Non-discrete effects in language

The problem
We tend to think about language as a system of discrete elements (phonemes, morphemes, words, sentences)
But this view does not survive an encounter with reality

Simple example:
morpheme fusion
детский
det-sk-ij ‘children’s, childish’
Root-Suffix-Ending
[deckij]
suffix
deck-ij
root

Similar exampes abound on all lingustic levels
Phonemes: coarticulation
cat keep cool
Words: clitics
iz mašiny ‘from the car’
iz ... mašiny ‘from ... the car’
iz taksi [is taksi] ‘from the taxi’
Clauses: parcellation
I’ll come, in a minute
These are primarily syntagmatic examples: non-discrete boundaries between linearly arranged units

Paradigmatics
The same problem applies to paradigmatic boundaries, that is boundaries between classes, types, or categories in an inventory
Questionable phonemes
Russian жюри žjuri ‘jury’
[ž’ur’i]
even though supposedly there is no palatalized [ž’] in Russian (in this position)
Questionable words and clauses
I want [to go]
particle infinitival clause
I wan[na go] ??
cf. жури žuri ‘rebuke’

Semantics
X said smth (Zaliznjak 2006: 186)
‘X uttered a sequence of sounds’
‘X meant smth’
‘X expressed his belief in smth’
‘X wanted Y to know smth’
‘X wanted Y to perform smth’
.................
Some of these meanings are shared
by X told smth, but some are not

Diachronic change
Russian писать pisat’ ‘write’
Funny slangish use:
popisal nozhom ‘cut/slashed someone with a knife’, lit. ‘wrote with a knife’
One of the Indo-European etymologies of the root pis- is ‘create image by cutting’
Apparently the ancient meaning of the root, several millennia old, is still present in a marginal usage of the modern verb

Language contact
The Baltic language Prussian, spoken in this area until the 16th – 17th century
Vladimir N. Toporov
In the existing texts Prussian syntax is almost fully copied from German (Luther’s Catechism)
In the 18th century, when Prussian was extinct, German-speaking peasants of the area used many Prussian words

Intermediate conclusion
Language simultaneously
longs for discrete, segmented structure
tries to avoid it
Non-discrete effects permeate every single aspect of language
This problem is in the core of theoretical debates about language

Possible reactions
“Digital” linguistics (de Saussure, Bloomfield, Chomsky...):
More inclusive (“analog”) linguistics:
often a mere statement of continuous boundaries and countless intermediate/borderline cases
ignore non-discrete
phenomena or dismiss them
as minor
Ferdinand de Saussure:
language only consists
of identities and differences
the discreteness delusion
a bit too simple-minded
appeal of scientific rigor but extreme reductionism

Cognitive science
Rosch: prototype theory
Lakoff: radial categories
A is the prototypical phoneme/word/clause/ meaning...
B, C, and D are less prototypical representatives
We still need a theory for:
boundaries between related categories
boundaries in the syntagmatic structure

My main suggestion
In the case of language we see the structure that combines the properties of discrete and non-discrete: focal structure
Focal phenomena are simultaneously distinct and related
Focal structure is a special kind of structure found in linguistic phenomena, alternative to the discrete structure
It is the hallmark of linguistic and, possibly, cognitive phenomena, in constrast to simpler kinds of matter

Various kinds of structures
▐
focal point 1
focal point 2
discrete structure
▐
continuous structure
focal structure
1
2
1
2

Still more realistic: amoeba structure

Examples
▐
focal point 1
focal point 2
det sk
said told
*pis- pis-
Prussian German
Syntagm.
Paradigm.
Diachr.
Lg.contact
etc., etc.

Peripheral status of non-discrete phenomena
Where does it stem from?
Objective properties of language?
I don’t think so
Or, perhaps, properties of the observing human mind?
This directly relates to one of the key issues in The Critique of Pure Reason

Kant’s puzzle
The role of observer, or cognizer, crucially
affects the knowledge of the world
“The schematicism by which our understanding deals with the phenomenal world ... is a skill so deeply hidden in the human soul that we shall hardly guess the secret trick that Nature here employs.”
NB: Standards of scientific thought have developed on the basis of physical, rather than cognitive, reality
Physical reality is much more prone to the discrete approach
Compared to physical world, in the case of language and other cognitive processes Kant’s problem is much more acute
because mind here functions both as an observer and an object of observation, so making the distinction between the two is difficult

Recapitulation:
A paradoxical state of affairs
Science is based on categorization (Aristotelian, “rationality”, “left-hemispheric”, etc.)
The scientific approach is inherently biased to noticing only the fitting phenomena
It is like eyeglasses filtering out a part of reality
Addressing another part of it is perceived as pseudo-science, or quasi-science at best
Language is unknowable, a Ding an sich?

What to do?
We need to develop a more embracing linguistics and cognitive science that address non-discrete phenomena:
not as exceptions or periphery of language and cognition
but rather as their core
Can we outwit our mind?
Several avenues towards this goal

1. Start with prosody
Prosody is the aspect of sound code
that is obviously non-discrete
Example: Sandro V. Kodzasov’s
analysis of formal quantity
iconically depicting mental quantity
It was lo-ong ago. Oh, tha-at’s the reason.
He just left. That’s clear.
Develop new approaches on the basis of prosody, then apply them to traditional, “segmental” language

2. Explore gesticulation
In addition to sound code, there is a visual code: gesticulation and generally “body language”
Michael Tomasello: in order to “understand how
humans communicate with one another using a
language <…> we must first understand how
humans communicate with one another using natural gestures”
Когда он ехал по дорóге, он поравнялся с дéвочкой,
(From the materials of Julia Nikolaeva)
Simultaneously: iconic gestures and pointing gestures

3. Employ mathematics appropriate for the “cognitive matter”
Methodological point
1960s: a fashion of “mathematical methods” in linguistics
This did not bring much fruit, primarily because of the non-discreteness effects
Time for another attempt of bringing in more useful kinds of mathematics
Ongoing project: study of non-categorical referential choice
When we mention a person/object, we choose from a set of options, such as a proper name (Kant), a common name (the philosopher), or a reduced form (he)
This choice is not always deterministic: sometimes both Kant and he are appropriate
Probabilistic modelling and machine learning techniques used to simulate human behavior in non-categorical situations

Conclusion
Just as we invoke scientific thinking, we tend to immediately turn to discrete analysis
This is why discrete linguistics is so popular, in spite of the omnipresence and obviousness of non-discrete effects
This may be our inherent bias, or a habit developed in natural sciences, or a cultural preference
But in the case of language and other cognitive processes we do see the limits of the traditional discrete approach
It remains an open question if cognitive scientists are able to eventually overcome the strong bias towards “pure reason” and discrete analysis, or language will remain a Ding an sich
But it is worth trying to circumvent this bias and to seriously explore the focal, non-discrete structure that is in the very core of language and cognition