates of the verb which indicate the circumstances of the action: time, place, manner, etc. The number of the

In order to remind ourselves that predication is the basic structure of both queries and

"In the sentence : *Alfred sings*, three questions may arise (which confirms that there are three

*gives*  /│\ *Alfred the book to Charles* 

*hits*  /\ *Alfred Bernard* 

The immediate subordinates of the verb are the **agents** and the **circonstants.** 

**Structural syntax** is the science which studies this architecture.

LINEAR STEMMA FORKED STEMMA Bifurcation Trifurcation

no organised thought.

or an even more complex ramification:

**structural function**. […]

*sings*  │ *Alfred* 

advantageous manner. […]

way in the action. […]

elements) :


a stemma, a good way is to start with the verb. […]

circonstants is unlimited. " (Tesnière, 1953).

answers, we refer to Tesnière's proposal about '*interrogation*':

[…]

*NUCLEAR INTERROGATION*. In the sentence: *Who sings?* the question concerns the subordinate **nucleus**, which is emptied of the meaning *Alfred*, and where only the interrogative word *Who? exists.* We would say that there is a **nuclear interrogation**.

When the nuclear interrogation is made with an empty nucleus, the corresponding response is made with a full nucleus: *Who sings? Alfred sings.* It is even enough to fill the nucleus without repeating the rest of the sentence: W*ho sings? Alfred.* 

The sentence: W*hat does Alfred do?* is also a nuclear interrogation. W*hat does Alfred do? Alfred sings* or simply: *He sings.* The only difference is that this time the question is on the controlling nucleus.

To summarise, the sentence: *Alfred sings*, having two nuclei, can give rise to two nuclear interrogations. We can see from this that a phrase can give rise to **as many nuclear interrogations as it has nuclei**.

Nuclear interrogations are made via **question words**, of which the main ones are:

For agents: *who? – what?*  For circonstants: *where? – when? – how?- why?*  For epithet: *which?*  For example: *Which book is Alfred looking at? Alfred is looking at the red book* or simply: *The red one.*

*CONNECTIONAL INTERROGATION*. In the sentence: *Does Alfred sing?* the two nuclei *Alfred* and *sings* are full. The question is therefore not nuclear. Effectively, *Alfred* and the action of *singing* are given. What we don't know is whether the two notions should be joined together, that is, if there is a **connection** between them. The questions is thus about the connection. We would say there is a **connectional interrogation.** […]

If the connectional interrogation is made with a full nucleus, the corresponding response is made with an empty one. This is why a single word is enough: *yes* or *no*:

Does Alfred sing? – Yes.

*Yes* means : *There is a connection.* 

*No* means *: There is not a connection.* 

To summarise, the phrase *Alfred sings* can give rise to three questions, two nuclear and one connectional." (Tesnière, 1953).

As far as Chomsky is concerned, here we shall only recall that in generative, or more precisely in phrase-structure grammar, the start variable (or start symbol) S represents the whole sentence.

Queries and Predicate – Argument Relationship 71

What we eventually want to do is to make explicit some conclusions which can be arrived at

1. Factual oversimplifications are not admitted: verbs usually cannot be alone, but sometimes they can (I'm not speaking about ellipses), given that zerovalent verbs exist

2. Metalinguistic oversimplifications are not admitted either: neither the correlation subject-property (suggested by Aristotle) nor that of agent-action (suggested by Tesnière's terminology) always stand, and not everywhere: they are merely *pars pro toto* 

3. However, what can be seen as an interesting, though covert, convergence between two main models of predication is something underlying the conviction about sentence unit: that is to say that both the Aristotelian paraphrase 'man is walking' for 'man walks' and the Fregean symbolic transcription W (m) = 1, or W (m) = 030 attest to the feeling of a relationship, of a reference from the foreground to the background, from the present being to the whole one, from the determined knowledge to the totality of what can be judged, as Frege calls it (*das Beurteilbare*, the judgeable), from the objects the sentence is

To better understand this fundamental belonging of the "case in question" to what it is included within, without being reducible to it, is a worthwhile goal: the result will be to understand that difficult but stimulating balance which is provided by relating something determined to something abstract, a dream – as Peirce would say – to an index31, thoughts

**3.4 Predication without or before judgement. Propositions vs. propositional functions** 

As widely considered, we need predication before judging32. We need it to ask questions, to make requests, to give orders, to plea, to pray, to express wonder and so on. Predication deserves attention as an act of thinking, as a logical and psychological matter, as a semiotic, linguistic ability, as a communicative deed. Before judgements we utter questions, doubts,

Formalising this distinction means distinguishing between propositional functions and propositions, between unsaturated connections and saturated ones. Saturated through what

In a sentence deprived of its context no linguistic evidence (in the etymological sense of the word, i.e. seeable verbal constituents) can be displayed as the marker of an accomplished

29 Regarding the importance of an ontology of events, for predicates referring to events, see (Davidson,

31 "A verb by itself signifies a mere dream, an imagination unattached to any particular occasion. It calls

30 The formula means that the predicate 'walk' being saturated by its argument identifies the truth

(as atmospheric verbs in many languages) (Malchukov, Sievierska, 2011).

about, to the world (actual or possible) it has been assigned to.

Just a couple of further statements before leaving the subject of predication.

hypotheses, shaping our thoughts while still suspending our evaluations.

from the wide perspective so far explored:

representations29.

to worlds and worlds to thoughts.

device? Completed by what?, if ever …

**3.5 Affirming or denying** 

value: either 1 (true) or 0 (false).

32 See (Davidson, 2005).

up in the mind an *icon*" (Peirce 3.459).

1980).

So far we have reached the 1950s.

For the 1960s I wish to mention two independent semantic turns within two different traditions: František Daneš' *Three-level Approach to Syntax* (1964) and following articles and Charles Fillmore's *The Case for Case* (1968) with its further developments.

Without being able to dwell upon each of these contributions, I think both of them deserve to be appreciated for their awareness of the importance of a sharp distinction and at the same time a strict correlation between the formal and the functional level (as typical of the Prague School) or, in other words, between the syntactic and the semantic levels of linguistic analysis (as was gradually being evidenced within the generative trend).

Distinction does not mean separation. On the contrary, distinction allows better outlined relations, those which let the new generation of Czech linguists identify semantic patterns (something like the predicational categories already investigated by Sundén) such as: *process; agent–action–the object of action; the bearer of state–state; individual–predication of a feature to it; individual–placing it into a class; etc.* (Daneš, 1964).

"The framework of Functional Generative Description [FGD]", states Petr Sgall, "has been designed so as to handle sentence structure in its anthropocentric aspects, i.e. based on syntactic dependency (the core of which, at least in most European languages, is the pattern of actor and action) and comprising the topic-focus articulation, i.e. specifying sentences not just as abstract objects, but as anchored in interactive context; this opens a way to understand them as operations on the hearer's states of mind.

FGD offers a basis for a relatively economic description, since the sentence representation having the shape of a dependency tree (with the verb at its root) contains only nodes corresponding to lexical items proper, rather than to nonterminals and function morphemes." (Sgall, 2006); paper originally published in 1997).

In the report of Charles Fillmore's *The Case for Case*, his work is introduced in these terms: "The grammatical notion 'case' deserves a place in the base component of the grammar of every language. It is argued that past research has not led to valid insights on case relationships and that what is needed is a conception of base structure in which case relationships are primitive terms of the theory and in which such concepts as 'subject' and 'direct object' are missing." (Fillmore, 1967).

More than forty years later, we can conclude that the cognitive turn in linguistics has become stronger. The notion of case has evolved into that of frame. The latter, together with the notion of script, had, in the meantime, gained ground26.

It would be fruitful to compare the finite set, the list of cases with the results of other similar enterprises: tectogrammatical roles in Prague Dependency Treebank27, Chomsky's thematic roles/Theta Roles28.

<sup>26 (</sup>Minsky, 1974); (Schank, Abelson,1977).

<sup>27</sup> http://ufal.mff.cuni.cz/pdt2.0/doc/manuals/en/t-layer/html/ch11s05s01.html

<sup>28</sup> In generative grammar, a theta role or θ-role is the formal device for representing syntactic argument structure (number and type of noun phrases) required by a particular verb. Thematic roles or relations are their semantic correspondents. Theta comes from thematic.

70 Semantics – Advances in Theories and Mathematical Models

For the 1960s I wish to mention two independent semantic turns within two different traditions: František Daneš' *Three-level Approach to Syntax* (1964) and following articles and

Without being able to dwell upon each of these contributions, I think both of them deserve to be appreciated for their awareness of the importance of a sharp distinction and at the same time a strict correlation between the formal and the functional level (as typical of the Prague School) or, in other words, between the syntactic and the semantic levels of linguistic

Distinction does not mean separation. On the contrary, distinction allows better outlined relations, those which let the new generation of Czech linguists identify semantic patterns (something like the predicational categories already investigated by Sundén) such as: *process; agent–action–the object of action; the bearer of state–state; individual–predication of a feature* 

"The framework of Functional Generative Description [FGD]", states Petr Sgall, "has been designed so as to handle sentence structure in its anthropocentric aspects, i.e. based on syntactic dependency (the core of which, at least in most European languages, is the pattern of actor and action) and comprising the topic-focus articulation, i.e. specifying sentences not just as abstract objects, but as anchored in interactive context; this opens a way to

FGD offers a basis for a relatively economic description, since the sentence representation having the shape of a dependency tree (with the verb at its root) contains only nodes corresponding to lexical items proper, rather than to nonterminals and function

In the report of Charles Fillmore's *The Case for Case*, his work is introduced in these terms: "The grammatical notion 'case' deserves a place in the base component of the grammar of every language. It is argued that past research has not led to valid insights on case relationships and that what is needed is a conception of base structure in which case relationships are primitive terms of the theory and in which such concepts as 'subject' and

More than forty years later, we can conclude that the cognitive turn in linguistics has become stronger. The notion of case has evolved into that of frame. The latter, together with

It would be fruitful to compare the finite set, the list of cases with the results of other similar enterprises: tectogrammatical roles in Prague Dependency Treebank27, Chomsky's thematic

28 In generative grammar, a theta role or θ-role is the formal device for representing syntactic argument structure (number and type of noun phrases) required by a particular verb. Thematic roles or relations

Charles Fillmore's *The Case for Case* (1968) with its further developments.

analysis (as was gradually being evidenced within the generative trend).

*to it; individual–placing it into a class; etc.* (Daneš, 1964).

understand them as operations on the hearer's states of mind.

morphemes." (Sgall, 2006); paper originally published in 1997).

the notion of script, had, in the meantime, gained ground26.

are their semantic correspondents. Theta comes from thematic.

27 http://ufal.mff.cuni.cz/pdt2.0/doc/manuals/en/t-layer/html/ch11s05s01.html

'direct object' are missing." (Fillmore, 1967).

26 (Minsky, 1974); (Schank, Abelson,1977).

roles/Theta Roles28.

So far we have reached the 1950s.

What we eventually want to do is to make explicit some conclusions which can be arrived at from the wide perspective so far explored:


To better understand this fundamental belonging of the "case in question" to what it is included within, without being reducible to it, is a worthwhile goal: the result will be to understand that difficult but stimulating balance which is provided by relating something determined to something abstract, a dream – as Peirce would say – to an index31, thoughts to worlds and worlds to thoughts.
