Point: Why Linguistics is Not a Science
[Editor’s Note: This opinion piece is the first of a contrasting pair discussing the relationship between Linguistics and Science. The opposing piece will run in the next issue of SpecGram.]
While many have claimed, and probably rightly so, that Linguistics
suffers from a bad case of Physics Envy, it is Mathematics, the Queen
of the Sciences, which is best suited to provide a role model for
bringing some sorely needed rigor to the field.
Any practicing mathematician will speak of the crucial role
intuition plays in the formulation of ideasthe mysterious spark, the
gut feeling, the leap of faith that points the way to a difficult but elegant theorem cannot
be replaced by any mechanical means. However, the intuitive leap is inspiration, and has no place in the final proof
of a claim. For decades every mathematician has known, instinctively,
that both Fermat’s Last “Theorem” and the Four Color Map Hypothesis
must be true. While there was little doubt among practitioners, all
agreed that neither was true until rigorously proven.
Linguistics as a whole lacks such a tradition of rigor, and
linguists sometimes show their incomplete appreciation of formalism in
interesting and even disturbing ways. Two anecdotes from my own
experience provide a sense of how things can go bizarrely wrong.
Formalism for the Sake of Formalism
First, I recall a paper that I read long ago, in which the author
introduced considerable and complex machinery, including advanced topics
in group theory and discrete mathematics, to say precisely what is meant
by the notion that “lines in diagrams should not cross.” The end result
was not appreciably distinguishable from the simple statement that
lines shouldn’t crossperhaps with the added caveat of “no cheating with
weird lines going around underneath or over the top of the diagram.”
The mathematics in this case was in fact correct, but was also
offputting and out of place. The entire linecrossingprevention
construct was in no way related to the main theory being presented, the
notions of line and crossing used were no different from
the well known entities used by tree diagram drawers from decades gone
by, and the entire enterprise was utterly abandoned once fully explicated.
The only value provided by all of this mathematics was several
additional pages in length, and a misleading air of formalism and
competence. Tellingly, while I recall the showy but misguided
mathematics, I have no recollection of the supposed main content of the
paper.
Trusting the Theory
I also recall another incident in an introductory linguistics course
concerning formal systems.
The instructor discussed a gavagaibrained interpretation of imaginary numbers I had
never encountered before, namely that i (the square root of 1) did not have a fixed value, but rather oscillated between +1 and 1.
On the surface this can seem quite clever. i^{ 2} = i · i
= (1) · (+1) = (+1) · (1). The class was made up mostly
of humanities
majors, and they seemed quite impressed with the intuitive sense that
this system makes. However, there was also the the usual smattering of
engineering typesmostly
programmers with the prototypical hackerish proclivity for
linguisticsand they objected strenuously.
They raised objections that ranged from the pointed but fairly trivial to the directly devastating, such as:
 Why not oscillate between ^{1}/_{2} and 2? No one ever asked that before.
 What is the speedor even the mediumof the oscillation? I don’t know.
 How do you know if you are on the upswing (1 to +1) or the
downswing (+1 to 1)? There have to actually be two distinct values of i: i_{1} (+1/1) and i_{2} (1/+1). So i_{1} · i_{2} = (1), but i_{1} · i_{1} is always 1. So i_{1}^{2} is just 1 again, which is clearly incorrect, unless 1 = 1. It just works out if you choose the details correctly.
These are questions in the Mathematical traditionthe devil is in
the details, so let’s beat them to death once and for all and be done with it. The answers are very much in
the Linguistic traditionsquishy answers with good, intuitive
interpretations: symmetrical seems better, so i obviously oscillates between 1 and +1, not ^{1}/_{2} and 2; the speed is irrelevant, since the numbers just sit there on the page and there is no medium of oscillation; i · i has to be aligned right to work so it aligns right and works. The reader can be trusted to do the right thing.
Continuing in the Mathematical tradition, I refused to let the matter go. i^{ 3}
is, at best, going to oscillate between (1) · (+1) ·
(1) and (+1) · (1) · (+1), or, between 1 and +1, which
is the original description of i. But in the classical theory of complex numbers, i^{ 3} = i. Now i = i, implying i = 0 !
Still this was not enough to convince the professor. Even the
computer science students, undergrads all, were losing their nerve to
fight with a distinguished professor. I dropped the matter in class,
but wrote up my final reductio ad absurdum (as if the previous two weren’t enough) in our next written assignment.
It is possible, you see, to do dark, foul things with complex
numbers. If you are mathematically masochistic enoughor if you are an
electrical engineer (which implies the previous condition, now that I
think of it). Horrid, evil things, like taking the complex cube roots
of regular numbers, such as 8. It turns out that the complex cube roots of 8 are:
1 + i · √3
and
1  i · √3
Oscillating values of i mean that each root actually oscillated with the otheran
almost elegant result on the surface. Multiplying through with
alternating values, though, we
get the result that vibrating at an unknown speed in an unknown medium
between the values of 1.464101... and 5.464101... is the same thing as
being 8a clear absurdity.
That short paper was the only one in my grad school career to get a
completely unacceptable grade. I knew better than to try to pursue the
physical interpretations of complex numbers that arise in electrical
engineering!
Perhaps this all seems irrelevant to the daytoday working of
linguistics, but I see a frightening analog between this incident and
another relayed to me by a colleague. At a conference, a linguist
presenting a theory made some startling but potentially powerful
theoretical claims about a particular language. Another linguist,
incidentally a native speaker of the language in question, stood up and
contradicted some of the obvious conclusions of the theory with simple
statements in his mother tongue. The presenter acknowledged that the
data did seem contradictory, but concluded that, “at some point, you
just have to put your trust in the theory.”
There is no coherent reply to such an incoherent assertion.
Rolling Eyes
At this point, I’m sure there has been a lot of eye rolling. Most
mathematically inclined readers, I expect, will
be shaking their heads at the lack of rigor and the lack of
understanding of rigor demonstrated above. Prototypical linguists, I
fear, will be shaking their heads at the excruciatingly boring
mathematical detail, which they’ve skimmed without really
internalizing. That’s the problem!
This is the same problem that hampers much work in linguistics.
Intuition without rigor is used to fill in the gaps in a theory. In
mathematics, this can lead one terribly astray when one’s intuitions
aren’t up to the challenge. In linguistics, the situation is actually
worse: what is essentially a theory of linguistic intuition has gaps, which are silently filled in by the reader, using their intuitions.
I’d say that the recursion is frightful, but no one other than old,
grey LISP programmers has really good intuitions about recursion.
Optimism for the Future
Despite the pessimistic tone so far, there is a cause for cautious optimism. The
best hope for remedying this situation is some sort of redemption
through the growing composite field of computational linguistics. You
have to remove all traces of intuition when instructing a computer in
how to perform any task, linguistic or otherwiseor you must at least
explicitly formalize those intuitions! There can be no magical jumping of
gaps with transparent, unconscious ‘just knowing’, at just the right timenot when your mind is crisp, cold silicon.
Alpberta CediumNdelemeiyerov 
Siberian Holographic Institute of Technology 

A Preliminary Field Guide to Linguists, Part TwoAthanasious Schadenpoodle 

Linguistic TopologyI. Juana PelotaGrande 

SpecGram Vol CL, No 2 Contents 
