vagueness

Huangshan area

Vagueness

According to A. Tarskis, the sentence “snow is white” is true if and only if snow is white.

If you do not have any snow now, what might this sentence refer to? In the same manner, Timothy Williamson describes the situation:

"If the term 'this dagger' has no referent, one might argue that no statement using that term is true. Consequently, neither "This dagger is sharp" nor "This dagger is not sharp" is true, and so "This dagger is sharp" is neither true nor false.” (Williamson 1995)

However, vagueness and the sorites paradox are more than a problem of the lack of a reference.

The theme of vagueness staggers the logical construct in the sense that something is either true or false. When is something a bunch and when no more. One also speaks of the sorites paradox when one removes a grain of sand again and again from a heap of sand grains, up to the last grain of sand. In terms of one grain of sand, however, no one can speak about a heap.

We have a heap of sand with n grains of sand and remove a grain of sand: n-1. After that, we still have a bunch of sand grains and remove a grain of sand. Thus, you could remove 100,000 grains of sand and still end up with a bunch that is no longer there, which is paradoxical.

A question is if we have an epistemic problem for which we can’t recognize the moment. The sorites problem is so determined that it is not the lack of recognizability. To be considered as vague, a term must be blurred and epistemically incomprehensible.

The Blue Book also provides an example of a psychological argument.

Other examples of vagueness would be adjectives, contextuality, special nouns, generalizations, or pronunciation of words.

Timothy Williamson states that vagueness is related to adjectives and a lack of reference. TW is thin, where thin is a vague predicate. TW is neither clearly thin nor clearly not thin. If an adjective is vague, it is then because of its property by which it cannot be clearly delimited and which is reference-less.

Vagueness can also be attached to the context. 100,000 euros are a lot of money, but not enough for a rich person:

"$100,000 makes a Haitian refugee rich. While $99,999 doesn't make an Arabian oil sheikh rich,” (Raffman 1994), argues Diana Raffman.

Vagueness is found not only in adjectives, but also in well-known nouns such as wing, bar, tit, trunk, pole, row, which have arbitrary double meanings. "Now I need a bar" might mean that I need something to eat or that I want to have a drink.

Similarly, generalizations are vague. Each generic term can refer to different things, e.g. Tree> Fruit Tree> Apple Tree> Jonagold.

The way a word is emphasized by a speaker can also change its meaning, and so vagueness is also found here. If one says "sheep", it might mean an animal, or if one says "ship", it would recur to a boat.

While the sorites paradox refers to the problem of the heap, vagueness is more general. Blurring goes in the direction of fuzzy logic, which is concerned with vague terms and can also be represented graphically, taking into account the gradual affiliations that are used in the language, e.g. linguistics such as less, something, very, pretty, truthfulness such as wrong, more or less wrong, right, very correct or measurement such as not, something, very. (R. Kruse, J. Gebhardt and F. Klawonn, 1994)

For example, take a kiwi and “be matured”. Very immature, immature, more or less mature, ripe, very ripe, overripe, all these could be converted into a coordinate system with parabolas to a fuzzy function.

Fuzzy logics are important in many different areas such as in the business and IT sectors.

Ludwig Wittgenstein

In Philosophical Investigations, Ludwig Wittgenstein refers verbally to the term "vagueness" twice and several times to related terms such as “blurred”, “boundary line”, and “rigid”/"sharp”.

Rule-following

Wittgenstein states in PU’s paragraph 99 that a blurred limitation is not a limitation, as if one closed someone in a room and left a door open. Paragraph 100 questions whether something is still a game when the rules are vague.

§ 100 "Still, it isn´t a game at all, if there is some vagueness in the rules.“ –But is it really not a game then? -

Wittgenstein himself gives an example of vagueness in rules in § 83 by stating, "make up the rules as we go along", which means that you can also change the rules.

Language

Vagueness as per Wittgenstein is particularly found in his distinction between ordinary language and the language of logic. Here, Wittgenstein makes it clear that even an imperfect sentence can have its high value, as it is known from everyday life.

§ 98 On the one hand, it is clear that every sentence in our language is 'in order as it is'. That is to say, we are not striving after an ideal: as if our ordinary vague sentences had not yet got a quite unexceptionable sense, and a perfect language still had to be constructed by us. - On the other hand, it seems clear that where there is sense, there must be perfect order. - So there must be perfect order even in the vaguest sentence.

Psychology

According to Wittgenstein, the psychological option of vagueness can be seen in our wishes. Desire is vague because different people want different things or the desire may not meet reality:

„If on the other hand, you wish to give a definition of wishing, i.e. to draw a sharp boundary, then you are free to draw it as you like; and this boundary will never entirely coincide with the actual usage, as this usage has no sharp boundary.“ (BB 1960)

Imagine a coffee drinker and a tea drinker, and both want a hot drink and come back for something different. This could be called a psychological cause of vagueness.

Family resemblance

Considering Wittgenstein’s themes such as family resemblance and language games, you might find a strong relationship towards vagueness. The family resemblance ultimately considers a multi-valued logic.

By family resemblance, Wittgenstein refers to similarities, e.g. between games that cannot be fixed by a certain thing.

Speech games are words interwoven with actions that might go along from being simple structures to complex structures.

§ 71 One can say that the concept of a game is a term with blurred edges. - "But is a blurred concept a concept at all?" - Is a photograph that is not sharp even a picture of a person at all? Is it even always an advantage to replace a picture that is not sharp by one that is. Isn´t one that isn´t sharp often just what we need?

In § 77, Wittgenstein refers to the blur. Perhaps one can take a blurred image and a sharp image to give an example of vagueness—a blurred image and one that that is a bit sharper—and then ask how "sharp" the picture is.

§ 77 And if we carry this comparison a little further, it is clear that the degree to which the sharp picture can resamble the blurred one depends on the degree to which the latter lacks sharpness.

The themes of language games and family resemblance are found in PU as in the Blue Book. The Blue Book is dedicated to vagueness that pertains to the vagueness in the language and the book starts by questioning the meaning of a word.

The family resemblance takes into account of the unsharpness of terms and it would summarize similarities, comparabel to the similarities of members of a family.

Wittgenstein uses the example of the various ways of expecting someone for an afternoon tea to describe his concept of family resemblance in the Blue Book. The various species show us a family of being one concept.

„If one asks what are the different processes of expecting someone to tea in common, the answer is that there is not a single feature in common to all of them, though there are many common features overlapping.“ (BB 1960)

This is also picked up in PU’s §67 that introduces the term family resemblance:

§ 67 I can think of no better expression to characterize these similarities than "family resemblances"; for the various resemblance between members of a family – build, features, colours of eyes, gait, temperament, and do on and so forth – overlap and criss-cross in the same way. - And I shall say: "games" form a family. (...)

With the progression of the text, Wittgenstein relates family resemblance to the term "good". And on how to learn this meaning, he includes language games and states a family of meanings. The term good is thus vaguely characterized and correlated with a very modern understanding.

§77 (...) In this sort of predicament, always ask yourself: How did we learn the meaning of this word ("good", for instance)? From what sort of examples? In what language games? Then it will be easier for you to see the word must have a family of meanings.

Hans Sluga

Hans Sluga has published an essay on family resemblance, in which he begins with the question of universals and refers to Bambrough’s Universals and Family Resemblance, 1968.

Sluga notes that both Nietzsche and Wittgenstein say something similar; Wittgenstein says that language is formed through analogy and Nietzsche states that language is formed by metaphors, and each is capable of producing philosophical illusions.

"What the Wittgenstein of the Blue Book shares, however, with Nietzsche is the conviction that human thought proceeds by analogies (as Wittgenstein says) or metaphors (as Nietzsche puts it) and that are capable of being built into our language the profound of philosophical illusions. "(Hans Sluga 2006)

However, Wittgenstein and Nietzsche used completely different languages. While Wittgenstein prefers a sober language, Nietzsche tends to exaggerate. The proximity between Wittgenstein and Nietzsche can be explained by Schopenhauer, whom both philosophers refer to.

Sluga:

"It was Schopenhauer, after all, who had argued that they are grounded in recognitions of similarity, that they express metaphors or analogies. In his Parerga and Paralipomena he had written: "Similes are of great value in so far as they refer to unknown relation to a known (...) Even the formation of concepts at bottom on similes in as far as it results from our taking up what is similar in things and discarding what is dissimilar "(Schopenhauer 1851, 550)" (Hans Sluga, 2006)

And the text continues to state that terms of family resemblance are a special form of general terms of higher determination that can overlap with one another:

"On The Blue Book view, concepts are based on recognitions of similarity, and general terms have an analogical structure. Family resemblance terms are, it seems, a special variety of general terms; they are like composite terms of higher determination; but the distinguishing mark and which they refer to as a network of overlapping and open ended similarities, not in conjunctive terms. Wittgenstein's remarks on family resemblance are linked to a comprehensive view of the nature of concepts or, as we might say, of the meaning of general terms. " (Hans Sluga, 2006)

The point is that Wittgenstein’s family resemblance shows that beyond ordinary terms, there are terms that are neither simple nor complex, but of a different kind:

“There are then at least two kinds of terms: basic and indefinable terms and composite and definable ones. Wittgenstein gets to understand that this easy division is insufficient, that there are other types of terms, and that family resemblance terms, in particular, are neither basic nor composite. They certainly do not pick out a single observable characteristic nor do they refer to a conjunction of distinguishing marks." (Hans Sluga 2006)

Hilary Putnam

Hilary Putnam writes in his essay on Vagueness and Alternative Logic that Quine distinguishes between ordinary language and a scientific language in such a way that the natural language is vague.

"Quine has suggested that it really does not matter if ordinary language is vague (or even locally inconsistent), as long as we can think of it as approximating a scientific language which is free of these defects.“ (Putnam 1983)

Putnam further states that Quine’s views about statements in normal language are not true or false, but they are true or false relative to the translation scheme of an ideal language.

„In Quines view, statements in ordinary langauge are not true or false relative to a translation scheme (or "regimentation") which maps ordinary language onto an ideal language - and there is no fact of the matter as to which is the "right "Translation.” (Putnam 1983)

Putnam continues that it is the standard version when Quine suggests that we shift the normal-language utterances that are not quite correct into a meta-language.

"Quines view does not bring in any sense", "that's right, there is no determinate truth or falsity in ordinary language", because we could "in principle" rationally reconstruct ordinary language, ie, replace it by an ideal language (The "what me worry?" move.)

This means that sentences in the normal language are true or false relative to their translation scheme in the ideal language.“ (Putnam 1983)

In this context, Putnam recalls Davidson’s argument that correspondence is—somehow—a vague term.

"Not only is truth philosophically prior to correspondence; truth, Davidson emphasizes, but not vague notion (when there are vague terms in the language). Correspondence, being implicitly defined (non-uniquely) in terms of truth, is then also a vague notion. We are not, Davidson has said (in conversation), going to say everything we want to say without using vague language. " (Putnam 1983)

In his book Truth, Language and History, Davidson refers to Quine, who in his essay Ontological Relativity characterizes ontology as being relative to a translation manual. Also, the ontology of one language to another language is relative, without being determined.

"Rather, as Quine points out in Ontological Relativity, it only relativizes the ontology of one language to the other without establishing the ontology of any one language." (Davidson 2008)

Like Quine, Davidson is known for the development of his communication theory. A part of these considerations about communication are the possible errors that might occur in a conversation while people still understand each other.

A well-known example pertains to two different types of boats.

In the communicative situation, a boat is roughly named and understood.

„If you see a ketch sailing by and your companion says, "Look at that handsome yawl," you may be faced with a problem of interpretation. One natural possibility is that your friend has mistaken a ketch for a yawl, and has formed a false belief. But if his vision is good and his line of sight favorable it is even more plausible that he does not use the word "yawl"quite as you do, and has made no mistake at all about the position of the jigger on the passing yacht. We do this sort of off the cuff inter- pretation all the time, deciding in favor of reinterpretation of words in order to preserve a reasonable theory of belief. As phi- losophers we are peculiarly tolerant of systematic malapropism, and practised at interpreting the result. The process is that of constructing a viable theory of belief and meaning from sentences held true.“ (Davidson 1999)

Bettina Mueller

Bibliography:

Davidson, Donald, (1999) Wahrheit und Interpretation, Frankfurt: Suhrkamp

Davidson, Donald, (2008) Wahrheit, Sprache und Geschichte, Frankfurt: Suhrkamp

Raffman, D, (1994) Vagueness Without Paradox. In: Philosophical Review 103, 41-74

Sluga, Hans (2006) Family Resemblances, Grazer Philosophische Studien, Amsterdam - New York: Rodopi

R. Kruse, J. Gebhardt and F. Klawonn, (1994) Foundations of Fuzzy Systems

Walter, Sven, (HG) (2005) Vagheit, Paderborn: Mentis

Williamson, T. (1995) Definiteness and Knowability, Southern Journal of Philosophy 33, S. 171-191

Vagueness, Daili Graff, Williamson, T., (2017) Routledge

Wittgenstein, Philosophical Investigation, (2009) ed. By Peter Hacker/Joachim Schulte, Oxford, Wiley-Blackwell

Wittgenstein, Ludwig, (2013) Das Blaue Buch, Frankfurt: Suhrkamp

Wittgenstein, Ludwig, (1960) The Blue and Brown Books, New York: Harper Perennial