# Much ado about intuition
**Part 2: Wittgenstein and vagueness**
### Introduction:
Last article I discussed two cases where "unification" bumped up against
empirical adequacy. I explained that "unification" is something like
Occam's Razor; we prefer scientific models that *explain* data in as few
hypotheses as possible. I related these two cases to machine learning,
suggesting that there may be no unifying theory for either case, and
threw out the idea that some of our intuitive decision making processes
(among other mental processes, like vision processing) may resemble deep
learning models in nature. Two conclusions may follow: (1) we may be
able to cite highly generalizable deep learning models as epistemic
sources. (2) we may have *independent* justification for relying on
intuition.
You rely on intuition more than you think. This article begins to put a
little shoe leather on that idea through the problem of vagueness.
### Sorites paradox:
Given any predicate P, The Sorites paradox contains two
premises:
Let P(n) := "A man with n strands of hair on his head is bald." The
first premise states that a man with 0 strands of hair on his head is
bald. The second premise states that if a man with n strands of hairs on
his head is bald, then he'll still be bald if you add one strand of hair
to his head. The conclusion, line 3, states that no matter how many
strands of hair are on a man's head, he's bald. In particular, the
conclusion entails that a man with a full head of hair is bald.
The paradox relies on two observations. First, predicates have clear cut
cases. If you have no hair, you're bald. Second, adding a strand of hair
to your head doesn't make any perceptible difference; if you're bald,
you're still bald after you acquire one more strand of hair.
The Sorites paradox might bug you because it seems to imply that either
premise (2) is incorrect -- there's some clearly bald person such that
adding one strand of hair to their head makes them clearly not
bald -- or, there's something wrong with classical logic, and we should
adopt a logic with different semantics that accounts for the cases
between 'clearly bald' and 'clearly not bald.'
The Sorites paradox is one way to introduce *vagueness*. You might call
a predicate P vague if you can use P to generate a Sorites paradox. From
this perspective, most categories in language are vague, such as "bald,"
"heap," "red," "tall," "wide," and so on.
### Wittgenstein:
Remarks 1-138 in Wittgenstein's Philosophical Investigations discuss
vagueness, language games, and what Wittgenstein refers to as
philosophy's confusion: applying the artificial, crystalline purity of
logic to everyday language and creating meaningless problems.
Recall the conceptual analysis of "knowledge" attempted in the last
article. We tried to reduce "knowledge" to "justified true belief." In
general, conceptual analysis tries to discover the *necessary and
sufficient* *conditions* required for concepts to attain -- a fruitless
endeavor.
Wittgenstein exemplifies the concept of "games." Do board games, card
games, ball games, video games, logic puzzle games, drinking games, and
so on, really have a common underlying definition? If so, what? "A form
of play"? Is "play" not essentially recreation? If so, that would
include playing guitar, drawing, or poking fun at a Twitter feed. But no
one calls these latter activities "games."
While discussing vagueness, Wittgenstein uses the analogy of blotches of
color, or blurry shapes:
> ...imagine having to sketch a sharply defined picture
> 'corresponding' to a blurred one. In the latter there is a blurred
> red rectangle: for it you put down a sharply defined one. Of
> course -- several such sharply defined rectangles can be drawn to
> correspond to the indefinite one. -- But if the colours in the original
> merge without a hint of any outline won't it become a hopeless task
> to draw a sharp picture corresponding to the blurred one? Won't you
> then have to say: "Here I might just as well draw a circle or heart
> as a rectangle, for all the colours merge. Anything -- and nothing -- is
> right." -- -- And this is the position you are in if you look for
> definitions corresponding to our concepts in aesthetics or ethics.
>
> In such a difficulty 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 that the word must have a family of meanings."
Note the "family of meanings." Instead of one definition, Wittgenstein
thinks the word "game" has a family of definitions. Instead of one
outline, we have an assortment of overlapping venn diagrams. Instead of
one red circle, we have an arrangement of red blotches. Board games and
drinking games are both social, and board games use pieces that follow
rules like card games use labeled cards that follow rules, and so on.
Also note the call out of "aesthetics or ethics." Philosophers ask
questions like "what is good?" and "what is beauty?" For Wittgenstein,
teleology rules the roost. The framing of such a question lacks the
*context* and *purpose* in which such words (beauty, good, ...) are
used. Without context, such a question is akin to asking "What is the
King piece (in a game of chess)?" You need the entire context of chess
to answer that question. Here, Wittgenstein relates a word's use in
language, which perhaps most aptly explains its meaning, to a chess
piece's function in a game of chess:
> But we talk about it [language] as we do about the pieces in chess
> when we are stating the rules of the game, not describing their
> physical properties.
>
> The question "What is a word really?" is analogous to "What is a
> piece in chess?
There are many ways to read the beginning of Philosophical
Investigations. One way: philosophy is not worthwhile. Another way:
philosophy submits to the primacy of everyday experience and language
use, not the other way round. From Wittgenstein:
> When I talk about language (words, sentences, etc.) I must speak the
> language of every day. Is this language somehow too coarse and
> material for what we want to say? Then how is another one to be
> constructed? -- And how strange that we should be able to do anything
> at all with the one we have!
>
> In giving explanations I already have to use language full-blown (not
> some sort of preparatory, provisional one); this by itself shows that
> I can adduce only exterior facts about language.
>
> Yes, but then how can these explanations satisfy us? -- Well, your very
> questions were framed in this language; they had to be expressed in
> this language, if there was anything to ask!
>
> And your scruples are misunderstandings.
Your questions refer to
> words; so I have to talk about words.
You say: the point isn't the
> word, but its meaning, and you think of the meaning as a thing of the
> same kind as the word, though also different from the word. Here the
> word, there the meaning. The money, and the cow that you can buy with
> it. (But contrast: money, and its use.)
In other words, if language were somehow too coarse or vague to
communicate explanations, and explanations were hopeless without further
precise definition, how would you give explanations that derive those
further precise definitions? Philosophy, at best, "leaves everything as
it is." And philosophically pondering what a word *really* means, or
expecting a word to behave like a precise mathematical definition, is a
phantasmic confusion:
> When we believe that we must find that order, must find the ideal, in
> our actual language, we become dissatisfied with what are ordinarily
> called "propositions", "words", "signs".
>
> The proposition and the word that logic deals with are supposed to be
> something pure and clear-cut. And we rack our brains over the nature
> of the *real* sign. -- It is perhaps the *idea* of the sign? or the
> idea at the present moment?
Depending on how you read it, you can get carried away with
Wittgenstein's conclusion. On one hand, it's a satisfying flame that
burns away the cold-to-the-touch analytic philosophy so influential in
contemporary ivory towers. On the other hand, if philosophy is only one
lens, is it not a perfectly valid lens? Or at least just as valid as any
other lens. Put another way: just because philosophy has not yet "found
a philosophical answer," does that mean it never will? Put yet another
way: in normal, everyday language, people find aesthetic and ethical
concepts perplexing, and wonder exactly *what* they are and *why* they
exist. Isn't it a bit facetious to pretend this is a mere philosophical
musing, only valid when language "goes on vacation"?
I especially don't find the section after remark 138 convincing.
Wittgenstein tries to argue that a language could never be private
(since a rule would have to be established to ever be followed in the
first place). This argument has a lot to do with the complexity of
ostension. More on that later.
**Exhibit A: the concept of "art"**
Morris Weitz applies Wittgenstein's approach to an end-all-be-all
critique of aesthetic theory. The concept of "art," according to Weitz,
is like the concept of "game." Art is part of a family of meaning.
Sculpture is only so much like painting, which is only so much like
theater, which is only so much like literature, and so on. Weitz labels
art as an "open concept." Every new artistic production may expand the
horizons of art. By effect, some closed definition of "art" is a logical
impossibility.
Maurice Mandelbaum responds a decade later. He critiques the idea of
family resemblances. For one thing, consider a family. You might try to
find some phenotypic trait that each member of the family exhibits and
use that to "define" the family. For example, suppose everyone has "the
same nose." Likely, this phenotypic approach will fail. Family members
differ physiologically and there will be exceptions.
You could not conclude, however, that *no* set of necessary and
sufficient conditions exist that demarcate families. There is, in fact,
some attribute that all members of a family share: genetic similarity,
or ancestral lineage. When it comes to art, are Weitz and Wittgenstein
unjustifiably giving up and failing to investigate more subtle
conditions?
Frank Sibley, in "Aesthetic Concepts," written around the same time,
questions relegating the ascription of *aesthetics terms* to defined
conditions and principles. Aesthetic terms are: "delicate," "trite,"
"balanced," "somber," "joyful," and so on. In other words, Sibley's
paper claims that aesthetic terms are vague. And aesthetic judgments are
not "mechanical." I imagine you're not protesting.
But Sibley is not simply claiming that aesthetic judgments are highly
varied or "subjective." Critics ascribe aesthetic qualities by relying
on non-aesthetic characteristics. A painting is "delicate" because of
its pale colors. A piece of music is "somber" because of its slow tempo
and minor key. But that same non-aesthetic characteristic may be used in
a slightly different piece to implicate a contradictory aesthetic
quality. The pale colors may make this new painting "bland," instead of
"delicate," and it could not be both.
Aesthetic judgment is highly individual *to each piece.* Sibley points
this out: imagine someone who's totally clueless artistically. Further,
imagine that this person, like a machine learning model trained for
sentiment analysis, tries to inductively reason towards some set of
rules or procedures they could use to ascribe aesthetic terms to pieces
of art. They may sometimes be right, but they'd never have great
confidence*.* In other words, since they could never rule out slightly
different states of affairs and/or epistemic positions that change their
answers and their confidence levels, they would never *know* what terms
were appropriate to apply.
Kind of like initial conditions in chaotic systems (and why weather
forecasts are still bad); here, too, "unification" may be impossible.
**Exhibit B: the concept of "species"**
Are categories (like such and such species) real? Do they have
ontological status (do they exist) or are they mere epistemic
*concepts*? You may think that only individual organisms exist and that
the classification into species is a convenience. Such a view is called
*nominalism*. On the other extreme, you may think that a species
classification is a "type" or "universal" -- just as real as the
individual organisms within it. The latter view is called "essentialism"
or "universalism."
Ernst Mayr defines "species":
> ...species are relationally defined. The word species corresponds very
> closely to other relational terms such as, for instance, the word
> *brother*. ... To be a different species is not a matter of degree of
> difference but of relational distinctness.
Being part of the same species, then, is like being part of the same
family tree, which is chalked up to causal, historical, and genetic
ties.
Ernst is trying to avoid vagueness, so that we can understand firm
epistemic grounds for grouping individuals into species, but his
definition is vague. Given any organism, assumedly a member of some
species, you should be able to work backwards causally and construct its
family tree:
The question becomes, then, at which previous generation N do we "prune"
the tree and declare that any further ancestor of N is part of species X
and any descendent of N is part of species Y? We have a Sorites-esque
situation.
Relatedly, there's a movement within philosophy of science towards
pluralism. Essentially (ha ha), some philosophers argue that different
concepts of "species" have different explanatory uses within biology,
eschewing the intuitive one ring to rule them all approach. Pluralism
paints a picture of science that explains the world's features
*piecemeal* instead of striving for the elusive "theory of everything."
Maybe there is no fundamental ontology -- no "carving" up of nature into
"natural kinds" -- but only many equally valid "carvings" that suit
different conceptual and explanatory needs.
(I doubt it.)
