CHAPTER 2

DIACRITIC SYMBOLOGY

Philip of Macedonia, warned by the oracle to beware of quadrigae, ordered their destruction and even avoided the so called region, nevertheless he was stabbed by Pausania's dagger, whose hilt represented a quadriga. Object, name, representation.

2.1. Diacritical and syncathegorematic symbology is a rather neglected matter although its shortcomings are much more detrimental than the shortcomings of the terminological endowment. For instance, it seems to me like a grotesquery that the English lexicon is so rich in terms expressing chromatic properties or fighting actions and so poor in terms expressing propositional connectives (disjunctions, in particular). Maliciously, I might suppose that the more ambiguous is a symbology, the more easy is to hide behind its ambiguity an insufficient perspicuity.

Mindful of the mentioned Morris's complaint I start improving the ‘metalinguistic' symbology.

2.1.1. The meticulous analysis of the distinction between tokens and types (Peirce), that is the distinction between sign event and sign design (Carnap) is deferred to the next chapter. For the present I speak of a word to mean just the type, that is the abstract syntactical entity whose instances are its various tokens.

2.2. In §2.1 above I enclosed

(2.i) metalinguistic

within single inverted commas to mean that

(2.ii) metalanguage

is a rough notion. Awaiting for a better convention I assume

dialanguage

as a synonym of (2.ii) in such a rough acceptation, and hyphens as a dialinguistic operator. I make my point clearer.

2.2.1. The scholastic distinction between suppositio materialis and suppositio formalis is the distinction between use and mention. For instance

(2.iii) indulgent

is used in

(2.iv) Bob is indulgent

since (2.iv) speaks of Bob's indulgence; on the contrary, both in

(2.v) -indulgent- is trisyllabic

and in

(2.vi) -indulgent- is commendatory

-indulgent- is mentioned. According to the current symbology, hyphens could be substituted by quotation marks ("...") both in (2.v) and in (2.vi); but I claim that this procedure is deeply misleading, since what (2.v) speaks of (a word, a syntactic entity) is not what (2.vi) speaks of (a meaning, a semantic entity). In fact, just as

(2.vii) "indulgent" is trisyllabic

is an unexceptionable statement, and

the meaning of "indulgent" is trisyllabic

is a senseless one (better: a sortally improper one) because meanings are not syllabic entities,

the meaning of "indulgent" is commendatory

is an unexceptionable statement, and

(2.viii) "indulgent" is commendatory

is a sortally improper one. In order to prove this last issue, it is sufficient to replace (2.iii) with

(2.ix) fond

and to remember the archaic meaning (-silly-) of (2.ix); since this meaning is not at all commendatory, if we insist claiming that the predicate refers to the word, we cannot avoid deriving

"fond" is commendatory and not commendatory

so falling into incoherence. On the contrary, as soon as we acknowledge that

commendatory

refers to meanings and that (2.ix) adduces two different meanings,

the present meaning of "fond" is commendatory

and

the archaic meaning of "fond" is not commendatory

become two sortally proper (and even true) statements.

2.2.2. To realize that we mention a linguistic entity with reference sometimes to the word and sometimes to its meaning (that is to the piece of information adduced by the same word) is so fundamental an achievement that I try to impress it through another example.

The editor is criticizing the too inflamed tones of an article:

-pusillanimous- is offensive

he says, suggesting the choice of a more moderate adjective. Yet the editor is referring to a meaning; in fact to substitute "pusillanimous" with "coward" would be derisive, since the change of the word would not entail any change in the meaning.

2.3. On this ground I say that a statement

- is protolinguistic iff it does not concern a linguistic referent (giving "linguistic" its widest acceptation)

- is dialinguistic iff it does concern a linguistic referent.

Then, for instance, while (2.iv) is a protolinguistic statement, (2.v) and (2.vi) are dialinguistic ones.

Moreover I say that a dialinguistic statement

- is metalinguistic iff , just as (2.v), it concerns a syntactic referent (an expression)

- is hyperlinguistic iff, just as (2.vi), it concerns a semantic referent (a piece of information, a meaning).

Analogously I speak of the protolinguistic (or dialinguistic, metalinguistic, hyperlinguistic) faculties of a language.

2.4. I call "asterisks" the (mute) symbol

* ... *

and I agree that asterisks are an abbreviation of

(2.x) the meaning of " ... "

(that is: I introduce asterisks as a semantic symbol, just as quotation marks are a syntactic symbol and hyphens are a bivalent, therefore an ambiguous symbol). Consequently, for instance

(2.xi) *indulgent* is commendatory

is the accurate symbolization of (2.vi).

There are two alternatives to the introduction of a specific (and mute) semantic symbol, and precisely

- to continue accepting quotation marks as an ambiguous symbol whose interpretation is sometimes syntactic (to mean the enclosed expression) and sometimes semantic (to mean the piece of information adduced by the enclosed expression)

- to use an explicit formulation like (2.x).

Yet both of them are unsatisfactory. The former because it does not overcome a general ambiguity, therefore it does not allow the great theoretical advantages we can draw from an accurate symbology. The latter because it does not account for the evidence that sentences like (2.v), where no "the meaning of" occurs, are perfectly grammatical in our usual practice. In other words: to introduce a periphrasis would not account for the silent ambiguity hidden under the lacking distinction between a metalinguistic and a hyperlinguistic mention. Only the introduction of a mute symbol different from the metalinguistic one can overcome the ambiguity affecting current languages; in this sense while (2.viii) is a wrong translation of (2.vi), (2.xi) is the right one.

2.4.1. The tripartition sign-meaning-referent (starting from the lekton of the Stoicism until the triangle of Ogden and Richard) is well known. Asterisks fulfil a symbolic lack, so satisfying the mentioned Morris's remark and, above all, so contributing to a clarification of our ideas about a very insidious topic.

2.4.2. An easy analogy. Besides using (spending) a banknote, people can speak of it. But while a discourse between two mint technicians appreciating its filigree is ‘syntactic', a discourse between two housewives complaining its poor purchasing power is ‘semantic'.

2.4.3. Here I could exhibit a lot of illustrious quotations where the lack of a semantic symbol constraints the authors to untenable formulations. I avoid it mainly because I am interested in exposing my ideas, not in censuring methodically other people's ones. Such a censure will be carried out only when necessary to support mine, and anyhow without any gossipy pleasure (in the most tedious way, then). Yet, if I were quite frank, I ought to confess that the strongest reason is the hope that my liberal attitude be reciprocated.

2.5. All the dialinguistic symbols (hyphens, quotation marks and asterisks) have a substantivizing effect. For instance (§2.7 as for the use of new lines)

indulgent

is an adjective, but

-indulgent-            "indulgent"            *indulgent*

are substantives; the same syntactic well formation of (2.v), (2.vii) and (2.xi) legitimates this conclusion. The obvious reason is that if we speak of words or of meanings, we speak of objects, therefore we need nouns.

2.5.1. The distinction between metalanguages and hyperlanguages, of course, is not the well known distinction between different metalinguistic orders. For instance

"indulgent" is an adjective

is a true metalinguistic statement and

" "indulgent" " is a substantive

is a true meta-metalinguistic statement, but surely it is not a hyperlinguistic statement, since it does not concern semantics.

2.5.2. Dialinguistic symbols are freely concatenable. For instance

" *nor* " is a substantive

is a formally correct (and true) statement saying that the expression obtained by enclosing between asterisks

nor

is a substantive naming the meaning of that conjunction. More about this point in §3.4.

2.5.3. There are contexts where the clear distinction between quotation marks and asterisks is nearly impossible, just owing to the ambiguity of the message.. For instance, strictly,

(2.xii) hyper derives from uper

is a syntactically incorrect sentence (it is a word salad) since the first and the last words are prefixes, not substantives; and the mere criterion of interpretative collaboration makes (2.xii) understandable. Yet both

"hyper" derives from "uper"

and

*hyper* derives from *uper*

are tenable correct formulations; while the former speaks of a historical link between signs, the latter speaks of a historical link between notions. The interesting peculiarity of (2.xii) is that the lack of a dialinguistic symbol, superficially, seems to concern only the first word, because the typographical peculiarities of the last word (the Greek type) favours (even improperly) its objectification. In other words, though

"hyper" derives from uper

instances a syntactically incorrect expression too, such a kind of incorrectness is rather current.

2.6. Cartesius taught us that the existence of our mental activity is even more unquestionable than the existence of the world around us. And a mental activity is the most essential factor in any linguistic process. In this sense to neglect such a factor entails the ‘topological deformation' (from tridimensionality to bidensionality) already denounced (§1.1). The worrying meta consideration is that the tacit acceptation of the inadequateness affecting the current (natural and artificial) languages reveals the intrinsic poorness of the ideas leading the approach. A poorness particularly prejudicial for logic, because to reason on the logos is necessarily to reason dialinguistically. First of all, in order to bridge the gap we must recognize that, besides the suppositio materialis and the suppositio formalis, a suppositio informationalis is also necessary (I apologize for the disconcerting expression, but more or less all new expressions, at their start, are disconcerting). Asterisks are just the first step to reaching this goal.

2.7. A very precious dialinguistic operator (whose detailed analysis, as far as I know, has never been proposed) is represented by the new line. In the current linguistic practice the new line is a highly polyvalent operator; the paradigm of its various functions follows.

2.7.1. The metalingustic use of a new line is exemplified by (2.i), since what can be enclosed within single inverted commas is an expression, not a meaning. A metalinguistic new line, of course, is an alternative to quotation marks; and actually (though at first sight more equivocal)

(2.xiii) In §2.1 I enclosed "metalinguistic" within single inverted commas

is a perfectly equivalent formulation (a pedantry: the same (2.xiii) is a new example of a metalinguistic new line, since it is used to speak of a formulation).

The comparison between (2.i) and (2.xiii) emphasizes that new lines, just because they consist of a spatial disposition without any intervention of graphic elements, are the cleanest dialinguistic operator.

2.7.2. The hyperlingustic use of a new line is exemplified by (2.ii) since what can be a rough notion is a meaning, not a sign. A hyperlinguistic new line, of course, is an alternative to asterisks; and actually

(2.xiv) *metalanguage* is a rough notion

is an alternative formulation (a pedantry: (2.xiv) too is an example of a metalinguistic new line, since it too speaks of a formulation).

2.7.3. The ambiguous dialinguistic use of a new line can be instanced by writing that

Bob bought a pen

is the message under scrutiny; in fact the same ambiguity of *message* forbids a specifically metalinguistic or hyperlinguistic interpretation of the new line. In this ambiguous use, the new line can be replaced by hyphens.

2.7.4. The mere emphasizing (therefore protolinguistic) use of a new line can be exemplified by enclosing (2.i) between quotation marks or (2.ii) between asterisks; in these new formulations the new line becomes only an emphasizing operator devoid of any dialinguistic import.

2.7.5. A new line is sometimes recycled, in the sense that a further reference may change the original use. A clear example is in Chapter 1, where (1.i) is introduced as a metalinguistic new line (if the speaker utters (1.i) ...) but few lines below is recycled hyperlinguistically (the piece of information... (1.i) ...). Did the reader realize it?

2.7.6. Of course, owing to the proliferation of their different uses, new lines, so to say, are strong homonymy bearers. Yet a homonymy bearer can act as a catalyser of incoherence only on condition that we are unaware of its status. And the proposed analysis not only allows us to exclude any risk of unawareness; it stimulates too a critical interpretation of the various new lines occurring in the text (for instance the new lines of §2.5, §2.5.1, §2.5.2). Anyway, in order to help the reader, from the start I will comment on the more interesting applications.

2.8. A meaning postulate (Carnap) associates a certain piece of information to a certain word, and in §1.6.1 I called "semantic" (symbolically "s") the respective relation. Obviously different languages (different linguistic codes) may associate different meanings to a same word. For instance "largo" adduces *long* in Spanish (S) and *broad* in Italian (I). Therefore

(2.xv) *largo*

(metalinguistic new line) is an elliptic expression since the omission of the linguistic code does not allow to single out the meaning (2.xv) speaks of. In order to overcome this ambiguity I agree that asterisks must be completed by an index specifying the linguistic code of reference; accordingly

*largo*S = *lungo*I = *long*E

is a sentence where the agreement is applied. Another way to present the same passage is referring the index to the s-relations, so writing

sS("largo")=sI("lungo") =sE("long")

in order to mean that the informational nucleus associated in Spanish with

"largo"

(merely emphasizing new line which becomes a metalinguistic new line if we cancel the pair of quotation marks) is the same associated in Italian with "lungo" et cetera. In other words: the English code book assigns to "long" the same attribute (characteristic, quality) the Spanish code book assigns to "largo" et cetera. For the sake of concision the index may be omitted when the linguistic code of reference is the contextual one (English, in this case).

2.8.1. Here too homonymy is a disagreeable enemy; in fact, for instance, in spite of its index,

(2.xvi) *sole*E

is an ambiguous expression, since in English "sole" is a homonymy bearer.

A first way out from this impasse is the appeal to another language where the various meanings are adduced by different words, as, with reference to (2.xvi),

*solo*I

(alone)

*suola*I

(bottom of a shoe) and

*sogliola*I

(flatfish).

Reciprocally as for

(2.xvii) *lira*I

(*lyre* and *lira*).

A second way out is the enrichment of the homonymy bearer by different graphic elements. So, for instance, the ambiguity of (2.xvii) disappears as soon as a "lira0" (that of course, owing to the index, would name my troubled national (ex)currency) were distinguished from a "lira1" (that would name the musical instrument played by Nero). Anyhow, since these minutiae do not influence my discourse, I remarked them only to underline (meta-theoretically) that also expressions like

the meaning of "..." in L

or like

the piece of information adduced by "..." in L

are ambiguous when the expression within inverted commas is a homonymy bearer in L.

2.9. Owing to the crucial role of asterisks I pay attention to the following objection.

There is no necessity to introduce a semantic symbol because even if actually some attributes pertain to meanings, no one can forbid us from defining their correspondents pertaining to the respective words: For instance, we can define

(2.xviii) commendophorous

(ambiguous new line, since we have not yet specified whether words or meanings are the real objects of definitions) by agreeing that an adjective is commendophorous iff its meaning (iff the attribute it adduces) is commendatory. Then the message transmitted by (2.xi) is also transmitted by

(2.xix) "indulgent" is commendophorous

and (2.xix) allows us to reason unobjectionably on signs, thus rendering asterisks a superfluous device.

As we shall see, the objection is very momentous; yet my first reply is playful. Ava, Bob's wife, is suspected of conjugal infidelity by her father-in-law Anyl (nomen omen). Indeed he thinks that a true gentleman cannot pay a detective to shadow a lady; then, since notoriously if a wife is conjugally infidel her husband is a cuckold, Anyl commissions the detective to shadow Bob in order to ascertain his eventual cuckoldness.

What of Anyl's idea?

2.9.1. Awaiting for a stricter approach to the notion of a dilemma (§6.7), here I recall Frege's notion of a Satzfrage: a Satzfrage contains a demand that we should either aknowledge the truth or reject it as false [Black and Geach, 1960]. Roughly, a dilemma is the cognitional situation where two opposite alternatives (the horns of the dilemma) are considered, but none of them is asserted. So, for instance

(2.xx) is Ava an infidel wife?

is Anyl's dilemma (the interrogation point is the spontaneous symbol to express a dilemma).

The (right or wrong) solution of a dilemma is the assignation of a ‘truth-value' to its horns.

The (basic) datum of a dilemma is the piece of information on whose ground the solution is attained.

The core of a dilemma is the fact whose knowledge constitutes the (basic) datum.

Therefore, while the core of Anyl'dilemma is Ava's behaviour, the datum is the piece of information on whose ground one horn of the dilemma is (rightly or wrongly) asserted. Evidently *core* and *datum* are two different notions; an easy way to understand the difference is to think of an untrustworthy detective who, instead of pursuing the datum of Anyl's dilemma, would pursue its core on his own account.

2.9.2. If the reality were made of monads, a dilemma could be proposed only by focusing on the concerned monad. Reality is an interrelated network of nearly unconceivable fineness, and just owing to these interrelations we can formulate various dilemmas whose core (then whose datum) is anyhow the same (I recall the Aristotelian pollakos legomenon, that is what can be said in many ways). In this sense to define consequent properties pertaining to Ava's husband (is he a cuckold?) or to her sons (are they sons of a promiscuous woman?) and so on, is a procedure which modifies only the superficial aspect of the discourse, since they all depend on the same factual evidence (they all concern Ava's corporeal liberality, which is anyhow the common core of all dilemmas).

The theoretically momentous distinction between pertinence and regard (of an attribute) is based just on this discriminating element. So, for instance, we say that cuckoldness pertains to husbands, but regards wifes. Consequently, among the various dilemmas concerning the same core, we can privilege the one where pertinence and regard coincide, that is, in the contingency, (2.xx).

Coming back to the objection of §2.9, (2.xviii) legitimately defines an attribute pertaining to adjectives, yet no definition can modify the core of the respective dilemma, whose solution continues depending on the commendableness of the attribute adduced by the adjective whose ‘commendophorablesness' we have to ascertain. Then , on the basis of the considerations proposed in §2.4, the use of a mute semantic symbol is not by-passable.

2.10. Synonymy is another topic directly affected by the mentioned distinction. In fact, as soon as we realize that any formal transformation of signs presupposes implicitly the signic nature of the same signs (no thing without a semantic dimension can be a sign) a conclusion becomes evident: synonymy is a relation whose pertinence is syntactic, but whose regard is semantic. I make my point clearer.

The formal approach to signs leaves their meanings out of consideration; nevertheless it concerns signs, whch is to say objects having that certain characteristics. We can reason on European citizens leaving their nationality out of consideration (for instance stating that they have the right to cross freely the European frontiers), yet we cannot extrapolate automatically our statements to persons who are not European citizens, so then we can leave their nationality out of consideration provided that they have a certain requisite. Analogously we can leave the meanings out of consideration, provided that the objects we are reasoning about have a meaning.

In formal treatments definitions are introduced as abbreviations, and abbreviations are managed through a purely syntactic approach. Yet no syntactical approach can overcome the semantic role of a given sign: to introduce an abbreviation in a formal theory is to agree that in every interpretation of the same theory, definiendum and definiens adduce the same piece of information, though any specific piece of information is left out of consideration.

In other words, the way we deal formally with signs (leaving their meanings out of consideration) is far from being the way we deal with arabesques (where the same notion of an abbreviation is meaningless).

2.10.1. The same current symbolization of synonymy through something like

"x"="y"

evidences my claim. Such a symbolization is surely misleading since manifestly the two synonymous expressions are not identical. As what is identical is their meaning,

*x*=*y*

is the correct symbolization; therefore by

"x"D"y" iff *x*=*y*

I introduce the symbol for synonymy

(2.xxi) D

which is called "inverted arrows". By definition (2.xxi) is a symbol of equivalence having syntactic pertinence (it is established between signs) and semantic regard (it depends on a relation between meanings). It plays an important role in definitions (§4.6)) allowing to adequate symbolic formulations to usual expressions.

2.10.2. An etymologic pedantry. Just as *synonymous* pertains to signs (which are synonymous iff they adduce the same meaning), *homonymous* pertains to meanings (which are homonymous iff they are adduced by the same sign). Then, since the two attributes pertain to heterogeneous referents, to give them a common ending ("onymous" from "onoma", where *onoma*Gr = *noun*) is misleading; while it is etymologically correct to say that different meanings adduced by a same word are homonymous, it would be better to say that different words having the same meaning are homosignificant. But of course this is not a proposal, this is only a pedantry, I repeat.

2.10.3. Synonymy (homosignificance) and homonymy are not absolute relations; they must bereferred to a language (*sideboard* and *belief* are homonymous in Italian, where "credenza" adduces both of them, but evidently they are not homonymous in English). And just because we write signs, not meanings, synonymy can be directly formulated ("wide" and "broad" are synonymous), but homonymy cannot (*pen* and *pen* are homonymous?). For instance,

in English *pen* is both *female swan* and *instrument for ink writing*

or

"pen" is in English a homonymy bearer for *female swan* and *instrument for ink writing*

are two correct (but indirect) ways to formulate a homonymy.