The logic of vagueness

Conversation degenerates when we lose sight of the polyversity of language, and of the ineluctable vagueness of our thoughts. According to Peirce, ‘No concept, not even those of mathematics, is absolutely precise; and some of the most important for everyday use are extremely vague’ (CP6.496, c. 1906). Genuinely informative communication depends on taking this necessary vagueness into account. Properly understanding any utterance requires you to interpret it with the degree of vagueness appropriate to the situational context. Every language user has to develop a sensitivity to context at an early age, though few are conscious of it.

The perspectival nature of linguistic systems means that as children learn to use words and linguistic constructions in the manner of adults, they come to see that the exact same phenomenon may be construed in many different ways for different communicative purposes depending on many factors in the communicative context.

— Tomasello (1999, 213)

To construe is to simplify, and to simplify is to generalize: a symbol, by referring to a type of experience, can thus refer to many tokens of it on various occasions, including future occasions. Even proper nouns (names of specific things, places, people etc.) are general signs, because each implies the continuity of its object through time: each momentary manifestation of the object is a token of that type, and some features of it may vary from one occurrence to another. (If you notice a difference in someone’s characteristic behavior, you might say, ‘It’s not like him to do that!’) And the more common a word is, the broader is its reference.

Things that you talk about, whether you perceive them to be in the external or internal world, are already construed, categorized and ‘framed’ by the time you mention them. But each actual reference to them can affect your framing habits; and these in turn affect your way of talking about them, or hearing others talk about them. Since everyone has a history of cycling through such loops countless times, and this history determines for each her ‘natural’ idiom, synchronizing reference between speakers is not always easy – hence polyversity.

The upshot of this in communication is that in trying to connect words with referents or experiences, ‘all sorts of risks are taken, assumptions and guesses made’ (Sperber and Wilson 1995, 19). This is the only practical way to reduce the many possible ‘construals’ of phenomena – or meanings of words – to the simplicity required for the maintenance of a conversation.

Sperber and Wilson take this as an argument against what they call ‘the mutual-knowledge hypothesis,’ but they are using the word knowledge here in an absolute sense, as equivalent to objective certainty (Sperber and Wilson 1995, 19-20). In reality, the common ground that people must have in order to carry on a conversation is a network of rather vague default assumptions. Actual conversation often consists of attempts to render some of the ‘mutual knowledge’ more precise, but in the actual context, there are pragmatic limits to this precision.

William James, in typically elegant fashion, gives a more psychologically realistic account of cognition as ‘virtual knowing.’

Now the immensely greater part of all our knowing never gets beyond this virtual stage. It never is completed or nailed down. … To continue thinking unchallenged is, ninety-nine times out of a hundred, our practical substitute for knowing in the completed sense. As each experience runs by cognitive transition into the next one, and we nowhere feel a collision with what we elsewhere count as truth or fact, we commit ourselves to the current as if the port were sure. We live, as it were, upon the front edge of an advancing wave-crest, and our sense of a determinate direction in falling forward is all we cover of the future of our path.

— James, ‘A World of Pure Experience’ (Kuklick 1172)

Merleau-Ponty’s Phenomenology of Perception takes a slightly different perspective:

My set of experiences is presented as a concordant whole, and the synthesis takes place not in so far as they all express a certain invariant, and in the identity of the object, but in that they are all collected together, by the last of their number, in the ipseity of the thing. The ipseity is, of course, never reached: each aspect of the thing which falls to our perception is still only an invitation to perceive beyond it, still only a momentary halt in the perceptual process. If the thing itself were reached, it would be from that moment arrayed before us and stripped of its mystery. It would cease to exist as a thing at the very moment when we thought to possess it. What makes the ‘reality’ of the thing is therefore precisely what snatches it from our grasp.

— Merleau-Ponty (1945, 271)

This is, in context, quite consistent with Peirce’s definition of ‘reality’:

I define the real as that which holds its characters on such a tenure that it makes not the slightest difference what any man or men may have thought them to be, or ever will have thought them to be, here using thought to include, imagining, opining, and willing (as long as forcible means are not used); but the real thing’s characters will remain absolutely untouched.

CP 6.495 (c. 1906)

In the process of inquiry or of learning, what James called ‘our sense of a determinate direction’ is a feeling that our knowledge of reality is becoming more precise, getting closer to the Truth. But semiotic experience teaches that our knowledge is never completely determinate.

No cognition and no Sign is absolutely precise, not even a Percept; and indefiniteness is of two kinds, indefiniteness as to what is the Object of the Sign, and indefiniteness as to its Interpretant, or indefiniteness in Breadth and in Depth.

— Peirce, CP 4.543 (1906)

Any knowledge that will prove useful as guidance into the future must be general, and thus indefinite in that sense.

Yet every proposition actually asserted must refer to some non-general subject …. Indeed, all propositions refer to one and the same determinately singular subject, well-understood between all utterers and interpreters; namely, to The Truth, which is the universe of all universes, and is assumed on all hands to be real. But besides that, there is some lesser environment of the utterer and interpreter of each proposition that actually gets conveyed, to which that proposition more particularly refers and which is not general.

CP 5.506

This ‘lesser environment’ is of course the more immediate context. Even if the dynamic Object of the sign is fully determinate, is The Whole Truth, the sign itself is still ‘indefinite as to its Interpretant,’ i.e. vague in that context.

No communication of one person to another can be entirely definite, i.e., non-vague. We may reasonably hope that physiologists will some day find some means of comparing the qualities of one person’s feelings with those of another, so that it would not be fair to insist upon their present incomparability as an inevitable source of misunderstanding. Besides, it does not affect the intellectual purport of communications. But wherever degree or any other possibility of continuous variation subsists, absolute precision is impossible. Much else must be vague, because no man’s interpretation of words is based on exactly the same experience as any other man’s. Even in our most intellectual conceptions, the more we strive to be precise, the more unattainable precision seems. It should never be forgotten that our own thinking is carried on as a dialogue, and though mostly in a lesser degree, is subject to almost every imperfection of language.

CP 5.506

Readers who want a more precise definition of vagueness, or a more specific definition of generality, might consult Peirce, EP2:350-53 (or CP 5.446-450, 1905).

Relevance in context

Sperber and Wilson (1995, 142) suggest that the goal of the comprehension process is

to maximize the relevance of any information being processed. … people hope that the assumption being processed is relevant (or else they would not bother to process it at all), and they try to select a context which will justify that hope: a context which will maximize relevance. In verbal comprehension in particular, it is relevance which is treated as given, and context which is treated as a variable.

This is another perspective on the process of ‘context construction’ described in Chapter 15. But context being holarchic, that process itself has a context. Relevance involves some relation to the known (or presupposed), but also some novelty; if i tell you what you already take for granted, that is not relevant. Relevance itself, then, is determined by context, i.e. by the ‘state of information’ (Peirce) in which the communication or ‘processing’ is situated – or in Peircean terms, in which the sign determines an interpretant.

Peirce in a 1906 text identified three kinds of interpretant:

In all cases, it includes feelings; for there must, at least, be a sense of comprehending the meaning of the sign. If it includes more than mere feeling, it must evoke some kind of effort. It may include something besides, which, for the present, may be vaguely called “thought.” I term these three kinds of interpretant the “emotional,” the “energetic,” and the “logical” interpretants.


Naturally it is the ‘logical interpretant, the conveyed thought’ (EP2:410) which is most crucial for a sign involved in a process of dialog or inquiry; and ‘the essence of the logical interpretant’ (EP2:412) is the habit which is established or modified by that semiosic process. Not all signs can have a logical interpretant, and even a sign which would have one if the semiotic process were completed may not produce it in an actual semiotic process, depending on the timing:

It is not to be supposed that upon every presentation of a sign capable of producing a logical interpretant, such interpretant is actually produced. The occasion may either be too early or too late. If it is too early, the semiosis will not be carried so far, the other interpretants sufficing for the rude functions for which the sign is used. On the other hand, the occasion will come too late if the interpreter be already familiar with the logical interpretant, since then it will be recalled to his mind by a process which affords no hint of how it was originally produced. Moreover, the great majority of instances in which formations of logical interpretants do take place are very unsuitable to serve as illustrations of the process, because in them the essentials of this semiosis are buried in masses of accidental and hardly relevant semioses that are mixed with the former.


What makes a semiosis ‘relevant’ or essential (rather than accidental) to the formation of a logical interpretant? To deal with this question, Peirce constructs a scenario of an inquiry process and conducts a thought-experiment to investigate how it works.

The best way that I have been able to hit upon for simplifying the illustrative example which is to serve as our matter upon which to experiment and observe is to suppose a man already skillful in handling a given sign (that has a logical interpretant) to begin now before our inner gaze for the first time, seriously to inquire what that interpretant is. It will be necessary to amplify this hypothesis by a specification of what his interest in the question is supposed to be.… unless our hypothesis be rendered specific as to that interest, it will be impossible to trace out its logical consequences, since the way the interpreter will conduct the inquiry will greatly depend upon the nature of his interest in it.


The inquirer’s ‘interest’ is part of the context of the inquiry – not the ‘context which is treated as a variable’ according to Sperber and Wilson, but the situational context which determines what is essential and what is irrelevant in the text.


Do you read me? Then you have to believe that your experience is cognate with mine. Co-gnatus, ‘born together’ (or ‘descended from the same ancestor’), derives from the Latin verb gigno (earlier geno), meaning ‘beget’ or ‘bring forth’. Its root forms -gn-, -gen- and-gon- have begotten the stems of many English words, along with its complement verb nascor (‘to be born’), through its participial form natus (or gnatus), source of English words such as nature and native.