We would always be in the case of a prosthesis-channel. Of course, we must necessarily assume that there is an odd number of mirrors. Only in this event would the mirror nearer to the observer give him an image of the original object as if it were reflected in the first mirror. With an even number of mirrors, in fact, the image would be ‘reversed’ twice, and we would not be in the presence of a simple prosthesis but, rather, of the effect of a more complex catoptric apparatus, this having translation functions. In any case, for the problem we are concerned with here, the observer need only know that there is an odd or even number of mirrors, and he will then behave as he does when facing his bathroom mirror or his barber’s mirrors. Now, on the grounds of the principles enunciated in our previous pragmatics of the mirror, the observer knows (a) that the final mirror is a mirror and (b) that it is telling the truth; therefore, he also knows (c) that, at that very moment, the reflected object does exist in point A. Through this causal chain, the final mirror image becomes a rigid designator of the object which is the source of stimuli; better still, we know that the final image ‘christens’, so to say, the initial object in that very moment.
Such catoptric apparatus would be a rigid-designation apparatus. There is no linguistic contrivance which would provide the same guaran-tee, not even a proper name, because in this event two conditions of absolutely rigid designation would be missing: (1) the original object might well not exist at the moment and also might never have existed; (2) there would be no guarantee that the name corresponds to that object alone and to no other having similar general characteristics.
We therefore come to discover that the semantics of rigid designation is in the end a (pseudo) semantics of the mirror image and that no linguistic term can be a rigid designator (just as there is no absolute icon). If it cannot be absolute, any rigid designator other than a mirror image, any rigid designator whose rigidity may be undermined in differ-ent ways and under different conditions, becomes a soft or slack de-signator. As absolutely rigid designators, mirror images alone cannot be questioned by counterfactuals. In fact, I could never ask myself (without violating the pragmatic principles regulating any relation with mirrors): «If the object whose image I am perceiving had properties other than those of the image I perceive, would it still be the same object?» But this guarantee is provided precisely by the threshold-phenomenon a mir-ror is. The theory of rigid designators falls a victim of the magic of mir-rors.
7.9. On signs
If the mirror has nothing to do with proper names, it has nothing to do with common nouns, either, which always refer (except with regard to their indexical use) to general concepts. But this does not mean that the mirror image is not a sign because semiotic tradition, from Hellenism to the present days, has developed a sign concept which goes beyond the mere concept of verbal sign.
According to the earliest definitions, a sign is aliquid which stat pro aliquo. The most elementary type of recollectable sign, as theorized by the Stoics, is smoke which stands for fire.
At this point, we should establish whether the mirror image stands for the body emanating it as a reflection just as smoke stands for the fire which produces it.
A correct understanding of the first and most thorough sign theory ever produced (that is, the Stoics theory) will inevitably lead us to as-sume that anything may be taken as a sign of anything else provided that it is an antecedent revealing a consequent —where antecedent and conse-quent have the value they assume according to the logical ratio of impli-cation p э q. Thus the consequent might well be the more or less chronologically remote cause of the antecedent—as it is in the case of fire and smoke.
However, this definition (as we have seen in chapter one of this book) is not sufficient to characterize a sign as such. The semiotic require-ments are the following:
(1) In order that the antecedent might become a sign of the consequent, the antecedent must be potentially present and perceptible while the consequent is usually absent. For the Stoic semeion, the absence of the consequent seems to be strictly necessary: if one sees smoke billowing out of flames, there is no need to consider it a sign of fire. Words and many nonverbal indexical devices can be produced while their referent is present, but their condition for being a sign is that they must be under-standable as sign even though their supposed referent is not there. The consequent may be absent whether because it is out the reach of my actual perceptibility or because it does not subsist any longer at the very moment in which I interpret the sign (think, for example, of the tracks of prehistorical animals). As Abelard said, the power of language is given by the fact that the expression nulla rosa est (translatable either as there is no rose or as such a thing like a rose has never existed) is fully comprehensible even though there are no roses.
(2) As a result, the antecedent may be produced even though the conse-quent does not subsist or has never subsisted. One can produce smoke by means of chemical substances thus pretending that there is (some-where) fire. Signs can be used to lie about the world’s state of affairs.
(3) Signs can be used to lie because the antecedent (expression) does not require the consequent as either its necessary or its efficient cause. The antecedent is only presumed to be caused by the consequent.
(4) This happens because the antecedent is not primarily related to an actual state of affairs but to a more or less general content. In every signification system, the consequent conveyed by the antecedent is only a class of possible consequents. Signs can be referred to referents because they are primarily correlated to a content (extensions are functions of the intentions). Even a gestural index, like a finger pointing at something, before being characterized by its contiguity to the object indicated, is characterized by the fact that, in a given gestural convention’s system, it signifies «focus your attention on the possible object in the radius of the digital apex»; in fact, I might indicate something which does not exist, and my (deceived) interlocutor will at first be led into thinking that something must be there. This something is the consequent content of the antecedent-expression /finger pointed at something/.
(5) But the Stoics’ semiotics tells us something more. It does not tell us that smoke as a sign is smoke as a material occurrence. The Stoics’ sign is incorporeal: it is the relationship of implication between two propositions (‘if there is smoke there must be fire’, which could also be translated in terms of a law: ‘each time there is smoke there must be fire’). The semiotic relationship is, therefore, a law correlating a type-antecedent to a type-consequent. The sign is not given by the fact that this smoke auto-matically leads me to that fire, but that a general class of occurrences recognizable as smoke automatically leads me to the general class of oc-currences definable as fire. The relationship exists between types rather than between tokens. In other words, the interpreter of certain semiotic situations makes them occur as relations between tokens owing to the fact that he knows (while the barbarian does not) that—first of all— the same relation holds between types.
(6) The fact that the semiotic relationship occurs between types makes it independent of the actual channel or medium in which and by which its corre-sponding occurrences are produced and conveyed. The smoke-to-fire sign relationship does not change whether or not the smoke is chemically produced or spoken about or portrayed by images. The relationship link-ing dots and dashes to the letters of the alphabet as codified by Morse code does not change according to whether the dots and dashes are con-veyed by electric signals or tapped out by a prisoner against the wall of his cell.
(7) Finally (and here the original Stoic concept is partially developed), the content of an expression may be interpreted. If after seeing smoke somebody tells me there is fire, I might ask him what he means by fire, and he might explain this by showing me some fire, or with the image of a flame, or by giving a verbal definition, or by causing me to recollect a sensation of heat, or by reminding me of a past event when I experi-enced the presence of fire. In the same way, when hearing the name John I might ask for the meaning of this name, and the speaker need not necessarily show me John, he only need define him in one way or an-other (Lucy’s husband, the guy you met yesterday, the one portrayed in this miniature, the guy who walks moving his head like this or like that, and so on . . .). Each interpretation not only defines the content of the expression, but also in its own
